Download - Stanford School of Earth Sciences - Stanford University
Download - Stanford School of Earth Sciences - Stanford University
Download - Stanford School of Earth Sciences - Stanford University
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
3D CHARACTERIZATION AND MECHANICS OF BRITTLE DEFORMATION IN<br />
THRUST FAULT RELATED FOLDS<br />
A DISSERTATION<br />
SUBMITTED TO THE DEPARTMENT<br />
OF GEOLOGICAL AND ENVIRONMENTAL SCIENCES<br />
AND THE COMMITTEE ON GRADUATE STUDIES<br />
OF STANFORD UNIVERSITY<br />
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS<br />
FOR THE DEGREE OF<br />
DOCTOR OF PHILOSOPHY<br />
Patricia E. Fiore<br />
November 2006
© Copyright by Patricia E. Fiore 2007<br />
All Rights Reserved<br />
ii
iii
Abstract<br />
This thesis addresses the proposition that a better understanding <strong>of</strong> fractures<br />
will aid in the optimization <strong>of</strong> hydrocarbon recovery in thrust fault related folds.<br />
Fault planes, stratigraphic layers, and stratigraphic growth features interpreted<br />
within a three-dimensional volume <strong>of</strong> seismic reflection data collected over the Elk<br />
Hills Oil Field, Kern County, CA are integrated with mechanical models to develop a<br />
four-dimensional fault evolution history that is structurally, stratigraphically, and<br />
mechanically consistent. The developed fault chronology has direct implications for<br />
the migration and emplacement <strong>of</strong> hydrocarbons. The method introduced here, by<br />
which structural and stratigraphic interpretations are incorporated into a sequence <strong>of</strong><br />
forward mechanical models, represents an effective means <strong>of</strong> constraining the<br />
structural evolution <strong>of</strong> a fault network that developed within a syn-depositional<br />
tectonic setting.<br />
The development <strong>of</strong> fractures in the sedimentary layers <strong>of</strong> Sheep Mountain<br />
anticline, a Laramide asymmetric fault-cored fold <strong>of</strong> the Bighorn Basin <strong>of</strong> Wyoming,<br />
is documented and interpreted as a method <strong>of</strong> constraining the kinematic evolution <strong>of</strong><br />
the fold. The relative chronology, mode <strong>of</strong> formation (opening vs. shearing), and<br />
structural locations <strong>of</strong> these fractures provide the following constraints interpretations<br />
<strong>of</strong> fold kinematics: there was little or no lateral fold propagation and no hinge<br />
migration; limb rotation or limb flexure and stretching operated at different structural<br />
locations during folding.<br />
Field observations <strong>of</strong> sheared fractures in various structural locations across<br />
Sheep Mountain document the role <strong>of</strong> fracture reactivation. Differences in<br />
observations <strong>of</strong> shearing constrain spatial and temporal variations <strong>of</strong> the stress state<br />
across the anticline during folding. Differences in both the formation and reactivation<br />
<strong>of</strong> fracture sets in the forelimb and backlimb indicate that the stress state in the<br />
forelimb was significantly influenced by the underlying fault.<br />
The coupling <strong>of</strong> fracture mapping with analysis <strong>of</strong> high precision GPS<br />
positions collected across patches <strong>of</strong> bedding surfaces at Sheep Mountain provides<br />
insight into the curvature-fracture relationship. Comparison <strong>of</strong> principal curvature<br />
v
magnitudes with fracture measurements indicates that greater curvature correlates with<br />
greater spherical variance <strong>of</strong> fracture sets. Fracture intensities, however, correlate only<br />
loosely with curvature, so fracturing mechanisms other than flexure must be taken into<br />
account.<br />
vi
Preface<br />
Small scale structural heterogeneities (joints, faults, sheared joints) affect the<br />
flow properties <strong>of</strong> reservoirs as discontinuities in the permeability <strong>of</strong> the rock volume,<br />
disrupting both the vertical and lateral transport <strong>of</strong> fluids. Accurate characterization <strong>of</strong><br />
these structures within reservoirs is thus sought for economic purposes. Typically,<br />
these structures are below seismic resolution and direct observation <strong>of</strong> their patterns is<br />
unfeasible, except within boreholes, where spatial coverage is limited. Fracture<br />
clusters <strong>of</strong>ten localize near faults or on folds. Thus, new multi-scale methods for<br />
predicting fracture patterns from subsurface data in which faults and folds are imaged<br />
would play a crucial role in the development <strong>of</strong> hydrocarbon reservoirs.<br />
Additionally, it is <strong>of</strong>ten beneficial from a geological point <strong>of</strong> view to reverse<br />
this relationship and consider faulting and folding with respect to observed fracturing.<br />
In this way, insight into the tectonic forces existing within the crust may be gained.<br />
The establishment <strong>of</strong> a link between faulting, folding, and fracturing would aid<br />
geologists in deducing the deformational history <strong>of</strong> a rock mass based on field<br />
interpretation <strong>of</strong> fractures present within thrust fault related folds. A complete<br />
understanding <strong>of</strong> the mechanics <strong>of</strong> faulting, folding and fracturing is a prerequisite for<br />
this process.<br />
This thesis consists <strong>of</strong> four chapters that are focused on relating common<br />
geological structures, namely faults, folds, and fractures. Elk Hills Anticline, a thrust<br />
fault related growth fold in Kern County, California, and Sheep Mountain Anticline, a<br />
Laramide thrust fault related fold in the Bighorn Basin <strong>of</strong> Wyoming, are two field sites<br />
that provide, respectively, the subsurface and the outcrop data that form the basis for<br />
the analyses included in this work. Three chapters provide insight into the link<br />
between fault and fold evolutions (chapters one, two, and three), two chapters have<br />
implications linking faulting and fracturing (chapters two and three), and three<br />
chapters link folding and fracturing (chapters two, three, and four).<br />
In chapter one, I use elastic models to investigate the evolution <strong>of</strong> the fault<br />
system beneath the Elk Hills anticline. My coauthors for this work are David Pollard,<br />
Bill Currin, and David Miner. Currin and Miner were employees at Occidental <strong>of</strong> Elk<br />
vii
Hills, Inc. at the time <strong>of</strong> the study. They provided the fault and horizon interpretations<br />
that served as input (fault surfaces) and calibration (structure contour maps <strong>of</strong> specific<br />
horizons) for the modeling effort. I interpreted growth structures within the seismic<br />
reflection data and worked with David Pollard to develop a method <strong>of</strong> forward<br />
modeling for observed deformation within a growth faulting environment through a<br />
series <strong>of</strong> iterative steps in which fault geometry evolves. I drafted the manuscript and<br />
all included figures with significant edits suggested by David Pollard. This manuscript<br />
has been accepted for publication in American Association <strong>of</strong> Petroleum Geologists<br />
Bulletin and is currently in press.<br />
The work presented in chapter two represents the initial results <strong>of</strong> a fruitful<br />
collaboration with Nicolas Bellahsen, who, at the time, was a post-doctorate fellow<br />
with David Pollard. Bellahsen spearheaded field efforts in which we collected fracture<br />
measurements at outcrops around Sheep Mountain Anticline. By considering fracture<br />
orientations, modes <strong>of</strong> deformation, and abutting relations, we developed a<br />
chronological fracturing story and were able to use this story to investigate the<br />
kinematics <strong>of</strong> folding at Sheep Mountain. I am second author on this paper after<br />
Bellahsen. I led the thin section interpretation and curvature analysis work, generating<br />
the corresponding figures. I also worked side-by-side with Bellahsen during the<br />
development <strong>of</strong> many <strong>of</strong> the concepts presented in the paper and through the drafting<br />
<strong>of</strong> the paper. David Pollard provided significant conceptual direction during the project<br />
and suggested significant reorganization and edits <strong>of</strong> the paper. This manuscript was<br />
published in the May 2006 issue <strong>of</strong> Journal <strong>of</strong> Structural Geology (v. 28, n.5).<br />
[Reprinted from Journal <strong>of</strong> Structural Geology, v. 28, Bellahsen, N., P. E. Fiore, and<br />
D. D. Pollard, The role <strong>of</strong> fractures in the structural interpretation <strong>of</strong> Sheep Mountain<br />
Anticline, Wyoming, p. 850-867, Copyright 2006, with permission from Elsevier.]<br />
In chapter three, I document the reactivation <strong>of</strong> fractures observed throughout<br />
Sheep Mountain Anticline. This work is coauthored with Nicolas Bellahsen and David<br />
Pollard. To dispel the notion that reactivation <strong>of</strong> fractures at Sheep Mountain may be<br />
lithology dependent, we first present fracture measurements in four different<br />
lithologies. We then discuss how differences observed in shearing at locations across<br />
the fold may constrain the state <strong>of</strong> stress at the time <strong>of</strong> deformation. Nicolas Bellahsen<br />
viii
worked with me in the field, identifying sheared fractures and investigating the spatial<br />
extent <strong>of</strong> shearing for different fracture sets. David Pollard also contributed to field<br />
work and provided invaluable direction and editing for a manuscript resulting from<br />
this work. Submission <strong>of</strong> this manuscript to Journal <strong>of</strong> Structural Geology is<br />
anticipated.<br />
In chapter four I compare characteristics <strong>of</strong> the fracture pattern mapped across<br />
patches <strong>of</strong> bedding surfaces with the magnitude <strong>of</strong> curvature <strong>of</strong> those surfaces.<br />
Although this was the last chapter completed, it was the first concept proposed to me<br />
by David Pollard upon my arrival at <strong>Stanford</strong> – that we should work toward a better<br />
understanding <strong>of</strong> how the shapes <strong>of</strong> surfaces relate to the fractures developed across<br />
those surfaces. I carried out all <strong>of</strong> the field work and analysis involved in this study<br />
and drafted the manuscript. Nicolas Bellahsen and David Pollard are coauthors on this<br />
paper. Work with Nicolas Bellahsen provided a foundation for the fracture<br />
characterization included in this project. David Pollard provided conceptual advice<br />
central to the development <strong>of</strong> the project. The manuscript is currently in preparation<br />
for submission to Journal <strong>of</strong> Structural Geology.<br />
Appendix one took shape while I was considering tectonic boundary conditions<br />
for the modeling included in chapter 1. During an internship at Occidental <strong>of</strong> Elk Hills,<br />
it became clear to me that geoscientists are still in debate over the tectonic setting in<br />
which the anticline formed. In part to justify my work at Elk Hills to Occidental<br />
employees, I felt it necessary to defend our view <strong>of</strong> Elk Hills as developing in response<br />
to a thrusting mechanism. David Pollard, my coauthor for this paper, suggested that we<br />
carry out kinematic calculations for suggested wrenching scenarios. The completion <strong>of</strong><br />
this task, and the results <strong>of</strong> a mechanical modeling effort in which wrenching drives<br />
the deformation, is summed up in a manuscript that has not yet been placed for<br />
publication.<br />
Appendix two is a field guide for Sheep Mountain anticline that I compiled with<br />
assistance from Nicolas Bellahsen and David Pollard for the June 2006 Rock Fracture<br />
Project field trip. It consists <strong>of</strong> a lengthy background section that includes excerpts<br />
from many previous studies at the anticline and then discusses much <strong>of</strong> the work<br />
conducted by Nicolas Bellahsen, David Pollard and me. Much <strong>of</strong> chapter two <strong>of</strong> this<br />
ix
thesis is included in the field guide. Some <strong>of</strong> the concepts developed in chapter three<br />
are included as well, although many <strong>of</strong> these concepts are in their infancy. Since<br />
publication is not intended, I have included the field guide as an appendix for archival<br />
purposes.<br />
x
Acknowledgements<br />
I am grateful to the many people who have contributed to the research presented<br />
in this thesis. Foremost, I thank Dave Pollard for his guidance over the past five years.<br />
He has been an excellent advisor and I truly appreciate the countless hours he has<br />
dedicated to helping me develop both my research and the ability to communicate it to<br />
others. In particular, I thank Dave for thinking <strong>of</strong> my future career when helping me to<br />
consider projects and internships. I also thank my committee members: Atilla Aydin,<br />
Mark Zoback, Steve Graham, and Ronnie Borja for invaluable suggestions and<br />
feedback over the years. I am appreciative <strong>of</strong> the GPS support provided by George<br />
Hilley and Trevor Hebert.<br />
Thanks to my fellow colleagues within the geomechanics research group who<br />
have engaged me in interesting research discussions and enlivened day to day tasks.<br />
Through the years, I have greatly benefited from the field assistance, technical<br />
discussion, and supportive working environment provided by Stephan Bergbauer, Phil<br />
Resor, Kurt Sternl<strong>of</strong>, Ian Mynatt, Ashley Griffith, Ole Kaven, Pete Lovely, Nico<br />
Bellahsen, Frantz Maerten, Laurent Maerten, Eric Flodin, Nick Davatzes, Brita<br />
Graham, Jordan Muller, Fabrizio Agosta, Laura Chiaramonte, Joe Gonzales, and Chris<br />
Wilson. In particular, Nico Bellahsen has been a great field partner and collaborator. I<br />
have learned a vast amount through interactions with Nico in both the field and the<br />
<strong>of</strong>fice, and much <strong>of</strong> my Sheep Mountain work would not have been possible without<br />
his efforts and enthusiasm.<br />
Beyond the <strong>Stanford</strong> community, I owe thanks to Stan Stearns and Radu<br />
Girbacea for helping turn a summer internship project with Occidental Oil and Gas<br />
into a true research project and to Peter Hennings for introducing me to Sheep<br />
Mountain six years ago during an internship at Phillips Petroleum Co.<br />
Financial support for my studies came from many sources. Project specific funds<br />
were provided by an NSF Tectonics Program Grant No. EAR-0125935 and an NSF<br />
Collaboration in Mathematical Geosciences Program Grant No. EAR-04177521.<br />
Additional funds were provided by the <strong>Stanford</strong> Rock Fracture Project, the <strong>Stanford</strong><br />
xi
<strong>University</strong> Department <strong>of</strong> Geological and Environmental <strong>Sciences</strong>, and the <strong>Stanford</strong><br />
McGee Grant.<br />
My family has provided endless support throughout my education. From an<br />
early age, my parents fueled my curiosity and encouraged my learning. I owe the<br />
dedication required to complete this thesis to them. My three sisters have been a<br />
constant source <strong>of</strong> personal support, providing prospective and a fun outlet from the<br />
geological world. Finally, I am indebted to my husband, Jeff, for his unwavering love,<br />
support, and patience during my final months at <strong>Stanford</strong>, despite the many miles<br />
between us.<br />
xii<br />
PEF, November 20 th , 2006
Table <strong>of</strong> Contents<br />
Abstract ………………………………...………………………………………….…. v<br />
Preface ………………………………………………………………………………. vii<br />
Acknowledgements ………………………………………………………………….. xi<br />
Table <strong>of</strong> Contents …………………………………………………………………... xiii<br />
List <strong>of</strong> Tables …………………………………………………………...………… xviii<br />
List <strong>of</strong> Illustrations …………………………………………………………………. xix<br />
Chapter 1: Mechanical and stratigraphic constraints on the evolution <strong>of</strong> faulting<br />
at Elk Hills, CA …………………………………………………………………. 1<br />
Abstract ....................................................................................................................1<br />
Introduction ..............................................................................................................1<br />
Regional geological setting ......................................................................................4<br />
Elk Hills Field .......................................................................................................... 6<br />
Structural interpretation............................................................................................7<br />
Velocity model .........................................................................................................9<br />
Stratigraphy ............................................................................................................10<br />
Stratigraphic constraints .........................................................................................10<br />
Pseudowells ........................................................................................................ 10<br />
Pseudowell interpretations: Western Elk Hills................................................ 12<br />
Pseudowell interpretations: Eastern Elk Hills ................................................. 15<br />
Bedding relationships ......................................................................................... 15<br />
Bedding relationship interpretations................................................................ 15<br />
Isochores............................................................................................................. 17<br />
Isochore interpretations: McDonald to Base Reef Ridge................................ 19<br />
Isochore interpretations: Base Reef Ridge to Calitroleum.............................. 21<br />
Isochore interpretations: Calitroleum to Wilhelm........................................... 23<br />
Isochore interpretations: Wilhelm to MYA 4-A ............................................. 24<br />
Stratigraphic constraints on fault evolution............................................................24<br />
Mechanical modeling ............................................................................................. 24<br />
Boundary conditions........................................................................................... 26<br />
Model increments................................................................................................ 30<br />
Model calibration ............................................................................................... 32<br />
Model results....................................................................................................... 33<br />
Discussion ..............................................................................................................35<br />
Modeled and interpreted discrepancies.............................................................. 36<br />
Tectonic strain analysis ...................................................................................... 37<br />
Implications for hydrocarbon migration ............................................................ 39<br />
Conclusions ............................................................................................................41<br />
Acknowledgements ................................................................................................42<br />
References ..............................................................................................................42<br />
xiii
Chapter 2: The role <strong>of</strong> fractures in the structural interpretation <strong>of</strong> Sheep<br />
Mountain anticline, Wyoming ………………………………………………… 49<br />
Abstract ..................................................................................................................49<br />
Introduction ............................................................................................................49<br />
Geological and tectonic setting ..............................................................................53<br />
Methods ..................................................................................................................56<br />
Fracture sampling .............................................................................................. 56<br />
Data processing .................................................................................................. 59<br />
Curvature calculation......................................................................................... 61<br />
Structural data ........................................................................................................63<br />
Northeastern forelimb ........................................................................................ 63<br />
Southwestern backlimb ...................................................................................... 68<br />
Hinge................................................................................................................... 71<br />
Northern nose ..................................................................................................... 75<br />
Interpretation .......................................................................................................... 76<br />
Pre-existing fractures ......................................................................................... 76<br />
Early Laramide compression: onset <strong>of</strong> faulting and folding .............................. 78<br />
Fold growth: intermediate stage......................................................................... 81<br />
Fold growth: late stage....................................................................................... 82<br />
Conclusions ............................................................................................................83<br />
Acknowledgements ................................................................................................84<br />
References ..............................................................................................................84<br />
Chapter 3: Fracture reactivation at Sheep Mountain anticline: insight on the<br />
mechanics <strong>of</strong> folding and constraints on the stress field …………………….. 91<br />
Abstract ..................................................................................................................91<br />
Introduction ............................................................................................................92<br />
Geological background...........................................................................................93<br />
Field data ................................................................................................................99<br />
Systematic fracture sets ...................................................................................... 99<br />
Forelimb ........................................................................................................ 102<br />
Backlimb........................................................................................................ 102<br />
Hinge ............................................................................................................. 104<br />
Shearing datas .................................................................................................. 104<br />
Forelimb ........................................................................................................ 106<br />
Backlimb........................................................................................................ 110<br />
Hinge ............................................................................................................. 113<br />
Analysis <strong>of</strong> field data............................................................................................113<br />
Interpretation <strong>of</strong> shearing................................................................................. 113<br />
Forelimb ........................................................................................................ 113<br />
Backlimb........................................................................................................ 115<br />
Lithological control on fracturing .................................................................... 115<br />
Set V fractures................................................................................................... 118<br />
Stress field constraints...................................................................................... 120<br />
Constraints on spatial variation in stress orientation: conjugate shearing..... 121<br />
xiv
Spatial variation in stress orientation: opposite senses <strong>of</strong> shearing............... 121<br />
Constraints on spatial variation in stress field magnitude: set I fractures ..... 128<br />
Discussion ............................................................................................................134<br />
Kinematics <strong>of</strong> shearing and folding.................................................................. 134<br />
Implications for the mechanics <strong>of</strong> fracturing in a thrust fault related folds..... 134<br />
Acknowledgements ..............................................................................................136<br />
References ............................................................................................................ 136<br />
Chapter 4: Curvature and fracturing based on GPS data collected at Sheep<br />
Mountain anticline, WY ……………………………………………………… 141<br />
Abstract ................................................................................................................141<br />
Introduction ..........................................................................................................141<br />
Geological setting.................................................................................................142<br />
Methodology ........................................................................................................143<br />
GPS data collection .......................................................................................... 143<br />
GPS data filtering ............................................................................................. 147<br />
Curvature calculation....................................................................................... 148<br />
Fracture data collection ................................................................................... 148<br />
Fracture data analysis...................................................................................... 148<br />
Field data ..............................................................................................................149<br />
GPS data........................................................................................................... 149<br />
Fracture data .................................................................................................... 151<br />
Curvature analysis ................................................................................................158<br />
Discussion ............................................................................................................ 163<br />
Curvature analyses ........................................................................................... 163<br />
Relating curvature analysis to fracture measurements .................................... 163<br />
Conclusions ..........................................................................................................167<br />
Acknowledgements .............................................................................................. 167<br />
References ............................................................................................................ 167<br />
Appendix 1: Tectonic shortening style in the Southern San Joaquin Valley,<br />
Revisited ………………………………………………………………………. 171<br />
Abstract ................................................................................................................171<br />
Introduction ..........................................................................................................172<br />
Previous work.......................................................................................................175<br />
Shearing calculations............................................................................................177<br />
Pure shear ...................................................................................................... 178<br />
Simple shear................................................................................................... 178<br />
Implications <strong>of</strong> shearing-related rotation on relative plate velocities........... 179<br />
Discussion ............................................................................................................180<br />
Analysis <strong>of</strong> shearing calculations................................................................... 180<br />
Variation in isochore trends at Elk Hills ....................................................... 184<br />
Analysis <strong>of</strong> a wrenching growth mechanism at Elk Hills............................... 184<br />
Conclusions ..........................................................................................................186<br />
Acknowledgements ..............................................................................................188<br />
References ............................................................................................................188<br />
xv
Appendix 2: The Rock Fracture Project field trip, Sheep Mountain Anticline,<br />
WY, 2006………………………………………………………………………. 193<br />
Introduction ..........................................................................................................194<br />
Themes: ................................................................................................................194<br />
Fracture characterization at the outcrop ......................................................... 194<br />
Fracture characterization over the fold............................................................ 195<br />
Fold-thrust fault relationships based on fracture patterns............................... 195<br />
Tectonic history revealed by fracture patterns................................................. 195<br />
Field Trip Stops:...................................................................................................196<br />
First Day ........................................................................................................ 196<br />
Second Day.................................................................................................... 196<br />
DAY 1 ..................................................................................................................199<br />
Stop 1: Geology <strong>of</strong> the greater region ..................................................................200<br />
Objectives.......................................................................................................... 200<br />
Key Points......................................................................................................... 200<br />
Tectonic setting <strong>of</strong> Laramide Orogeny ............................................................. 200<br />
Structural styles <strong>of</strong> Laramide folds and thrust faults........................................ 202<br />
Stratigraphy <strong>of</strong> the Bighorn Basin.................................................................... 204<br />
Structures surrounding Sheep Mountain .......................................................... 207<br />
Structural interpretations for Sheep Mountain anticline.................................. 213<br />
Stop 2: Fold shape ................................................................................................222<br />
Objectives.......................................................................................................... 222<br />
Key Points......................................................................................................... 222<br />
Stop 3: Fracture introduction; nose fractures .......................................................224<br />
Objectives.......................................................................................................... 224<br />
Key Points......................................................................................................... 224<br />
Previous fracture studies at Sheep Mountain................................................... 224<br />
Methods <strong>of</strong> fracture characterization ............................................................... 229<br />
Fracture interpretation..................................................................................... 231<br />
Fracture characterization in the nose .............................................................. 233<br />
DAY 2 ..................................................................................................................237<br />
Stop 4: Backlimb fractures ...................................................................................238<br />
Objectives.......................................................................................................... 238<br />
Key Points......................................................................................................... 238<br />
Overview ........................................................................................................... 239<br />
Kinematic Indicators ........................................................................................ 241<br />
Fracture characterization in the backlimb ....................................................... 242<br />
Stop 5: Backlimb fractures and shearing <strong>of</strong> Set I.................................................248<br />
Objectives.......................................................................................................... 248<br />
Key Points......................................................................................................... 248<br />
Shearing <strong>of</strong> Set I fractures in the backlimb....................................................... 249<br />
Stop 6: Backlimb fractures ...................................................................................253<br />
Objectives.......................................................................................................... 253<br />
Key Points......................................................................................................... 253<br />
Fracture characterization................................................................................. 254<br />
Shearing at site ................................................................................................. 258<br />
xvi
Role <strong>of</strong> thumb in fracture variation .................................................................. 264<br />
Stop 7: Forelimb and hinge fractures ...................................................................267<br />
Objectives.......................................................................................................... 267<br />
Key Points......................................................................................................... 267<br />
Fracture characterization in the forelimb ........................................................ 268<br />
Shearing (reactivation) <strong>of</strong> Set I fractures in the forelimb................................. 271<br />
Bedding plane slip in the forelimb.................................................................... 272<br />
Fracture characterization at site ...................................................................... 275<br />
Fracture characterization in the hinge............................................................. 281<br />
Shearing in the hinge ........................................................................................ 285<br />
Stop 8: Fracture synthesis..................................................................................... 286<br />
Objectives.......................................................................................................... 286<br />
Key Points......................................................................................................... 286<br />
Stages <strong>of</strong> fracturing........................................................................................... 288<br />
Pre-existing fractures..................................................................................... 288<br />
Early Laramide compression: onset <strong>of</strong> faulting and folding ......................... 288<br />
Fold growth: intermediate stage .................................................................... 289<br />
Fold growth: late stage .................................................................................. 289<br />
Constraints on fold kinematics ......................................................................... 292<br />
Fixed hinge .................................................................................................... 292<br />
Understanding spatial variations .................................................................... 293<br />
Set III fractures.............................................................................................. 293<br />
Set II fractures ............................................................................................... 295<br />
Role <strong>of</strong> shearing <strong>of</strong> set I fractures..................................................................... 299<br />
References ............................................................................................................ 302<br />
xvii
List <strong>of</strong> Tables<br />
Table 1.1. Ages <strong>of</strong> stratigraphic horizons; model increments; applied strains.............31<br />
Table 4.1. Fisher statistics for fracture sets at surveyed pavements...........................155<br />
Table 4.2. Extreme values <strong>of</strong> principal normal curvatures.........................................159<br />
xviii
List <strong>of</strong> Illustrations<br />
Figure 1.1. Location <strong>of</strong> the Elk Hills Oil Field...............................................................5<br />
Figure 1.2. Structure <strong>of</strong> the Elk Hills Oil Field ..............................................................8<br />
Figure 1.3. Tertiary stratigraphic column for the Elk Hills Oil Field...........................11<br />
Figure 1.4. Cross sections and pseudowells .................................................................13<br />
Figure 1.5. Stratigraphic bedding relationships............................................................16<br />
Figure 1.6. Tracing <strong>of</strong> seismic line exhibiting stratigraphic bedding relationships......18<br />
Figure 1.7 Interpreted and modeled isochore maps.....................................................20<br />
Figure 1.8. Isochore signatures related to fault activity................................................22<br />
Figure 1.9. Conceptual model <strong>of</strong> fault evolution..........................................................25<br />
Figure 1.10. Remote boundary conditions applied to one step models ........................29<br />
Figure 1.11. Interpreted and modeled structure contour maps .....................................34<br />
Figure 1.12. Remote boundary conditions applied to iterative models ........................38<br />
Figure 2.1. Geology <strong>of</strong> Sheep Mt. ................................................................................52<br />
Figure 2.2. Cross section through Sheep Mt.................................................................54<br />
Figure 2.3. Stratigraphic column for Sheep Mt. ...........................................................54<br />
Figure 2.4. Fracture measurements in the limbs and hinge at Sheep Mt......................57<br />
Figure 2.5. Fracture measurements in the nose at Sheep Mt. .......................................58<br />
Figure 2.6. Sample sites for microscope analysis.........................................................60<br />
Figure 2.7. Curvature map <strong>of</strong> Sheep Mt. ......................................................................62<br />
Figure 2.8. Fracture patterns in the forelimb ................................................................64<br />
Figure 2.9. Thin section <strong>of</strong> a set I fracture in the forelimb...........................................65<br />
Figure 2.10. Reactivated set I fractures in the forelimb................................................66<br />
Figure 2.11. Fracture pattern in the backlimb...............................................................67<br />
Figure 2.12. Thin section <strong>of</strong> a set I fracture in the backlimb........................................67<br />
Figure 2.13. Thin sections <strong>of</strong> set II, III, and IV fractures in the backlimb ...................69<br />
Figure 2.14. Set IV fractures in the backlimb...............................................................70<br />
Figure 2.15. Thin sections <strong>of</strong> set I and II fractures in the hinge ...................................70<br />
Figure 2.16. Fracture pattern in the hinge.....................................................................72<br />
Figure 2.17. Fracture pattern in the hinge <strong>of</strong> the nose ..................................................73<br />
Figure 2.18. Fracture pattern in the backlimb <strong>of</strong> the nose ............................................74<br />
Figure 2.19. Stages <strong>of</strong> fracturing at Sheep Mt..............................................................77<br />
Figure 3.1. Geology <strong>of</strong> the Bighorn Mts./Bighorn Basin area......................................94<br />
Figure 3.2. Geological map <strong>of</strong> Sheep Mt......................................................................96<br />
Figure 3.3. Stratigraphic column for the Bighorn Basin ..............................................97<br />
Figure 3.4. Schematic drawing <strong>of</strong> Sheep Mt. fracture pattern .....................................98<br />
Figure 3.5. Forelimb, backlimb, and hinge fracture measurements ...........................100<br />
Figure 3.6. Abutting relationships for set V joints .....................................................103<br />
Figure 3.7. Locations and types <strong>of</strong> shearing observations at Sheep Mt. ....................105<br />
Figure 3.8. Set I reactivated fractures in the forelimb ................................................107<br />
Figure 3.9. Sheared set I fracture in the forelimb .......................................................108<br />
Figure 3.10. Sheared set I fractures and set II joints in the backlimb.........................109<br />
Figure 3.11. Sheared set V joints in the backlimb......................................................111<br />
Figure 3.12. Sheared set I fractures in the backlimb ..................................................112<br />
Figure 3.13. Fracture pattern in the hinge...................................................................112<br />
xix
Figure 3.14. Shearing domains ...................................................................................114<br />
Figure 3.15. Conceptual model <strong>of</strong> fracture, fold, and shearing development ............116<br />
Figure 3.16. Sets II and V abutting relationship.........................................................119<br />
Figure 3.17. Conjugate shearing along sets II and V..................................................122<br />
Figure 3.18. Spatial constraints on local principal stress directions...........................123<br />
Figure 3.19. Conceptual drawing <strong>of</strong> opposite senses <strong>of</strong> shear along parallel joints...123<br />
Figure 3.20. Stress states for which pre-existing fractures will slip...........................126<br />
Figure 3.21. Remote strains consistent with shearing observations ...........................129<br />
Figure 3.22. Mohr-Coulomb analysis investigating mechanics <strong>of</strong> set I reactivation 131<br />
Figure 3.23. Thin sections <strong>of</strong> set I fractures in the hinge and backlimb.....................133<br />
Figure 3.24. Kinematics <strong>of</strong> shearing at Sheep Mt. .....................................................135<br />
Figure 4.1. Geological map <strong>of</strong> Sheep Mt....................................................................144<br />
Figure 4.2. Various methods <strong>of</strong> post-processing GPS data ........................................146<br />
Figure 4.3. GPS data collected at Sheep Mt. ..............................................................150<br />
Figure 4.4. Fracture orientation data...........................................................................152<br />
Figure 4.5. Fracture sets present at studied pavements ..............................................154<br />
Figure 4.6. Intensity mesurements..............................................................................157<br />
Figure 4.7. Relative elevations <strong>of</strong> collected GPS data................................................160<br />
Figure 4.8. Filtered GPS data .....................................................................................161<br />
Figure 4.9. Maximum and minimum normal curvatures across GPS6 and GPS7 .....162<br />
Figure 4.10. Photographs <strong>of</strong> GPS6 and GPS7 ............................................................164<br />
Figure 4.11. Spherical variance <strong>of</strong> fracture sets at study sites....................................165<br />
Figure A1.1. Location <strong>of</strong> Elk Hills .............................................................................173<br />
Figure A1.2. Schematic model <strong>of</strong> a compressional flower structure..........................174<br />
Figure A1.3. Structure <strong>of</strong> Elk Hills.............................................................................181<br />
Figure A1.4. Isochore maps at Elk Hills.....................................................................183<br />
Figure A1.5. Elastic displacement field for a flower structure model <strong>of</strong> Elk Hills ... 187<br />
Figure A2.0. Aerial photograph <strong>of</strong> Sheep Mt.............................................................193<br />
Figure A2.1. Tectonic map <strong>of</strong> Wyoming....................................................................194<br />
Figure A2.2. Sheep Mt. field trip stops ......................................................................196<br />
Figure A2.3. Geological map <strong>of</strong> Sheep Mt.................................................................197<br />
Figure A2.4. Structural map <strong>of</strong> Sheep Mt...................................................................198<br />
Figure A2.5. Road map to Sheep Mt. .........................................................................199<br />
Figure A2.6. Day 1 field trip stops .............................................................................199<br />
Figure A2.7. Two modes <strong>of</strong> subduction .....................................................................201<br />
Figure A2.8. Thrust fault interpretation <strong>of</strong> Laramide deformation ............................202<br />
Figure A2.9. Drape fold interpretation <strong>of</strong> Laramide deformation ..............................203<br />
Figure A2.10. Stratigraphic column <strong>of</strong> Bighorn Basin...............................................205<br />
Figure A2.11. Photograph <strong>of</strong> stratigraphy at the NW nose <strong>of</strong> Sheep Mt....................206<br />
Figure A2.12. Stratigraphic column <strong>of</strong> Sheep Mt.......................................................206<br />
Figure A2.13. Geological map <strong>of</strong> the NE Bighorn Basin...........................................207<br />
Figure A2.14. Major folds within the NE Bighorn Basin...........................................208<br />
Figure A2.15. Synthetic structure contour map <strong>of</strong> the NE Bighorn Basin .................209<br />
Figure A2.16. Strain energy density models <strong>of</strong> the NE Bighorn Basin......................211<br />
Figure A2.17. Cross section through the Bighorn Mts. and NE Bighorn Basin.........212<br />
Figure A2.18. Interpretation <strong>of</strong> Sheep Mt. structure: Hennier and Spang, 1983........313<br />
xx
Figure A2.19. Interpretation <strong>of</strong> Sheep Mt. structure: Forster et al., 1996 ..................214<br />
Figure A2.20. Interpretation <strong>of</strong> Sheep Mt. structure: Brown, 1984 ...........................214<br />
Figure A2.21. Relationship btwn Sheep Mt. and Bighorn Mts.: Forster et al., 1996 .215<br />
Figure A2.22. Interpretation <strong>of</strong> Sheep Mt. structure: Stanton and Erslev, 2002 ........215<br />
Figure A2.23. Structure <strong>of</strong> the Torchlight Field ........................................................216<br />
Figure A2.24. Tectonic map <strong>of</strong> the NE Bighorn Basin ..............................................217<br />
Figure A2.25. Structure contour map <strong>of</strong> Sheep Mt. ...................................................218<br />
Figure A2.26. Model setup to test fault geometry at Sheep Mt..................................219<br />
Figure A2.27. Results <strong>of</strong> heuristic tests <strong>of</strong> fault geometry at Sheep Mt.....................220<br />
Figure A2.28. Basemap for 2D seismic reflection pr<strong>of</strong>iles near Sheep Mt................221<br />
Figure A2.29. Photographs <strong>of</strong> hinge...........................................................................222<br />
Figure A2.30. Photograph showing topographic high................................................223<br />
Figure A2.31. Fracture pattern map: Harris et al., 1960.............................................225<br />
Figure A2.32. Iso-fracture map: Harris et al., 1960....................................................226<br />
Figure A2.33. Joint frequencies: Johnson et al., 1965................................................228<br />
Figure A2.34. Characterizing fracture orientations ....................................................229<br />
Figure A2.35. Characterizing mode <strong>of</strong> deformation...................................................229<br />
Figure A2.36. Characterizing abutting relationships..................................................230<br />
Figure A2.37. Fracture pattern in the hinge <strong>of</strong> the nose .............................................231<br />
Figure A2.38. Stereonets for fracture measurements at site 2....................................231<br />
Figure A2.39. Photo and interpretation <strong>of</strong> fractures at site 2......................................232<br />
Figure A2.40. Photo and interpretation <strong>of</strong> fractures at site 2......................................232<br />
Figure A2.41. Rose diagrams <strong>of</strong> fracture measurements in the nose ........................ 234<br />
Figure A2.42. Fracture pattern in the hinge <strong>of</strong> the nose .............................................235<br />
Figure A2.43. Fracture pattern in the backlimb <strong>of</strong> the nose .......................................236<br />
Figure A2.44. Field trip driving route ........................................................................237<br />
Figure A2.45. Stop 4 location.....................................................................................238<br />
Figure A2.46. Pavement at site 8................................................................................239<br />
Figure A2.47. Fracture pattern at site 8 ......................................................................240<br />
Figure A2.48. Rib marks and hackle along joint surface at site 8..............................241<br />
Figure A2.49. Shear along a set II fracture at site 8 ...................................................241<br />
Figure A2.50. Aerial photograph <strong>of</strong> backlimb <strong>of</strong> Sheep Mt.......................................242<br />
Figure A2.51. Backlimb stereonet..............................................................................243<br />
Figure A2.52. Backlimb fracture measurements ........................................................244<br />
Figure A2.53. Thin section <strong>of</strong> a set I fracture in the backlimb...................................245<br />
Figure A2.54. Thin section <strong>of</strong> a set II fracture in the backlimb..................................245<br />
Figure A2.55. Thin section <strong>of</strong> a set III fracture in the backlimb ................................246<br />
Figure A2.56. Thin section <strong>of</strong> a set IV fracture in the backlimb .............................. 246<br />
Figure A2.57. Photographs <strong>of</strong> set IV fractures in the backlimb .................................247<br />
Figure A2.58. Fractured pavement at site 72 in the backlimb....................................248<br />
Figure A2.59. Left-lateral shear along set I fractures at site 72 in the backlimb........249<br />
Figure A2.60. Left-lateral shear along a set I fracture at site 72 in the backlimb ......250<br />
Figure A2.61. Left-lateral shear along a set I fracture at site 72 in the backlimb ......250<br />
Figure A2.62. Left-lateral shear along set I fractures at site 74 in the backlimb........251<br />
Figure A2.63. Interpretation <strong>of</strong> fractured pavement at site 72....................................252<br />
Figure A2.64. Photograph <strong>of</strong> stop 6 sites ...................................................................253<br />
xxi
Figure A2.65. Stereonets <strong>of</strong> fracture measurements at stop 6 sites ............................254<br />
Figure A2.66. Interpretation <strong>of</strong> fractured pavement at site 81....................................255<br />
Figure A2.67. Set IV fractures at site 81 ....................................................................255<br />
Figure A2.68. Photograph and interpretation <strong>of</strong> site 22 pavement.............................256<br />
Figure A2.69. Photograph and interpretation <strong>of</strong> fractures at site 22 ..........................257<br />
Figure A2.70. Interpretation <strong>of</strong> stages <strong>of</strong> fracture formation at site 22 ......................257<br />
Figure A2.71. Photograph and interpretation <strong>of</strong> conjugate shearing at site 22 ..........258<br />
Figure A2.72. Left-lateral shear along a set V fracture at site 22...............................259<br />
Figure A2.73. Right-lateral shear along a set II fracture at site 22.............................259<br />
Figure A2.74. Interpretation <strong>of</strong> a sheared set V fracture at site 22.............................260<br />
Figure A2.75. Left-lateral shear along a set V fracture at site 22...............................261<br />
Figure A2.76. Right-lateral shear along a set II fracture at site 15............................ 262<br />
Figure A2.77. Bedding plane slip at site 22 in the backlimb......................................263<br />
Figure A2.78. Backlimb fracture data highlighting set V fractures ...........................264<br />
Figure A2.79. Left-lateral shear along a set V fracture in the backlimb ....................265<br />
Figure A2.80. Elastic model setup with idealized main and thumb thrust faults .......266<br />
Figure A2.81. Most tensile stress field resulting from slip along underlying faults...266<br />
Figure A2.82. Photograph <strong>of</strong> the forelimb <strong>of</strong> Sheep Mt.............................................267<br />
Figure A2.83. Forelimb fracture measurements.........................................................268<br />
Figure A2.84. Forelimb fracture patterns ...................................................................269<br />
Figure A2.85. Thin section <strong>of</strong> a set I fracture in the forelimb ....................................270<br />
Figure A2.86. Reactivated set I fractures in the forelimb...........................................271<br />
Figure A2.87. Splay fractures indicating bedding plane slip in the forelimb.............272<br />
Figure A2.88. Polished underside <strong>of</strong> a bedding plane in the forelimb .......................273<br />
Figure A2.89. Slickenlines along a bedding plane in the forelimb ............................273<br />
Figure A2.90. Conceptual model <strong>of</strong> flexural slip: Twiss and Moores, 1992..............274<br />
Figure A2.91. Interpretation <strong>of</strong> bedding plane slip along the rivercut at Sheep Mt. ..274<br />
Figure A2.92. Photograph <strong>of</strong> the forelimb; location <strong>of</strong> site 12...................................275<br />
Figure A2.93. Stratigraphy at site 12..........................................................................276<br />
Figure A2.94. Tensleep pavement at site 12...............................................................276<br />
Figure A2.95. Stereonets <strong>of</strong> measurements in the Tensleep at site 12. ......................277<br />
Figure A2.96. Set I reactivated fractures at site 12.....................................................277<br />
Figure A2.97. Slickenlines along set I reactivated fracture surfaces at site 12 ..........278<br />
Figure A2.98. Limey sandstone pavement at site 12..................................................279<br />
Figure A2.99. Stereonets <strong>of</strong> measurements in the limey sandstone at site 12............279<br />
Figure A2.100. Phosphoria pavement SE <strong>of</strong> site 11...................................................280<br />
Figure A2.101. Stereonets <strong>of</strong> measurements in the Phosphoria at site 12..................280<br />
Figure A2.102. Photograph <strong>of</strong> the hinge ....................................................................281<br />
Figure A2.103. Hinge fracture measurements............................................................282<br />
Figure A2.104. Thin sections <strong>of</strong> set I and set II fractures in the hinge.......................283<br />
Figure A2.105. Fracture pattern in the hinge..............................................................284<br />
Figure A2.106. Dispersion in orientation <strong>of</strong> hinge fracture sets.................................285<br />
Figure A2.107. Intense fracturing within the Madison Fm. in the hinge ...................285<br />
Figure A2.108. Photograph <strong>of</strong> site 10.........................................................................286<br />
Figure A2.109. Sandstone fracture measurements in the limbs and hinge.................287<br />
Figure A2.110. Stages <strong>of</strong> fracture and fold development...........................................291<br />
xxii
Figure A2.111. Mechanism <strong>of</strong> hinge perpendicular jointing: Gross et al., 1998 .......292<br />
Figure A2.112. Curvature map <strong>of</strong> Sheep Mt. .............................................................293<br />
Figure A2.113. Geometry for elastic model investigating set II development...........295<br />
Figure A2.114. Modeled elastic displacements and most tensile stress field.............296<br />
Figure A2.115. Correlation <strong>of</strong> model results and field observations..........................297<br />
Figure A2.116. Conceptual model <strong>of</strong> folding at Sheep Mt.........................................298<br />
Figure A2.117. Conceptual model <strong>of</strong> set IR fractures formed in the forelimb...........299<br />
Figure A2.118. Stages <strong>of</strong> fracturing and shearing <strong>of</strong> set I fractures ...........................300<br />
Figure A2.119. Proximity <strong>of</strong> a stress state to brittle failure........................................301<br />
xxiii
xxiv
Chapter 1<br />
Mechanical and stratigraphic constraints on the evolution <strong>of</strong> faulting<br />
at Elk Hills, CA<br />
Abstract<br />
To unravel the four-dimensional evolution <strong>of</strong> the Elk Hills Oil Field, Kern<br />
County, CA we integrate seismically interpreted fault surfaces, stratigraphic units, and<br />
stratigraphic features with mechanical models. Correspondence <strong>of</strong> synthetic<br />
stratigraphic surfaces, deformed by modeled vertical displacement fields, to<br />
seismically interpreted stratigraphic surfaces represented on structure contour maps<br />
suggests that the tectonic history described here is structurally, stratigraphically, and<br />
mechanically consistent, placing constraints on the regional deformation mechanism<br />
and local structure. During the time period investigated, Middle Miocene to present,<br />
the eastern and the western parts <strong>of</strong> the Elk Hills Anticline developed in response to a<br />
regional horizontal shortening oriented at about 035°. The apparent bend in the trend<br />
<strong>of</strong> the anticline, from northwest-southeast in the western part <strong>of</strong> the field, to east-west<br />
in the eastern part <strong>of</strong> the field is generated by the intersection <strong>of</strong> two distinct fault<br />
systems. In both fault systems, north dipping fault surfaces are backthrusts <strong>of</strong> older<br />
south dipping faults. These results have direct implications for the migration and<br />
emplacement <strong>of</strong> hydrocarbons at Elk Hills, suggesting that Upper Miocene Stevens<br />
turbidite oil pools were derived from sources to the south. Additionally, this study<br />
indicates that the method by which stratigraphic and structural interpretations are<br />
incorporated into a sequence <strong>of</strong> forward mechanical models represents an effective<br />
means <strong>of</strong> constraining the structural evolution <strong>of</strong> a fault network that developed within<br />
a syn-depositional tectonic setting.<br />
Introduction<br />
At Elk Hills Oil Field, Kern County, CA better knowledge <strong>of</strong> the present day and<br />
evolutionary structure <strong>of</strong> the underlying faults would improve recovery efforts. Gross<br />
fault geometry has implications for the existence <strong>of</strong> hydrocarbon traps and the<br />
trajectories <strong>of</strong> wellbores, while evolutionary structure has implications for the timing<br />
1
<strong>of</strong> hydrocarbon migration and entrapment. Previous studies have considered the<br />
current day fault geometry at Elk Hills (Nicholson, 1990; Imperato, 1995), and a<br />
recently published geochemical analysis <strong>of</strong> various oils constrains the timing <strong>of</strong><br />
emplacement <strong>of</strong> specific oil pools (Zumberge et al., 2005). To date, however, there has<br />
not been a well documented study <strong>of</strong> the growth <strong>of</strong> the subsurface faults at Elk Hills<br />
through time.<br />
A three-dimensional seismic reflection volume acquired over the field in 1999<br />
images the shallow fold and fault geometry, for the first time making such a study<br />
feasible. Although the existence <strong>of</strong> this seismic reflection volume greatly enhances<br />
efforts to determine the history <strong>of</strong> faulting at Elk Hills, two issues require further<br />
attention. As in many cases, the resolution <strong>of</strong> the data at Elk Hills decreases with<br />
depth, and so the deep fault geometry, specifically how faults intersect at depth,<br />
remains debatable. Additionally, evolutionary structure is not directly observable<br />
within the three-dimensional seismic reflection data volume, as time is not<br />
represented.<br />
Recent literature <strong>of</strong>fers a methodology to help constrain fault geometry and<br />
timing using mechanical models. Savage and Cooke (2004) present the displacement<br />
fields resulting from heuristic models with simple fault geometries for a field area<br />
where no faults are directly observable, asserting that the geometry <strong>of</strong> mechanically<br />
interacting faults can be constrained by the distributions <strong>of</strong> their displacement fields.<br />
Muller and Aydin (2005) and Resor et al. (2005) use mechanical models to investigate<br />
recent earthquakes where fault geometry is obscure, citing plausible fault geometries<br />
as those that produce modeled elastic displacement fields closely resembling observed<br />
displacements. These studies represent one episode <strong>of</strong> deformation, wherein fault<br />
geometry is static. Elk Hills is a growth fold, and the seismic reflection data reveal that<br />
not all faults have the same history <strong>of</strong> activity, so this modeling approach must be<br />
tailored to incorporate the different stages <strong>of</strong> fault evolution.<br />
Prior structural studies document how various geological and geophysical<br />
observations can be integrated to constrain the growth history <strong>of</strong> faults in cases where<br />
faults and folds are imaged adequately. For example, Medwedeff (1989), Suppe et al.<br />
(1992), Bloch et al. (1993), Shaw and Suppe (1996), and Shaw et al. (2002) show that<br />
2
growth wedges can be analyzed to determine intervals <strong>of</strong> fault movement along a<br />
single fault plane and to distinguish pre-, syn-, and post-faulting strata. Stratigraphic<br />
signatures present within the seismic reflection data at the Elk Hills Oil Field indicate<br />
that structural development and deposition were coeval, thus motivating a similar<br />
analysis. At Elk Hills, however, activity along multiple intersecting faults presents a<br />
complex history, requiring that numerous growth signatures be interpreted.<br />
In our study <strong>of</strong> Elk Hills, we show how these two previously published<br />
techniques can be combined to develop a fault history that is structurally,<br />
stratigraphically, and mechanically consistent. In light <strong>of</strong> pr<strong>of</strong>iles <strong>of</strong> interval<br />
thicknesses, stratigraphic bedding relationships, and isochore maps, we constrain the<br />
sequence <strong>of</strong> faulting. This interpreted growth sequence is then tested by comparing the<br />
displacement field inferred from structure contour maps to model displacement fields.<br />
The structure contour maps are taken as a cumulative representation <strong>of</strong> the elastic<br />
displacement fields modeled through each stage <strong>of</strong> fault evolution. It is tacitly<br />
assumed that the elastic stress perturbations due to individual slip events relax<br />
between events in such a way that the displacement fields for multiple events over ten<br />
million years are simply additive.<br />
Where stratigraphic signatures are not adequate to determine the activity <strong>of</strong> a<br />
specific fault during a given period, or the resolution <strong>of</strong> the data does not permit a<br />
complete understanding <strong>of</strong> fault geometry with depth, alternate fault geometries and<br />
faulting histories were considered. A series <strong>of</strong> forward mechanical models was<br />
constructed to test each possible fault network evolution. In this paper, we focus on<br />
the growth sequence that led to the best correlation between modeled and interpreted<br />
displacement fields. We note in the sections on structural interpretation and<br />
stratigraphic constraints on fault evolution where certain interpretations required<br />
additional testing.<br />
This study uses stratigraphic and mechanical principles to constrain the four-<br />
dimensional evolution <strong>of</strong> the fault system beneath the Elk Hills Anticline. It provides<br />
insight into the tectonic framework in which the field developed and the geometry and<br />
timing <strong>of</strong> faulting, thus having significant implications for hydrocarbon migration.<br />
Additionally, this study represents an extension <strong>of</strong> previous work on mechanical<br />
3
forward modeling <strong>of</strong> deformation in compressional tectonic settings (Shamir and Eyal,<br />
1995; Savage and Cooke, 2004), developing a methodology to consider both multiple<br />
faults and multiple time steps in an analysis that combines faulting kinematics and<br />
mechanics.<br />
Regional Geological Setting<br />
Elk Hills is located 25 km (15.5 mi) north <strong>of</strong> the bend in the San Andreas Fault<br />
(Fig. 1.1) in the southern San Joaquin Valley within the fold and thrust belt that lines<br />
the west side <strong>of</strong> the valley (Nicholson, 1990). Deformation within this belt is linked to<br />
tectonism along the San Andreas Fault, which lies just west <strong>of</strong> the Temblor Range that<br />
bounds the western limit <strong>of</strong> the valley. Coalinga, Kettleman Hills, and Lost Hills are<br />
similarly oriented antiforms proximal to Elk Hills. Interpretation <strong>of</strong> the causal tectonic<br />
mechanism for these folds has varied. In the 1970s, Wilcox et al. (1973) and Harding<br />
(1974, 1976) suggested that these echelon folds are the result <strong>of</strong> a wrenching<br />
mechanism related to slip along the San Andreas Fault. In the following decade,<br />
interpretation <strong>of</strong> a seismic reflection pr<strong>of</strong>ile across Kettleman Hills (Wentworth et al.,<br />
1984) led to the reclassification <strong>of</strong> these anticlines as thrust related. This interpretation<br />
was later strengthened by the analysis <strong>of</strong> earthquakes near New Idria in 1982 (M=5.5),<br />
Coalinga in 1983 (M=6.5) and Kettleman Hills North Dome in 1985 (M=6.1), which<br />
indicated the activity <strong>of</strong> thrust faults striking subparallel to the trend <strong>of</strong> these folds<br />
(e.g. Namson and Davis, 1988; Ekstrom et al., 1992; Stein and Ekstrom, 1992). In situ<br />
borehole studies that estimated the regional maximum horizontal compression<br />
direction as northeast-southwest (e.g. Mount and Suppe, 1987; Zoback et al., 1987;<br />
Castillo and Zoback, 1994), when combined with the northwest-southeast trend <strong>of</strong> the<br />
anticlinal hinges, are also consistent with the thrust related hypothesis.<br />
A proposition that the folds formed initially with trends oblique to the San<br />
Andreas Fault and subsequently were rotated to their subparallel orientations, with<br />
deformation style transitioning from wrench-related shearing to fault-perpendicular<br />
shortening (Miller, 1998). In this paper, we show that mechanical models do not<br />
generate representative uplift at Elk Hills when the slip along the underlying faults is<br />
4
36 0 00’<br />
Diablo Range<br />
New Idria<br />
Coalinga<br />
Coalinga<br />
120 0 00’<br />
San Andreas Fault<br />
N<br />
Kettleman Hills<br />
Temblor Range<br />
0 mile 20<br />
0 km 30<br />
120 0 00’<br />
San Joaquin<br />
Valley<br />
Lost Hills<br />
Elk Hills<br />
Buena Vista<br />
119 0 00’<br />
Taft<br />
Midway Sunset<br />
Sierra Nevada Range<br />
Bakersfield<br />
San Emigdio Mtns<br />
119 0 00’<br />
Figure 1.1. Location <strong>of</strong> the Elk Hills Oil Field within the southwestern San Joaquin<br />
Valley <strong>of</strong> California.<br />
5<br />
36 0 00’<br />
35 0 00’
predominantly strike-slip; and we present mechanical model results for the data<br />
included in this study that are consistent with a thrust fault related growth mechanism.<br />
Elk Hills Field<br />
Elk Hills was first classified as oil land based on field work by Arnold and<br />
Johnson (1910) that correlated surface morphology and lithologies at Elk Hills to that<br />
<strong>of</strong> other known oil fields in the San Joaquin Valley. Shallow tests proved the existence<br />
<strong>of</strong> oil in 1911 (Maher et al., 1975). In 1912, Elk Hills was set aside as Naval<br />
Petroleum Reserve No. 1 and remained largely shut-in until 1976 (Reid and McIntyre,<br />
2001). During this time, several geological studies, based on field data and<br />
increasingly deeper subsurface data, were conducted at Elk Hills (e.g. Thoms and<br />
Smith, 1922; Pemberton, 1929; Woodring et al., 1932; Maher et al., 1975).<br />
As a result <strong>of</strong> the multitude <strong>of</strong> wells drilled on site since the discovery <strong>of</strong> oil and<br />
field studies carried out within the greater San Joaquin Valley, the upper Tertiary<br />
stratigraphy at Elk Hills is well documented (e.g. Maher et al., 1975; Sarna-Wojcicki<br />
et al., 1979; Loomis, 1990; Sarna-Wojcicki et al., 1990; Bloch, 1992; Miller, 1999).<br />
The Monterey Formation, comprising the mid to late Miocene interval, is the best<br />
known stratigraphic sequence at Elk Hills. It has been the subject <strong>of</strong> much study in the<br />
past few decades due to its function as both source rock and reservoir for<br />
hydrocarbons, with the diagenesis <strong>of</strong> its constituent porcelanites (e.g. Graham and<br />
Williams, 1985; Eichhubl and Behl, 1998; Reid and McIntyre, 2001) and the<br />
deposition and trapping mechanisms <strong>of</strong> its constituent turbidites (e.g. MacPherson,<br />
1978; Webb, 1981; Reid, 1990; Reid, 1995; Shultz, 2003) receiving specific attention.<br />
These studies combined with investigations into the larger San Joaquin Valley<br />
petroleum system (e.g. Peters et al., 1994), have bolstered recovery efforts at Elk Hills.<br />
Today, over 2,000 wells are producing from four petroleum zones. As <strong>of</strong> 2004,<br />
cumulative production at Elk Hills exceeded 1.2 billion barrels <strong>of</strong> oil and 1.8 trillion<br />
cubic feet <strong>of</strong> natural gas, making it the seventh largest oil field in the continental U.S<br />
(California Division <strong>of</strong> Oil and Gas, 2005).<br />
6
Structural Interpretation<br />
The Elk Hills structure has an overall northwest-southeast anticlinal trend (Fig.<br />
1.2a, 1.2b). At shallow depths, Elk Hills is a broad structure with two slight highs<br />
representing left stepping echelon anticlines called 29R and 31S (Fig. 1.2a). At depth,<br />
these anticlines are distinct and a much lower amplitude fold called the Northwest<br />
Stevens structure lies to the northwest <strong>of</strong> the echelon folds (Fig. 1.2b). Collectively,<br />
these three structures constitute the Elk Hills Anticline and Oil Field.<br />
The fault interpretation at Elk Hills is based primarily upon the three-<br />
dimensional volume <strong>of</strong> seismic reflection data that was collected over the field from<br />
1999 to 2000. Along with borehole data from over 700 wells, the seismic data place<br />
constraints on the large scale faulting in the field. In the western part <strong>of</strong> the field, four<br />
main structure bounding faults have been identified, all <strong>of</strong> which strike northwest-<br />
southeast (Fig. 1.2a and 1.2b). Three <strong>of</strong> these faults, 1R, 2R, and 3R, are thrust faults<br />
with dips that decrease with depth (Fig. 1.2c). The decollement surface for the 1R fault<br />
is placed within the Late Oligocene Lower Santos shale, approximately 1 km above<br />
that inferred for the 2R and 3R faults, which sole into the Early Oligocene Tumey<br />
shale. These decollement levels are somewhat ambiguous within the seismic reflection<br />
data, and have been located with the help <strong>of</strong> mechanical models. Mechanical models<br />
have also helped to interpret the fourth fault, 5R, as a backthrust <strong>of</strong> the 1R fault.<br />
Correlating the spatial location <strong>of</strong> these faults with the shape <strong>of</strong> deformed seismic<br />
reflectors as displayed on structure contour maps, we associate the 2R fault with the<br />
Northwest Stevens anticline, the 3R fault with the 31S anticline, and the 1R and 5R<br />
faults with the 29R anticline (Fig. 1.2).<br />
Cross sections through the eastern part <strong>of</strong> the field reveal a different structural<br />
configuration (Fig. 1.2d). Here, the 7 fault is a steep and nearly planar fault dipping to<br />
the south. It trends east-west, as does the 6R fault, which dips to the north.<br />
Stratigraphic features within the seismic data imply that the 6R fault is much younger<br />
than the 7 fault (Fig. 1.2c). An anticlinal crest comparable to the anticlinal crest<br />
located slightly to the south <strong>of</strong> the 7 fault has not developed adjacent to the 6R fault at<br />
depth, suggesting that early in the structural history <strong>of</strong> Elk Hills, the 7 fault was the<br />
only fold forming fault present in the eastern part <strong>of</strong> the field. Mechanical<br />
7
SW NE<br />
S N<br />
8<br />
8<br />
0 km 2<br />
0 km 2<br />
7<br />
0 mile 1<br />
7<br />
0 mile 1<br />
6<br />
6<br />
5<br />
5<br />
depth (km) 0<br />
McDONALD<br />
3R<br />
2R<br />
1R<br />
4<br />
BASE REEF RIDGE<br />
3<br />
5R<br />
CALITROLEUM<br />
2<br />
NWS<br />
anticline<br />
WILHELM<br />
31S<br />
anticline<br />
MYA4-A<br />
1<br />
29R<br />
anticline<br />
depth (km) 0<br />
6R<br />
4<br />
McDONALD<br />
7<br />
BASEREEFRIDGE<br />
3<br />
2<br />
CALITROLEUM<br />
31S<br />
anticline<br />
WILHELM<br />
1<br />
MYA4-A<br />
(c) (d)<br />
A A’<br />
B B’<br />
NE<br />
119 0 32’00”<br />
119 0 26’00”<br />
119 0 20’00”<br />
119 0 32’00”<br />
119 0 26’00”<br />
119 0 20’00”<br />
0 km 2<br />
8<br />
B<br />
0 km 2<br />
B<br />
0mile1 6R<br />
1829<br />
305<br />
0mile 1<br />
N<br />
2438<br />
A<br />
N<br />
6R<br />
1R<br />
610<br />
A<br />
1R<br />
5R<br />
3048<br />
35 0 16’00” 35 0 20’00”<br />
914<br />
3658<br />
7<br />
5R<br />
31S anticline<br />
31S anticline<br />
29R anticline<br />
1219<br />
4267<br />
7<br />
1524<br />
29R anticline<br />
4877<br />
3R<br />
depth (m)<br />
3R<br />
depth (m)<br />
NWS anticline<br />
B’<br />
NWS anticline<br />
B’<br />
2R<br />
A’<br />
35 0 20’00”<br />
35 0 16’00” 35 0 20’00”<br />
2R<br />
A’<br />
35 0 20’00”<br />
C.I. = 76 m (250 ft)<br />
C.I. = 152 m (500 ft)<br />
(a) (b)<br />
119 0 32’00”<br />
119 0 26’00”<br />
119 0 20’00”<br />
119 0 32’00”<br />
119 0 26’00”<br />
119 0 20’00”
Figure 1.2 (opposite page). (a) Structure contour map <strong>of</strong> a Late Pliocene stratigraphic<br />
unit. The traces <strong>of</strong> the six seismically interpreted, structure bounding faults are drawn<br />
on the map and labeled. Dashed lines represent faults that are below the contoured<br />
surface. (b) Structure contour map <strong>of</strong> a Middle Miocene stratigraphic unit. At this<br />
depth, the slight highs seen in figure 1.2a, the 31S and the 29R anticlines, are clearly<br />
two distinct anticlines. A fold <strong>of</strong> much lower amplitude, the Northwest Stevens<br />
structure, lies to the north. (c) A cross section through the western part <strong>of</strong> the field<br />
running along the line A to A’ in (a) and (b). (d) A cross section through the eastern<br />
part <strong>of</strong> the field running along the line B to B’ in (a) and (b). Labeled anticlinal crests,<br />
faults, and marker horizons are the structural and stratigraphic elements factoring into<br />
this study.<br />
modeling has indicated that the 6R fault is a backthrust <strong>of</strong> the 7 fault and does not<br />
cross-cut the 7 fault.<br />
Velocity Model<br />
We created a three-dimensional velocity model to convert surfaces interpreted<br />
within the seismic data volume from the time domain to the depth domain. The three<br />
dimensionality <strong>of</strong> this model is very important to the preservation <strong>of</strong> the shapes <strong>of</strong> the<br />
faults as they are interpreted, and these shapes provide the input geometry for the<br />
mechanical models. As noted, the majority <strong>of</strong> faults at Elk Hills are not planar. Thus,<br />
the two-dimensional method, commonly applied within fields where planar faults<br />
exist, <strong>of</strong> converting fault polygons (hanging wall and footwall cuts) from time to depth<br />
at various horizons and then extending a planar surface between these polygons to<br />
generate a three-dimensional fault surface, is not adequate for the Elk Hills field.<br />
The velocity model was calibrated with the Base Reef Ridge horizon (see<br />
below). This horizon was selected as a calibration surface based primarily on the<br />
exceptional well control <strong>of</strong> 704 data points. It was chosen over other surfaces <strong>of</strong><br />
comparable well control due to its position lower in the stratigraphic column, thus<br />
providing calibration to deeper levels. The velocities within the model range from<br />
1,400 m/sec (4,600 ft/sec) near the surface to 6,000 m/sec (19,700 ft/sec) at depth.<br />
This velocity pr<strong>of</strong>ile corresponds to the two-way travel time interval extending from 0<br />
to 5 seconds, the lower limit <strong>of</strong> the seismic volume.<br />
9
Stratigraphy<br />
Five stratigraphic markers were selected for use in this study: the Middle<br />
Miocene McDonald horizon, the Early Pliocene Base Reef Ridge horizon (BRR), the<br />
Early Pliocene Calitroleum horizon, the Middle Pliocene Wilhelm horizon, and the<br />
Late Pliocene Mya 4-A horizon (Fig. 1.3). Due to strong seismic reflections (large<br />
impedance contrasts), each horizon can be correlated throughout the three-dimensional<br />
volume. Well picks, numbering into the hundreds for each <strong>of</strong> these horizons, serve as<br />
calibration for the geophysical seismic reflection volume. No horizons older than the<br />
mid Miocene McDonald horizon are included in this study because both well control<br />
and clarity <strong>of</strong> the seismic reflection imaging diminish greatly below the McDonald<br />
marker. The results <strong>of</strong> this study therefore have implications for the development <strong>of</strong><br />
Elk Hills during the time period extending from the Middle Miocene to the present.<br />
Stratigraphic constraints<br />
Stratigraphic analyses contribute significantly to the interpretation <strong>of</strong> fault<br />
evolution at Elk Hills because the faulting is syn-depositional growth faulting. As<br />
evident in cross sectional views (Fig. 1.2c and 1.2d), stratigraphic intervals thin<br />
toward faults within their hanging wall and thicken discontinuously across the fault<br />
planes into the footwall. These and similar stratigraphic features can be identified and<br />
used to interpret the timing <strong>of</strong> relative motion. These techniques provide sufficient<br />
constraints on fault evolution so particular fault initiations can be bracketed between<br />
the deposition times <strong>of</strong> different stratigraphic layers.<br />
Pseudowells<br />
We term the first method <strong>of</strong> stratigraphic analysis pseudowells because they are<br />
artificial pr<strong>of</strong>iles <strong>of</strong> interval thicknesses. To construct pseudowells, we generated<br />
depth converted cross-sections running perpendicular to the strike <strong>of</strong> the faults. We<br />
then drew two well-path trajectories for each fault, one in the hanging wall and the<br />
other in the footwall, both parallel to and equidistant from the fault (Fig. 1.4a). Where<br />
a trajectory intersects with the center <strong>of</strong> an interval, a bedding perpendicular<br />
10
PERIOD<br />
QUAT.<br />
NEOGENE<br />
PALEOGENE<br />
EPOCH<br />
PLEIST.<br />
PLIOCENE<br />
MIOCENE<br />
OLIGOCENE<br />
EOCENE<br />
FORMATION MEMBER / ZONE<br />
SAN JOAQUIN<br />
ETCHEGOIN<br />
MONTEREY<br />
TEMBLOR<br />
sandstone<br />
pebbly sand<br />
clay shale<br />
silty shale<br />
TULARE<br />
DRY GAS ZONE<br />
SHALLOW OIL ZONE<br />
REEF RIDGE<br />
ANTELOPE SHALE /<br />
MCDONALD<br />
DEVILWATER / GOULD<br />
MEDIA<br />
CARNEROS<br />
UPPER SANTOS<br />
CASTLEROCK<br />
LOWER SANTOS<br />
SALT CREEK / CYMRIC<br />
OCEANIC<br />
TUMEY<br />
STEVENS<br />
PHACOIDES<br />
KREYENHAGEN<br />
siliceous shale<br />
dolomitic shale<br />
LITH.<br />
interbedded sandstone<br />
and siltstone<br />
sandstone lens<br />
Mya 4-A<br />
Wilhelm<br />
Calitroleum<br />
Base Reef<br />
Ridge<br />
(BRR)<br />
McDonald<br />
Figure 1.3. Stratigraphic column <strong>of</strong> the mid to upper tertiary sediments at Elk Hills<br />
based on Maher et al. (1975). The stratigraphic positions <strong>of</strong> the five markers used in<br />
this study are noted to the right <strong>of</strong> the column. The lithology column is highly<br />
simplified.<br />
11
thickness was measured and plotted. The thickness <strong>of</strong> each interval is hung on the top<br />
horizon <strong>of</strong> that interval (Fig. 1.4b). Because the strike <strong>of</strong> the faults in the eastern part<br />
<strong>of</strong> the Elk Hills field is much different from that in the western part, we consider these<br />
parts separately.<br />
Pseudowell interpretation relied heavily upon cross-sections. For instance, the<br />
cross section in figure 1.4a shows a regional thickening <strong>of</strong> sediments toward the<br />
southwest during McDonald to BRR time <strong>of</strong> depostion. For the other three time<br />
intervals considered, the regional thickening direction is reversed, with thickening<br />
toward the northeast. When looking at the pseudowell plot (Fig. 1.4b), we note<br />
interruptions in the regional trends. Fault activity is identified based on both<br />
stratigraphic thinning and sharp changes in thickness across faults. An anomalously<br />
thin interval is correlated with the location <strong>of</strong> a structural high, where thinning is<br />
interpreted as the result <strong>of</strong> erosion (or lesser deposition) <strong>of</strong> sediments caused by uplift<br />
associated with slip on the underlying fault. Eroded sediments from the uplifted<br />
hanging walls are subsequently deposited on the footwalls, creating a difference in<br />
thickness <strong>of</strong> the interval from one side <strong>of</strong> the fault to the other.<br />
Pseudowell interpretations: Western Elk Hills<br />
Figure 1.4b shows that during the period from McDonald to BRR time, there is a<br />
departure from the trend <strong>of</strong> thickening toward the southwest at pseudowells H2R and<br />
H3R. These pseudowells are positioned in the hanging walls <strong>of</strong> the 2R and 3R faults,<br />
respectively. The cross section in figure 1.4a shows a change in thickness across the<br />
2R fault and a larger change across the 3R fault, suggesting that both faults were<br />
active during this interval. The thickness <strong>of</strong> the McDonald to BRR interval in figure<br />
1.4a is slightly different across the 1R fault. We tentatively infer that 1R was less<br />
active (or inactive) during this time relative to 2R and 3R, but reexamine this activity<br />
more closely in subsequent examples. There is no thinning <strong>of</strong> the McDonald to BRR<br />
interval in the 29R anticline during this time, and the hanging wall and footwall<br />
thicknesses across the 5R fault are constant, indicating that the 5R fault was inactive.<br />
12
(a)<br />
depth (km)<br />
0<br />
1<br />
2<br />
3<br />
4<br />
5<br />
6<br />
7<br />
8<br />
(c)<br />
1<br />
2<br />
3<br />
4<br />
5<br />
depth (km) 0<br />
6<br />
7<br />
8<br />
0 mile 1<br />
0 km 2<br />
SW NE<br />
H6R<br />
F6R<br />
0 mile 1<br />
0 km 2<br />
F5R H5R<br />
1R<br />
31S<br />
anticline<br />
6R<br />
29R<br />
anticline<br />
7<br />
5R<br />
H1R F1R H3R F3R<br />
3R<br />
H7 F7<br />
31S<br />
anticline<br />
2R<br />
NWS<br />
anticline<br />
MYA4- A<br />
S N<br />
H2R F2R<br />
NE<br />
MYA4-A<br />
(b)<br />
(d)<br />
m<br />
0<br />
400<br />
0<br />
400<br />
800<br />
0<br />
400<br />
800<br />
1200<br />
0<br />
400<br />
800<br />
F5R H5R H1R F1R H3R F3R H2R F2R<br />
MYA4-A<br />
WILHELM<br />
CALITROLEUM<br />
BRR<br />
1200<br />
SW NE<br />
m<br />
0<br />
400<br />
0<br />
400<br />
0<br />
400<br />
0<br />
400<br />
800<br />
F6R H6R H7 F7<br />
MYA4-A<br />
WILHELM<br />
CALITROLEUM<br />
BRR<br />
S N<br />
Figure 1.4. Cross sections through the (a) western and (c) eastern parts <strong>of</strong> the field<br />
showing the locations <strong>of</strong> pseudowells used for stratigraphic analysis. The orientation<br />
<strong>of</strong> the cross sections run from A to A’ and B to B’ in figure 1.2a. Dashed gray lines<br />
represent pseudowell paths and white dots represent the intersection points <strong>of</strong> these<br />
wellpaths with the centers <strong>of</strong> stratigraphic intervals. White lines represent the bedding<br />
perpendicular thickness measurements made for each interval along wellpaths.<br />
Pseudowell plot <strong>of</strong> the thicknesses in meters <strong>of</strong> the four stratigraphic intervals in each<br />
well location for the (b) western and (d) eastern parts <strong>of</strong> the field.<br />
13
The most notable feature in the interval from BRR to Calitroleum time is the<br />
large contrast in hanging wall and footwall thickness across the 2R fault (Fig. 1.4a).<br />
This observation is mirrored in the pseudowell plot at well F2R, where the thickness is<br />
much greater than in well H2R, departing from the slight thickening trend. We infer<br />
that the 2R fault was very active during this period. Similarly, this interval in well<br />
H3R in the hanging wall <strong>of</strong> the 3R fault is thin compared to that in well F3R in the<br />
footwall, suggesting continued slip along 3R. Little can be deduced about the activity<br />
<strong>of</strong> the 1R fault from these plots. As in the earlier interval, the hanging wall and<br />
footwall thicknesses across the 5R fault are constant, suggesting that no slip occurred<br />
from BRR to Calitroleum time.<br />
The Calitroleum to Wilhelm interval is thin in pseudowell H5R compared to<br />
both F5R and H1R (Fig. 1.4b). This suggests that the area near H5R was a structural<br />
high, and implies the presence <strong>of</strong> an active fault beneath the interval. Slip along either<br />
or both the 1R and 5R faults could produce uplift at H5R. A disparity in the<br />
thicknesses <strong>of</strong> the Calitroleum to Wilhelm interval between the hanging wall and<br />
footwall <strong>of</strong> the 5R fault indicates that it was active during this period. It is not possible<br />
to determine from the cross section and pseudowell plots (Fig. 1.4) how large a role, if<br />
any, fault 1R played in the development <strong>of</strong> the structural high near well H5R. There is<br />
no diagnostic evidence for slip on the 2R fault from Calitroleum to Wilhelm time<br />
based on figure 1.5.<br />
In the final interval, Wilhelm to Mya 4-A, the structure was apparently<br />
composed <strong>of</strong> a single broad anticline. The pseudowells on the flanks <strong>of</strong> the structure,<br />
wells F5R, H2R, and F2R, are thick compared with other wells. Based on the thin<br />
intervals in the H1R, F1R, and F3R pseudowells, we deduce that uplift was still<br />
occurring due to slip on faults in both the northeast and the southwest parts <strong>of</strong> the<br />
field.<br />
Through this analysis, we recognize that slip along the northeastern faults, 2R<br />
and 3R, affected depositional patterns during the Late Miocene, whereas Pliocene<br />
depositional patterns suggest slip along all <strong>of</strong> the major faults. We conclude that slip<br />
along the 2R and 3R faults initiated before slip along the 1R and 5R faults, but that<br />
motion along the earlier faults continued as slip along the 1R and 5R faults initiated.<br />
14
Pseudowell interpretations: Eastern Elk Hills<br />
The most interesting stratigraphic constraints on faulting in the eastern part <strong>of</strong><br />
the Elk Hills Oil Field pertain to the 7 fault and can be seen in both cross-section (Fig.<br />
1.4c) and pseudowell analysis (Fig. 1.4d). The differences in interval thickness across<br />
the 7 fault from well H7 to well F7, as well as the differences in interval thickness<br />
across the anticline from well H7 to well H6R, indicate that activity along the 7 fault<br />
decreased after the deposition <strong>of</strong> the Base Reef Ridge to Calitroleum interval.<br />
Pseudowell analysis indicates that wells located in the hanging wall and footwall <strong>of</strong><br />
the 6R fault, wells H6R and F6R, have equivalent thickness for each <strong>of</strong> the studied<br />
intervals. The 6R fault was not active during these intervals.<br />
Bedding relationships<br />
The second technique for constraining fault timing is the examination <strong>of</strong><br />
stratigraphic bedding relationships that are indicators <strong>of</strong> fault movement. Figure 1.5<br />
provides schematic drawings <strong>of</strong> the five relationships considered: divergent fill,<br />
disrupted reflectors, onlap fill, divergent reflectors, and disrupted fill (Mitchum et al.,<br />
1977). Interpretation <strong>of</strong> these relationships is based upon the interaction <strong>of</strong> structure<br />
and stratigraphy. Divergent fill indicates syn-faulting strata, disrupted reflectors<br />
indicate pre-faulting strata, onlap fill indicates post-faulting strata, divergent reflectors<br />
indicate syn- to post-faulting strata, and disrupted fill indicates syn-faulting strata<br />
relative to one fault and pre-faulting strata relative to the second fault. Many such<br />
bedding relationships are imaged within the Elk Hills seismic reflection dataset and<br />
these provide important constraints on fault activity (Fig. 1.6).<br />
Bedding relationship interpretations<br />
Divergent fill is shown in figure 1.6, where beds thin onto, and truncate against,<br />
the anticlinal crest in the hanging wall <strong>of</strong> the 3R fault within the McDonald to BRR<br />
interval. The 3R fault was thus active during the deposition <strong>of</strong> this interval. The 1R<br />
fault <strong>of</strong>fsets this same stratigraphic package with no apparent across fault thickness<br />
change. Consideration <strong>of</strong> the kinematics involved in the process <strong>of</strong> <strong>of</strong>fsetting divergent<br />
15
(a) (d)<br />
(b)<br />
(c)<br />
(e)<br />
2 1<br />
Figure 1.5. The five stratigraphic bedding relationships considered in this study. Each<br />
suggests a timing relationship between faulting and the deposition <strong>of</strong> sediments. (a)<br />
Divergent fill indicating syn-faulting strata. (b) Disrupted reflectors <strong>of</strong> equal thickness<br />
indicating pre-faulting strata. (c) Onlap fill indicating post faulting strata. (d) Divergent<br />
reflectors indicating syn-faulting to post faulting strata. (e) Disrupted fill indicating that<br />
the strata are syn-faulting relative to fault 1 and pre-faulting relative to fault 2<br />
(Mitchum et al., 1977). This figure also suggests a timing relationship between the<br />
two faults, with fault 1 being older than fault 2.<br />
16
fill leads to the following conclusions: (1) the 3R fault is older than the 1R fault; (2)<br />
stratigraphic layers above the base <strong>of</strong> the divergent fill post-date the initiation <strong>of</strong> slip<br />
along the 3R fault; (3) the entire divergent fill package is older than slip along the 1R<br />
fault that <strong>of</strong>fsets it.<br />
Onlap fill and divergent reflectors are seen in figure 1.6 as sags in the BRR,<br />
Calitroleum, and Wilhelm horizons above the 1R fault. These features reflect a<br />
slowing or termination <strong>of</strong> slip along the 1R fault at the time <strong>of</strong> deposition <strong>of</strong> the<br />
deformed horizons. Just above the Wilhelm horizon, however, the next resolvable<br />
reflector is fairly straight, with no kink above the 1R fault. This geometry leads to the<br />
deduction that 1R fault activity slowed after the deposition <strong>of</strong> the Wilhelm horizon.<br />
The interval <strong>of</strong> rock between the bent and straight reflectors consists <strong>of</strong> post faulting<br />
strata that leveled out the paleotopography that was generated by previous slip along<br />
the 1R fault.<br />
At the northeast end <strong>of</strong> the cross section shown in figure 1.6, divergent<br />
reflectors are labeled above the 2R fault. These reflectors document an incremental<br />
infilling <strong>of</strong> paleotopography. Reflectors one through four are sequentially less<br />
divergent, indicating that each layer was subjected to less deformation subsequent to<br />
its deposition than the previous layer. The degree to which these reflectors are<br />
divergent indicates that slip along the 2R fault slowed during Calitroleum to Wilhelm<br />
time and may have ceased shortly after Wilhelm time.<br />
Disrupted reflectors <strong>of</strong> equal thickness occur across the 5R fault just above the<br />
Calitroleum horizon. Because there is no discrepancy in the thickness <strong>of</strong> hanging wall<br />
and footwall beds, it is inferred that movement along the 5R fault postdates the<br />
deposition <strong>of</strong> the Calitroleum horizon.<br />
Isochores<br />
The final technique for stratigraphic analysis constrains both fault height and the<br />
timing between deposition and faulting using isochore maps that provide contours <strong>of</strong><br />
the vertical thickness <strong>of</strong> a given interval. We have removed overthickening effects due<br />
to repeated sections across thrust faults from the isochore maps. Four isochore maps<br />
17
two-way time (s)<br />
1.0<br />
2.0<br />
3.0<br />
4.0<br />
5R<br />
29R<br />
anticline<br />
onlap fill<br />
1R<br />
divergent fill<br />
0 mile 1<br />
31S<br />
anticline<br />
0 km 2<br />
3R<br />
2R<br />
1<br />
4<br />
3<br />
2<br />
divergent<br />
reflectors<br />
SW NE<br />
Figure 1.6. Line drawing <strong>of</strong> a seismic line exhibiting each <strong>of</strong> the stratigraphic bedding<br />
relationships shown in figure 1.5. Timing relationships can be deduced from analysis<br />
<strong>of</strong> these indicators.<br />
18<br />
1<br />
2<br />
3<br />
4<br />
5<br />
approximate depth (km)
were interpreted, representing each <strong>of</strong> the studied time intervals (Fig. 1.7a, 1.7c, 1.7e,<br />
1.7g). In analyzing these maps, we focused on two fault-related signatures, contour<br />
merging and bed thinning. Closely spaced and merging contours (Fig. 1.8a) may<br />
indicate that a fault cut the interval at the time <strong>of</strong> deposition (Fig. 1.8b). Sediments<br />
eroded <strong>of</strong>f the hanging wall may be deposited on the footwall side <strong>of</strong> the fault,<br />
resulting in a sharp thickness contrast across the fault. The thinning <strong>of</strong> beds may<br />
indicate a structural high (Fig. 1.8c). Isochore maps do not contain information about<br />
the relative depths <strong>of</strong> any two points within a layer. Thus, thinning intervals could<br />
result from syn-depositional faulting below the interval, so the beds <strong>of</strong> interest are<br />
uplifted (Fig. 1.8di), or post-tectonic infilling by sediments <strong>of</strong> paleotopography (Fig.<br />
1.8dii). We use the seismic character <strong>of</strong> divergent reflectors, as previously illustrated<br />
in figure 1.6, to determine which interpretation is more representative <strong>of</strong> the faulting in<br />
question.<br />
Isochore interpretations: McDonald to Base Reef Ridge<br />
Isochores <strong>of</strong> vertical thickness between the McDonald and the Base Reef Ridge<br />
markers (Fig. 1.7a) show that a structural high is present along the trace <strong>of</strong> the 2R<br />
fault, indicating an active fault beneath the interval at the time <strong>of</strong> deposition. The<br />
structural high and close contours along the trace <strong>of</strong> the 3R fault indicate that it cut the<br />
interval during the time <strong>of</strong> deposition. Both <strong>of</strong> these faults were previously determined<br />
to be active prior to McDonald deposition, based on fault movement indicators.<br />
Isochore interpretation presents an additional conclusion in terms <strong>of</strong> the relative ages<br />
<strong>of</strong> these faults. Because the 3R fault cut further up section than the 2R fault during this<br />
time interval and the two faults sole to the same decollement level (Fig. 1.2b and<br />
1.4a), we infer that the 3R fault is older than the 2R fault.<br />
A few small isolated structural highs exist along the trace <strong>of</strong> the 1R fault,<br />
indicating that it was not slipping along its entire present day length. We infer that this<br />
isochore map captures the very early stages <strong>of</strong> growth <strong>of</strong> the 1R fault. Because the<br />
thickness <strong>of</strong> the McDonald to BRR interval remains roughly constant across the<br />
location <strong>of</strong> the trace <strong>of</strong> the 5R fault, we infer that the 5R fault was inactive during this<br />
time interval.<br />
19
(a)<br />
35 0 16’00” 35 0 20’00”<br />
(c)<br />
35 0 16’00” 35 0 20’00”<br />
(e)<br />
35 0 16’00” 35 0 20’00”<br />
(g)<br />
35 0 16’00” 35 0 20’00”<br />
N<br />
0mile1 0 km 2<br />
N<br />
0mile1 0 km 2<br />
N<br />
0mile1 0 km 2<br />
N<br />
0mile1 0 km 2<br />
119 0 32’00”<br />
2R<br />
2R<br />
2R<br />
2R<br />
119 0 32’00”<br />
5R<br />
5R<br />
5R<br />
5R<br />
3R<br />
1R<br />
119 0 26’00”<br />
3R<br />
1R<br />
1R<br />
3R<br />
3R<br />
1R<br />
119 0 26’00”<br />
C.I. = 76 m (250 ft)<br />
7<br />
6R<br />
119 0 20’00”<br />
C.I. = 76 m (250 ft)<br />
7<br />
C.I. = 15 m (50 ft)<br />
7<br />
6R<br />
6R<br />
C.I. = 15 m (50 ft)<br />
7<br />
6R<br />
119 0 20’00”<br />
35 0 20’00”<br />
thickness<br />
(m)<br />
1524<br />
1219<br />
914<br />
610<br />
305<br />
35 0 20’00” thickness<br />
(m)<br />
35 0 20’00”<br />
thickness<br />
(m)<br />
35 0 20’00”<br />
1829<br />
1524<br />
1219<br />
914<br />
610<br />
305<br />
427<br />
366<br />
305<br />
244<br />
183<br />
122<br />
thickness<br />
(m)<br />
366<br />
305<br />
244<br />
183<br />
122<br />
(b)<br />
35 0 16’00” 35 0 20’00”<br />
(d)<br />
35 0 16’00” 35 0 20’00”<br />
(f)<br />
35 0 16’00” 35 0 20’00”<br />
(h)<br />
35 0 16’00” 35 0 20’00”<br />
20<br />
119 0 32’00”<br />
119 0 32’00”<br />
119 0 32’00”<br />
119 0 32’00”<br />
119 0 26’00”<br />
119 0 26’00”<br />
119 0 26’00”<br />
119 0 26’00”<br />
119 0 20’00”<br />
N<br />
0 km 2<br />
119 0 20’00”<br />
N<br />
0 km 2<br />
119 0 20’00”<br />
N<br />
0 km 2<br />
119 0 20’00”<br />
N<br />
0 km 2<br />
35 0 20’00”<br />
35 0 20’00”<br />
35 0 20’00”<br />
35 0 20’00”<br />
1<br />
0.95<br />
0.9<br />
0.85<br />
0.8<br />
0.75<br />
0.7<br />
0.65<br />
0.6<br />
0.55<br />
1<br />
0.95<br />
0.9<br />
0.85<br />
0.8<br />
0.75<br />
0.7<br />
0.65<br />
0.6<br />
1<br />
0.95<br />
0.9<br />
0.85<br />
0.8<br />
0.75<br />
0.7<br />
1<br />
0.95<br />
0.9<br />
0.85<br />
0.8<br />
0.75<br />
0.7<br />
normalized thickness normalized thickness normalized thickness normalized thickness
Figure 1.7 (opposite page). Isochore maps <strong>of</strong> the intervals: McDonald to Base Reef<br />
Ridge (a) as interpreted, (b) as modeled; Base Reef Ridge to Calitroleum (c) as<br />
interpreted, (d) as modeled; Calitroleum to Wilhelm, (e) as interpreted, (f) as modeled;<br />
Wilhelm to Mya 4-A (g) as interpreted, (h) as modeled. Fault traces have been plotted<br />
and labeled on the interpreted isochore maps with solid lines representing faults that<br />
cut through the interval at the time <strong>of</strong> deposition, dashed lines representing faults that<br />
were below the interval at the time <strong>of</strong> deposition, and dotted line representing faults<br />
that had not yet begun to slip at the time <strong>of</strong> deposition <strong>of</strong> the interval. The thickness<br />
colorbar and contours for the interpreted isochores have been converted from feet<br />
into meters. Modeled isochores show normalized thicknesses with a 0.1 contour<br />
interval. For location referencing, an index map outlining the production blocks <strong>of</strong> the<br />
field has been plotted on both interpreted and modeled isochore maps.<br />
In the eastern part <strong>of</strong> the field, the structural high and close contours along the<br />
trace <strong>of</strong> the 7 fault indicate that it was active and cut up through the McDonald to Base<br />
Reef Ridge interval during the time <strong>of</strong> its deposition. Further to the south, along the<br />
present day trace <strong>of</strong> the 6R fault, there is no evidence <strong>of</strong> fault activity. The 6R fault<br />
trace lays in a low that is most likely an expression <strong>of</strong> the hanging wall subsidence that<br />
occurs well behind the tipline <strong>of</strong> a thrust fault as a result <strong>of</strong> displacement <strong>of</strong> material<br />
up the fault plane (Savage and Cooke, 2004).<br />
Isochore interpretations: Base Reef Ridge to Calitroleum<br />
The isochore map representing the time interval from Base Reef Ridge to<br />
Calitroleum deposition (Fig. 1.7b), highlights a few changes in fault activity from the<br />
previous interval. The very close contours and large difference in contour values<br />
across the 2R fault (about 1000 feet), indicate that this fault was active and cut up<br />
through the section, uplifting Base Reef Ridge to Calitroleum sediments in the<br />
hanging wall, much <strong>of</strong> which were eroded <strong>of</strong>f to create the large disparity in thickness<br />
<strong>of</strong> this interval across the 2R fault. The 3R fault apparently was still active during this<br />
interval based on the adjacent structural high, and the fact that it cut through this<br />
interval. If we compare the extent <strong>of</strong> the expression <strong>of</strong> the 3R fault in the Base Reef<br />
Ridge to Calitroleum interval with the previous interval, we see that slip migrated<br />
toward the southeastern end <strong>of</strong> the fault, which cuts through the interval, as indicated<br />
by the pattern <strong>of</strong> thinning across the crest <strong>of</strong> the 31S anticline. The east-west portion<br />
<strong>of</strong> the 31S anticline is thin during this interval, indicating that uplift along the 7 fault<br />
21
Figure 1.8. Fault related signatures seen within isochore maps. (a) Close contours<br />
are indicative <strong>of</strong> a fault cutting the interval during deposition. (b) A cross sectional<br />
view through the anticline along line C to C’ shown in (a). (c) Thin beds are indicative<br />
<strong>of</strong> a structural high. The line D to D’ shows the location <strong>of</strong> a cross-section through the<br />
anticline that can have two possible configurations: (di) thinning beds can result from<br />
an active fault beneath the interval, causing syn-depositional uplift, (dii) thinning beds<br />
can result from infill <strong>of</strong> paleotopography after fault slip.<br />
22
continued into Base Reef Ridge to Calitroleum time. In contrast with the previous<br />
interval, however, there is not a jump in the contour values along the trace <strong>of</strong> the fault,<br />
so it did not cut through the interval. The highly asymmetric shape <strong>of</strong> the thinning<br />
pattern, with a much steeper gradient on the northern side <strong>of</strong> the structural high,<br />
suggests that the sediments <strong>of</strong> this interval were draped over the tip <strong>of</strong> an active fault.<br />
To the south, in the vicinity <strong>of</strong> the 6R fault trace, the absence <strong>of</strong> a structural high, and<br />
<strong>of</strong> close contours, reveal that the fault had not yet developed at the time the<br />
Calitroleum was deposited.<br />
During this interval, the 1R fault was slipping along the entire length <strong>of</strong> the<br />
present day fault, as indicated by the extent <strong>of</strong> the structural high. To the southwest <strong>of</strong><br />
this structural high, where the thickness <strong>of</strong> the interval is fairly constant, there are no<br />
signs <strong>of</strong> activity along the 5R fault. We interpret the structural highs to the southeast<br />
<strong>of</strong> the 29R anticline as being related to uplift along faults associated with the Buena<br />
Vista and Midway-Sunset fields (Fig. 1.1).<br />
Isochore interpretations: Calitroleum to Wilhelm<br />
Isochore thickness patterns and fault activity change drastically after Calitroleum<br />
time. In the Calitroleum to Wilhelm isochore map (Fig. 1.7c), there is little<br />
disturbance <strong>of</strong> contours in the area <strong>of</strong> the 2R fault. During this interval, the 2R fault<br />
slipped much less than in the previous time interval, if at all. Similarly, slip along the 7<br />
fault virtually shut <strong>of</strong>f, as the average strike <strong>of</strong> the 31S anticline in this isochore map is<br />
oriented more northwest-southeast than previously, with the east-west section not as<br />
well-defined. The 3R fault was still active from Calitroleum to Wilhelm time, as the<br />
northwest-southeast part <strong>of</strong> the 31S anticline remained thin. In the southwestern part<br />
<strong>of</strong> the study area, a northwest-southeast striking depression bounded on the northeast<br />
by close contours appears along the trace <strong>of</strong> the 5R fault. This marks the beginning <strong>of</strong><br />
slip along the 5R fault and expresses the uplift and erosion <strong>of</strong> hanging wall sediments.<br />
Judging from the pattern <strong>of</strong> thinning over the 29R structure, where the gradient along<br />
the northern limb is steep, the 1R fault also was active during the Calitroleum to<br />
Wilhelm interval.<br />
23
Isochore interpretations: Wilhelm to Mya 4-A<br />
The isochore map (Fig. 1.7d) <strong>of</strong> the time from Wilhelm deposition to Mya 4-A<br />
deposition, depicts a relatively thin stratigraphic interval. The difference between the<br />
thickest and thinnest sections is small, and thus the contour map appears very noisy<br />
and is more difficult to interpret, but trends are noticeable. The 31S and 29R anticline<br />
locations remain thin through this time period, indicating that the 3R, 1R, and 5R<br />
faults were still active. As in the previous interval, little evidence for motion along the<br />
2R fault exists. Examination <strong>of</strong> the southern part <strong>of</strong> the isochore map indicates that the<br />
5R fault remained active beneath the interval while the 6R fault had not yet begun to<br />
slip.<br />
Stratigraphic Constraints on Fault Evolution<br />
The pseudowell, bedding relationship, and isochore interpretations made at Elk<br />
Hills allow us to place constraints on the evolution <strong>of</strong> the fault system beneath the<br />
anticline (Fig. 1.9). These stratigraphic interpretations indicate that in the western part<br />
<strong>of</strong> Elk Hills, both the 2R and 3R faults were active prior to deposition <strong>of</strong> the<br />
McDonald horizon. Initiation <strong>of</strong> slip along isolated segments <strong>of</strong> the 1R fault occurred<br />
at some time after McDonald deposition, but before Base Reef Ridge deposition and<br />
the 1R fault began slipping as a whole after Base Reef Ridge deposition. The 5R fault<br />
formed during the interval between Calitroleum and Wilhelm deposition.<br />
Interpretations for the eastern part <strong>of</strong> the field indicate that the 7 fault was active prior<br />
to McDonald deposition and slowed greatly after Calitroleum deposition and that the<br />
6R fault formed very late in the evolution <strong>of</strong> the anticline.<br />
Mechanical Modeling<br />
To test the mechanical viability <strong>of</strong> the stratigraphically interpreted fault<br />
chronology, and to further refine the evolution (both timing and geometry) <strong>of</strong> the fault<br />
network at Elk Hills, we turn to forward numerical models. The remainder <strong>of</strong> this<br />
paper focuses on the method involved in developing a mechanical model to apply to<br />
growth faulting. We do not show the results <strong>of</strong> all the scenarios tested, but only the<br />
model that provided the best fit for the data at Elk Hills. From this model, we<br />
24
(a)<br />
A A’<br />
3R<br />
pre-McDonald<br />
(Middle Miocene)<br />
A A‘<br />
A A‘<br />
1R<br />
5R<br />
3R<br />
2R<br />
pre-Base Reef Ridge<br />
(Early Pliocene)<br />
A A‘<br />
1R<br />
3R<br />
3R<br />
2R<br />
pre-McDonald<br />
(Middle Miocene)<br />
2R<br />
pre-Wilhlem<br />
(Middle Pliocene)<br />
(b)<br />
B B’<br />
7<br />
pre-McDonald<br />
(Middle Miocene)<br />
B B’<br />
6R<br />
7<br />
post Mya-4A<br />
(Late Pliocene)<br />
Figure 1.9. Conceptual model <strong>of</strong> fault evolution in (a) the western part and (b) the<br />
eastern part <strong>of</strong> the Elk Hills oil field. Each box represents a distinct stage in the<br />
faulting history in which a new fault, shown in black, begins to slip. Faults shown in<br />
gray have been active during a prior stage <strong>of</strong> evolution. These schematic fault crosssections<br />
are located along lines A to A’ and B to B’ in figures 1.2a and 1.2b.<br />
25
determined: (1) the 6R fault formed as a backthrust <strong>of</strong> the 7 fault sometime after Mya<br />
4-A deposition; (2) the 5R fault is a backthrust <strong>of</strong> the 1R fault; (3) the 1R fault has a<br />
different decollement surface than the 2R and 3R faults, which sole at a deeper<br />
stratigraphic level; and (4) <strong>of</strong> the major faults included in this study, only the 7 and 2R<br />
faults are inactive today. For all <strong>of</strong> the remaining faults, additional increments <strong>of</strong> slip<br />
accumulated in each successive stage <strong>of</strong> deformation once the fault initiated.<br />
For the mechanical modeling involved in this study, we use Poly3D (Thomas,<br />
1993), a boundary element computer program based on the deformation <strong>of</strong> a linear<br />
elastic, homogeneous, and isotropic solid. It is a three-dimensional displacement<br />
discontinuity program that solves for the elastic stress, strain, and displacement fields<br />
resulting from fault slip. Complex fault geometries can be investigated because the<br />
program models faults as assemblages <strong>of</strong> triangular elements <strong>of</strong> displacecment<br />
discontinuity. Each element is constructed by the superposition <strong>of</strong> angular dislocations<br />
(Comninou and Dunders, 1975; Jeyakumaran et al., 1992). Previous investigators have<br />
documented agreement between numerical approximations resulting from Poly3D and<br />
related analytical solutions (Thomas, 1993; Willemse et al., 1996; Crider and Pollard,<br />
1998); thus validating the reliability <strong>of</strong> the code.<br />
Our hypothesis for Elk Hills is that the faults are first order heterogeneities and<br />
that heterogeneity in mechanical properties <strong>of</strong> the stratigraphic layering contributed to<br />
a lesser degree to the shape <strong>of</strong> the folds. Dealing with a homogeneous model space<br />
allows us to investigate deformation related to fault heterogeneity in an otherwise<br />
simple and well-constrained setting. We show that significant insight can be gained<br />
from this approach which has the advantage <strong>of</strong> being more efficient to implement than<br />
approaches that could address the material heterogeneities.<br />
Boundary Conditions<br />
Local boundary conditions are specified on each triangular element as three<br />
components <strong>of</strong> a uniform displacement discontinuity or <strong>of</strong> the traction at the midpoint.<br />
We prescribe local zero traction in the strike and dip directions and zero displacement<br />
discontinuity in the direction perpendicular to the elements. These conditions allow<br />
26
the two surfaces <strong>of</strong> each element to slip freely in a strike-slip and dip-slip sense, but<br />
restrict the element surfaces from opening or interpenetrating.<br />
We consider several different remote (tectonic) strain boundary conditions,<br />
depicted in the insets in figures 1.10a – 1.10f, and observe how points along an<br />
originally flat observation grid are displaced as the Elk Hills faults respond to the<br />
remote loading. For this analysis <strong>of</strong> the remote boundary conditions, we simplify the<br />
model to the application <strong>of</strong> one strain step to build a basic intuition as to how variation<br />
in remote strain direction affects the deformation. We observe the pattern <strong>of</strong> uplift,<br />
noting where it has the same general trends as those seen in the interpreted structure<br />
contour maps (e.g. Fig. 1.2a). The following discussion examines these correlations<br />
for each <strong>of</strong> the boundary conditions. We disregard slip along the 6R fault because<br />
stratigraphic analysis has shown it to be very recent.<br />
The first loading condition tests whether slip along the San Andreas Fault could<br />
be wholly responsible for the deformation at Elk Hills. We specify a zero remote stress<br />
field and apply a right lateral displacement discontinuity <strong>of</strong> 33 mm, representing the<br />
slip accrued in one year (Toda and Stein, 2002), on a model San Andreas Fault that<br />
extends to 1000 km depth. The use <strong>of</strong> this deep dislocation is based on studies <strong>of</strong><br />
transform plate boundaries using GPS data that indicate such a dislocation embedded<br />
in an elastic half-space produces a displacement field at the free surface that is<br />
comparable with the measured displacement field (e.g. Savage, 1990; Muller et al.,<br />
2003). The uplift pattern mapped within the seismic volume (Fig. 1.2a) is not similar<br />
to the computed displacement field (Fig. 1.10a), so we conclude that slip on the plate<br />
boundary is unlikely to generate the Elk Hills uplift.<br />
In an Elk Hills structural overview paper, Nicholson (1990) suggested that the<br />
slip <strong>of</strong> the Elk Hills faults that generated the uplift we see today was driven by a deep<br />
seated left lateral strike-slip fault into which the shallower faults converge. In a<br />
representative mechanical model (Fig. 1.10b), left lateral motion along such a deep<br />
seated fault serves as the loading for the shallower, Elk Hills faults. At shallow depths,<br />
the model fault geometry is similar to that shown in figures 1.2, 1.4a, 1.6, and 1.9. At<br />
depth, however, where the seismic data do not resolve the faults well, we take the<br />
liberty <strong>of</strong> converging the faults into the proposed strike slip fault. The interpreted<br />
27
shallow fault geometry does not converge simply into one deep strike slip fault, so two<br />
distinct, <strong>of</strong>fset, vertical fault segments are used (Fig. 1.10b). A left-lateral<br />
displacement discontinuity <strong>of</strong> 33 mm is applied along these faults within a zero remote<br />
stress field. A map view representation <strong>of</strong> the vertical displacement field at a<br />
stratigraphic level comparable to the level <strong>of</strong> the Mya 4-A horizon is shown in figure<br />
4b. No uplift is generated in the area <strong>of</strong> the 31S and 29R anticlines. Based on these<br />
results, it seems improbable that the uplift at Elk Hills was generated by strike-slip<br />
motion along a deep-seated left-lateral fault.<br />
The displacement fields in figures 1.10c through 1.10f assess the orientation <strong>of</strong><br />
the maximum horizontal tectonic contraction on the pattern <strong>of</strong> uplift. In the first two<br />
examples, applied remote contractions <strong>of</strong> one percent at 110° (Fig. 1.10c) and<br />
140° (Fig. 1.10d), have only small components normal to the western faults. These<br />
cases resolve predominantly left-lateral and right-lateral motion along the Elk Hills<br />
faults, respectively. Neither <strong>of</strong> these examples produce results that correlate well with<br />
the interpreted displacement fields.<br />
Concluding that the greatest uplift is generated by a horizontal tectonic<br />
contraction oriented perpendicular to the strike <strong>of</strong> the dipping faults, we consider<br />
strain fields in which the maximum contraction is at 035° and 000°, perpendicular to<br />
the average strike <strong>of</strong> the western faults (125°) and that <strong>of</strong> the eastern faults (090°),<br />
respectively. Both displacement fields (Fig. 1.10e and 1.10f) replicate the northwest-<br />
southeast anticlinal trend in the western part <strong>of</strong> the field and the east-west trend in the<br />
eastern part <strong>of</strong> the field. The displacement associated with the north-south contraction<br />
correlates better in the eastern part <strong>of</strong> the field as a larger east-west trending high<br />
develops at the eastern end <strong>of</strong> the 31S anticline. In the western part <strong>of</strong> the field,<br />
however, this model correlates more poorly because a localized high is generated far<br />
to the northwest, at the tip <strong>of</strong> the 2R fault. As in figure 10d, this is a reflection <strong>of</strong> the<br />
right lateral strike-slip that occurs along the western faults. The best correlations are<br />
found for a tectonic strain field in which the horizontal contraction is perpendicular to<br />
the majority <strong>of</strong> the structures. We proceed by applying a 035° contraction to the<br />
models. To ensure that our models replicate deformation in a thrust<br />
28
35 0 16’00” 35 0 20’00”<br />
35 0 16’00” 35 0 20’00”<br />
35 0 16’00” 35 0 20’00”<br />
(a) (b)<br />
N<br />
0 km 2<br />
(c) (d)<br />
N<br />
0 km 2<br />
(e) (f)<br />
N<br />
0 km 2<br />
119 0 32’00”<br />
119 0 32’00”<br />
119 0 26’00”<br />
119 0 26’00”<br />
SAF<br />
119 0 20’00”<br />
119 0 20’00”<br />
35 0 20’00”<br />
35 0 16’00”<br />
35 0 20’00”<br />
35 0 16’00”<br />
35 0 20’00”<br />
35 0 16’00”<br />
35 0 16’00” 35 0 20’00”<br />
35 0 16’00” 35 0 20’00”<br />
N<br />
0 km 2<br />
N<br />
0 km 2<br />
N<br />
0 km 2<br />
normalized displacement<br />
Figure 1.10. Model results <strong>of</strong> test cases in which one step models were run under<br />
various remote boundary conditions. Plotted are the normalized vertical displacement<br />
fields resulting from driving mechanisms <strong>of</strong> (a) right-lateral slip along the San Andreas<br />
Fault; (b) slip along deep seated left-lateral strike-slip faults; (c) remote horizontal<br />
contraction oriented at 110°; (d) remote horizontal contraction oriented at 140°; (e)<br />
remote horizontal contraction oriented at 035°; (f) remote horizontal contraction<br />
oriented at 000°. Insets show the geometry <strong>of</strong> the model setup with red arrows<br />
indicating the driving mechanism for each scenario. With the exception <strong>of</strong> (b), all<br />
insets are in map view with the Elk Hills index map shown in blue for reference. The<br />
inset for model (b) is a three-dimensional view with the geometry <strong>of</strong> the hypothetical<br />
deep vertical strike-slip faults drawn in dashed lines.<br />
29<br />
35 0 16’00” 35 0 20’00”<br />
119 0 32’00”<br />
119 0 32’00”<br />
119 0 26’00”<br />
119 0 26’00”<br />
119 0 20’00”<br />
119 0 20’00”<br />
35 0 20’00”<br />
35 0 16’00”<br />
35 0 20’00”<br />
35 0 16’00”<br />
35 0 20’00”<br />
35 0 16’00”
environment, where the minimum principal compressive stress is vertical, we apply a<br />
small contraction <strong>of</strong> 0.1 percent in the minimum horizontal strain direction.<br />
Model Increments<br />
A fault chronology relative to specific stratigraphic horizons has been<br />
constrained above. Each interval bracketed by two horizons can be represented by an<br />
individual model step. Because certain faults are active only during the deposition <strong>of</strong><br />
specific stratigraphic intervals, we begin by prescribing an appropriate amount <strong>of</strong><br />
strain for each interval. To stay within the elastic limit <strong>of</strong> a few percent, we set a total<br />
maximum horizontal strain <strong>of</strong> one percent from McDonald time <strong>of</strong> deposition through<br />
the present day. We then partition this strain into increments proportional to the length<br />
<strong>of</strong> time represented by each interval (Table 1.1a). We further partition increments<br />
during which new faults begin to slip by assigning half <strong>of</strong> the allotted strain to a step<br />
in which the new fault is not yet active and the remaining half <strong>of</strong> the allotted strain to a<br />
step in which the new fault is allowed to slip. Increments 9 and 10 are an exception<br />
because fault 6R has been found to be much younger than the Mya 4-A horizon, and<br />
so it is allowed to slip for only one quarter <strong>of</strong> the time represented by the Mya 4-A to<br />
surface interval.<br />
Although a constant strain rate is questionable, it provides a basis from which to<br />
make first order evaluations <strong>of</strong> similarities between modeled and mapped deformation.<br />
Table 1.1a documents the ages selected for each <strong>of</strong> the horizons and the corresponding<br />
strains applied to each stratigraphic interval. Table 1.1b documents the strains applied<br />
to model increments that have been defined based on fault activity. Because the total<br />
strain is less than the actual tectonic strain, the models cannot reproduce the<br />
magnitudes <strong>of</strong> uplift. However, we postulate that the patterns <strong>of</strong> uplift are set by the<br />
geometry and sequence <strong>of</strong> faulting and the relative magnitudes <strong>of</strong> uplift are set by the<br />
relative magnitude <strong>of</strong> applied strain.<br />
To address the fact that some paleotopography may have been present at the time<br />
<strong>of</strong> deposition <strong>of</strong> each layer, we apply a pre-deformation step. An undeformed<br />
observation grid, representing the newly deposited, undeformed horizon, is given ten<br />
percent <strong>of</strong> the deformation that occurred across the next oldest surface during the<br />
30
Table 1.1. (a) Documentation <strong>of</strong> the ages assigned to each horizon (approximate<br />
error bars are given), the time period represented by each stratigraphic interval (∆t),<br />
and the corresponding applied strains. Ages gathered from Sarna-Wojcicki et al.,<br />
1979; Loomis, 1990; Sarna-Wojcicki et al., 1990; Bloch, 1992; Miller, 1999. Refer to<br />
the stratigraphic column shown in figure 1.3. (b) Documentation <strong>of</strong> the model<br />
increments defined based on fault activity, and the corresponding applied remote<br />
strain in the maximum contraction direction, active faults, and stratigraphic interval.<br />
Abbreviations: McD = McDonald, BRR = Base Reef Ridge, CLLM = Calitroleum,<br />
WILM = Wilhelm.<br />
31
previous interval to account for paleotopography. The figure <strong>of</strong> ten percent is not well<br />
constrained, but was applied to the Base Reef Ridge, Calitroleum, Wilhelm, and Mya<br />
4-A horizons. The McDonald horizon required special attention, as cross sections<br />
showing the geometries <strong>of</strong> the faults (Fig. 1.2c and 1.2d) indicate that its topography<br />
was influenced by slip prior to McDonald deposition along the 7 fault for a greater<br />
period <strong>of</strong> time than by slip along the 2R and 3R faults. We ran a pre-deformation step<br />
as discussed above for an interval in which the 7, 2R, and 3R faults were all active.<br />
The amount <strong>of</strong> strain applied to this increment was a small percentage <strong>of</strong> the total<br />
strain applied to the model from McDonald time <strong>of</strong> deposition to the present time<br />
(Table 1.1). Before this step, we applied a deformation step in which the McDonald<br />
horizon was at the surface, but only the 7 fault was active. We tested how differing<br />
amounts <strong>of</strong> strain applied in this step affected the overall deformation <strong>of</strong> the<br />
McDonald horizon.<br />
Model Calibration<br />
The deformed shapes <strong>of</strong> stratigraphic horizons as interpreted in the seismic data<br />
volume were used to calibrate the model. A planar observation grid represents an<br />
undeformed stratigraphic horizon. After the grid is slightly deformed to account for<br />
the paleotopography at its time <strong>of</strong> deposition, the locations <strong>of</strong> points across this grid<br />
are tracked in three dimensions through the deformation stages as faults are generated<br />
and slip. After the final stage <strong>of</strong> deformation, the shape <strong>of</strong> the modeled horizon is<br />
compared with the shape <strong>of</strong> a horizon at a similar stratigraphic level as interpreted<br />
within the seismic volume. A representative model should reproduce comparable<br />
trends and relative magnitudes <strong>of</strong> uplift in the areas <strong>of</strong> the 31S and 29R anticlines.<br />
Depending on the depth <strong>of</strong> the specific horizon, various fault cuts should also be<br />
reproduced. The sequence <strong>of</strong> steps that most closely reproduces the shape <strong>of</strong> the<br />
interpreted horizon is considered to be the best model to fit the fault evolution at Elk<br />
Hills.<br />
Because the faults at Elk Hills developed in a syn-depositional setting, the<br />
horizons interpreted within the seismic data volume record deformation due<br />
32
predominantly to slip on faults during the time period since deposition <strong>of</strong> the horizon,<br />
with a small amount <strong>of</strong> recorded deformation attributed to the existing topography at<br />
the time <strong>of</strong> deposition <strong>of</strong> the surface. Thus, the deformation <strong>of</strong> several surfaces can be<br />
modeled, and the results compared with the interpreted deformation <strong>of</strong> the surfaces, to<br />
ensure that the fault system evolution through time is consistent. Therefore, we<br />
include all five <strong>of</strong> the horizons considered within the stratigraphic analysis in the<br />
model.<br />
Model Results<br />
The forward modeled deformation <strong>of</strong> the McDonald, Base Reef Ridge, and<br />
Wilhelm surfaces (Fig. 1.11a, 1.11c, and 1.11e) and the corresponding interpreted<br />
surfaces (Fig. 1.11b, 1.11d, and 1.11f) show that the long wavelength deformation <strong>of</strong><br />
Elk Hills is well represented by the models. At each <strong>of</strong> the tested levels, there is<br />
correlation in the general trend <strong>of</strong> the Elk Hills field, with the structure trending<br />
northwest-southeast in the western part <strong>of</strong> the field and transitioning in the middle <strong>of</strong><br />
the field to trending east-west in the eastern part <strong>of</strong> the field. The Calitroleum and Mya<br />
4-A surfaces have similar deformational features as the Wilhelm surface, respectively<br />
more and less pronounced. We omit the analysis <strong>of</strong> these results in favor <strong>of</strong> focusing<br />
on the deeper horizons with more complicated deformation patterns.<br />
The McDonald surface, cut by all faults included in this study and subjected to the<br />
largest amount <strong>of</strong> cumulative strain, is expected to be the most difficult to reproduce.<br />
Regardless, model results (Fig. 1.11a) indicate that we have accounted for all <strong>of</strong> the<br />
major deformational features noticeable across the interpreted surface (Fig. 1.11b).<br />
Fault cuts <strong>of</strong> the 2R, 3R, 1R, 5R, 6R, and 7 faults can be seen on the modeled surface.<br />
The 31S, 29R, and Northwest Stevens anticlines are present, are located at reasonable<br />
spatial positions, and are <strong>of</strong> similar relative magnitudes as in the interpreted surface.<br />
31S is slightly more uplifted than 29R, and both <strong>of</strong> these structures are much higher<br />
than the Northwest Stevens anticline. The east-west trending portion <strong>of</strong> the 31S<br />
anticline also is present. The asymmetry <strong>of</strong> the 31S and Northwest Stevens anticlines<br />
are well represented in the model results, with the steeper limb <strong>of</strong> the 31S being that<br />
33
(a)<br />
35 0 16’00” 35 0 20’00”<br />
(c)<br />
35 0 16’00” 35 0 20’00”<br />
(e)<br />
35 0 16’00” 35 0 20’00”<br />
N<br />
0mile1 0<br />
0<br />
0 km 2<br />
N<br />
mile1<br />
km 2<br />
N<br />
0mile1 0 km 2<br />
119 0 32’00”<br />
24Z sand body<br />
2R<br />
119 0 32’00”<br />
119 0 32’00”<br />
2R<br />
119 0 32’00”<br />
119 0 32’00”<br />
2R<br />
119 0 32’00”<br />
26R sand body<br />
5R<br />
5R<br />
5R<br />
1R<br />
3R<br />
3R<br />
1R<br />
119 0 26’00”<br />
1R<br />
119 0 26’00”<br />
119 0 26’00”<br />
119 0 26’00”<br />
119 0 26’00”<br />
3R<br />
119 0 26’00”<br />
C.I. = 152 m (500 ft)<br />
7<br />
6R<br />
C.I. = 152 m (500 ft)<br />
7<br />
6R<br />
C.I. = 76 m (250 ft)<br />
7<br />
119 0 20’00”<br />
119 0 20’00”<br />
119 0 20’00”<br />
119 0 20’00”<br />
119 0 20’00”<br />
6R<br />
119 0 20’00”<br />
35 0 20’00”<br />
depth (m)<br />
35 0 20’00”<br />
depth (m)<br />
35 0 20’00”<br />
4877<br />
4267<br />
3658<br />
3048<br />
2438<br />
1829<br />
3658<br />
3048<br />
2438<br />
1829<br />
1219<br />
depth (m)<br />
1829<br />
1524<br />
1219<br />
914<br />
607<br />
305<br />
(b)<br />
(d)<br />
(f)<br />
35 0 16’00” 35 0 20’00”<br />
35 0 16’00” 35 0 20’00”<br />
119 0 32’00”<br />
119 0 32’00”<br />
119 0 32’00”<br />
119 0 32’00”<br />
119 0 26’00”<br />
119 0 26’00”<br />
119 0 26’00”<br />
119 0 26’00”<br />
119 0 20’00”<br />
N<br />
0 km 2<br />
119 0 20’00”<br />
119 0 20’00”<br />
N<br />
0 km 2<br />
119 0 20’00”<br />
N<br />
0 km 2<br />
Figure 1.11. Interpreted and modeled vertical displacement fields for three stratigraphic<br />
horizons: McDonald (a) as interpreted, (b) as modeled; Base Reef Ridge (c)<br />
as interpreted, (d) as modeled; Wilhelm (e) as interpreted, (f) as modeled. The<br />
colorbars and contours for the interpreted maps have been converted from feet into<br />
meters. The traces <strong>of</strong> the six seismically interpreted, structure bounding faults are<br />
plotted on the interpreted map with dashed lines representing faults that are below<br />
the stratigraphic surface. For location referencing, an index map outlining the<br />
production blocks <strong>of</strong> the field has been plotted on all vertical displacement fields. In<br />
(a), the locations <strong>of</strong> the Stevens sands reservoirs <strong>of</strong> the 31S anticline, the 2B<br />
reservoir at the western nose <strong>of</strong> the 29R anticline, and the Asphalto field to the<br />
southwest <strong>of</strong> the 29R anticline are outlined in solid white, while turbidite sand bodies<br />
are outlined in dashed white (after Zumberge et al., 2005). See text for a discussion<br />
<strong>of</strong> how fault evolution may have played a role in the charging <strong>of</strong> Stevens reservoirs.<br />
35 0 16’00” 35 0 20’00”<br />
34<br />
119 0 32’00”<br />
119 0 32’00”<br />
119 0 26’00”<br />
119 0 26’00”<br />
119 0 20’00”<br />
119 0 20’00”<br />
35 0 20’00”<br />
35 0 20’00”<br />
35 0 20’00”<br />
0<br />
0.1<br />
0.2<br />
0.3<br />
0.4<br />
0.5<br />
0.6<br />
0.7<br />
0.8<br />
0.9<br />
1<br />
0<br />
0.1<br />
0.2<br />
0.3<br />
0.4<br />
0.5<br />
0.6<br />
0.7<br />
0.8<br />
0.9<br />
1<br />
0<br />
0.1<br />
0.2<br />
0.3<br />
0.4<br />
0.5<br />
0.6<br />
0.7<br />
0.8<br />
0.9<br />
1<br />
normalized displacement normalized displacement normalized displacement
which lies along the 3R and 7 faults, and the steeper limb <strong>of</strong> the Northwest Stevens<br />
anticline being the limb that lies along the 2R fault.<br />
At the Base Reef Ridge level, the model outputs a surface that is cut by faults<br />
2R, 3R, 1R, 5R, and 6R (Fig. 1.11c). The uplift <strong>of</strong> the 31S and 29R anticlines is <strong>of</strong><br />
virtually the same magnitude, and the Northwest Stevens anticline is a lower<br />
amplitude feature. Although the east-west portion <strong>of</strong> the 31S anticline is present in the<br />
modeled surface, the model has not produced sufficient uplift at this location. A<br />
structure that the model has reproduced nicely is the 29R anticline. If we compare the<br />
modeled surface (Fig. 1.11c) with the interpreted surface (Fig. 1.11d), we see that in<br />
both cases, the steeper anticlinal limb is along the 1R fault at the northwestern extent<br />
<strong>of</strong> the structure, but that at the southeastern extent <strong>of</strong> the structure, the steeper<br />
anticlinal limb is along the 5R fault.<br />
At the shallow level <strong>of</strong> the Wilhelm surface, the three distinct anticlines <strong>of</strong> the<br />
Elk Hills field have coalesced into one broad structure (Fig. 1.11e and 1.11f). The<br />
model shows two localized highs in positions corresponding to the 31S and 29R<br />
anticlines. The magnitude <strong>of</strong> uplift at the location <strong>of</strong> the 29R anticline is slightly<br />
greater than that at the 31S anticline. The Northwest Stevens structure cannot be<br />
distinguished as a separate feature. The east-west portion <strong>of</strong> the 31S anticline, again, is<br />
not reproduced with sufficient uplift.<br />
Discussion<br />
The mechanical modeling undertaken in this study has refined the interpreted<br />
fault activity and geometric constraints at Elk Hills. If the deformation at Elk Hills<br />
occurred in a manner that can be approximated by linear elastic behavior during<br />
faulting with stress relaxation between events, then the suggested fault evolution is<br />
physically realistic. We acknowledge, however, that if the deformation at Elk Hills<br />
occurred in a manner that differs significantly from the postulated behavior, then<br />
faulting scenarios that our modeling efforts have deemed physically impossible, such<br />
as continued slip along the 2R fault to present, or a common decollement surface for<br />
the 1R and 3R faults, may in fact be possible. Correspondence between interpreted and<br />
modeled displacement fields indicates that the models presented here do approximate<br />
35
the deformation at Elk Hills. This method <strong>of</strong> sequential forward modeling for the total<br />
observed deformation therefore provides an opportunity to investigate deformational<br />
processes in an environment wherein fault geometry evolves.<br />
Modeled and Interpreted Discrepancies<br />
The most noticeable difference between the modeled and mapped surfaces is to<br />
the southwest <strong>of</strong> the Elk Hills structure, where all model results show a pronounced<br />
depression and the interpreted structure maps do not. Figures 1.11b, 1.11d, and 1.11f<br />
show highs in this corner <strong>of</strong> the maps, related to uplift within the Midway Sunset field<br />
(Fig. 1.1). We would not expect our models to replicate these features because we<br />
have not included faults outside the Elk Hills field.<br />
A discontinuity in the uplift <strong>of</strong> the 31S anticline is seen in all <strong>of</strong> the model<br />
results where the strike <strong>of</strong> the anticline changes from northwest-southeast to east-west.<br />
We suggest that this is a result <strong>of</strong> the limits <strong>of</strong> seismic resolution, because the data are<br />
very noisy at this location. A complete understanding <strong>of</strong> how the northwest-southeast<br />
and east-west fault systems intersect cannot be gained from examination <strong>of</strong> the seismic<br />
data. The faults were extrapolated across this data gap, but the resulting geometry is<br />
awkward and may not accurately represent the intersection <strong>of</strong> the two fault systems.<br />
The final noteworthy difference between the modeled and interpreted<br />
deformation for each surface is the inability <strong>of</strong> the model to reproduce the east-west<br />
trending portion <strong>of</strong> the 31S uplift. Varying fault frictional properties and the extent <strong>of</strong><br />
pre-McDonald uplift are two possible explanations that we do not address in this<br />
study. Modeling a more pronounced eastern section <strong>of</strong> the 31S anticline through time<br />
could also be accomplished by applying a remote strain oriented more normal to the<br />
eastern faults. We assess this possibility in the following section.<br />
To further assess the correspondence between modeled and interpreted<br />
deformation, we present modeled isochores <strong>of</strong> the four intervals that were<br />
stratigraphically analyzed (Fig. 1.7b, 1.7d, 1.7f, 1.7h). These synthetic isochores have<br />
been edited to remove overthickening effects along fault traces and thus can be<br />
directly compared with the interpreted isochores (Fig. 1.7a, 1.7c, 1.7e, 1.7f). Many <strong>of</strong><br />
36
the features within the interpreted isochore maps are also present in the synthetic<br />
isochore maps.<br />
Tectonic Strain Analysis<br />
We explore the effects <strong>of</strong> a clockwise rotation in relative plate motion between<br />
the North American and Pacific plates that occurred between 5 and 8 Ma (Atwater,<br />
1970; Engebretson et al., 1985). If the tectonic strain direction had rotated along with<br />
this plate motion rotation, then the remote contraction direction during the early stages<br />
<strong>of</strong> structural evolution at Elk Hills would have been oriented more N-S than the<br />
applied 035° remote contraction. The cumulative deformation field <strong>of</strong> the McDonald<br />
surface is shown in figure 1.12a. For this modeling scenario a remote contraction at<br />
000° was applied for steps 1-5 (Table 1.1b), representing growth prior to 5 Ma, and a<br />
remote contraction at 035° was applied for steps 6-10 (Table 1.1b), representing<br />
growth after 5 Ma. As compared with figure 1.11a, figure 1.12a shows greater uplift<br />
along the 7 fault, the oldest fault in the field that strikes sub-perpendicular to this early<br />
contraction direction. This comparison indicates that the 7 fault accrued significant<br />
slip during the period <strong>of</strong> structural development represented by model steps 1-5. By<br />
applying a two step deformation pathway, we may more closely replicate the<br />
interpreted deformation fields.<br />
Noting that a change in remote strain applied to half <strong>of</strong> the modeling steps does<br />
not drastically change the uplift modeled along the western faults, we revisited the<br />
possibility <strong>of</strong> having a remote contraction oriented at 000° throughout the period <strong>of</strong><br />
Elk Hills growth investigated by this study using the full ten step model and observing<br />
the modeled deformation <strong>of</strong> the McDonald surface. Figure 1.12b shows the resulting<br />
cumulative deformation field. In comparing figure 1.12b with the interpreted<br />
McDonald surface in figure 1.11b, we suggest that this constant 000° remote strain<br />
results in an east-west trending uplift that is too high relative to the northwest-<br />
southeast trending portion <strong>of</strong> the 31S anticline. This discrepancy could be reconciled<br />
by readjusting the amount <strong>of</strong> strain applied to model increments representing<br />
deformation occurring prior to McDonald deposition. A second discrepancy that we<br />
37
(a) (b)<br />
35 0 16’00” 35 0 20’00”<br />
119 0 32’00”<br />
119 0 32’00”<br />
119 0 26’00”<br />
119 0 26’00”<br />
119 0 20’00”<br />
N<br />
0 km 2<br />
119 0 20’00”<br />
35 0 20’00”<br />
35 0 16’00”<br />
35 0 16’00” 35 0 20’00”<br />
normalized displacement<br />
119 0 32’00”<br />
119 0 32’00”<br />
119 0 26’00”<br />
119 0 26’00”<br />
119 0 20’00”<br />
N<br />
0 km 2<br />
Figure 1.12. Normalized modeled vertical displacement fields for the McDonald<br />
surface resulting from: (a) a two step remote strain history in which a change from a<br />
remote contraction oriented at 000° to one oriented at 035° replicates the change in<br />
relative plate motion that occurred 5 Ma., and (b) a constant remote strain oriented at<br />
000°. For location referencing, an index map outlining the production blocks <strong>of</strong> the<br />
field has been plotted on the vertical displacement fields.<br />
38<br />
119 0 20’00”<br />
35 0 20’00”<br />
35 0 16’00”
cannot explain away is the location <strong>of</strong> the northwest-southeast trending portion <strong>of</strong> the<br />
31S anticline. As referenced by the index map shown in black in figure 1.12b, the<br />
mapped location <strong>of</strong> the maximum uplift has been translated to the northwest as<br />
compared with figures 1.11a and 1.11b. Although this tectonic strain sensitivity<br />
analysis has indicated that changes in the orientation <strong>of</strong> the contraction between 000°<br />
and 035° do not drastically affect the resulting deformation, we suggest that the small<br />
change in location <strong>of</strong> the 31S anticline when modeled with a tectonic contraction at<br />
000° provides justification for using the 035° direction.<br />
Additional support for a remote strain oriented perpendicularly to the western<br />
faults is derived from consideration <strong>of</strong> the relative ages <strong>of</strong> the eastern and western<br />
faults and the mechanics <strong>of</strong> fault formation. The 7 fault (in the east <strong>of</strong> the field) strikes<br />
E-W and is a steeply dipping planar feature. It is the oldest fault in the model and<br />
could be a remnant <strong>of</strong> an older structural fabric. Extensional basins formed throughout<br />
Southern California beginning around 18Ma as the triple junction passed through the<br />
area. Maps from Tennyson (1989) show that some <strong>of</strong> these basins were oriented E-W.<br />
Thus, it is possible that the 7 fault is a remnant <strong>of</strong> one <strong>of</strong> these basins linked to the<br />
formation <strong>of</strong> the San Andreas Fault. With the change in the tectonic regime to<br />
contraction after the migration <strong>of</strong> the triple junction, strain could have first localized<br />
along this normal fault, reactivating it in reverse motion. As contraction continued, the<br />
deformation was too great to be accommodated by this fault alone, so the fault system<br />
in the western part <strong>of</strong> the field developed, striking perpendicular to the remote<br />
contraction. The later development <strong>of</strong> the 6R fault in an E-W orientation could also be<br />
attributed to the older structural fabric. Although the 035° orientation <strong>of</strong> the tectonic<br />
contraction does not produce the optimal deformation pattern in the eastern part <strong>of</strong> the<br />
Elk Hills field, it is the most sound orientation mechanically when we consider the<br />
development <strong>of</strong> the thrust faults in the western part <strong>of</strong> the field.<br />
Implications for Hydrocarbon Migration<br />
When integrated with results from a recent geochemical study investigating<br />
reservoir charging at Elk Hills (Zumberge et al., 2005), the structural history presented<br />
here may constrain the direction from which hydrocarbons charged the 31S Stevens<br />
39
turbidite oil pools. The 31S anticline is located updip from subbasins both to the north<br />
and to the south, making migration pathways from either direction a possibility<br />
(Zumberge et al., 2005). Biomarker maturity indicators for the 31S reservoirs show<br />
very little thermal-maturity variation, indicating quick flooding <strong>of</strong> the reservoirs in the<br />
Late Pliocene or Pleistocene that was possibly due to the development <strong>of</strong> a fault<br />
system on the flanks <strong>of</strong> the anticline (Zumberge et al., 2005). Our structural study<br />
suggests that the 7 fault on the northern flank <strong>of</strong> the anticline developed very little past<br />
the Early Pliocene, while the 6R fault on the southern flank <strong>of</strong> the anticline began to<br />
form during the Pleistocene. We therefore hypothesize that the oil pools residing<br />
within the 31S Stevens turbidite sands migrated from the south.<br />
The structural evolution <strong>of</strong> the fault system beneath Elk Hills may also explain<br />
the existence <strong>of</strong> the oil pool within the Stevens turbidite sands at the Asphalto field,<br />
located to the southwest <strong>of</strong> the 29R anticline (Fig. 1.11a). The geochemistry <strong>of</strong> this oil<br />
pool matches the geochemistry <strong>of</strong> the oil pools found within the Stevens sands in the<br />
2B reservoir at the southeast nose <strong>of</strong> the 29R anticline and across the 31S anticline<br />
(Fig. 1.11a). The 2B reservoir was most likely charged by spillage from the 31S oil<br />
pool. As Zumberge et al. (2005) explain, however, the existence <strong>of</strong> the Asphalto oil<br />
pool in the Stevens turbidite sands is enigmatic. Geochemical data imply that this<br />
reservoir was not charged by the same oils that exist in the other reservoirs in the<br />
western part <strong>of</strong> the field, and the low permeability porcelanite within the crest <strong>of</strong> the<br />
29R anticline should have impeded migration <strong>of</strong> oils within the 2B pool to the<br />
Asphalto field (Zumberge et al., 2005). The 2B reservoir lies near the southeast lateral<br />
termination <strong>of</strong> the 5R fault and the Asphalto oil field lies near the northwest lateral<br />
termination <strong>of</strong> the 5R fault (Fig. 1.11a). Perhaps motion along the 5R fault allowed the<br />
fault to act as a conduit (Antonellini and Aydin, 1994; Barton et al., 1995; Caine et al.,<br />
1996; Huang et al., 1998; Aydin, 2000; Wiprut and Zoback, 2000), transporting oil<br />
from the turbidite sands within the 2B reservoir through the porcelanite along the<br />
length <strong>of</strong> the 29R anticline and depositing it in the turbidite sands to the southwest <strong>of</strong><br />
the 29R anticline. In this case, the migration <strong>of</strong> these oils would have been during<br />
Pleistocene time, as the sequence <strong>of</strong> events would have been: (1) development <strong>of</strong> the<br />
6R fault and charging <strong>of</strong> the 31S Stevens reservoirs; (2) spillage <strong>of</strong> oil into the 2B<br />
40
eservoir; (3) migration <strong>of</strong> oil along the 5R fault from the 2B reservoir to the Asphalto<br />
field.<br />
Pleistocene migration <strong>of</strong> hydrocarbons into the 31S turbidites is feasible as long<br />
as two conditions are met: the migration preceded the increase in Monterey<br />
porcelanite permeability resulting from the diagenetic conversion <strong>of</strong> opal CT to quartz;<br />
and either no other migration pathways into the 31S sands were established, or no trap<br />
existed, prior to development <strong>of</strong> the 6R fault (S. A. Reid, 2006, personal<br />
communication). Migration <strong>of</strong> hydrocarbons along the 5R fault into the Asphalto field<br />
rather than the updip 24Z field is feasible as the migrating oil would not have been<br />
able to displace oil out <strong>of</strong> the steep 24Z structure but could flood and displace oil from<br />
Asphalto (S. A. Reid, 2006, personal communication). Although further work is<br />
required to asses the soundness <strong>of</strong> the suggested migration constraints, the charging <strong>of</strong><br />
reservoirs at Elk Hills was most likely influenced by the evolving fault system.<br />
Conclusions<br />
The integration <strong>of</strong> numerical modeling with stratigraphic interpretation <strong>of</strong><br />
seismic data has refined our understanding <strong>of</strong> the fault evolution at Elk Hills, placing<br />
constraints on decollement levels, the chronology <strong>of</strong> faulting, and the timing <strong>of</strong><br />
faulting relative to reference horizons. These constraints have important implications<br />
for oil migration routes and reservoir charging histories. North dipping faults 5R and<br />
6R are backthrusts <strong>of</strong> older south dipping faults. Consideration <strong>of</strong> the locations and<br />
timing <strong>of</strong> these faults indicates that they have likely played a significant role in the<br />
migration <strong>of</strong> oil from a source south <strong>of</strong> the Elk Hills oil field into Pleistocene age traps<br />
within the Stevens sands <strong>of</strong> the Monterey Formation on the 31S anticline and, in<br />
limited locations, the 29R anticline.<br />
Consideration <strong>of</strong> the driving mechanism for the deformation at Elk Hills<br />
suggests that since ~ 10 Ma, Elk Hills has been subjected to thrusting related,<br />
predominantly northeast-southwest directed compressional tectonics. Within this<br />
compressional setting, the apparent bend in the trend <strong>of</strong> the Elk Hills Oil Field has<br />
developed due to the intersection <strong>of</strong> two distinct fault systems. Modeling indicates that<br />
the faults in the east <strong>of</strong> the field are most likely the remnants <strong>of</strong> an older structural<br />
41
fabric trending east-west, whereas the northwest-southeast trending faults to the west<br />
are oriented perpendicularly to the tectonic compression.<br />
Iterative mechanical models adequately approximate the deformation <strong>of</strong><br />
stratigraphic horizons interpreted within the seismic volume. This correlation has<br />
provided constraints on the fault evolution at Elk Hills. More generally, the correlation<br />
indicates that sequences <strong>of</strong> mechanical models can be used to better understand<br />
deformation within growth-faulting settings.<br />
Acknowledgements<br />
This study was supported by <strong>Stanford</strong> Rock Fracture Project funds as well as<br />
grant EAR-0125935 from the National Science Foundation Tectonics Program.<br />
Fiore’s research was supported by an internship at Occidental Oil and Gas. The<br />
authors thank Bill Long for obtaining permission from Occidental Oil and Gas to work<br />
with and present results from the Elk Hills seismic data set. Discussions with Steve<br />
Graham, Radu Girbacea, Stan Stearns, and Tony Reid significantly contributed to this<br />
study. Critical reviews by Russell Davies, Raymond Sorenson, Laird Thompson, and<br />
Bruce Trudgill improved earlier versions <strong>of</strong> the manuscript.<br />
References<br />
Antonellini, M. A., and A. Aydin, 1994, Effect <strong>of</strong> faulting on fluid flow in porous<br />
sandstones: petrophysical properties: AAPG Bulletin, v. 78, p. 355-377.<br />
Arnold, R., and H. R. Johnson, 1910, Preliminary report on the McKittrick-Sunset oil<br />
region, Kern and San Luis Obispo Counties, California: U.S. Geological<br />
Survey Bulletin 406, 225 p.<br />
Atwater, T., 1970, Implications <strong>of</strong> plate tectonics for the Cenozoic tectonic evolution<br />
<strong>of</strong> western North America: Geological Society <strong>of</strong> America Bulletin, v. 81, p.<br />
3513-3535.<br />
Aydin, A., 2000, Fractures, faults, and hydrocarbon entrapment, migration and flow:<br />
Marine and Petroleum Geology, v. 17, p. 797-814.<br />
Barton, C. A., M. D. Zoback, and D. Moos, 1995, Fluid flow along potentially active<br />
faults in crystalline rock: Geology, v. 23, p. 683-686.<br />
Bloch, R. B., 1992, Studies <strong>of</strong> the stratigraphy and structure <strong>of</strong> the San Joaquin Basin,<br />
California: PhD dissertation, <strong>Stanford</strong> <strong>University</strong>, <strong>Stanford</strong>, CA, 480 p.<br />
42
Bloch, R. B., R. Von Huene, P. E. Hart, and C. M. Wentworth, 1993, Style and<br />
magnitude <strong>of</strong> tectonic shortening normal to the San Andreas fault across<br />
Pyramid Hills and Kettleman Hills South Dome, California: Geological<br />
Society <strong>of</strong> America Bulletin, v. 105, p. 464-478.<br />
Caine, J. S., J. P. Evans, and F. C. B., 1996, Fault zone architecture and permeability<br />
structure: Geology, v. 24, p. 1025-1028.<br />
California Division <strong>of</strong> Oil and Gas, 2005, 2004 annual report <strong>of</strong> the State Oil and Gas<br />
Supervisor: Sacramento, California, California Department <strong>of</strong> Conservation<br />
publication no. PR06, 270 p.<br />
Castillo, D. A., and M. D. Zoback, 1994, Systematic variations in stress state in the<br />
Southern San Joaquin Valley: inferences based on well-bore data and<br />
comtemporary seismicity: AAPG Bulletin, v. 78, p. 1257-1275.<br />
Comninou, M. A., and J. Dunders, 1975, The angular dislocation in a half-space:<br />
Journal <strong>of</strong> Elasticity, v. 5, p. 203-216.<br />
Crider, J. G., and D. D. Pollard, 1998, Fault linkage: Three-dimensional mechanical<br />
interaction between echelon normal faults: Journal <strong>of</strong> Geophysical Research, v.<br />
103, p. 24,373-24,391.<br />
Eichhubl, P., and R. J. Behl, 1998, Diagenesis, deformation, and fluid flow in the<br />
Miocene Monterey Formation, in P. Eichhubl, ed., Diagenesis, deformation,<br />
and fluid flow in the Miocene Monterey Formation: Pacific Section SEPM,<br />
book 83, p. 5-13.<br />
Ekstrom, G., R. S. Stein, J. P. Eaton, and D. Eberhart-Phillips, 1992, Seismicity and<br />
geometry <strong>of</strong> a 110-km-long blind thrust fault; 1. The 1985 Kettleman Hills,<br />
California, earthquake: Journal <strong>of</strong> Geophysical Research, v. 97, p. 4843-4864.<br />
Engebretson, D. C., A. Cox, and R. G. Gordon, 1985, Relative motion between<br />
oceanic and continental plates in the Pacific basin: Geological Society <strong>of</strong><br />
America Special Paper 206, 59 p.<br />
Graham, S. A., and L. A. Williams, 1985, Tectonic, depositional, and diagenetic<br />
history <strong>of</strong> Monterey Formation (Miocene), central San Joaquin basin,<br />
California: AAPG Bulletin, v. 69, p. 365-411.<br />
Harding, T. P., 1974, Petroleum traps associated with wrench faults: AAPG Bulletin,<br />
v. 58, p. 1290-1304.<br />
Harding, T. P., 1976, Tectonic significance and hydrocarbon trapping consequences <strong>of</strong><br />
sequential folding synchronous with San Andreas faulting, San Joaquin Valley,<br />
California: AAPG Bulletin, v. 60, p. 356-378.<br />
43
Huang, J. J., P. J. Hicks Jr., J. P. Ashbaush, and P. B. Flemmings, 1998, Coupling <strong>of</strong><br />
along-fault migration and hydrocarbon entrapment in stacked reservoirs (abs.):<br />
AAPG and SEPM Annual Convention Abstract.<br />
Imperato, D. P., 1995, Studies <strong>of</strong> the stratigraphy and structure <strong>of</strong> the Great Valley <strong>of</strong><br />
California and implications for plate tectonics: Ph.D. dissertation, <strong>University</strong><br />
<strong>of</strong> California at Santa Barbara, Santa Barbara, California, 271 p.<br />
Jeyakumaran, M., J. W. Rudnicki, and L. M. Keer, 1992, Modeling <strong>of</strong> slip zones with<br />
triangular dislocation elements: Bulletin <strong>of</strong> the Seismological Society <strong>of</strong><br />
America, v. 82, p. 2,153-2,169.<br />
Loomis, K. B., ed., 1990, Depositional environments and sedimentary history <strong>of</strong> the<br />
Etchegoin Group, west-central San Joaquin Valley, California: Studies <strong>of</strong> the<br />
Geology <strong>of</strong> the San Joaquin Basin,, in J. G. Kuespert and S. A. Reid, eds.,<br />
Structure, stratigraphy and hydrocarbon occurrences <strong>of</strong> the San Joaquin Basin,<br />
California: Pacific Section AAPG, guidebook, v. 64, p. 231-247.<br />
MacPherson, B. A., 1978, Sedimentation and trapping mechanism in upper Miocene<br />
Stevens and older turbidite fans <strong>of</strong> southeastern San Joaquin Valley,<br />
California: AAPG Bulletin, v. 62, p. 2243-2278.<br />
Maher, J. C., R. D. Carter, and R. J. Lantz, 1975, Petroleum geology <strong>of</strong> Naval<br />
Petroleum Reserve No. 1, Elk Hills, Kern County, California: U.S. Geological<br />
Survey Pr<strong>of</strong>essional Paper 912,109 p.<br />
Medwedeff, D. A., 1989, Growth fault-bend folding at southeast Lost Hills, San<br />
Joaquin Valley, California: AAPG Bulletin, v. 73, p. 54-67.<br />
Miller, D. D., 1998, Distributed shear, rotation, and partitioned strain along the San<br />
Andreas fault, central California: Geology, v. 26, p. 867-870.<br />
Miller, D. D., 1999, Sequence stratigraphy and controls on deposition <strong>of</strong> the Upper<br />
Cenozoic Tulare Formation, San Joaquin Valley, California: PhD dissertation,<br />
<strong>Stanford</strong> <strong>University</strong>, <strong>Stanford</strong>, CA, 170 p.<br />
Mitchum, R. M., P. R. Vail, and J. B. Sangree, 1977, Seismic stratigraphy and global<br />
changes <strong>of</strong> sea level, part 6: Stratigraphic interpretation <strong>of</strong> seismic reflection<br />
patterns in depositional sequences, in C. E. Payton, ed., Seismic stratigraphy -<br />
applications to hydrocarbon exploration: AAPG Memoir, 26, p. 117-133.<br />
Mount, V. S., and J. Suppe, 1987, State <strong>of</strong> stress near the San Andreas fault:<br />
Implications for wrench tectonics: Geology, v. 15, p. 1143 - 1146.<br />
44
Muller, J. R., and A. Aydin, 2005, Using mechanical modeling to constrain fault<br />
geometries proposed for the northern Marmara Sea: Journal <strong>of</strong> Geophysical<br />
Research, v. 110, B03407, doi: 10.1029/2004JB003226.<br />
Muller, J. R., A. Aydin, and F. Maerten, 2003, Investigating the transition between the<br />
1967 Mudurnu Valley and 1999 Izmit earthquakes along the North Anatolian<br />
fault with static stress changes: Geophysics Journal International, v. 154, p.<br />
471-482.<br />
Namson, J. S., and T. L. Davis, 1988, Seismically active fold and thrust belt in the San<br />
Joaquin Valley, central California: Geological Society <strong>of</strong> America Bulletin, v.<br />
100, p. 257-273.<br />
Nicholson, G. E., 1990, Structural overview <strong>of</strong> Elk Hills, in J. G. Kuespert and S. A.<br />
Reid, eds., Structure, stratigraphy and hydrocarbon occurrences <strong>of</strong> the San<br />
Joaquin Basin, CA: Pacific Section AAPG, guidebook, v. 64, p. 133-140.<br />
Pemberton, J. R., 1929, Kern County, California, in Structure <strong>of</strong> typical American oil<br />
fields: AAPG Sidney Powers memorial Volume 2, v. A003, p. 44-61.<br />
Peters, K. E., M. H. Pytte, T. D. Elam, and P. Sundararaman, 1994, Identification <strong>of</strong><br />
petroleum systems adjacent to the San Andreas fault, California, U.S.A., in L.<br />
B. Magoon and W. G. Dow, eds., The petroleum system - From source to trap:<br />
AAPG Memoir 60, p. 423-436.<br />
Reid, S. A., 1990, Trapping characteristics <strong>of</strong> upper Miocene turbidite deposits, Elk<br />
Hills field, Kern County, California, in J. G. Kuespert and S. A. Reid, eds.,<br />
Structure, stratigraphy, and hydrocarbon occurrences <strong>of</strong> the San Joaquin basin,<br />
California: Pacific Section AAPG, guidebook, v. 64, p. 319-329.<br />
Reid, S. A., 1995, Miocene and Pliocene depositional systems <strong>of</strong> the southern San<br />
Joaquin basin and formation <strong>of</strong> sandstone reservoirs in the Elk Hills area,<br />
California, in A. E. Fritsche, ed., Cenozoic paleogeography <strong>of</strong> the western<br />
United States-II: Pacific Section SEPM, book 75, p. 131-150.<br />
Reid, S. A., and J. L. McIntyre, 2001, Monterey Formation porcelanite reservoirs <strong>of</strong><br />
the Elk Hills field, Kern County, California: AAPG Bulletin, v. 85, p.169-189.<br />
Resor, P. G., D. D. Pollard, T. J. Wright, T. J., and G. C. Beroza, 2005, Integrating<br />
high-precision aftershock locations and geodetic observations to model<br />
coseismic deformation associated with the 1995 Kozani-Grevena earthquake,<br />
Greece: Journal <strong>of</strong> Geophysical Research, v. 110, doi: 10.1029/2004JB003263.<br />
Sarna-Wojcicki, A. M., H. W. Bowman, and P. C. Russell, 1979, Chemical correlation<br />
<strong>of</strong> some Late Cenozoic tuffs <strong>of</strong> northern and central California by neutron<br />
45
activation analysis <strong>of</strong> glass and comparison with x-ray fluorescence analysis:<br />
U. S. Geological Survey Pr<strong>of</strong>essional Paper P1147, 15 p.<br />
Sarna-Wojcicki, A. M., K. R. Lajoie, C. E. Meyer, D. P. Adam, and H. J. Rieck, 1990,<br />
Tephrochronologic correlation <strong>of</strong> upper Miocene sediments along the Pacific<br />
margin, coterminous United States, in R. M. Morrison, ed., Quaternary <strong>of</strong> the<br />
Non-Glacial United States, Decade <strong>of</strong> North American Geology, v. K-2.<br />
Savage, H., and M. L. Cooke, 2004, The effect <strong>of</strong> non-parallel fault interaction on fold<br />
patterns: Journal <strong>of</strong> Structural Geology, v. 26, p. 905-917.<br />
Savage, J. C., 1990, Equivalent strike-slip earthquake cycles in half-space and<br />
lithosphere-asthenosphere <strong>Earth</strong> models: Journal <strong>of</strong> Geophysical Research, v.<br />
95, p. 4873-4879.<br />
Shamir, G., and Y. Eyal, 1995, Elastic modeling <strong>of</strong> fault-driven monoclinal fold<br />
patterns: Tectonophysics, v. 245, p. 13-24.<br />
Shaw, J. H., A. Plesch, J. F. Dolan, T. L. Pratt, and P. Fiore, 2002, Puente Hills blindthrust<br />
system, Los Angeles, California: Bulletin <strong>of</strong> the Seismological Society<br />
<strong>of</strong> America, v. 92, p. 2946-2960.<br />
Shaw, J. H., and J. Suppe, 1996, Earhquake hazards <strong>of</strong> active blind-thrust faults under<br />
the central Los Angeles basin, California: Journal <strong>of</strong> Geophysical Research, v.<br />
101, p. 8623-8642.<br />
Shultz, M. R., 2004, Stratigraphic architecture <strong>of</strong> two deep-water depositional<br />
systems: The Tres Pasos formation, Chilean Patagonia, and the Stevens<br />
Sandstone, Elk Hills: PhD dissertation, <strong>Stanford</strong> <strong>University</strong>, <strong>Stanford</strong>,<br />
California, 284 p.<br />
Stein, R. S., and G. Ekstrom, 1992, Seismicity and geometry <strong>of</strong> a 110-km-long blind<br />
thrust fault, 2. synthesis <strong>of</strong> the 1982-1985 California earthquake sequence:<br />
Journal <strong>of</strong> Geophysical Research, v. 97, p. 4865-4883.<br />
Suppe, J., G. T. Chou, and S. C. Hook, 1992, Rates <strong>of</strong> folding and faulting determined<br />
from growth strata, in K. R. McClay, ed., Thrust Tectonics: New York,<br />
Chapman & Hall, p. 105-122.<br />
Tennyson, M., 1989, Pre-transform early Miocene extension in western California:<br />
Geology, v. 17, p. 792-796.<br />
Thomas, A. L., 1993, Poly3D: a three-dimensional, polygonal element, displacement<br />
discontinuity boundary element computer program with applications to<br />
fractures, faults, and cavities in the <strong>Earth</strong>'s crust: MS thesis, <strong>Stanford</strong><br />
<strong>University</strong>, <strong>Stanford</strong>, CA, 97 p.<br />
46
Thoms, C. C., and F. M. Smith, 1922, Notes on Elk Hills oil field: California State<br />
Mining Bureau, 7 th State Mineralogists Report, 1921, p. 7-19.<br />
Toda, S., and R. S. Stein, 2002, Response <strong>of</strong> the San Andreas Fault to the 1983<br />
Coalinga-Nunez earthquakes; an application <strong>of</strong> interaction-based probabilities<br />
for Parkfield: Journal <strong>of</strong> Geophysical Research, v. 107, B6, doi:<br />
10.1029/2001JB000172.<br />
Webb, G. W., 1981, Stevens and earlier Miocene turbidite sandstone, southern San<br />
Joaquin Valley, California: AAPG Bulletin, v. 65, p. 438-465.<br />
Wentworth, C. M., M. C. Blake, Jr., D. L. Jones, A. W. Walter, and M. D. Zoback,<br />
1984, Tectonic wedging associated with emplacement <strong>of</strong> the Franciscan<br />
assemblage, California Coast Ranges, in, M. C. Blake, ed., Franciscan geology<br />
<strong>of</strong> northern California: Pacific Section SEPM, book 43, p. 163-173.<br />
White, R. E., 1987, Paleomagnetism <strong>of</strong> the Tulare Formation from cores and surface<br />
exposures west-central and southwestern San Joaquin Valley, California: MS<br />
thesis, Long Beach State <strong>University</strong>, Long Beach, California, 272 p.<br />
Wilcox, R. E., T. P. Harding, and D. R. Seely, 1973, Basic wrench tectonics: AAPG<br />
Bulletin, v. 57, p. 74-96.<br />
Willemse, E. J. M., D. D. Pollard, and A. Aydin, 1996, Three-dimensional analyses <strong>of</strong><br />
slip distributions on normal fault arrays with consequences for fault scaling:<br />
Journal <strong>of</strong> Structural Geology, v. 18, p. 295-309.<br />
Wiprut, D., and M. D. Zoback, 2000, Fault reactivation and fluid flow along a<br />
previously dormant normal fault in the northern North Sea: Geology, v. 28, p.<br />
595-598.<br />
Woodring, W. P., P. V. Roundy, and H. R. Farnsworth, 1932, Geology and oil<br />
resources <strong>of</strong> the Elk Hills, California, including Naval Petroleum Reserve No.<br />
1: U. S. Geological Survey Bulletin 835, 82 p.<br />
Zoback, M. D., M. L. Zoback, V. S. Mount, J. Suppe, J. P. Eaton, J. H. Healy, D.<br />
Oppenheimer, P. Reasenberg, L. M. Jones, C. B. Raleigh, I. G. Wong, O.<br />
Scotti, and C. M. Wentworth, 1987, New evidence on the state <strong>of</strong> stress <strong>of</strong> the<br />
San Andreas fault system: Science, v. 238, p. 1105-1111.<br />
Zumberge, J. E., J. A. Russell, and S. A. Reid, 2005, Charging <strong>of</strong> Elk Hills reservoirs<br />
as determined by oil geochemistry: AAPG Bulletin, v. 89, p. 1347-1371.<br />
47
Abstract<br />
Chapter 2<br />
The role <strong>of</strong> fractures in the structural interpretation <strong>of</strong> Sheep<br />
Mountain anticline, Wyoming<br />
The development <strong>of</strong> fractures in the sedimentary layers <strong>of</strong> Sheep Mountain<br />
anticline, a Laramide asymmetric fault-cored fold <strong>of</strong> the Bighorn Basin, is documented<br />
and interpreted as a method <strong>of</strong> constraining the kinematic evolution <strong>of</strong> the fold. This<br />
study suggests the existence <strong>of</strong> a regional fracture set (set I) predating the Laramide<br />
compression, and striking 110°, oblique to the future fold trend. A joint set (set II),<br />
striking 045° and present in the hinge and backlimb, is associated with the NE-<br />
oriented Laramide compression. Joints striking 135° (set III; fold parallel) are found<br />
within the hinge and are interpreted to have developed in response to the bending <strong>of</strong><br />
stratigraphic layers. The two youngest fracture sets are attributed to a late stage <strong>of</strong> fold<br />
growth: a joint set (set IV) in the backlimb striking parallel to the set I fractures, but<br />
vertical; and a fracture set in the forelimb consisting <strong>of</strong> set I fractures reactivated as<br />
reverse faults. The relative chronology, mode <strong>of</strong> formation (opening vs. shearing), and<br />
structural locations <strong>of</strong> these fractures provide the following constraints on fold<br />
kinematics: there was little or no lateral fold propagation and no hinge migration; limb<br />
rotation or limb flexure and stretching operated at different structural locations during<br />
folding.<br />
Introduction<br />
Fold-fracture relationships were conceptualized in the late 1960s and 1970s by<br />
Price (1967), Stearns (1968), Friedman (1969), and Stearns and Friedman (1972).<br />
These conceptual models have three shortcomings, which have been addressed in<br />
recent investigations. First, they do not consider the temporal evolution <strong>of</strong> the fold.<br />
The fractures described in these models are correlated with final fold geometry,<br />
without consideration <strong>of</strong> either the effect <strong>of</strong> the initial and transitional fold shapes on<br />
fracture development, or fracture evolution during fold growth (Fischer and<br />
Wilkerson, 2000). Second, they neglect to account for the influence <strong>of</strong> pre-existing<br />
49
fractures (Guiton et al., 2003a; 2003b; Bergbauer and Pollard, 2004). Third, they<br />
disregard the effect <strong>of</strong> primary faults, which are <strong>of</strong>ten associated with fold formation<br />
(Johnson and Johnson, 2002; Savage and Cooke, 2004). Fault slip perturbs the<br />
surrounding stress field on the scale <strong>of</strong> fault length and can affect fracture formation<br />
within this zone <strong>of</strong> influence. In this paper, we document the distribution and<br />
characteristics <strong>of</strong> fractures at Sheep Mountain anticline and use these data to interpret<br />
the evolution <strong>of</strong> the fold.<br />
Kinematic models attempt to unravel the evolution <strong>of</strong> a fold with time through<br />
both backward and forward modeling, with the present-day shape <strong>of</strong> the fold as<br />
calibration (Suppe, 1985; Jamison, 1987; Mitra, 1990; Erslev, 1991; Cristallini and<br />
Allmendinger, 2002; Bump, 2003). These models are based on kinematic assumptions<br />
such as hinge migration (Suppe, 1983; Beutner and Diegel, 1985; Allmendinger,<br />
1998) or fixed hinge (Erslev, 1991; McConnell, 1994; Spang and McConnell, 1997),<br />
rotating limbs (Erslev, 1991) or fixed limb dip (Suppe, 1983; Suppe and Medwedeff,<br />
1990). Recent studies have suggested that a fold may attain its maximum (along<br />
strike) length very early during its evolution (Armstrong and Bartley, 1993; Cristallini<br />
and Allmendinger, 2001; Bernal and Hardy, 2002; Fischer and Christensen, 2004). In<br />
contrast, other workers have inferred that fold tips propagate laterally through time<br />
(Fischer and Wilkerson, 2000), maintaining that vertical displacement on a fault is<br />
accompanied by increasing length (Cowie and Scholz, 1992; Dawers et al., 1993;<br />
Peacock and Sanderson, 1996). We propose that the kinematics <strong>of</strong> a thrust fault related<br />
fold can be constrained through an examination <strong>of</strong> the deformation recorded within the<br />
folded layers. This deformation includes the brittle fracturing <strong>of</strong> sedimentary layers as<br />
recorded by joints, faults, and deformation bands. The chronology <strong>of</strong> these structural<br />
features, when combined with their geometry and modes <strong>of</strong> deformation, provide<br />
insight into the structural setting at the time <strong>of</strong> their formation. We show how<br />
inferences can be made that associate each fracture set with a particular stage <strong>of</strong> fold<br />
evolution (pre-, early-, syn-, late, or post-folding). The timing and locations <strong>of</strong> these<br />
fractures, thereby help to inform an improved kinematic model.<br />
Recent studies have attempted to constrain the unknown parameters <strong>of</strong> folding at<br />
various field sites, making use <strong>of</strong> mechanical models, for which the present-day fold<br />
50
shape and fracture distributions serve as calibration (e.g. Shamir and Eyal, 1995; Nino<br />
et al., 1998; Zhang et al., 2000; Johnson and Johnson, 2002; Savage and Cooke, 2004,<br />
and references therein). For example, Nino et al. (1998) examined the role <strong>of</strong> fault dip,<br />
layer thickness, and bedding-parallel slip with elasto-plastic models that replicate the<br />
shape <strong>of</strong> the Jabal Mquebra anticline in Syria. Johnson and Johnson (2002) showed<br />
that viscous models reproduce the shape <strong>of</strong> some <strong>of</strong> the Rocky Mountain foreland<br />
basement-involved folds when the appropriate underlying fault geometry, magnitude<br />
<strong>of</strong> cover anisotropy, and nature <strong>of</strong> the basement-cover contact are prescribed. Savage<br />
and Cooke (2004) showed how the geometry <strong>of</strong> a parasitic fault at Sheep Mountain,<br />
Wyoming can be developed using elastic models. The mechanical models also provide<br />
the opportunity to investigate fold-fracture relationships that may constrain fold<br />
evolution. Theoretical fracture patterns derived from the stress fields computed in a<br />
mechanical analysis can be compared with fracture data collected in the field to test<br />
hypotheses about fold evolution (Guiton et al., 2003a, 2003b).<br />
Sheep Mountain anticline, Wyoming (Fig. 2.1) is widely known for its<br />
exceptional outcrops, most notably in the canyon cut by the Bighorn River,<br />
approximately perpendicular to the axial trend <strong>of</strong> the anticline. Studies over the past<br />
two decades have contributed to an understanding <strong>of</strong> the large scale deformation at<br />
Sheep Mountain (Gries, 1983; Hennier and Spang, 1983; Stone, 1993; Brown, 1993;<br />
Forster et al., 1996; Savage and Cooke, 2002), particularly the underlying fault<br />
geometry. Recently, a new geometric model was developed for the subsurface<br />
structure <strong>of</strong> the anticline (Stanton and Erslev, 2004). From the interpretation <strong>of</strong> a few<br />
2D seismic reflection lines, as well as surface maps from previous studies (Rioux,<br />
1958; Hennier 1984; Rioux, 1995) and stratigraphic picks within exploration wells,<br />
Stanton and Erslev (2004) interpreted the fold to have resulted from slip along a<br />
basement fault dipping SW that was followed by slip on a NE-dipping fault (Fig. 2.2).<br />
Although the underlying fault geometry at Sheep Mountain has received<br />
attention, knowledge <strong>of</strong> the fracture patterns is limited. Harris et al. (1960) described<br />
several fracture sets in the Sheep Mountain area and related these to bed thickness and<br />
lithology. They interpreted the systematic (planar, parallel, repetitious) fracture sets as<br />
“<strong>of</strong> compressional deformational origin” and “related to shear stresses”. However,<br />
51
N<br />
(b)<br />
108°12'<br />
subsidiary<br />
structure<br />
Quaternary<br />
Cretaceous<br />
Jurassic<br />
Triassic<br />
A<br />
108°10'<br />
Permian (Phosphoria Fm)<br />
Carboniferous (Pennsylvanian, Tensleep Fm)<br />
Carboniferous (Pennsylvanian, Amsden Fm)<br />
Carboniferous (Mississipian, Madison Fm)<br />
Anticlinal axis Synclinal axis<br />
108°08'<br />
A'<br />
Big Horn River<br />
Sheep<br />
Mountain<br />
anticline<br />
1 km<br />
(a)<br />
44°<br />
43°<br />
45°<br />
110°<br />
Absaroka Mnts<br />
WIND RIVER<br />
RANGE<br />
108°04'<br />
109°<br />
BIG<br />
HORN<br />
WIND RIVER<br />
108°02'<br />
BASIN<br />
BASIN<br />
Owl Creek Mnts<br />
108°<br />
Big Horn Mnts<br />
107°<br />
100 km<br />
POWDER<br />
Figure 2.1. Geologic and tectonic maps <strong>of</strong> the Sheep Mountain anticline. (a) Detail <strong>of</strong><br />
the Wyoming tectonic map, with a square outlining the location <strong>of</strong> the anticline. (b)<br />
Geological map <strong>of</strong> the anticline from Rioux (1994). The line A-A’ is the location <strong>of</strong> the<br />
cross-section shown in figure 2.2.<br />
52<br />
44°36'<br />
44°34'<br />
Casper Arch<br />
RIVER<br />
BASIN
diagnostic evidence for such an interpretation (see Pollard and Aydin, 1988) was not<br />
obtained. Furthermore, the fracture orientations were not recorded, nor were they<br />
rotated to remove the effect <strong>of</strong> bedding orientation, and the relative age relationships<br />
<strong>of</strong> the fracture sets were not deduced from the field observations. Johnson et al. (1965)<br />
studied fracture geometries within two formations <strong>of</strong> significantly different ages, one<br />
pre-Laramide and one post-Laramide, in the Bighorn Basin. The study was designed<br />
to test the premise that differences between the fracture patterns within the two<br />
lithologies would suggest that a pre-Laramide orogeny had occurred in the Bighorn<br />
Basin. Although the study was inconclusive, fracture orientation (strike and dip) and<br />
length data were collected and interpreted to suggest the mechanism by which each<br />
fracture set formed. Two major joint sets were recorded: one trending east-west and<br />
one trending between 105° and 155°; two minor joint sets were recorded: one trending<br />
north-south and one trending between 025° and 065°. The modes <strong>of</strong> deformation <strong>of</strong><br />
these fracture sets were not observed in the field, but were instead suggested based on<br />
angular relationships between fracture sets and fold axes.<br />
In this paper, we present new field data collected at 60 sites across the<br />
northwestern half <strong>of</strong> the anticline that consist <strong>of</strong> fracture mode (opening or shear) and<br />
geometry (orientation, size, and spacing) at the macro- and microscale, along with the<br />
chronological relationships among the fracture sets. We focus on the interpretation <strong>of</strong><br />
these data as an indicator <strong>of</strong> fold kinematics.<br />
Geological and tectonic setting<br />
Sheep Mountain anticline is located along the eastern flank <strong>of</strong> the Bighorn basin,<br />
which trends NW/SE and is bounded to the east by the Bighorn Mountains, to the<br />
south by the Owl Creek Mountains, to the west by the Absaroka and Beartooth<br />
Mountains, and to the north by the Nye-Bowler Lineament (Fig. 2.1). During the<br />
Paleozoic and Mesozoic, this basin filled with approximately 3000 m <strong>of</strong> sediments<br />
(Thomas, 1965; Ladd, 1979). The oldest formation exposed at Sheep Mountain is the<br />
Lower Carboniferous Madison limestone (Fig. 2.3), which is about 200m thick, and is<br />
topped by a paleokarst surface. The Madison Formation is unconformably overlain by<br />
the Upper Carboniferous Amsden Formation. The base <strong>of</strong> the Amsden Formation is<br />
53
SW<br />
0 m<br />
2000 m<br />
4000 m<br />
T. P. P.<br />
Bighorn basin<br />
Cambrian<br />
pre-Cambrian basement<br />
Sheep Mountain<br />
Figure 2.2. Cross section through Sheep Mountain (see Fig. 1b for location) as<br />
interpreted by Stanton and Erslev (2004). The fold is asymmetric and underlain by a<br />
basement (gray shading) thrust fault verging toward the northeast and cross cutting<br />
only the lower sedimentary layers. Stanton and Erslev (2004) interpreted this fault to<br />
be later cut by a southwest-verging thrust fault. The formation above the Cambrian<br />
formation is the Madison Fm. T.P.P. is for the Amsden (Pennsylvanian), Tensleep<br />
(Pennsylvanian), Phosphoria (Permian) and Chugwater (Triassic) Fm.<br />
Perimian Trias<br />
Carb.<br />
(Penn.)<br />
Carboniferous (Miss.)<br />
250 Ma<br />
292 Ma<br />
320 Ma<br />
Chugwater<br />
174m<br />
Phosphoria<br />
68m<br />
Tens<br />
29m<br />
Ams<br />
35m<br />
Madison<br />
230m<br />
Figure 2.3. Stratigraphic section for formations that outcrop at Sheep Mountain after<br />
Ladd (1979). Miss. is for Mississipian. Penn. is for Pennsylvanian.<br />
54<br />
NE
marked by a crossbedded, light gray fine grained quartz arenite (Ladd, 1979). The<br />
remainder <strong>of</strong> the formation consists <strong>of</strong> thick siltstones, sandstones, shales and<br />
carbonates. Above the Amsden formation, the Tensleep Formation (also Upper<br />
Carboniferous in age) is composed <strong>of</strong> interbedded thin sandstones, shales, and<br />
carbonates in its lower part and thicker beds <strong>of</strong> crossbedded quartz arenite in its upper<br />
part. Above the Carboniferous section is the Phosphoria Formation, Permain in age.<br />
The lower beds <strong>of</strong> the Phosphoria Fm. are predominantly siltstones and shales, with a<br />
thin interbedded gypsum layer (Ladd, 1979). Higher in section, the formation is<br />
composed <strong>of</strong> thick carbonates (biolithite, micrite and biosparite). Due to minor<br />
Ancestral Rocky Mountains uplift, the Tensleep Fm. and Phosphoria Fm. are thinned<br />
at Sheep Mountain (Simmons and Scholle, 1990). Above these units, the base <strong>of</strong> the<br />
Mesozoic rocks is defined by the Triassic Chugwater Formation, distinctive due to its<br />
red color. The overlying sediments are composed <strong>of</strong> sandstones and shales that have<br />
been eroded in the Sheep Mountain area.<br />
At the end <strong>of</strong> the Maastrichtian and during Paleocene times, the Laramide<br />
orogeny produced a NE-trending compression (Dickinson and Snyder, 1978;<br />
Engebretson et al., 1985; Bird, 1998; Bird, 2002). Sheep Mountain anticline formed<br />
during the Laramide orogeny as a basement cored, doubly-plunging, asymmetric fold<br />
(Fig. 2.1 and 2.2). Given its orientation (NW-SE), the fold formed perpendicular to the<br />
Laramide direction <strong>of</strong> compression (NE-SW). This orientation is similar to the<br />
orientation <strong>of</strong> many folds within the Rocky Mountains, although others formed at<br />
acute angles to the regional compression (Erslev, 1993). At Sheep Mountain, the steep<br />
northeastern limb (forelimb) dips between 40° and 90° northeast. This dip is shallower<br />
near the fold noses and steeper in the central part <strong>of</strong> the fold. In the southwestern<br />
backlimb, bedding dips are between 10° and 40° southwest. The shape <strong>of</strong> Sheep<br />
Mountain anticline changes along the fold axis. Near the northern termination, the fold<br />
plunges approximately 20° northwest and the pr<strong>of</strong>ile is very tight (Twiss and Moores,<br />
1992, p.228). Toward the south, the asymmetry increases while the fold hinge<br />
becomes rounder. At the southern termination, the plunge <strong>of</strong> the fold axis is<br />
approximately 10° southwest.<br />
55
The fold overlies a fault that has been interpreted as a southwest-dipping thrust<br />
(Hennier and Spang, 1983; Forster et al., 1996; Stanton and Erslev, 2004). Stanton and<br />
Erslev (2004) suggest the displacement along this fault reaches a maximum beneath<br />
the central section <strong>of</strong> the anticline and decreases toward the north and south noses.<br />
They conclude that this southwest-dipping thrust was later cut by a northeast-dipping<br />
thrust (Fig. 2). This faulting chronology is in opposition to the studies <strong>of</strong> Hennier and<br />
Spang (1983) and Forster et al. (1996), which suggest that the fault responsible for the<br />
formation <strong>of</strong> Sheep Mountain Anticline is a SW dipping backthrust <strong>of</strong> an older NE<br />
dipping thrust, and Stone (2004), which suggests that the SW and NE dipping thrusts<br />
developed contemporaneously in early Laramide time.<br />
Smaller scale faults are present at Sheep Mountain Anticline. Slickensides are<br />
present on bedding (Hennier and Spang, 1983), indicating a component <strong>of</strong> flexural-slip<br />
folding with slip directions approximately normal to the fold axis. Additionally, some<br />
small reverse faults are present in the hinge and the backlimb <strong>of</strong> the anticline (Hennier<br />
and Spang, 1983; Forster et al., 1996). In the backlimb, a smaller fold branches from<br />
the main anticline and has an axis trending NNW-SSE. This structure apparently is<br />
associated with a shallower thrust fault that is not linked to any basement fault<br />
(Hennier and Spang, 1983; Forster, 1996; Savage and Cooke, 2004; Stanton and<br />
Erslev, 2004).<br />
Methods<br />
Fracture sampling<br />
Fracture populations were sampled only in the part <strong>of</strong> the anticline north <strong>of</strong> the<br />
Bighorn River (Fig. 2.4, 2.5, 2.6). Sandstones were sampled from the Tensleep Fm. in<br />
the anticlinal limbs and from the Amsden Fm. in the hinge. The limestone <strong>of</strong> the<br />
Phosphoria Fm. was sampled in the fold nose to increase data coverage and to assess<br />
fracture formation as a function <strong>of</strong> lithology. The fracture orientation data, mode <strong>of</strong><br />
deformation (opening or shearing), termination relationships, and evidence for<br />
reactivation are the key data sets incorporated into our analysis <strong>of</strong> fracture evolution.<br />
Fracture infilling, length, and spacing also were studied. Spacing measurements are<br />
56
Site 27<br />
N<br />
31<br />
Site 36<br />
N<br />
31<br />
Site 08<br />
N<br />
NOSE<br />
Site 28<br />
N<br />
Site 02<br />
N<br />
Site 07<br />
N<br />
36<br />
116<br />
78<br />
57<br />
N<br />
Site 23<br />
N<br />
HINGE<br />
86<br />
Site 39<br />
N<br />
108°10'<br />
Site 18<br />
N<br />
42<br />
Site 40<br />
N<br />
27<br />
02 36<br />
28<br />
29<br />
39<br />
41<br />
07<br />
40<br />
30<br />
14<br />
43<br />
08<br />
44<br />
51 Site 17<br />
N<br />
BACKLIMB<br />
62<br />
42<br />
Site 29<br />
N<br />
Site 41<br />
N<br />
12<br />
23<br />
44°39'<br />
Site 16<br />
N<br />
35<br />
Site 43<br />
N<br />
13<br />
18<br />
44<br />
45<br />
Site 30<br />
N<br />
53<br />
12<br />
17<br />
16<br />
Site 01<br />
N<br />
Site 44<br />
N<br />
37<br />
01<br />
26<br />
19<br />
Site 45<br />
N<br />
Site 19<br />
N<br />
20<br />
47<br />
49<br />
Site 46<br />
N<br />
21<br />
Site 20<br />
N<br />
19<br />
44<br />
FORELIMB<br />
Figure 2.4. Aerial photograph <strong>of</strong> Sheep Mountain with the backlimb, forelimb, and<br />
hinge fracture measurement sites and the corresponding polar stereonets shown.<br />
Great circles represent the average bedding corrected orientations <strong>of</strong> fracture sets<br />
measured within the sandstones <strong>of</strong> the Tensleep and Amsden Formations. Black<br />
great circles correspond to the major fracture sets that are used in the analysis <strong>of</strong> fold<br />
kinematics. Gray great circles correspond to minor fracture sets that are most likely<br />
due to local deformation. These minor fracture sets are not considered in the present<br />
analysis <strong>of</strong> fold evolution. The backlimb contains four fracture sets: striking 110° and<br />
bedding perpendicular (set I), striking 045° and bedding perpendicular (set II), striking<br />
135° and bedding perpendicular (set III), and striking 110° and oblique to bedding (set<br />
IV). The forelimb contains one abundant systematic set that strikes 110° and is<br />
perpendicular to bedding (set I). Other fracture sets (are much less numerous and<br />
predominantly trend N-S. In the hinge, three fracture sets are found: striking 110° and<br />
bedding perpendicular (set I), striking 045° and bedding perpendicular (set II), and<br />
striking 135° and bedding perpendicular (set III). The fractures <strong>of</strong> set III are largely<br />
restricted to the hinge.<br />
22<br />
57<br />
108°10'<br />
Site 14<br />
N<br />
11<br />
46<br />
63<br />
Site 13<br />
N<br />
51<br />
35<br />
50<br />
Site 12<br />
N<br />
44°38'<br />
101<br />
10<br />
1 km<br />
Site 50<br />
N<br />
Site 11<br />
N<br />
24<br />
31<br />
32<br />
Site 21<br />
N<br />
63<br />
24<br />
Site 51<br />
N<br />
Site 10<br />
N<br />
47, 48<br />
26<br />
108°08'<br />
37<br />
Site 31<br />
N<br />
Site 47<br />
N<br />
38<br />
44°37'<br />
39<br />
Site 32<br />
N<br />
Site 48<br />
N<br />
49<br />
37
Jurassic<br />
Trias<br />
Permian (Phospphoria Fm)<br />
Carboniferous<br />
(Pennsylvanien, Tensleep Fm)<br />
Carboniferous<br />
(Pennsylvanian, Amsden Fm)<br />
Carboniferous<br />
(Mississipian, Madison Fm)<br />
Anticlinal axis<br />
Hinge<br />
site 66<br />
N<br />
site 65<br />
N<br />
46<br />
50<br />
site 57<br />
site 64<br />
N<br />
N<br />
Backlimb<br />
N<br />
37<br />
250 m<br />
54<br />
site 56<br />
site 63<br />
N<br />
N<br />
site 67<br />
site 55<br />
57<br />
66 56<br />
55 67<br />
65 68<br />
26<br />
64<br />
54<br />
63 53<br />
62<br />
N<br />
N<br />
61<br />
60<br />
2<br />
site 68<br />
site 54<br />
Forelimb<br />
site 26<br />
site 53<br />
site 02<br />
site 62 site 61 site 60<br />
Figure 2.5. Geologic map from Rioux (1995) <strong>of</strong> the nose <strong>of</strong> Sheep Mountain with the<br />
nose fracture measurement sites and the corresponding polar stereonets shown.<br />
Great circles represent the average bedding corrected orientations <strong>of</strong> fracture sets<br />
measured within the limestone <strong>of</strong> the Phosphoria Fm. Black great circles correspond<br />
to the major fracture sets that are used in the analysis <strong>of</strong> fold kinematics. Gray great<br />
circles correspond to minor fracture sets not used in the analysis.<br />
58<br />
52<br />
46<br />
N<br />
58<br />
56<br />
36<br />
N<br />
N<br />
N<br />
31<br />
53<br />
57<br />
N<br />
N<br />
N<br />
N<br />
31<br />
78<br />
61<br />
79
parallel to the bedding and are not normalized to bed thickness. At each outcrop,<br />
fractures were sampled in areas typically a few tens <strong>of</strong> meters on a side.<br />
The data presented here include evidence from thin sections cut perpendicular to<br />
fracture strike (Fig. 2.6). The samples were collected at the same sites at which<br />
fracture orientations were measured. The samples were collected to confirm, at the<br />
microscale, the macroscopic determination <strong>of</strong> deformation mode. When the mode is<br />
ambiguous, the structures are called fractures, where confirmed they are referred to as<br />
joints or shear fractures. We collected several samples for each set <strong>of</strong> fractures in each<br />
structural position. Thus, we believe that the samples are representative <strong>of</strong> the<br />
deformation modes observed throughout the northern part <strong>of</strong> the anticline. For brevity,<br />
we show only a few typical thin sections (Fig. 2.6).<br />
Data processing<br />
Four fracture sets are defined based on both orientation data and mode <strong>of</strong><br />
deformation. Members <strong>of</strong> a fracture set share both a common range <strong>of</strong> strike and dip<br />
orientation, and, with the exception <strong>of</strong> set I, a common deformation mode. With one<br />
exception, common orientation can be identified only after removal <strong>of</strong> bedding dip by<br />
stereographic rotation. Fold plunge was not removed because it is less than 20° and it<br />
does not significantly impact the determination <strong>of</strong> prefolding fracture orientation.<br />
Commonality <strong>of</strong> fracture orientation after removal <strong>of</strong> bedding dip is taken as<br />
supportive <strong>of</strong> a prefolding origin (Hancock, 1985). Fracture strikes either<br />
perpendicular or parallel to bedding strike are not affected by rotation <strong>of</strong> bedding to<br />
remove the dip and may be interpreted as occurring during any stage <strong>of</strong> fold growth.<br />
We present stereonets <strong>of</strong> the orientation data at each measurement site that are not<br />
weighted by abundance, as we believe that this can be biased by outcrop conditions.<br />
However, we note when a fracture set is less systematic and abundant than others.<br />
The stereonets presented in this paper have been produced with a prototype<br />
computer code developed in the Structural Geology Department <strong>of</strong> the Institut<br />
Français du Pétrole, using an original method for the automatic definition <strong>of</strong> fracture<br />
clusters. As a standard represention, each fracture is represented locally as a plane<br />
with an orientation given by the unit normal vector as a point (pole) on the unit sphere.<br />
59
N<br />
108°10'<br />
SM 41, 41b<br />
44°39'<br />
SM 44<br />
SM 13<br />
SM 08 SM 44b<br />
SM 23<br />
SM 45<br />
SM 18<br />
SM 16<br />
108°10'<br />
44°38'<br />
1 km<br />
108°08'<br />
Figure 2.6. Sample sites for microscale analysis. Samples SM08, SM13, SM16,<br />
SM18, and SM23 are within the Tensleep Formation. Samples SM41, SM44, and<br />
SM45 are within the Amsden Formation. All sites relate to sites shown in figure 2.4<br />
where fracture data were collected.<br />
60<br />
44°37
The density <strong>of</strong> fractures is estimated at each point on this sphere using an<br />
Epanechnikov kernel (see Diggle and Fisher, 1985 for examples with other kernels).<br />
Outliers (fractures associated with a small density) are removed by filtering and the<br />
density distribution is smoothed manually changing the variance <strong>of</strong> the kernel<br />
(Wollmer, 1995). In a first step, cluster centers are identified by searching for local<br />
maxima <strong>of</strong> the density map using the method introduced by Kittler (1976). This step<br />
results in the definition <strong>of</strong> number <strong>of</strong> sets and a guess for the mean pole <strong>of</strong> each set.<br />
This guess allows each fracture to be classified probabilistically using its distance<br />
from each cluster center. Then the algorithm presented by Marcotte and Henry (2002)<br />
is used to finalize the fracture classification. This method is based on the assumption<br />
<strong>of</strong> a bivariate normal distribution <strong>of</strong> fractures within a set. The results <strong>of</strong> this analysis<br />
are presented in a polar stereonet using the Lambert projection on the lower<br />
hemisphere with great circles representing the mean plane <strong>of</strong> each fracture set (Fig.<br />
2.4, 2.5, 2.7, 2.9, 2.10, 2.13, 2.15, 2.16, and 2.17). In these figures, the polar stereonets<br />
depict, from left to right: fractures in present-day orientations, fractures in pre-folding<br />
orientations, and the great circle <strong>of</strong> the calculated mean orientation <strong>of</strong> the fracture sets.<br />
Curvature calculation<br />
We computed a curvature map (Fig. 2.7) to assess the relative curvature <strong>of</strong><br />
various fold locations. Forster et al. (1996) published a structure contour map <strong>of</strong> a<br />
reference horizon at the base <strong>of</strong> a Jurassic formation (Sundance Fm.). This map was<br />
generated through field mapping and the construction <strong>of</strong> serial cross sections that<br />
predict the elevation <strong>of</strong> the formation in areas where it has been eroded. We digitized<br />
the structure contour map and calculated the maximum curvature across the resulting<br />
three dimensional surface. The curvature was calculated using gOcad, a 3D<br />
geomodeling s<strong>of</strong>tware program (Mallet, 2002). The algorithm for maximum curvature<br />
selects the prinicipal curvature with the greater absolute value and plots that curvature.<br />
Thus, positive curvature, representative <strong>of</strong> synclinal features, may be differentiated<br />
from negative curvature, representative <strong>of</strong> anticlinal features. In figure 2.7, areas <strong>of</strong><br />
lighter shades <strong>of</strong> gray have positive curvature and areas <strong>of</strong> darker shades <strong>of</strong> gray have<br />
negative curvature.<br />
61
Hinge<br />
Backlimb<br />
curvature (m -1 )<br />
x10 -3<br />
6<br />
4<br />
2<br />
0<br />
-2<br />
-4<br />
-6<br />
Hinge<br />
Subsidiary fold<br />
Forelimb<br />
Syncline<br />
Figure 2.7. Curvature map <strong>of</strong> Sheep Mountain anticline calculated from the map in<br />
Forster et al. (1996). See text for calculation details. Light colors represent synclinal<br />
folding and dark colors represent anticlinal folding.<br />
62
Structural Data<br />
Northeastern forelimb<br />
In the forelimb, we observe one systematic fracture set within the Tensleep<br />
sandstone, trending 110° (Fig. 2.4, sites 10 to 14 and 29 to 32). From abutting<br />
relationships in other structural positions <strong>of</strong> the fold, this set is interpreted as the first<br />
formed in the area, and is thus called set I. Additionally, non-systematic sets are<br />
locally developed (striking primarily 070° and 180°, Fig. 2.4) and are interpreted to<br />
reflect more local rather than fold-scale or regional deformation, and so are not further<br />
considered (Fig. 2.4).<br />
Set I fractures are linear and several meters long (Fig. 2.8). Their spacing is on<br />
the order <strong>of</strong> a few tens <strong>of</strong> cm. In the field, their mode <strong>of</strong> deformation is difficult to<br />
determine, as different fractures within the set exhibit characteristics <strong>of</strong> either joint or<br />
shear band morphology. In some cases, the fractures are open with or without mineral<br />
fill, and in other cases, they have small positive relief. This latter attribute may be<br />
related to either cementing (for the case <strong>of</strong> joints or dilational bands) or tighter<br />
packing <strong>of</strong> grains within the fracture (for the case <strong>of</strong> deformation bands). At the<br />
microscale, the fractures are defined by zones that contain smaller quartz grains with<br />
more angular shapes, poorer sorting, less porosity, and smaller calcite cement crystals<br />
than the surrounding rock (Fig. 2.9). These features are characteristic <strong>of</strong> deformation<br />
bands (Aydin, 1978; Antonellini et al. 1994), and we interpret set I fractures to be such<br />
brittle structures. However, no <strong>of</strong>fset or sense <strong>of</strong> shearing was obvious either in thin<br />
sections or in the field. Thus, we are unable to suggest a mode <strong>of</strong> deformation for<br />
these fractures.<br />
Bed-normal reverse faults that strike 110° and dip 30° south are present along<br />
the forelimb (at sites 11, 13, 14, and 30 to 32 on Fig. 2.4. and see Fig. 2.10). The faults<br />
are oblique to the fold axis and the Laramide regional compression. The oblique<br />
striations noticeable along the fault planes indicate oblique slip, consistent with the<br />
resolution <strong>of</strong> shear stress from the NE directed compression onto these planes (Fig.<br />
2.10).<br />
63
S N<br />
a)<br />
Nb planes 94<br />
SE<br />
b)<br />
Nb planes 35<br />
N<br />
N<br />
N<br />
Figure 2.8. Field photographs <strong>of</strong> fracture patterns on a tilted bedding surface taken<br />
at forelimb sites 12 (a) and 32 (b). Note the abundance and small spacing <strong>of</strong> set I<br />
fractures (striking 110°). Numerous fractures <strong>of</strong> different orientations can be observed<br />
but are non-systematic and are not considered in this paper.<br />
N<br />
set I<br />
64<br />
set I<br />
N<br />
N<br />
1 m<br />
1 m<br />
NW
zone <strong>of</strong> def.<br />
0.5 mm<br />
Figure 2.9. Microscopic detail <strong>of</strong> a set I fracture in the forelimb from site SM13. This<br />
fracture strikes 110° and dips perpendicular to bedding. In the deformed zone, there<br />
is less porosity than in the surrounding matrix. There are also more angular quartz<br />
grains, that are, for the most part, smaller in size than those within the matrix. There<br />
is also a larger amount <strong>of</strong> calcitic cement within the deformed zone.<br />
65
SE NW<br />
a)<br />
d)<br />
SE<br />
c)<br />
S 0<br />
N<br />
Nb planes34<br />
1 m<br />
N<br />
b)<br />
N<br />
10 cm<br />
N<br />
NW<br />
10 cm<br />
Figure 2.10. Reactivated set I fractures in the forelimb. (a) Field photograph <strong>of</strong> set I<br />
(110°) small reverse faults within the sandstone <strong>of</strong> the Tensleep Fm. at site 13 that<br />
cut a bedding surface. (b) Cross sectional view <strong>of</strong> the photograph in (a) showing<br />
<strong>of</strong>fset bedding. (c) Close up <strong>of</strong> one fault: the slip decreases toward fault tips. (d)<br />
Striation data (thin arrows on the fault planes) that indicate an oblique reverse slip<br />
along the faults. The large arrows are inferred direction <strong>of</strong> compression that is<br />
compatible with the striations.<br />
66
a)<br />
NW SE<br />
b)<br />
Nb planes116<br />
set I<br />
N<br />
set II<br />
Figure 2.11. Fracture pattern in the backlimb. (a) Field photograph <strong>of</strong> the fracture<br />
pattern at site 8 within the Tensleep sandstone on the backlimb. (b) Line drawing <strong>of</strong><br />
the outcrop in (a) that shows set II fractures (strike <strong>of</strong> 045°) terminating at set I<br />
fractures (strike <strong>of</strong> 110°).<br />
zone <strong>of</strong> def.<br />
N<br />
N<br />
0.5 mm<br />
Figure 2.12. Microscopic details <strong>of</strong> a set I (110°) fracture in the Tensleep sandstone<br />
<strong>of</strong> the backlimb at site SM16. The fracture is characterized by a zone with less<br />
porosity, smaller quartz grains and a larger amount <strong>of</strong> calcite cement as compared to<br />
the host rock.<br />
67<br />
3 m
Southwestern backlimb<br />
In the backlimb, four fracture sets are observed in the Tensleep sandstone (Fig.<br />
2.4, site 1, 7-8, 16-21, 23). These sets strike 110°, 045°, 135°, and 110° again.<br />
Set I fractures trend 110° (Fig. 2.4 and 2.11) and are bed-normal. These fractures<br />
are 10-20 m long as compared to a height <strong>of</strong> a few meters that equals bed thickness.<br />
The fractures are linear and their spacing varies from 1 to 3 m. They lack tail cracks,<br />
riedel fractures, or other shearing-related secondary structures. As in the forelimb,<br />
their mode <strong>of</strong> deformation is difficult to determine in the field. They sometimes<br />
ressemble joints and other times ressemble deformation bands. Microscopically, set I<br />
fractures are characterized by a decrease <strong>of</strong> grain size, a decrease <strong>of</strong> porosity, and an<br />
increase in amount <strong>of</strong> cement (calcite) as compared to the surrounding host rock (Fig.<br />
2.12). Again, these fractures show no kinematic evidence <strong>of</strong> shearing.<br />
Set II fractures trend 045° (Fig. 2.4 and 2.11) and are bed-normal. They<br />
terminate against set I fractures (Fig. 2.11) and, as a result, are only a few meters in<br />
length. They are quite linear and their spacing is approximately 1 meter. In the field,<br />
they have a joint morphology and a cement-filling indicating an opening mode <strong>of</strong><br />
deformation. As seen in thin section, the fill typically consists <strong>of</strong> large calcite crystals<br />
without evidence <strong>of</strong> fracturing or crushing, which supports a strictly dilational origin<br />
(Fig. 2.13a).<br />
Set III fractures have a more restricted occurrence than sets I and II (Fig. 2.4, site<br />
18-20, 52). They trend 135°, are bed-normal, and contain a coarse calcite mineral fill<br />
(Fig. 2.13b) that is indicative <strong>of</strong> opening mode. The length <strong>of</strong> these fractures is on the<br />
order <strong>of</strong> a few meters. The termination relationships with other fracture sets are<br />
difficult to determine because <strong>of</strong> the small number <strong>of</strong> these fractures. Age<br />
relationships are more easily determined from observations within the fold hinge,<br />
where these fractures are more numerous.<br />
Set IV fractures trend 110° and are parallel to set I fractures but are vertical and<br />
not bed-normal (Fig. 2.4 and 2.14). Abutting relationships are difficult to establish<br />
because they have been observed mainly in cross-section, which reveals only their<br />
vertical dip. These fractures are several meters long with an approximate spacing <strong>of</strong><br />
one meter. In the field, most set IV fractures are open, and all lack evidence <strong>of</strong><br />
68
a)<br />
b)<br />
c)<br />
0.5 mm<br />
0.5 mm<br />
0.5 mm<br />
Figure 2.13. Microscopic detail <strong>of</strong> fractures in the Tensleep sandstone <strong>of</strong> the<br />
backlimb. These photomicrographs all show features with distinct fracture walls and a<br />
large crystal calcite fill. (a) Microscopic structure <strong>of</strong> a set II (045°) fracture at SM8. (b)<br />
Microscopic structure <strong>of</strong> a set III (135°) fracture at SM23. (c) Microscopic structure <strong>of</strong><br />
a set IV (110°) fracture at SM18. In addition to the characteristics seen in the previous<br />
two photomicrographs, this photomicrograph has crushed grains along the walls <strong>of</strong><br />
the fracture.<br />
69
)<br />
Nb planes 22<br />
N<br />
NE SW<br />
1 m<br />
Figure 2.14. Vertical set IV fractures in the backlimb. (a) and (b) Field photographs<br />
<strong>of</strong> set IV (110°) fractures at site 23 in the Tensleep sandstone. (b) is a close-up<br />
photograph. These fractures do not show any evidence <strong>of</strong> shearing.<br />
a)<br />
b)<br />
N<br />
N<br />
0.5 mm<br />
0.5 mm<br />
Figure 2.15. (a) Microstructure <strong>of</strong> a set I (110°) fracture in the sandstone <strong>of</strong> the<br />
Amsden Fm. in the hinge at site SM44. The fracture is composed <strong>of</strong> crushed matrix<br />
grains surrounded by quartz cement. (b) Microstructure <strong>of</strong> a set II (045°) fracture in<br />
the sandstone <strong>of</strong> the Amsden Fm. in hinge at site SM41. The fracture has distinct<br />
walls and is filled with large crystals <strong>of</strong> calcite cement.<br />
70<br />
a)
shearing. Microstructural examination <strong>of</strong> preserved calcite fill shows a difference from<br />
set II and set III morphology (Fig. 2.13c). Matrix grains at joint walls are crushed and<br />
display an elongation direction, suggesting a shearing event prior to vein filling.<br />
Hinge<br />
In the hinge, fracture measurements were made in the Amsden Fm. sandstone<br />
beds (Fig. 2.4). We observed three sets <strong>of</strong> fractures with orientations: 110°, 045°, 135°<br />
(Fig. 2.4, sites 39 to 41, 43 to 48, and 50 and 51).<br />
Set I fractures trend 110° and are bed-normal. They are less numerous in the<br />
hinge than in the limbs, and their spacing is greater. In thin section (Fig. 2.15a and b),<br />
these fractures are marked by reduced grain size and porosity as compared to the host<br />
rock, similar to the set I fractures in the forelimb (Fig. 2.8). The alignment <strong>of</strong> elongate<br />
grains seen in thin section (Fig. 2.15b) may be indicative <strong>of</strong> shearing during<br />
deformation. As can be noted from figure 2.4 and 2.5, this set is not visible at many<br />
locations. Looking at the data (Fig. 2.16), we see that the fracture set striking SE (see<br />
below, set III) is actually composed <strong>of</strong> fractures striking from ESE to SE. The set I<br />
fractures are thus <strong>of</strong>ten clustered with set III, because their strike is similar. This<br />
observation is also valid for most <strong>of</strong> the sites <strong>of</strong> measurements in the hinge. This<br />
explains why there seem to be fewer set I fractures in the hinge. It is actually only due<br />
to the automatic cluster analysis. However, as is represented in figure 2.16, we will<br />
consider set I fractures to be as numerous in the hinge as in the limbs.<br />
Set II fractures trend 45°, are bed-normal, and have a coarse calcite fill similar to<br />
that seen in the backlimb (Fig. 2.4, 2.15c, and 2.15). These fractures are joints, with<br />
lengths <strong>of</strong> a few meters and 1 meter spacing.<br />
Set III fractures trend 135° (parallel to the fold axis), are bed-normal, and are<br />
observed mainly in the hinge. Set III fractures abut set II fractures in the hinge and<br />
thus postdate set II (Fig. 2.16). Set II fractures abut set I fractures in the backlimb, so<br />
we infer that set III fractures also postdate set I fractures.<br />
71
a)<br />
Nb planes 42<br />
b)<br />
N<br />
N N<br />
10 cm<br />
Set II<br />
N<br />
Set III<br />
Figure 2.16. Fracture pattern in the hinge. (a) Field photograph showing the<br />
termination relationships between set II (045°) and III (135°) at site 39 in the<br />
sandstone <strong>of</strong> the Amsden Fm. (b) Line drawing <strong>of</strong> the outcrop in (a) showing that 8 <strong>of</strong><br />
13 set III fractures terminate at set II fractures and no set II fractures terminate at set<br />
III.<br />
72
a)<br />
NW<br />
b)<br />
Nb planes 77<br />
Set III<br />
N N<br />
Set II<br />
N<br />
SE<br />
10 cm<br />
Figure 2.17. Fracture pattern in the hinge <strong>of</strong> the fold nose. (a) Field photograph<br />
showing the fracture pattern in the sandstone <strong>of</strong> the Tensleep Fm. at site 2. (b) Line<br />
drawing <strong>of</strong> the outcrop in (a) showing that set III (135°) fractures terminate at set II<br />
(045°) fractures more times than set II fractures terminate at set II fractures.<br />
73
a)<br />
NW SE<br />
b)<br />
Set II<br />
Nb planes 61<br />
Set III<br />
N N<br />
N<br />
10 cm<br />
Figure 2.18. Fracture pattern in the backlimb <strong>of</strong> the fold nose. (a) Field photograph<br />
showing the fracture pattern in the Phosphoria Formation at site 2. (b) Line drawing <strong>of</strong><br />
the outcrop in (a) showing that the chronology <strong>of</strong> fracture sets II (045°) and III (135°)<br />
is hard to determine from abutting relationships at this location.<br />
74
Northern nose<br />
The fold nose is defined as the area NW <strong>of</strong> the position in the backlimb where,<br />
due to the fold shape, bedding strike has rotated to 150° from the typical value <strong>of</strong> 135°<br />
along the limbs (Fig. 2.4). In the nose, fracture data were collected primarily from<br />
limestones within the Phosphoria Formation because the Tensleep Formation crops<br />
out in limited locations (Fig. 2.4 and 2.5). Outcrops <strong>of</strong> both the Tensleep and<br />
Phosphoria Formations are present at the southern extent <strong>of</strong> the nose, and we compare<br />
measurements from these two formations to determine similarities and differences<br />
between fractures within the two lithologies. The comparison was done at sites 2, 27,<br />
and 36 in the Tensleep Fm. (Fig. 2.4) and sites 2 and 60 in the Phosphoria Fm. (Fig.<br />
2.5).<br />
Close to the nose hinge, in the Tensleep Fm., as described earlier, the fractures<br />
consist <strong>of</strong> two main joint sets trending 045° (set II) and 135° (set III) (Fig. 2.4, sites 2,<br />
27, and 36 and Fig. 2.17). From abutting relationships, the set II joints predate set III<br />
joints (Fig. 2.16). In the Phosphoria Fm., in the nose hinge, we also observe two main<br />
fracture sets (Fig. 2.5, site 2). One set is NE-trending and composed <strong>of</strong> joints (Fig. 2.5,<br />
site 2 and Fig. 2.18). Another set is SE-trending (Fig. 2.5, site 2 and Fig. 2.18) and<br />
also composed <strong>of</strong> joints. The chronology is difficult to determine (Fig. 2.18) as the<br />
abutting relationships are not entirely consistent. However, based on strike and mode<br />
<strong>of</strong> deformation, we suggest that theses two joint sets are similar to set II and III<br />
described throughout the fold.The fracture pattern in the backlimb (Fig. 2.4, site 7) is<br />
similar to the fracture pattern in the nose backlimb (Fig. 2.5, site 60). The fracture<br />
pattern in the forelimb (Fig. 2.4, site 29) also is similar to the fracture pattern in the<br />
nose forelimb (Fig. 2.5, site 26). The common occurrence <strong>of</strong> both set II and set III in<br />
the sandstones and limestones at the selected sites is used to infer that fracture data<br />
recorded within the limestones is a reasonable proxy for the fracture pattern that<br />
existed within the eroded sandstone beds <strong>of</strong> the fold nose.<br />
Throughout the nose, we observe that the NE-trending set II joints vary in<br />
orientation from 045° to 070° toward the nose (Fig. 2.5). Fractures trend 045°at sites<br />
2, 26, 53, and 60 and 070° at all but one <strong>of</strong> the remaining sites. The SE-trending set III<br />
joints also vary in orientation throughout the nose, but to the largest extent within the<br />
75
nose backlimb (Fig. 2.5). They trend 135° at sites 60, 61, and 62, and trend 160° at<br />
sites 64, 65, and 66. In the nose hinge, these SE-trending joints maintain an average<br />
orientation <strong>of</strong> 140° at all sites except site 57 (Fig. 2.5).<br />
Interpretation<br />
The four fracture sets found at Sheep Mountain anticline provide qualitative<br />
constraints for the temporal and spatial evolution <strong>of</strong> deformation <strong>of</strong> the sedimentary<br />
layers within the anticline. The following discussion synthesizes field and thin-section<br />
observations to first present an interpretive chronological history <strong>of</strong> fracture<br />
development and to then make inferences about fold kinematics.<br />
Pre-existing fractures<br />
Set I fractures are observed in most <strong>of</strong> the locations across the fold and are<br />
systematically perpendicular to bedding. The exact nature <strong>of</strong> these fractures remains<br />
uncertain (see previous sections and Fig. 2.9, 2.12, 2.15a and b) because we do not<br />
know if they initiated in a shearing mode (e.g. as deformation bands) or in an opening<br />
mode (as joints) and subsequently were sheared.<br />
Fracture set I is oblique to the fold, striking approximately 25° counterclockwise<br />
from the fold axis. Additionally, abutting relationships indicate that set I predates all<br />
other fracture sets. Thus, we interpret set I as the oldest set and as having initiated<br />
prior to the Laramide orogeny (Fig. 2.19). A similar interpretation was made by<br />
Silliphant et al. (2002) at Split Mountain in Utah and Hennings et al. (2000) at Oil<br />
Mountain in Wyoming, where a fracture set <strong>of</strong> similar strike (WNW-trending) was<br />
present at nearby locations where bed dips are approximately horizontal, as well as in<br />
each position <strong>of</strong> the fold after rotation <strong>of</strong> the bedding to horizontal.<br />
Fractures, striking 110° when bedding is restored to horizontal, and dipping<br />
perpendicular to bedding, also are found regionally near Sheep Mountain in the Black<br />
Hills <strong>of</strong> western South Dakota and northeastern Wyoming (Wicks et al., 2000). In this<br />
location, the fracture set was interpreted to predate Laramide compression.<br />
Conversely, a set <strong>of</strong> fractures <strong>of</strong> this orientation was found near the Tensleep fault in<br />
the Southeast Bighorn basin (Allison, 1983) and was interpreted as a late joint set. The<br />
76
(c)<br />
Set I<br />
(d)<br />
(a)<br />
(b)<br />
Set I<br />
Set III<br />
Set III<br />
Set II<br />
Set II<br />
N E<br />
Set IV<br />
Figure 2.19. Schematic representation <strong>of</strong> the fracturing history at Sheep Mountain<br />
anticline. (a) Set I (110°) fractures form prior to the Laramide compression in<br />
horizontal beds. (b) Set II (045°) joints are initiated as early compression-parallel<br />
fractures. (c) Set III (135°) joints develop in the hinge during folding. (d) Vertical set IV<br />
(110°) joints initiate parallel to set I fractures in the backlimb, while in the forelimb, set<br />
I fractures are reactivated as reverse faults during a late stage <strong>of</strong> (or posterior to)<br />
folding.<br />
77
chronology, however, was deduced from a statistical analysis <strong>of</strong> the number and<br />
scatter <strong>of</strong> joint measurements and not from abutting relationships observed in the field.<br />
In other places in Wyoming and Montana, fractures sub-parallel to set I have not been<br />
observed: for example at Elk Basin in Montana (Engelder et al., 1997), at Garland and<br />
Little Sand Draw in the southeast Bighorn basin (Garfield et al., 1992), and at Teapot<br />
Dome (Allison, 1983; Cooper et al., 1998). This suggests that set I did not develop<br />
uniformly across the region. Similarly, at Sheep Mountain, set I fractures are present<br />
primarily within the limbs, are less abundant within the hinge and the nose. One<br />
explanation is that this fracture population did not form homogeneously but left<br />
undisturbed patches in a given layer, due to subtle differences in diagenesis or stress<br />
state. Another explanation is that this fracture set is not well expressed in limestone<br />
(the dominant formation cropping out in the nose) due to material properties differing<br />
from those <strong>of</strong> the sandstone and/or the higher position in the stratigraphic column. Set<br />
II and III however are expressed both in the Tensleep Fm. and in the Phosphoria Fm.<br />
Lastly, these fractures may be fold-related, which would explain the heterogenous<br />
distribution. However, we have documented that these fractures are older than those<br />
interpreted as the Laramide compression-related fractures and other studies have<br />
shown that they are present in places where no fold formed (Allison, 1983; Hennings<br />
et al., 2000; Wicks et al., 2000). Thus, in the following, we consider these fractures to<br />
be pre-Laramide in age.<br />
If the set I fractures formed as shear fractures, they would have formed oblique<br />
to the direction <strong>of</strong> greatest compression. Taking an estimated 30° angle, the tectonic<br />
compression would have been in a direction <strong>of</strong> either 080° or 140°. If they formed as<br />
joints, they would be associated with a 110°E directed compression. Further study is<br />
needed to constrain the nature and origin <strong>of</strong> this fracture set, but this is not crucial for<br />
constraining the fold growth as we view set I as having formed before folding.<br />
Early Laramide compression: onset <strong>of</strong> faulting and folding<br />
Set II joints strike parallel to the NE-SW direction <strong>of</strong> Laramide compression<br />
(Dickinson and Snyder, 1978; Engebretson et al., 1985; Bird, 2002) and are<br />
78
perpendicular to bedding. We showed that set II joints predate the fold-parallel hinge-<br />
restricted set III joints. Thus, we interpret the set II joints as having formed in response<br />
to early Laramide compression, prior to significant development <strong>of</strong> the fold (Fig.<br />
2.19).<br />
Joints initiating parallel to an early compressive event are documented in the<br />
literature (Engelder and Geiser, 1980; Engelder et al., 1997). Joints with the same<br />
orientation as set II are found in several locations in proximity to Sheep Mountain: at<br />
Garland and Little Sand Draw in the southeast Bighorn basin (Garfield et al., 1992), at<br />
Teapot Dome in Wyoming (Allison, 1983; Cooper et al., 1998) and in the southeast<br />
Bighorn basin near the Tensleep fault (Allison, 1983), confirming their regional status.<br />
Additionally, through pressure-interference tests in seven reservoirs throughout the<br />
Bighorn basin, Haws and Hurley (1992) found a consistent permeability anisotropy in<br />
the NE direction, supporting our interpretation <strong>of</strong> set II as a regional fracture set. At<br />
Sheep Mountain, we find set II joints in the backlimb, the hinge, and the nose (Fig.<br />
2.4, 2.5, and 2.19). Fractures <strong>of</strong> this set are notably absent in the forelimb, however,<br />
suggesting that an early structure, most likely the incipient fold or the underlying<br />
thrust fault, may have influenced their formation (Fig. 2.19).<br />
Sheep Mountain is interpreted as a fault-related fold, and the thrust fault causing<br />
the uplift <strong>of</strong> the anticline dips around 50° SW (Stanton and Erslev, 2004). Slip along<br />
the thrust fault may induce a zone <strong>of</strong> enhanced compression above the fault tip<br />
(compressive quadrant <strong>of</strong> a shearing mode discontinuity; Pollard and Segall, 1987).<br />
We suggest that such a stress perturbation inhibited the formation <strong>of</strong> the set II<br />
fractures in the overlying layers at a location corresponding to the forelimb during and<br />
after folding. Set II can thus be considered a regional fracture set with local zones<br />
where its formation was inhibited. Other studies have documented the influence <strong>of</strong><br />
perturbed stress fields on fracture orientation and location in extensional (Kattenhorn<br />
et al., 2000; Maerten et al., 2002) or strike slip (Bourne and Willemse, 2001)<br />
environments, as well as in salt tectonics settings (Cruikshank and Aydin, 1995).<br />
We have shown that field evidence supports the interpretation that set II fractures<br />
predate all fracture sets except set I, and thus they predate the hinge parallel set III<br />
joints that are inferred to be fold related. Yet, these timing relationships do not require<br />
79
set II to be pre-folding. Set III may have initiated during a later stage <strong>of</strong> the fold<br />
evolution rather than at the onset <strong>of</strong> folding. In this case, set II joints could have<br />
formed after the beginning <strong>of</strong> fold evolution but before the formation <strong>of</strong> set III, and<br />
would thus be fold-related.<br />
At Elk Basin Anticline, a basement-cored fold in Montana and Wyoming, fold<br />
perpendicular fractures comprise only a minor fracture set, and they are interpreted as<br />
a late set formed in response to an axis-parallel stretching (Gross and Engelder, 1995).<br />
A mechanism for this type <strong>of</strong> joint formation is curvature related to a doubly-plunging,<br />
non cylindrical fold geometry (Fischer and Wilkerson, 2000). For such a mechanism,<br />
rather than a regional deformation, to be an explanation for set II fractures at Sheep<br />
Mountain anticline, the present-day fold shape (quite cylindrical in its central part)<br />
would have had to have evolved from a more non-cylindrical shape. However, a<br />
perturbation in the strike <strong>of</strong> set II fractures occurs only in the present-day fold nose,<br />
and similar perturbations, which would represent previous locations <strong>of</strong> the fold nose,<br />
are not found. Therefore, we infer that the fold nose did not migrate laterally, and the<br />
early fold length was very similar to the current fold length.<br />
We consider a regional deformation as the most likely formation mechanism for<br />
set II fractures and suggest that the paucity <strong>of</strong> set II joints in the forelimb is due to a<br />
stress perturbation resulting from slip on the underlying basement thrust fault. The<br />
rotation in strike <strong>of</strong> set II fractures in the nose is then most likely also related to stress<br />
perturbations from the underlying fault. In such a case, the underlying fault would<br />
have established its horizontal dimension prior to significant slip. This concept has<br />
been documented for faults in extensional domains (Walsh et al., 2002) and inferred<br />
for faults in compressional domains (Julian and Wiltschko, 1983; Armstrong and<br />
Bartley, 1993; Fischer and Christensen, 2004). Such a mechanism is usually explained<br />
by invoking fault reactivation (Walsh et al., 2002). Reactivated faults do not grow<br />
laterally until their slip reaches a great enough value in comparison to length to trigger<br />
lateral propagation. At Sheep Mountain, the view <strong>of</strong> the underlying basement fault as a<br />
reactivated fault is consistent with previous studies (Simmons and Scholle, 1990; Ye<br />
et al., 1996).<br />
80
Fold growth: intermediate stage<br />
In the hinge, joints striking parallel to the fold axis and dipping perpendicular to<br />
bedding are classified as fracture set III. As previously noted, they could have formed<br />
at any time during folding (Fig. 2.19). Despite this ambiguity, the localized occurence<br />
<strong>of</strong> these joints is consistent with a fixed-hinge model <strong>of</strong> fold evolution (Allmendinger,<br />
1982; Fischer et al., 1992; Fisher and Anastasio, 1994; McConnell, 1994). Had the<br />
hinge migrated, we would expect to find fold-parallel joints elsewhere. The hinge is<br />
very tight, so it is unlikely that the observed hinge curvature could have been<br />
accommodated without joint formation.<br />
We do find some fold-parallel joints in the backlimb (Fig. 2.4, sites 18 to 20).<br />
These joints might be related to areas where layer curvature is greater (Fig. 2.7). The<br />
darkening <strong>of</strong> the curvature plot toward the north along the fold axis reflects the<br />
tightening <strong>of</strong> the fold in this direction. As we look along lines perpendicular to the fold<br />
axis, we see that in the north, zero or near zero curvature values are reached just a<br />
short distance from the fold axis, whereas further south, this distance is greater. The<br />
number <strong>of</strong> set II joints increases toward the south, the direction in which the fold<br />
shape changes from a tight to a more rounded pr<strong>of</strong>ile (Fig. 2.7). This supports our<br />
hypothesis that there is a link between curvature and the existence <strong>of</strong> set III joints.<br />
Where the hinge is tight in the north, the limbs are virtually planar with near zero<br />
curvature and set III is confined to the hinge.<br />
Set III joints also are found in the fold nose. In the backlimb <strong>of</strong> the nose, the<br />
joint strike changes along the fold from 135° to 160° (Fig. 2.5). This change roughly<br />
coincides with the change in fold limb orientation, as the strike <strong>of</strong> the layers changes<br />
from 130° to 150°, south to north (Fig. 2.5). The layers in this area are curved and this<br />
layer bending can explain the rotation <strong>of</strong> the set III joints. In the nose hinge zone, set<br />
III is the main joint set, where it most likely initiated due to layer curvature. The<br />
variation in orientation <strong>of</strong> fractures within this set also suggests that there was no fold<br />
propagation, as we do not observe any analogous change <strong>of</strong> set III joint strike along<br />
the cylindrical part <strong>of</strong> the fold.<br />
81
Fold growth: late stage<br />
During the late stage <strong>of</strong> fold growth, the fracture patterns in the hinge and in the<br />
nose did not change, although some fold-parallel joints may have continued to form.<br />
In the limbs, however, new fractures initiated and others were reactivated (Fig. 2.19).<br />
In the forelimb, we observe small thrust faults with oblique slip (Fig. 2.10 and<br />
2.19). Given the geometric similarities to set I fractures, these structures are<br />
interpreted as reactivated set I fractures. The present orientation <strong>of</strong> the faults is in<br />
agreement with Andersonian theory: they are reverse faults that dip approximately 30°<br />
from the horizontal, perpendicular to bedding. Thus, we infer that the reactivation<br />
occurred late in the fold evolution. Incorporated into this interpretation is the<br />
assumption that the set I fractures rotated passively with the strata and were<br />
reactivated when their dip reached a value low enough to allow a thrust <strong>of</strong>fset along<br />
them. This mechanism implies a horizontal greatest compressive stress striking<br />
perpendicular to the fold and a vertical least compressive stress.<br />
The set I fractures also could have been reactivated earlier during the fold<br />
growth. In some kinematic models <strong>of</strong> fault propagation folding, it is suggested that<br />
thickening and thinning <strong>of</strong> the forelimb occurs (Jamison, 1987; Chester and Chester,<br />
1990, Erslev, 1991, McConnell, 1994, Hardy and Ford, 1997, Allmendinger, 1998).<br />
This thinning is apparent on cross-sections shown by Frizon de Lamotte et al. (1997),<br />
Storti et al. (1997), and Grelaud et al. (2000). The presence <strong>of</strong> the reverse faults in the<br />
forelimb <strong>of</strong> Sheep Mountain may be consistent with shearing <strong>of</strong> the layer<br />
contemporaneous with this forelimb rotation and deformation.<br />
The present orientation <strong>of</strong> set I fractures suggests that they sheared after the beds<br />
were tilted. Reches (1978) and Allmendinger (1982) showed that compression at high<br />
angle to fold limbs is generally characterized by conjugate reverse faults whose<br />
bisector angle is horizontal and perpendicular to the fold. This compression is linked<br />
to a late stage <strong>of</strong> fold evolution when the forelimb is steep and the upper fault tip is<br />
locked such that additional slip events generate compressive stresses that could<br />
reactivate older fractures.<br />
Stanton and Erslev (2004) suggested that the thrust fault that created Sheep<br />
Mountain anticline was cut by a later NE-dippping thrust fault. This event may have<br />
82
occurred when the Sheep Mountain fault was locked and unable to propagate.<br />
Moreover, this younger fault would uplift the anticline. In the backlimb, we observed<br />
a second late fracture set, set IV, which is composed <strong>of</strong> vertical joints striking 110°<br />
(Fig. 2.14 and 2.19). They are interpreted as late due to their vertical dip that is<br />
oblique to bedding. These joints may be related to the uplift. We suggest that this joint<br />
set was influenced by the presence <strong>of</strong> the earlier set I fractures, because they strike<br />
oblique to the fold axis and parallel to the set I fractures. Such influence by pre-<br />
existing fractures has been suggested recently in Guiton et al. (2003a, 2003b) and<br />
Bergbauer and Pollard (2004).<br />
Conclusions<br />
The field data collected at Sheep Mountain anticline on fracture chronology and<br />
mode <strong>of</strong> formation (opening vs. shearing) help us to constrain the deformation and<br />
structural evolution <strong>of</strong> this anticline. We interpret these data to show that: (i) A<br />
fracture set (set I, 110°) was present before the onset <strong>of</strong> the Laramide compression. (ii)<br />
An early joint set (set II, 045°) initiated during the beginning <strong>of</strong> the Laramide<br />
compression, however, the formation <strong>of</strong> this set may be influenced by the onset <strong>of</strong><br />
faulting and/or folding. (iii) Set III joints (135°) localized in the hinge during layer<br />
bending related to fold evolution. Such joints also formed in the limbs where<br />
significant limb curvature developed (south part <strong>of</strong> the fold). (iv) In the forelimb,<br />
during late fold evolution, set I fractures were reactivated as reverse faults. (v) Also<br />
during this late stage, vertical joints (set IV, 110°) oblique to the fold axis initiated in<br />
the backlimb. Their strike direction was controlled by the pre-existing fractures <strong>of</strong> set<br />
I. These fracture data provide constraints on the folding kinematics. They suggest a<br />
fixed-hinge mechanism <strong>of</strong> folding in which little lateral propagation <strong>of</strong> the thrust fault<br />
and fold occurred. The data also indicate that little deformation <strong>of</strong> fold limbs occurred<br />
during fold growth, except where the curvature is significant, and during late stages <strong>of</strong><br />
fold growth.<br />
83
Aknowledgements<br />
This paper benefited from discussions with M. Cooke, J.M. Daniel, M. Guiton,<br />
and Y. Leroy. We thank E. Erslev and H. Stanton for providing a pre-print <strong>of</strong> their<br />
paper and I. Mynatt and Y. Fujii for assistance in the collection <strong>of</strong> fracture data in the<br />
field. J.M. Daniel and M. Guiton (Institut Français du Pétrole) are thanked for their<br />
help and for providing the s<strong>of</strong>tware used to calculate mean fracture orientations and<br />
plot the data. The manuscript greatly benefited from the reviews <strong>of</strong> W. Dunne and C.<br />
Zahm. This work was supported by the National Science Foundation Tectonics<br />
Program Grant No. EAR-012935 and the Collaboration in Mathematical Geosciences<br />
Program Grant No. EAR-04177521, the <strong>Stanford</strong> Rock Fracture Project, and the<br />
Institut Français du Pétrole.<br />
References<br />
Allison, M. L., 1983, Deformation styles along the Tensleep fault, Bighorn Basin,<br />
Wyoming: Wyoming Geol. Assoc. Guidebook Thirty-Fourth Annual Field<br />
Conference.<br />
Allmendinger, R. W., 1982, Analysis <strong>of</strong> microstructures in the Meade plate <strong>of</strong> the<br />
Idaho-Wyoming foreland thrust belt: Tectonophysics, v. 85, p. 221-251.<br />
Allmendinger, R. W., 1998, Inverse and forward numerical modeling <strong>of</strong> trishear faultpropagation<br />
folds: Tectonics, v. 17, p. 640-656.<br />
Armstrong, P.A., and J. M. Bartley, 1993, Displacement and deformation associated<br />
with a lateral thrust termination, southern Golden Gate Range, southern<br />
Nevada, U.S.A: Journal <strong>of</strong> Structural Geology, v. 15, p. 721-735.<br />
Antonellini, M.A., Aydin, A., and D. D. Pollard, 1994, Microstructure <strong>of</strong> deformation<br />
bands in porous sandstones at Arches National Park, Utah: Journal <strong>of</strong><br />
Structural Geology, v. 16, p. 941-959.<br />
Aydin, A., 1978, Small faults formed as deformation bands in sandstone: Pure and<br />
Applied Geophysics, v. 116, p. 913-930.<br />
Bergbauer, S. and D. D. Pollard, 2004, A new conceptual fold-fracture model<br />
including prefolding joints, based on field data from the Emigrant Gap<br />
anticline, Wyoming: GSA Bulletin, v. 116, p. 294-307<br />
Bernal, A. and S. Hardy, 2002, Syn-tectonic sedimentation associated with threedimensional<br />
fault-bend fold structures; a numerical approach: Journal <strong>of</strong><br />
Structural Geology, v. 24, p. 609-635.<br />
84
Beutner, E.C. and F. A. Diegel, 1985, Determination <strong>of</strong> fold kinematics from<br />
syntectonic fibers in pressure shadows, Marinsburg Slate, New Jersey:<br />
American Journal <strong>of</strong> Science v. 285, p. 16-50.<br />
Bird, P., 1998, Kinematic history <strong>of</strong> the Laramide orogeny in latitudes 35°-49°N,<br />
western United States: Tectonics, v. 17, p.780-801.<br />
Bird, P., 2002, Stress direction history <strong>of</strong> the Western United States and Mexico since<br />
85 Ma: Tectonics, v. 21, p. 1014, doi:10.1019/2001TC001319.<br />
Bourne, S. J. and E. J. M. Willemse, 2001, Elastic stress control on the pattern <strong>of</strong><br />
tensile fracturing around a small fault network at Nash Point, UK: Journal <strong>of</strong><br />
Structural Geology, v. 23, p. 1753-1770.<br />
Bump, A. P., 2003, Reactivation, trishear modeling, and folded basement in Laramide<br />
uplifts; implications for the origins <strong>of</strong> intra-continental faults: GSA Today, v.<br />
13, p. 4-10.<br />
Chester, J. and F. Chester, 1990, Fault-propagation folds above thrusts with constant<br />
dip: Journal <strong>of</strong> Structural Geology, v. 12, p. 903-910.<br />
Cooper, S. P., Goodwin, L. B., Lorenz, J. C., Teufel, L. W., and B. S. Hart, 1998,<br />
Geometric and genetic relationships between fractures, normal faults, and a<br />
doubly plunging anticline; Teapot Dome, Wyoming:. Geological Society <strong>of</strong><br />
America, Abstracts with Programs, v. 30, p. 62.<br />
Cowie, P. A. and C. H. Scholz, 1992, Physical explanation for the displacement-length<br />
relationship <strong>of</strong> faults using a post-yield fracture mechanics model: Journal <strong>of</strong><br />
Structural Geology, v. 14, p. 1113-1148.<br />
Cristallini, E. O. and R. W. Allmendinger, 2001, Pseudo 3-D modelling <strong>of</strong> trishear<br />
fault-propagation folding: Journal <strong>of</strong> Structural Geology, v. 23, p. 1883-1899.<br />
Cristallini, E. O. and R. W. Allmendinger, 2002, Backlimb trishear; a kinematic model<br />
for curved folds developed over angular fault bends: Journal <strong>of</strong> Structural<br />
Geology, v. 24, p. 289-295.<br />
Cruikshank, K.M. and A. Aydin, 1995, Unweaving the joints in Entrada Sandstone,<br />
southwest limb <strong>of</strong> the Salt Valley anticline, Arches National Park, Utah,<br />
U.S.A.: Journal <strong>of</strong> Structural Geology, v. 17, p. 409-421.<br />
Dawers, N. H., Anders, M. H., and C. H. Scholz, 1993, Growth <strong>of</strong> normal faults:<br />
displacement-length scaling: Geology, v. 21, p. 1107-1110.<br />
Dickinson, W. R. and W. S. Snyder, 1978, Plate tectonics <strong>of</strong> the Laramide orogeny:<br />
Geological Society <strong>of</strong> America Memoir 151, p. 355-366.<br />
85
Engebretson, D. C., A. Cox, and R. G. Gordon, 1985, Relative motion between<br />
oceanic and continental plates in the Pacific basin: Geological Society <strong>of</strong><br />
America Special Paper 206, 59 pp.<br />
Engelder, T. and P. Geiser, 1980, On the use <strong>of</strong> regional joint sets as trajectories <strong>of</strong><br />
paleostress fields during the development <strong>of</strong> the Appalachian Plateau, New<br />
York: Journal <strong>of</strong> Geophysical Research, v. 85, p. 6,319-6,341.<br />
Engelder, T., M. R. Gross, and P. Pinkerton, 1997, An analysis <strong>of</strong> joint development<br />
in thick sandstone beds <strong>of</strong> the Elk Basin Anticline, Montana-Wyoming: Rocky<br />
Mountain Association <strong>of</strong> Geologists 1997 Guidebook, p. 1-18.<br />
Erslev, E. A., 1991, Trishear fault-propagation folding: Geology, v. 19, p. 617-620.<br />
Erslev, E. A., 1993, Thrusts, back-thrusts, and detachments <strong>of</strong> Rocky Mountain<br />
foreland arches, in Schmidt, C.J., Chase, R.B., and Erslev, E.A., eds.,<br />
Laramide Basement Deformation in the Rocky Mountain Foreland <strong>of</strong> the<br />
Western United States: Boulder, Colorado, Geological Society <strong>of</strong> America<br />
Special Paper 280, p. 339-358.<br />
Fisher, D. and D. Anastasio, 1994, Kinematic analysis <strong>of</strong> a large-scale leading-edge<br />
fold, Lost River range, Idaho: Journal <strong>of</strong> Structural Geology, v. 16, p. 337-354.<br />
Fischer, M. P., and M. S. Wilkerson, 2000, Predicting the orientation <strong>of</strong> joints from<br />
fold shape: Results <strong>of</strong> pseudo-three-dimensional modeling and curvature<br />
analysis: Geology, v. 28, p. 15-18.<br />
Fischer, M., N. Woodward, and M. Mitchell, 1992, The kinematics <strong>of</strong> break-thrust<br />
folds: Journal <strong>of</strong> Structural Geology, v. 14, p. 451-460.<br />
Fischer, M. P. and R. D. Christensen, 2004, Insights into the growth <strong>of</strong> basement<br />
uplifts deduced from a study <strong>of</strong> fracture systems in the San Rafael monocline,<br />
east central Utah: Tectonics, v. 23, TC1018, doi:10.1029/2002TC001470.<br />
Forster, A., A. P. Irmen, and C. Vondra, 1996, Structural interpretation <strong>of</strong> Sheep<br />
Mountain Anticline, Bighorn Basin, Wyoming: Wyoming Geological<br />
Association Guidebook, v. 47, p. 239-251.<br />
Friedman, M., 1969, Structural analysis <strong>of</strong> fractures in cores from the Saticoy Field,<br />
Ventura Co., California: Am. Soc. Pet. Geol. Bulletin., v. 53, p. 367-389.<br />
Frizon de Lamotte, D., E. Mercier, A. Dupre de la Tour, and O. Averbuch, 1997,<br />
Cinématique du Plissement et Déformation Interne des Roches; l'exemple du<br />
pli de Lagrasse (Aude, France) : C. R. Acad. <strong>Sciences</strong>, v. 324, p. 591-598.<br />
86
Garfield, T. R., N. F. Hurley, and D. A. Budd, 1992, Little Sand Draw File, Big Horn<br />
Basin, Wyoming: a hybrid dual-porosity and single-porosity reservoir in the<br />
Phosphoria Formation: AAPG Bulletin, v. 76, p. 371-391.<br />
Grelaud, S., D. Buil, S. Hardy, and D. Frizon de Lamotte, 2000, Trishear kinematic<br />
model <strong>of</strong> fault-propagation folding and sequential development <strong>of</strong> minor<br />
structures: the Oupia anticline (NE Pyrenees, France) case study: Bulletin de la<br />
Société Géologique de France, v. 171, p. 441-449.<br />
Gross, M. R. and T. Engelder, 1995, Strain accommodated by brittle failure in<br />
adjacent units <strong>of</strong> the Monterey Formation, U.S.A.; scale effects and evidence<br />
for uniform displacement boundary conditions: Journal <strong>of</strong> Structural Geology,<br />
v. 17, p. 1303-1318.<br />
Guiton, M., Y. Leroy, W. and Sassi, 2003, Activation <strong>of</strong> diffuse discontinuities and<br />
folding <strong>of</strong> the sedimentary layers: Journal <strong>of</strong> Geophysical Research, v. 108, p.<br />
2183, doi:10.1029/2002JB001770.<br />
Guiton, M., W. Sassi, Y. Leroy, and B. Gauthier, 2003, Mechanical constraints on the<br />
chronology <strong>of</strong> fracture activation in the folded Devonian sandstone <strong>of</strong> the<br />
western Moroccan Anti-Atlas: Journal <strong>of</strong> Structural Geology, v. 25, p.1317-<br />
1330.<br />
Hancock, P. L., 1985, Brittle microtectonics; principles and practice: Journal <strong>of</strong><br />
Structural Geology, v. 7, p. 437-457.<br />
Harris, J. F., G. L. Taylor, and J. L. Walper, 1960, Relation <strong>of</strong> deformational fractures<br />
in sedimentary rocks to regional and local structures: AAPG Bulletin v. 44, p.<br />
1853-1873.<br />
Hardy, S. and M. Ford, 1997, Numerical modeling <strong>of</strong> trishear fault propagation<br />
folding: Tectonics, v. 16, p. 841-854.<br />
Haws, G. W. and N. F. Hurley, 1992. Applications <strong>of</strong> pressure-interference data in<br />
reservoir characterization studies, Big Horn basin, Wyoming: SPE 24668,<br />
1992 Annual Conference and Exhibition, p. 53- 62.<br />
Hennier, J., 1984, Sheep Mountain Anticline, Bighorn Basin, Wyoming: Unpublished<br />
MS thesis, Texas A&M <strong>University</strong>, 118 p.<br />
Hennier, J., and J. Spang, 1983, Mechanisms for deformation <strong>of</strong> sedimentary strata at<br />
Sheep Mountain anticline, Big Horn Basin, Wyoming: Wyoming Geological<br />
Association Guidebook, v. 34, p. 97-111.<br />
Hennings, P. H., J. E. Olson, and L. B. Thompson, 2000, Combining outcrop data and<br />
three-dimensional structural models to characterize fractured reservoirs; an<br />
example from Wyoming: AAPG Bulletin, v. 84, p. 830-849.<br />
87
Hyett, A. J., 1990, Deformation around a thrust tip in Carboniferous limestone at Tutt<br />
Head, near Swansea, South Wales: Journal <strong>of</strong> Structural Geology, v. 12, p. 47-<br />
58.<br />
Johnson G. D., L. J. Garside, and A. J. Warner, 1965, A study <strong>of</strong> the structure and<br />
associated features <strong>of</strong> Sheep Mountain Anticline, Big Horn County, Wyoming:<br />
Iowa Academy <strong>of</strong> Science, v. 72, p. 332-342.<br />
Johnson, K. M., and A. M. Johnson, 2002, Mechanical analysis <strong>of</strong> the geometry <strong>of</strong><br />
forced-folds: Journal <strong>of</strong> Structural Geology, v. 24, p. 401-410.<br />
Jamison, W. R., 1987, Geometric analysis <strong>of</strong> fold development in overthrust terranes:<br />
Journal <strong>of</strong> Structural Geology, v. 9, p. 207-220.<br />
Julian, F. E., and D. V. Wiltschko, 1983, Deformation mechanism in a terminating<br />
thrust anticline: GSA Program with abstract, v. 15, p. 606.<br />
Kattenhorn, S. A., A. Aydin, and D. D. Pollard, 2000, Joints at high angles to normal<br />
fault strike; an explanation using 3-D numerical models <strong>of</strong> fault-perturbed<br />
stress fields: Journal <strong>of</strong> Structural Geology, v. 22, p. 1-23.<br />
Kittler, J., 1976, A locally sensitive method for cluster analysis: Pattern Recognition,<br />
v. 8, p. 23-33.<br />
Ladd, R. E., 1979, The geology <strong>of</strong> Sheep Canyon Quadrangle: Wyoming: PhD<br />
dissertation. Ames, Iowa State <strong>University</strong>, 124 p.<br />
Maerten, L., P. Gillespie, and D. D. Pollard, 2002, Effects <strong>of</strong> local stress perturbation<br />
on secondary fault development. Journal <strong>of</strong> Structural Geology, v. 24, p. 145-<br />
153.<br />
Mallet, J. L., 2002, Geomodeling: Oxford <strong>University</strong> Press, New York, 599 p.<br />
Marcotte, D. and E. Henry, 2002, Automatic joint set clustering using a mixture <strong>of</strong><br />
bivariate normal distributions: International Journal <strong>of</strong> Rock Mechanics &<br />
Mining <strong>Sciences</strong>, v. 39, p. 323-334.<br />
McConnell, D.A., 1994, Fixed-hinge, basement-involved fault-propagation folds,<br />
Wyoming: Geological Society <strong>of</strong> America Bulletin, v. 106, p. 1583-1593.<br />
Mitra, S., 1990, Fault-propagation folds: Geometry, kinematic evolution, and<br />
hydrocarbon traps. AAPG Bulletin, v. 74, p. 921-045.<br />
Nino, F, H. Philip, and J. Chery, 1998, The role <strong>of</strong> bed-parallel slip in the formation <strong>of</strong><br />
blind thrust faults: Journal <strong>of</strong> Structural Geology, v. 20, p. 503-516.<br />
88
Peacock, D.C.P. and D. J. Sanderson, 1991, Displacements, segment linkage and relay<br />
ramps in normal fault zones: Journal <strong>of</strong> Structural Geology, v. 13, p. 721-733.<br />
Pollard, D. D. and P. Segall, 1987, Theoretical displacements and stresses near<br />
fractures in rocks: with applications to faults, joints, veins, dikes, and solution<br />
surfaces, in: B.K. Atkinson, ed., Fracture Mechanics <strong>of</strong> Rock: Academic Press,<br />
London, p. 277-349.<br />
Price, R. A., 1967, The tectonic significance <strong>of</strong> mesoscopic fabrics in the southern<br />
Rocky Mountains <strong>of</strong> Alberta and British Columbia: Canadian Journal <strong>of</strong> <strong>Earth</strong><br />
<strong>Sciences</strong>, v. 4, p. 39-70.<br />
Reches, Z., 1978, Development <strong>of</strong> monoclines: Part I. Structure <strong>of</strong> the Palisades Creek<br />
branch <strong>of</strong> the East Kaibab monocline, Grand Canyon, Arizona: Geological<br />
Society <strong>of</strong> America Memoir 151, p. 235-271.<br />
Renshaw, C. E., T. A., Myse, and S. R. Brown, 2003, Role <strong>of</strong> heterogeneity in elastic<br />
properties and layer thickness in the jointing <strong>of</strong> layered sedimentary rocks,<br />
Geophysical Research Letters, v. 30, p. 2295.<br />
Rioux, R. L., 1958, Geology <strong>of</strong> the Spence-Kane area, Bighorn County, Wyoming:<br />
Ph.D. thesis, <strong>University</strong> <strong>of</strong> Illinois, 182 p.<br />
Rioux, R. L., 1994, Geologic map <strong>of</strong> the Sheep Mountain-Little Sheep Mountain area,<br />
Big Horn County, Wyoming. Scale 1:31,680: USGS open-file report 94-191.<br />
Savage, H. M. and M. L. Cooke, 2004, The effect <strong>of</strong> non-parallel thrust fault<br />
interaction on fold pattern: Journal <strong>of</strong> Structural Geology, v. 26, p. 905-917.<br />
Silliphant, L. J., T. Engelder, and M. R. Gross, 2002, The state <strong>of</strong> stress in the limb <strong>of</strong><br />
the Split Mountain anticline, Utah: constraints placed by transected joints:<br />
Journal <strong>of</strong> Structural Geology, v. 24, p. 155-172.<br />
Simmons, S. P. and P. A. Scholle, 1990, Late Paleozoic uplift and sedimentation,<br />
Northeast Bighorn Basin, Wyoming: Wyoming Geological Association,<br />
Guidebook, v. 41, p. 39-55.<br />
Shamir, G. and Y. Eyal, 1995, Elastic modeling <strong>of</strong> fault-driven monoclinal fold<br />
patterns: Tectonophysics, v. 245, p. 13-24.<br />
Spang, J. H. and D. A. McConnell, 1997, Effect <strong>of</strong> initial fault geometry on the<br />
development <strong>of</strong> fixed-hinge, fault-propagation folds: Journal <strong>of</strong> Structural<br />
Geology, v. 19, p. 1537-1541.<br />
Stanton, H. I. and E. A. Erslev, 2004, Sheep Mountain Anticline: Backlimb<br />
Tightening and Sequential Deformation in the Bighorn Basin, Wyoming:<br />
Wyoming Geological Association Guidebook, v. 53, p. 75-87.<br />
89
Stearns, D. W., 1968, Certain aspects <strong>of</strong> fractures in naturally deformed rocks. Rock<br />
mechanics seminar: Bedford, Terrestrial <strong>Sciences</strong> Laboratory, p. 97-118.<br />
Stearns, D. W., and M. Friedman, 1972, Reservoirs in fractured rocks: AAPG Memoir<br />
16, p. 82-100.<br />
Stone, D. S., 1993, Basement-involved thrust generated folds as seismically imaged in<br />
sub-surface <strong>of</strong> the central Rocky Mountain foreland, in Schmidt, C.J., Chase,<br />
R. B., and E. A. Erslev, eds. Laramide basement deformation in the Rocky<br />
Mountain foreland <strong>of</strong> the Western United States: GSA SP 280, p. 271-318.<br />
Stone, D. S., 2004, Rio thrusting, multi-stage migration, and formation <strong>of</strong> vertically<br />
segregated Paleozoic oil pools at Torchlight Field on the Greybull Platform:<br />
Implications for exploration. The Mountain Geologist v. 41, p. 119-138.<br />
Storti, F., Salvini, F., and K. McClay, 1997, Fault-related folding in sandbox analogue<br />
models <strong>of</strong> thrust wedges. Journal <strong>of</strong> Structural Geology, v. 19, p. 583-602.<br />
Suppe, J., 1983, Geometry and kinematics <strong>of</strong> fault-bend folding. American Journal <strong>of</strong><br />
Science, v. 283, p. 684-721.<br />
Suppe, J., 1985, Principles <strong>of</strong> Structural Geology: Prentice-Hall, New Jersey, 537 p.<br />
Suppe, J., D. A. and Medwedeff, 1990, Geometry and kinematics <strong>of</strong> fault-propagation<br />
folding: Ecologae Geol. Helv., v. 83, p. 409-454.<br />
Thomas, L. E. 1965, Sedimentation and structural development <strong>of</strong> the Bighorn Basin:<br />
AAPG Bulletin, v. 49, p. 1867-1877.<br />
Twiss, R. J., and Moore, E. M., 1992, Structural Geology: Freeman, New York, 532 p.<br />
Walsh, J. J., A. Nicol, and C. Childs, 2002, An alternative model for the growth <strong>of</strong><br />
faults: Journal <strong>of</strong> Structural Geology, v. 24, p. 1669-1675.<br />
Wicks, J. L., S. L. Dean, and B. R. Kulander, 2000, Regional tectonics and fracture<br />
patterns in the Fall River Formation (Lower Cretaceous) around the Black<br />
Hills foreland uplifts, western South Dakota and northeastern Wyoming, in<br />
Cosgrove, J. W., and M. S. Ameen, eds., Forced Folds and Fractures:<br />
Geological Society <strong>of</strong> London Special Publication 169, p. 145-165.<br />
Wollmer F. W., 1995, C Program for automatic contouring <strong>of</strong> spherical orientation<br />
data using a modified Kamb method: Computers & Geosciences v.21, p.31-49.<br />
Ye, H., L. Royden, C. Burchfiel, and M. Schuepbach, 1996, Late Paleozoic<br />
deformation <strong>of</strong> interior North America: the Greater Ancestral Rocky<br />
Mountains: AAPG Bulletin, v. 80, p. 1397-1432.<br />
Zhang, Y., N. S. Mancktelow, B. E. Hobbs, A. Ord, and H. B. Mühlhaus, 2000,<br />
Numerical modelling <strong>of</strong> single-layer folding: clarification <strong>of</strong> an issue regarding<br />
the effect <strong>of</strong> computer codes and the influence <strong>of</strong> initial irregularities: Journal<br />
<strong>of</strong> Structural Geology, v. 22, p. 1511-1522.<br />
90
Chapter 3<br />
Fracture reactivation at Sheep Mountain Anticline: insight on the<br />
mechanics <strong>of</strong> folding and constraints on the stress field<br />
Abstract<br />
Field observations <strong>of</strong> sheared fractures in various structural locations across<br />
Sheep Mountain Anticline, Wyoming, document the role <strong>of</strong> fracture reactivation in<br />
folding related deformation. Most <strong>of</strong> the observed shearing is kinematically consistent.<br />
Differences in both the formation and reactivation <strong>of</strong> fracture sets in the forelimb and<br />
backlimb indicate that the stress state in the forelimb was highly influenced by the<br />
underlying fault.<br />
Differences in observations <strong>of</strong> shearing also constrain spatial and temporal<br />
variations <strong>of</strong> the stress state across the anticline during folding. At some locations,<br />
conjugate shearing has occurred along a set <strong>of</strong> joints (striking 045°) that formed early<br />
in the folding process and a set <strong>of</strong> joints (striking 075°) that formed during the<br />
development <strong>of</strong> a secondary fold at Sheep Mountain. These observations constrain the<br />
local principal stress directions if both sets sheared at the same time. The local σ1<br />
direction (maximum compression) is further constrained at locations where we have<br />
recorded left-lateral and right-lateral conjugate shearing <strong>of</strong> selected members <strong>of</strong> single<br />
sets <strong>of</strong> joints. Temporally, the σ1 direction apparently varied enough to resolve shear<br />
stress with opposite senses on these sub parallel joints. Frictional faulting analysis<br />
allows constraints to be placed on the state <strong>of</strong> stress prevailing during the reactivation<br />
<strong>of</strong> these joints. A fracture set that pre-dates the folding has sheared in the limbs in a<br />
sense that is consistent with the kinematics <strong>of</strong> folding, but no shearing <strong>of</strong> this fracture<br />
set has been recorded in the hinge. Again, frictional faulting theory is implemented to<br />
understand what physical conditions may allow for this variation in deformation. We<br />
determine that the pre-existing fracture set must have been infilled at the time <strong>of</strong><br />
reactivation.<br />
91
Introduction<br />
Multi-scale problems in which patterns <strong>of</strong> secondary deformation are derived<br />
from knowledge <strong>of</strong> a larger scale <strong>of</strong> deformation have gained attention over the last<br />
decade (e.g. Sassi and Faure, 1996; Allmendinger, 1998; Fischer and Wilkerson, 2000;<br />
Hart, 2006; 2006 AGU Fall Meeting session entitled: Fracturing and Faulting During<br />
Folding <strong>of</strong> Sedimentary Strata: Field Observations and Mechanical Models), in part<br />
due to economic motivations to better understand poorly observed fractured reservoirs.<br />
Ultimately, mechanical models, which track stress, strain, and displacement fields<br />
related to an imposed deformation, have the ability to predict physically plausible<br />
fracture patterns relating to observable deformations. The use <strong>of</strong> mechanical models is<br />
becoming more prevalent, but as indicated by sensitivity analyses carried out in prior<br />
studies (e.g. Kattenhorn et al., 2000; Bourne and Willemse, 2001; Maerten et al.,<br />
2002; Maerten et al., 2006), boundary conditions have a significant effect on the<br />
resulting stress calculations. For problems in which few data are available for<br />
calibration, methods <strong>of</strong> constraining boundary conditions with these small quantities<br />
<strong>of</strong> data become crucial. We suggest that observations <strong>of</strong> reactivated fractures can be<br />
used to constrain plausible boundary conditions.<br />
Two types <strong>of</strong> fractures exhibit slip (displacement discontinuity parallel to the<br />
fracture surfaces), but have formed under different circumstances. Shear fractures (e.g.<br />
Griggs and Handin, 1960; Stearns, 1968; Bergbauer and Pollard, 2004) initiate and<br />
propagate while slipping within the same remote stress field. Shear fractures are<br />
interpreted to contain the intermediate principal stress (σ2) and are inclined at an angle<br />
<strong>of</strong> less than 45° to the most compressive principal stress (σ1) based on analogous<br />
relationships documented in lab rock mechanics experiments (e.g. Griggs and Handin,<br />
1960). In contrast, sheared joints (e.g. Peacock, 2001; Bergbauer and Pollard, 2004;<br />
Myers and Aydin, 2004; Davatzes et al., 2005) or faulted joints (e.g. Segall and<br />
Pollard, 1983; Cruikshank et al., 1991; Willemse and Pollard, 1998; Wilkins et al.,<br />
2001; Silliphant et al., 2002) initiate and propagate while opening and later are sheared<br />
under different remote stress conditions. Sheared joints form as dominantly opening<br />
mode fractures, with surfaces normal to the least compressive principal stress (σ3;<br />
Pollard and Segall, 1987; Renshaw and Pollard, 1994). At some later time, the joints<br />
92
close and become misaligned with the principal stress axes due to either a material or<br />
stress field rotation, so shear traction is resolved along joint surfaces. Under suitable<br />
combinations <strong>of</strong> shear and normal (compressive) tractions, a slip event initiates and<br />
propagates along these surfaces and a sheared joint is born. We refer to this<br />
phenomenon as “fracture reactivation”. Clarification <strong>of</strong> the class <strong>of</strong> fracture studied at<br />
a field site is essential to understanding the evolution <strong>of</strong> the stress field through time,<br />
as shear fractures and sheared joints imply different alignment <strong>of</strong> fracture planes with<br />
the principal stresses.<br />
In this study, we investigate fracture reactivation at Sheep Mountain anticline<br />
(SMA) and, more generally, demonstrate how shearing observations can be used to (1)<br />
place quantitative constraints on the principal stresses and strains active within a fold<br />
at the time <strong>of</strong> deformation, and (2) identify the mechanical processes involved in the<br />
development <strong>of</strong> the fracture pattern. We present fracture data collected from different<br />
lithologies within the same structural locations, documenting the location, orientation,<br />
and sense <strong>of</strong> motion <strong>of</strong> sheared fractures. With these data we are able to investigate<br />
what effect, if any, lithological differences have on the formation and reactivation <strong>of</strong><br />
systematic fracture sets and to interpret spatial and temporal variations in shearing<br />
directions and magnitudes. Analyses implementing frictional faulting theory place<br />
constraints on the relative magnitudes <strong>of</strong> principal strains active during the Laramide.<br />
Geological background<br />
SMA is a northwest-southeast trending anticline located west <strong>of</strong> the Bighorn<br />
Mountains on the eastern flank <strong>of</strong> the Bighorn Basin within the Laramide Rocky<br />
Mountain foreland <strong>of</strong> Wyoming (Fig. 3.1a). Structurally, the fold is interpreted as a<br />
third order feature. Gravity magnetic pr<strong>of</strong>iles, seismic reflection pr<strong>of</strong>iles, and borehole<br />
data indicate that the eastern thrust <strong>of</strong> the Bighorn Mountains is a basin boundary fault<br />
that thrusts the Bighorn Mountains over the Powder River Basin to the northeast and<br />
triggers deformation distributed throughout the Bighorn Basin to the southwest (Fig.<br />
3.1b; Robbins and Grow, 1992; Stone, 1993). At the latitude <strong>of</strong> Sheep Mountain, this<br />
deformation is linked to slip along a northeast dipping backthrust, the Rio thrust<br />
(Gries, 1983; Stone 2004). Based on cross sections drawn through the<br />
93
(a)<br />
(b)<br />
(c)<br />
43°<br />
45°<br />
44°<br />
110°<br />
Absaroka Mnts<br />
A<br />
WIND RIVER<br />
RANGE<br />
Bighorn Basin<br />
A<br />
109°<br />
BIGHORN<br />
WIND RIVER<br />
BASIN<br />
Sheep Mt.<br />
BASIN<br />
Owl Creek Mnts<br />
108°<br />
Bighorn Mnts<br />
107°<br />
100 km<br />
Rio<br />
Thrust<br />
POWDER<br />
Casper Arch<br />
RIVER<br />
BASIN<br />
SMA<br />
Thrust<br />
Bighorn Mts.<br />
Western Thrus t<br />
Bighorn<br />
Mountains<br />
Bighorn Mts.<br />
Eastern Thrust<br />
Powder<br />
River<br />
Basin<br />
N<br />
10 km<br />
Figure 3.1. (a) Tectonic map <strong>of</strong> Wyoming showing the location <strong>of</strong> SMA as the doubly<br />
plunging fold represented by the thick black line and the area <strong>of</strong> (b) in gray. Modified<br />
from Bellahsen et al., 2006a. (b) Digital Orthophoto Quarter Quadrangles (DOQQs) <strong>of</strong><br />
the Bighorn Mt. and Bighorn Basin area. Quadrangles downloaded from<br />
http://wgiac.state.wy.us/. Black line shows the location <strong>of</strong> SMA. Dashed white lines<br />
trace the surface projections <strong>of</strong> major thrust faults. Light gray line shows the location<br />
<strong>of</strong> the cross-section in (c). (c) Schematic cross section through the Bighorn Basin and<br />
Bighorn Mountains. The SMA thrust can be considered a third order structure related<br />
to the Rio thrust fault and the eastern thrust <strong>of</strong> the Bighorn Mts.<br />
94<br />
A‘<br />
A‘
Bighorn Mountain eastern thrust fault and the Rio thrust fault to the south (Stone,<br />
1993; Stone 2004), we interpret the Sheep Mountain thrust fault to be a southwest<br />
dipping backthrust <strong>of</strong> the Rio thrust fault (Fig. 3.1c).<br />
Uplift at SMA is measured by more than 1 km <strong>of</strong> structural relief across pre-<br />
Laramide bedding that is accommodated primarily through folding. Three hundred<br />
meters <strong>of</strong> this structural relief can be viewed in cross-section where the Bighorn River<br />
transects the fold almost perpendicular to the hinge (Fig. 3.2), which strikes<br />
approximately 135°. The steeply dipping (40° to 90° NE) forelimb <strong>of</strong> SMA lies to the<br />
northeast <strong>of</strong> the hinge, and the more gently dipping (10° to 40° SW) backlimb lies to<br />
the southwest <strong>of</strong> the hinge. Approximately 2 km northwest <strong>of</strong> the river cut, a<br />
secondary fold intersects the backlimb <strong>of</strong> SMA with a trend that is rotated 20°<br />
clockwise from that <strong>of</strong> the main fold. After Savage and Cooke (2004), we call this<br />
secondary fold the thumb.<br />
At SMA, Paleozoic and Mesozoic marginal marine sedimentary rocks overlay<br />
granitic PreCambrian basement (Thomas, 1965; Fig. 3.3). The Cambrian, Ordovician,<br />
and Devonian sequence consists <strong>of</strong> about 500 meters <strong>of</strong> shale, limestone, and dolomite<br />
that are not exposed at SMA. The Mississippian Madison Fm. is comprised <strong>of</strong> massive<br />
limestone and interbedded dolomite and represents the oldest formation that outcrops<br />
at Sheep Mountain, as well as the oldest lithology examined in this study (Fig. 3.2).<br />
Above the Madison Fm., the Pennsylvanian Amsden and Tensleep Fms. consist <strong>of</strong><br />
interbedded sandstones, shales, and limestones. The sandstone beds provide many <strong>of</strong><br />
the outcrops where fractures that form the basis for this study were measured. The<br />
Permian Phosphoria limestone forms the resistant, outermost beds on both the<br />
forelimb and backlimb <strong>of</strong> the anticlinal edifice. The Triassic Chugwater Formation lies<br />
stratigraphically above the Phosphoria. At SMA, the Chugwater shales and younger<br />
Triassic, Jurassic, and Cretaceous Bighorn Basin sediments have all been eroded <strong>of</strong>f<br />
the topographic high.<br />
95
N<br />
108°12'<br />
Quaternary<br />
Cretaceous<br />
Jurassic<br />
Backlimb<br />
Thumb<br />
Forelimb<br />
108°10'<br />
Triassic (Chugwater Fm)<br />
Permian (Phosphoria Fm)<br />
Carboniferous (Pennsylvanian, Tensleep Fm)<br />
Carboniferous (Pennsylvanian, Amsden Fm)<br />
Carboniferous (Mississipian, Madison Fm)<br />
Anticlinal axis Synclinal axis<br />
Bighorn River<br />
108°08'<br />
44°38'<br />
108°06'<br />
1 km<br />
108°04'<br />
44°36'<br />
Figure 3.2. (a) Geological map <strong>of</strong> SMA after Rioux, 1994 and modified from<br />
Bellahsen et al., 2006a. Fracture data were collected from outcrops northwest <strong>of</strong> the<br />
river cut.<br />
96
K<br />
J<br />
TR<br />
P<br />
P<br />
M<br />
D<br />
O<br />
C<br />
pC<br />
Mesa Verde<br />
Cody<br />
Frontier<br />
Mowry<br />
Thermopolis<br />
Cloverly<br />
Morrison<br />
Sundance<br />
Gypsum Springs<br />
Chugwater<br />
Phosphoria<br />
Tensleep<br />
Amsden<br />
Madison<br />
Jefferson -<br />
Three Forks<br />
Bighorn<br />
Gallatin<br />
Gros Ventre<br />
Flathead<br />
Granite<br />
Shale<br />
Sandstone<br />
Limestone<br />
Dolomite<br />
Gypsum<br />
Granite<br />
Figure 3.3. Stratigraphic column for the Bighorn Basin. After Hennier, 1984.<br />
97
Set II<br />
Set IV<br />
Set III<br />
Set I<br />
Set I<br />
reactivated<br />
Figure 3.4. Schematic cross-section for SMA depicting the orientations <strong>of</strong> four<br />
previously interpreted fracture sets. The hinge <strong>of</strong> the fold trends approximately 135°.<br />
From Bellahsen et al., 2006a.<br />
98
Field data<br />
Systematic fracture sets<br />
Previous work at SMA based on sandstone outcrops <strong>of</strong> both the Tensleep and<br />
Amsden Fms. has defined four systematic fracture sets (Fig. 3.4; Bellahsen et al,<br />
2006a). Set I is found in all structural locations on the fold, strikes 110° when bedding<br />
is rotated to horizontal, is perpendicular to bedding, and is interpreted as forming<br />
before the folding event. Set II strikes 045°, is perpendicular to bedding, and formed<br />
early in the folding process, parallel to the inferred maximum regional compression<br />
direction. This set is sparse in the fold forelimb. Set III, striking 130°, is parallel to the<br />
fold hinge and perpendicular to bedding. It is interpreted as the primary folding-related<br />
fracture set and is localized in areas <strong>of</strong> greatest curvature. Set IV is interpreted as a<br />
late-folding fracture set that strikes 110°, parallel to set I fractures, but dips obliquely<br />
to bedding and is vertical as observed in the field. Both field observations <strong>of</strong> hackle<br />
along fracture walls and thin section identification <strong>of</strong> distinct vein boundaries support<br />
the interpretation <strong>of</strong> sets II, III, and IV initiating as joints with purely opening mode<br />
<strong>of</strong>fset between adjacent fracture surfaces (Bellahsen et al, 2006a). Field and<br />
microscopic observations <strong>of</strong> set I fractures have been inconclusive: they may have<br />
formed either in a shearing mode or in an opening mode and then were sheared.<br />
For this study, we highlight an additional set <strong>of</strong> systematic joints striking 075°<br />
and perpendicular to bedding. This was noted as minor in the Bellahsen et al. (2006a)<br />
study because it was found in limited locations. We refer to these joints as set V.<br />
Evidence for reactivation was collected within the Tensleep sandstone and Phosphoria<br />
limestone along the limbs, and in the Madison limestone and Amsden sandstone along<br />
the hinge. An understanding <strong>of</strong> the distribution <strong>of</strong> systematic joint sets in the different<br />
lithologies at SMA required additional data relative to those previously studied.<br />
In figure 3.5, we provide data documenting the locations and orientations <strong>of</strong><br />
systematic joint sets in four stratigraphic units: Madison Fm. limestone, Amsden Fm.<br />
sandstone, Tensleep Fm. sandstone, and Phosphoria Fm. limestone. Study sites were<br />
exposures <strong>of</strong> dimensions typically tens <strong>of</strong> meters on a side. At each study site, fracture<br />
sets were distinguished based on orientation data, abutting relations, and deformation<br />
mode. The average orientations <strong>of</strong> the sets at each site are represented by great circles<br />
99
(a)<br />
(b)<br />
Site 7-8<br />
N<br />
Site 18<br />
N<br />
40<br />
20<br />
N<br />
Site 58<br />
N<br />
N<br />
91<br />
108°10'<br />
Site 25<br />
N<br />
Site 72<br />
N<br />
108°10'<br />
38<br />
Site 77a<br />
N<br />
Site 12<br />
N<br />
15<br />
40<br />
21<br />
Site 71<br />
N<br />
Site 80<br />
N<br />
Site 84<br />
N<br />
Site 14<br />
N<br />
Fracture Sets<br />
Set I<br />
Set II<br />
Set III<br />
Set IV<br />
Set V<br />
minor set<br />
7-8<br />
26<br />
24<br />
07<br />
37<br />
25<br />
Site 78<br />
N<br />
Site 22<br />
N<br />
08<br />
26<br />
Site 07<br />
25<br />
N<br />
23<br />
44°39'<br />
29<br />
58<br />
30<br />
14<br />
14<br />
13<br />
13<br />
17<br />
Site 13<br />
N<br />
Site 29<br />
N<br />
25<br />
44°39'<br />
36<br />
35<br />
Site 08<br />
N<br />
116<br />
108°09'<br />
Site 23<br />
N<br />
18 18<br />
71 17<br />
72 16<br />
80<br />
01<br />
78<br />
19<br />
20<br />
81<br />
15<br />
22<br />
22<br />
Site 81<br />
N<br />
Site 76<br />
N<br />
Site11<br />
N<br />
35<br />
32<br />
Site 30<br />
N<br />
40<br />
Site 77b<br />
N<br />
22<br />
12<br />
12<br />
108°09'<br />
Site 10<br />
N<br />
N<br />
77<br />
76<br />
30<br />
Site 85<br />
100<br />
Site 14<br />
N<br />
63<br />
84<br />
25<br />
63<br />
11<br />
11<br />
86<br />
85<br />
Site 13<br />
N<br />
Site 18<br />
N<br />
N<br />
Site 83<br />
N<br />
51<br />
Site 17<br />
83<br />
21<br />
29<br />
35<br />
Site 33<br />
N<br />
42<br />
59<br />
Site11<br />
N<br />
Site 12<br />
N<br />
16<br />
44°38'<br />
Site 16<br />
N<br />
Site 15<br />
N<br />
24<br />
74<br />
1 km<br />
Site 59<br />
N<br />
101<br />
10<br />
10<br />
44<br />
48<br />
139<br />
73<br />
Site 31<br />
N<br />
Site 70<br />
N<br />
75<br />
31<br />
33<br />
32<br />
Site 01<br />
N<br />
N<br />
37<br />
Site 22<br />
Site 74<br />
N<br />
39<br />
Site 10<br />
N<br />
10<br />
37<br />
Site 69<br />
N<br />
44<br />
Site 19<br />
36<br />
Site 32<br />
N<br />
108°08'<br />
70<br />
69<br />
N<br />
108°08'<br />
N<br />
56<br />
37<br />
47<br />
Site 20<br />
N<br />
44<br />
Site 73<br />
44°37'<br />
Site 21<br />
N<br />
44°37'<br />
35<br />
N<br />
63<br />
Site 75<br />
22
(c)<br />
Site 39<br />
N<br />
Site 40<br />
N<br />
62<br />
42<br />
N<br />
108°10'<br />
Site 41<br />
N<br />
Site 43<br />
N<br />
53<br />
12<br />
Site 44<br />
N<br />
Site 45<br />
N<br />
49<br />
26<br />
Site 46<br />
N<br />
Site 51<br />
N<br />
26<br />
19<br />
Site 37<br />
N<br />
44°39'<br />
Site 50<br />
N<br />
Site 47<br />
N<br />
38<br />
21<br />
24<br />
Site 38<br />
N<br />
Site 48<br />
N<br />
Figure 3.5. DOQQs showing locations <strong>of</strong> fracture measurements and their<br />
orientations. (a) Forelimb and (b) backlimb fracture measurements. Phosphoria sites<br />
are labeled with white numbers and dots with the corresponding stereonets to the<br />
lower left <strong>of</strong> the DOQQs. Tensleep sites are labeled in black numbers and dots with<br />
the corresponding stereonets to the upper right <strong>of</strong> the DOQQs. (c) Hinge fracture<br />
measurements. Amsden sites are labeled with white numbers and dots with the<br />
corresponding stereonets to the lower left <strong>of</strong> the DOQQs. Madison sites are labeled in<br />
black numbers and dots with the corresponding stereonets to the upper right <strong>of</strong> the<br />
DOQQs.<br />
101<br />
108°09'<br />
49<br />
35<br />
Site 42<br />
N<br />
36<br />
Site 25<br />
N<br />
44°38'<br />
40<br />
1 km<br />
Site 49<br />
N<br />
43<br />
108°08'<br />
44°37'
in lower hemisphere stereonets. The number <strong>of</strong> fracture measurements represented is<br />
at the lower right <strong>of</strong> the stereonet and a total <strong>of</strong> nine orientations (five major, four<br />
minor) are represented in this data set from 150 measurement sites. All orientations<br />
have been unfolded before plotting on these stereonets so they are shown as relative to<br />
horizontal bedding. For analysis purposes, we present data for the forelimb, backlimb,<br />
and hinge separately.<br />
Forelimb<br />
Fracture data in the forelimb are taken from the Tensleep sandstone and<br />
Phosphoria limestone (Fig. 3.5a). In the Tensleep, set I is the dominant fracture set,<br />
found at nine <strong>of</strong> the ten observations sites; sets II and III are sparse; a minor north-<br />
south fracture set is present at seven sites; and fracture set V is present at six sites. The<br />
characteristics <strong>of</strong> set V are most evident in the backlimb and are discussed below. In<br />
the Phosphoria, set V is the only consistent fracture set present, occurring in five <strong>of</strong><br />
eight measurement sites. Set I, set II and the minor north-south set are found locally.<br />
Backlimb<br />
Tensleep sandstone and Phosphoria limestone units provide outcrops for study<br />
and data collection in the backlimb (Fig. 3.5b). Set V fractures are found in both<br />
lithologies, and are perpendicular to bedding and several meters long, with an average<br />
spacing on the order <strong>of</strong> meters. These fractures are typically joints with weathered<br />
surfaces and apertures <strong>of</strong> a few centimeters in the Phosphoria Fm. and veins filled with<br />
calcite in the Tensleep Fm.. Data collected from sites 16, 81, 101, 109, and 110 in the<br />
backlimb (Fig. 3.5) provide the clearest abutting relationships for set V fractures (Fig.<br />
3.6). There, set V abuts consistently against set I fractures and is abutted consistently<br />
by set III fractures. Set V and set II termination relationships alternate, although set V<br />
abuts against set II for seventy percent <strong>of</strong> the observed occurrences. Set V is found in<br />
nine <strong>of</strong> the thirteen Tensleep sites, with most occurrences in the area where the thumb<br />
intersects the main fold. In the Phosphoria, set V is found in seven <strong>of</strong> eighteen sites.<br />
Fracture sets I, II, III, and IV also are found in the backlimb. Set I is found in<br />
eight <strong>of</strong> thirteen sites in the Tensleep; but in only eight <strong>of</strong> eighteen sites in the<br />
102
N S<br />
0.5 m<br />
N S<br />
0.5 m<br />
set I<br />
set II<br />
set III<br />
set V<br />
N-S set<br />
Figure 3.6. Field photograph and interpretation <strong>of</strong> set III (heavy gray lines) and set V<br />
(heavy black lines) abutting relationships at site 15 in the backlimb.<br />
103
Phosphoria, and is absent in many <strong>of</strong> the sites along the thumb. Set II is found in<br />
eleven <strong>of</strong> the thirteen Tensleep sites and ten <strong>of</strong> the eighteen Phosphoria sites.<br />
Occurrences <strong>of</strong> set III fractures increase toward the southeast in the Tensleep. In the<br />
Phosphoria set III is more widespread, and is present at all but one <strong>of</strong> the sites to the<br />
southeast <strong>of</strong> the thumb intersection. Set IV is found in sparse locations in both the<br />
Tensleep (at six sites) and the Phosphoria (at two sites); all but one are in the area near<br />
the intersection <strong>of</strong> the thumb with the main fold.<br />
Hinge<br />
In the hinge, fracture data were collected in the Madison limestone and Amsden<br />
sandstone (Fig. 3.5c). Amsden measurement sites are spread along the length <strong>of</strong> the<br />
anticline. For exposure reasons, Madison sites are absent for over one kilometer<br />
northwest and two kilometers southeast <strong>of</strong> the thumb intersection with the main fold.<br />
Set I is found at three <strong>of</strong> five measurement sites in the Madison and four <strong>of</strong> eleven<br />
sites in the Amsden. Set II is found at all five sites in the Madison and eight <strong>of</strong> eleven<br />
sites in the Amsden. Set III is found at four <strong>of</strong> five sites in the Madison and eight <strong>of</strong><br />
eleven sites in the Amsden. Set IV is present in just one site in the hinge, Amsden<br />
measurement site 48 (Fig. 3.5). Set V is present at two sites in the Madison and three<br />
sites in the Amsden.<br />
Shearing data<br />
Fractures were classified as having sheared where distinct and consistent <strong>of</strong>fsets<br />
<strong>of</strong> markers and splay cracks were found. Sheared fractures were documented at just<br />
over fifty <strong>of</strong> the one hundred fifty visited sites. Admittedly, numerous outcrops in the<br />
nose, hinge, and forelimb are so intensely fractured that shearing-related features may<br />
be present but are impossible to distinguish. Alone, apparent <strong>of</strong>fset <strong>of</strong> one fracture<br />
along another fracture was commonly not diagnostic <strong>of</strong> shear, as the direction <strong>of</strong> <strong>of</strong>fset<br />
<strong>of</strong> different fractures within the same set varied along the length <strong>of</strong> the fracture in<br />
question. The interpretation in these cases was that the apparently <strong>of</strong>fset fractures<br />
actually are the terminations <strong>of</strong> two different fractures within that set, rather than a<br />
through-going fracture that was later <strong>of</strong>fset. Along the same lines, at certain outcrops,<br />
104
Set I - thrust Phosphoria<br />
Set I - LL Tensleep<br />
Set II - RL<br />
Set II - LL<br />
Set V - RL<br />
Set V - LL<br />
km<br />
0 0.25 0.5 1<br />
Figure 3.7. DOQQs <strong>of</strong> the NW part <strong>of</strong> SMA. Locations and types <strong>of</strong> shearing<br />
observations in the Tensleep sandstone are shown in black and in the Phosphoria<br />
limestone are shown in white.<br />
105
fractures one might identify as splay cracks are subparallel to minor fracture sets, and<br />
thus are interpreted to be fractures <strong>of</strong> a later set abutting obliquely against earlier<br />
formed fractures. As a result, few fractures were identified as sheared based on <strong>of</strong>fset<br />
alone. The most diagnostic evidence for shear was derived from observations <strong>of</strong><br />
isolated fractures with distinct splay cracks. In figure 3.7, the location, sense <strong>of</strong><br />
shearing (RL = right lateral, LL = left lateral), lithology, and set classification <strong>of</strong><br />
sheared fractures are plotted on the Digital Orthophoto Quarter Quadrangles (DOQQs)<br />
that span the field area. Shear has been detected along fractures <strong>of</strong> sets I, II, and V.<br />
Forelimb<br />
In the forelimb, the most prevalent form <strong>of</strong> <strong>of</strong>fset is thrusting along set I<br />
fractures (Fig. 3.8). Where this thrusting occurs, with <strong>of</strong>fset on the order <strong>of</strong><br />
centimeters, it is distributed along most, if not all, <strong>of</strong> the fractures within that set.<br />
Small thrust faults were noted at six measurement sites along the length <strong>of</strong> the fold,<br />
primarily in the Tensleep Formation (Fig. 3.8b). Morphologies <strong>of</strong> Madison outcrops in<br />
the forelimb (Fig. 3.8a) suggest the existence <strong>of</strong> thrust faults as well. Where outcrops<br />
are accessible, however, weathering has smoothed fracture walls, eliminating the<br />
prospect <strong>of</strong> finding kinematic indicators.<br />
Strike-slip shearing in the forelimb has been found only within Tensleep<br />
outcrops. Field evidence suggests this shearing is not widespread. Where found, it<br />
exists along a few members <strong>of</strong> the fracture set at most. The only consistent sense <strong>of</strong><br />
strike-slip shearing found in the forelimb is left-lateral slip along set I fractures. Splays<br />
emanating from set I fractures were found at sites 145, 13, 12, 11, 10, and 146 (Fig.<br />
3.9). These sites are northwest <strong>of</strong>, southeast <strong>of</strong>, and at the thumb intersection; and they<br />
span a distance <strong>of</strong> three kilometers along the fold. Shear along set II fractures has been<br />
recorded at three sites, all more than a kilometer northwest <strong>of</strong> the thumb intersection.<br />
Right-lateral motion is found along set II at sites 131 and 145, whereas left-lateral<br />
motion is found along set II at site 13. Instances <strong>of</strong> shear along set V are also recorded.<br />
The sense <strong>of</strong> motion along this set is in some cases inconsistent within the same<br />
measurement site. Right-lateral motion along set V is found at sites 10, 11, 12, and<br />
150, and left-lateral motion is found at sites 10, 12, 13, 145 (Fig. 3.7).<br />
106
E W SE NW<br />
(b)<br />
(a) 5 m (c)<br />
0.5 m<br />
SE NW<br />
Figure 3.8. (a) Madison limestone; (b) Tensleep sandstone; (c) Phosphoria<br />
limestone outcrops with set I fractures reactivated as small thrust faults. The<br />
orientation and thrust direction <strong>of</strong> these fractures are shown in white lines and barbs.<br />
Black traces in (a) represent bedding planes.<br />
107<br />
5 m
SE NW<br />
0.5 m<br />
SE NW<br />
0.5 m<br />
Figure 3.9. Field photograph and interpretation <strong>of</strong> a set I fracture sheared leftlaterally<br />
in the Tensleep sandstone <strong>of</strong> site 10.<br />
108
N<br />
N<br />
(a)<br />
10 cm<br />
10 cm<br />
N<br />
10 cm<br />
N<br />
10 cm<br />
(b)<br />
N<br />
N<br />
(c)<br />
10 cm<br />
10 cm<br />
Figure 3.10. Field photographs and line interpretations <strong>of</strong> sheared fractures in the<br />
backlimb. (a) Left-lateral shear along a set I fracture at site 72 in the Phosphoria Fm.<br />
(b) Left-lateral shear along a set II fracture at site 8 in the Tensleep Fm. (c) Rightlateral<br />
shear along a set II fracture at site 16 in the Tensleep Fm.<br />
109
Backlimb<br />
Sheared set I fractures consistently display left-lateral motion in the backlimb.<br />
This shearing is found throughout the backlimb: in the area around sites 141 and 142<br />
near the nose; in the area around sites 8, 135, and 124 along the backlimb <strong>of</strong> the main<br />
fold northwest <strong>of</strong> the thumb intersection; along the thumb at sites 101, 81, and 115; at<br />
the intersection <strong>of</strong> the thumb with the main fold around site 122; and east <strong>of</strong> the thumb<br />
along the backlimb <strong>of</strong> the main fold around sites 130 and 114 (Fig. 3.10a). Set I<br />
fractures are sheared in both Tensleep and Phosphoria outcrops.<br />
Left-lateral shearing along set II (Fig. 3.10b) is found at five locations, all<br />
northwest <strong>of</strong> the thumb intersection. Three <strong>of</strong> the sites where left-lateral shear is<br />
recorded also contain or are within tens <strong>of</strong> meters <strong>of</strong> right-lateral shearing along set II<br />
(Fig. 3.10c). Additional observations <strong>of</strong> right-lateral shearing along set II in the<br />
backlimb were made in the nose area, along the thumb, at the thumb intersection, and<br />
along the main fold southeast <strong>of</strong> this intersection. Like set I, set II fractures are sheared<br />
in both the Tensleep Fm. and the Phosphoria Fm.<br />
Set V also is sheared in opposite senses in the backlimb, <strong>of</strong>ten along members <strong>of</strong><br />
the set that are meters, or even decimeters (Fig. 3.11a), apart. These opposite<br />
directions <strong>of</strong> shearing along set V are found in the nose area, at the intersection <strong>of</strong> the<br />
thumb with the main fold, and along the backlimb <strong>of</strong> the main fold southeast <strong>of</strong> the<br />
thumb intersection. Set V is sheared in an exclusively left-lateral sense (Fig. 3.11b) in<br />
the area immediately northwest <strong>of</strong> the thumb intersection. Exclusively right-lateral<br />
shearing along set V (Fig. 3.11c) has been recorded along the thumb and northwest <strong>of</strong><br />
the thumb intersection in the area around site 8 for a stretch <strong>of</strong> one kilometer along the<br />
backlimb. Set V shearing occurs in left-lateral and right-lateral senses at both Tensleep<br />
and Phosphoria outcrops, although the occurrence <strong>of</strong> opposite senses <strong>of</strong> shearing at the<br />
same site has been noted only at Tensleep outcrops.<br />
In most locations where shearing is recorded in the backlimb, it is detected along<br />
just a handful <strong>of</strong> fractures within the set. Exceptions occur at sites 72, 144, 74, 16, and<br />
22, where more than half <strong>of</strong> the fractures <strong>of</strong> a given set sheared: set I at sites 72, 114,<br />
and 74, set II at site 16, and sets II and V at site 22 (Fig. 3.12).<br />
110
N<br />
N<br />
(a)<br />
10 cm<br />
10 cm<br />
N<br />
N<br />
N<br />
N<br />
(b)<br />
10 cm<br />
10 cm<br />
(c)<br />
10 cm<br />
10 cm<br />
Figure 3.11. Field photographs and line interpretations <strong>of</strong> sheared set V fractures in<br />
the Tensleep Fm. at site 130 in the backlimb. (a) Opposite directions <strong>of</strong> shear along<br />
set V fractures that are within decimeters <strong>of</strong> each other. (b) Left-lateral motion along<br />
an isolated set V fracture. (c) Right-lateral motion along an isolated set V fracture.<br />
111
N<br />
10 cm<br />
Figure 3.12. Field photograph and interpretation <strong>of</strong> a number <strong>of</strong> set I fractures<br />
reactivated in left-lateral motion in the Phosphoria Fm. at site 74 in the backlimb.<br />
10 cm<br />
Figure 3.13. Field photograph and interpretation <strong>of</strong> fractures at site 44 in the<br />
Madison Fm. in the hinge. Gray areas are rubble zones where it is difficult to view or<br />
interpret fractures.<br />
112<br />
N<br />
N<br />
10 cm
Hinge<br />
No evidence for shearing was found along the hinge (Fig. 3.7). The major<br />
notable observation within the hinge is the occurrence <strong>of</strong> set III fold parallel joints.<br />
Where found, set III is a regularly formed set with individual fractures spaced on the<br />
order <strong>of</strong> ten centimeters apart (Fig. 3.13).<br />
Analysis <strong>of</strong> field data<br />
Interpretations <strong>of</strong> shearing<br />
To interpret the shearing <strong>of</strong> fractures at Sheep Mountain, we divide the fold into<br />
six domains, discussing the shearing specific to each domain (Fig. 3.14). Because no<br />
shearing has been documented in the hinge (Fig. 3.14, domain 6) we do not discuss it<br />
here. The forelimb is referred to as domain one. The backlimb, because the thumb<br />
creates distinct, second order structural units, is subdivided into four different<br />
structural domains. Domain two represents the backlimb <strong>of</strong> the nose, defined to be the<br />
area northwest <strong>of</strong> where backlimb bedding strike changes from 135° to 150°<br />
(Bellahsen et al., 2006a). Domain three represents the area along the backlimb <strong>of</strong> the<br />
main fold to the northwest <strong>of</strong>, and removed from, the thumb intersection. Domain four<br />
includes the areas <strong>of</strong> both the main fold backlimb in the vicinity <strong>of</strong> the intersection <strong>of</strong><br />
the thumb and the thumb structure itself. The boundary between domains three and<br />
four is drawn about a half kilometer northwest <strong>of</strong> the thumb intersection. Domain five<br />
is the area <strong>of</strong> the main fold backlimb at and to the southeast <strong>of</strong> the thumb intersection.<br />
Forelimb<br />
In the forelimb, two forms <strong>of</strong> reactivation in shear are observed, both occurring<br />
along the set <strong>of</strong> fractures that pre-dates the fold, set I (Fig. 3.14). A small number <strong>of</strong><br />
these fractures have slipped in a left-lateral sense (note apparent RL sense on view <strong>of</strong><br />
underside <strong>of</strong> bedding in Fig. 3.16). We interpret this shearing to have occurred during<br />
folding, while set I fractures were subjected to Laramide compression (Fig. 3.15c,<br />
3.15d, 3.15e). Other set I fractures now are small thrust faults, having been reactivated<br />
during folding. A previous study has suggested that this motion occurred late in the<br />
folding history, when the fractures had achieved dips shallow enough to promote<br />
113
V<br />
III<br />
I<br />
II<br />
II<br />
V<br />
V<br />
III<br />
V<br />
I<br />
III<br />
III<br />
I<br />
I<br />
II<br />
II<br />
III<br />
V<br />
2<br />
I<br />
II<br />
3<br />
6<br />
Figure 3.14. Six shearing related structural domains at SMA: one in the forelimb,<br />
four in the backlimb, where the shearing pattern is complex due to the existence <strong>of</strong><br />
the thumb, and one in the hinge. Gray ellipses represent centers <strong>of</strong> domains and<br />
block diagrams illustrate the fracture sets and shearing directions observed in each<br />
domain.<br />
4<br />
114<br />
I<br />
II<br />
1<br />
5<br />
III<br />
I<br />
IR
thrust <strong>of</strong>fset (Fig. 3.15f; Bellahsen et al., 2006a). Evidence for shearing along the other<br />
fracture sets in the forelimb is both sparse and inconsistent (Fig. 3.7). Perturbations in<br />
fold shape are common in the forelimb, where bedding approaches vertical, leading to<br />
the interpretation <strong>of</strong> the rare instances <strong>of</strong> shear along set II and V fractures as resulting<br />
from local phenomena.<br />
Backlimb<br />
Throughout the backlimb, left-lateral shearing along set I fractures is attributed to the<br />
same mechanism as in the forelimb: oblique Laramide compression during folding<br />
(Fig. 3.15c, 3.15d, 3.15e). In domain three, set II fractures show mixed directions <strong>of</strong><br />
shearing, sometimes within the same site (Fig. 3.7). We suggest that this represents<br />
minor changes in a stress field in which the local maximum principal compressive<br />
stress (σ1) was oriented subparallel to set II fractures, but varied enough temporally to<br />
resolve shearing in different directions along the fractures. Set V is sheared in a left-<br />
lateral sense, most likely the result <strong>of</strong> a northeast directed compression resolved along<br />
the fracture planes (Fig. 3.15e). In domain four, the lack or degradation <strong>of</strong> outcrops<br />
near the thumb intersection has limited the number <strong>of</strong> observation sites. To the<br />
northwest <strong>of</strong> this domain, we see left-lateral slip along set II fractures and right-lateral<br />
slip along set V fractures. These slip directions reverse toward the southeast <strong>of</strong> the<br />
domain (Fig. 3.7; Fig. 3.14). An explanation for the shearing observed within this<br />
domain will be investigated below. Domain five contains set II fractures that have<br />
sheared in a right-lateral sense and set V fractures that have sheared in opposite senses<br />
(Fig. 3.14). We interpret the observed shearing as a result <strong>of</strong> a local clockwise rotation<br />
in the σ1 direction: set II sheared as σ1 rotated away from the northeast direction and,<br />
just as in domain three, set V sheared in the opposite sense when σ1 was oriented<br />
subparallel to set V fractures, but varied slightly temporally.<br />
Lithological control on fracturing<br />
Analysis <strong>of</strong> stereonets for sites within the Madison, Amsden, Tensleep, and<br />
Phosphoria Fms. at SMA (Fig. 3.5) leads to the deduction that lithological differences<br />
account for little variation in the average orientations <strong>of</strong> the main fracture sets at SMA.<br />
115
(a)<br />
(b)<br />
(c)<br />
Set II<br />
Set III<br />
Set I<br />
(d)<br />
(e)<br />
(f)<br />
Set IV<br />
thumb thrust<br />
Set V<br />
1<br />
thumb thrust<br />
3<br />
thumb thrust<br />
2<br />
SMA thrust<br />
SMA thrust<br />
SMA thrust<br />
Set I<br />
reactivated<br />
Figure 3.15. Conceptual model <strong>of</strong> fracture, fold, and shearing development modified<br />
from that for folding and fracturing presented in Bellahsen et al. (2006a) to include the<br />
initiation <strong>of</strong> set V fractures, the development <strong>of</strong> the thumb, and shearing along set I, II,<br />
and V fractures. (a) Set I fractures in undeformed rock. (b) Set II forms as Laramide<br />
contraction and slip along the SMA thrust begin. (c) Set I shears in a left-lateral sense<br />
in the backlimb and forelimb; set III forms in the hinge; additional set II fractures form<br />
as contraction continues and sedimentary layers begin to bend. (d) The thumb thrust<br />
begins to slip, accommodating some <strong>of</strong> the strain at SMA, causing slip along the SMA<br />
thrust to decrease; set V forms as either local or remote maximum principal<br />
compressive stress rotates; set II shears in a right-lateral sense; set I continues to<br />
shear in a left-lateral sense; additional set III fractures form. (e) Continued folding <strong>of</strong><br />
both the thumb and main fold lead to the formation <strong>of</strong> additional set II, III, and V<br />
fractures and increased shearing along sets I, II, and V. At this late stage <strong>of</strong> fold<br />
development, several shearing signatures constrain the stress field, including: (1)<br />
conjugate shearing along sets II and V (1); (2 & 3) opposite senses <strong>of</strong> shear along<br />
fractures <strong>of</strong> the same set. (f) A late stage <strong>of</strong> fold growth in which set I fractures in the<br />
forelimb reactivate with small thrust <strong>of</strong>fset and set IV fractures form in the backlimb,<br />
with the same strike as set I fractures, but oblique to bedding.<br />
116
Observations <strong>of</strong> reactivation further discredit a large lithological influence, as sets I, II,<br />
and V have sheared in both limestone and sandstone layers (Fig. 3.7).<br />
In the backlimb, set I may appear to be influenced by lithology. In the<br />
Phosphoria Fm., set I is present at notably fewer sites than in the Tensleep Fm. The<br />
majority <strong>of</strong> these Phosphoria sites are in the thumb, however. The two Tensleep sites<br />
in the thumb, site 15 and site 22, also lack set I fractures. This variation in the spatial<br />
location <strong>of</strong> set I fractures is attributed to a heterogeneity in the stress field in the future<br />
location <strong>of</strong> the thumb while set I was forming, and not a lithological difference.<br />
Furthermore, it cannot be attributed to any structural phenomena as the thumb<br />
uplifted, because set II also is interpreted to pre-date the thumb, and it is found in both<br />
Tensleep and Phosphoria sites throughout the thumb with the same orientation as at<br />
other locations on the fold.<br />
Trends in the occurrence <strong>of</strong> sets III and IV in the backlimb also suggest a lack <strong>of</strong><br />
lithological control on fracturing. Set III exists primarily in the area around and to the<br />
southeast <strong>of</strong> the thumb intersection. Set IV exists primarily in the area surrounding the<br />
thumb intersection. The spatial locations in which these fractures formed imply that<br />
the development <strong>of</strong> these two sets is related to localized structure-related stress<br />
perturbations. Because the sets formed in both the Tensleep sandstone and Phosphoria<br />
limestone, one may deduce that the two lithologies respond similarly to stress<br />
perturbations.<br />
No significant differences are noticeable in the orientation <strong>of</strong> fracture sets<br />
formed in the Madison and Amsden Fms. in the hinge. Joints <strong>of</strong> set II and III are the<br />
most commonly formed fractures in sites within both layers. Neither lithology<br />
provides evidence for fracture reactivation.<br />
As noted at other field locations, the forelimb <strong>of</strong> the fold shows more variability<br />
in fracture orientations than other structural positions (Jamison, 1997; Wennberg et al.,<br />
2007). One apparent difference based on lithology is that set I fractures are more<br />
populous in the Tensleep sandstone than the Phosphoria limestone. We argue that set I<br />
fractures do exist in many Phosphoria sites in the forelimb, but are underrepresented in<br />
figure 3.5a due to geometric complications. The Phosphoria Fm. forms the uppermost<br />
layer exposed in the steeply dipping forelimb, and thus access is limited. In these<br />
117
steeply dipping beds striking approximately 320°, not many set I fractures extend to<br />
the bottom <strong>of</strong> the exposed pavement where measurement is possible. As an example<br />
set I fractures are visible in figure 3.8c, but most cannot be measured. Sets that are<br />
found at numerous sites, set V and a minor N-S set, are present in both the Tensleep<br />
Fm. and the Phosphoria Fm., while the set that is sparse, set II, is sparse in both<br />
lithologies. Although at the microscale, mechanisms <strong>of</strong> deformation within sandstone<br />
and limestone are different, field observations indicate that at SMA, macroscale<br />
deformation is consistent from one lithology to another.<br />
Set V fractures<br />
Based on abutting relationships, we interpret set V to be composed <strong>of</strong> early syn-<br />
folding joints that formed after set II joints and before set III joints. Although most<br />
field observations suggest that set II predates set V, alternating termination<br />
relationships exist at specific locations (e.g. sites 1, 16, 8). These few abutments <strong>of</strong> set<br />
II on set V do not explicitly imply that the local principal stresses rotated back and<br />
forth. As illustrated in figure 3.16, set II joints in some locations formed as echelon<br />
<strong>of</strong>fset segments. With a change in direction <strong>of</strong> the least principal stress (σ3), set V<br />
fractures initiated and propagated, in some cases through the gaps between echelon set<br />
II segments (location (a) in Fig. 3.16). The sigmoidal shape <strong>of</strong> the segment marked (b)<br />
in figure 3.16 may record the transition <strong>of</strong> σ1 from 045 o to 075 o . The segment initiated<br />
as a set II joint. With the transition in direction <strong>of</strong> σ1, the tips <strong>of</strong> the original segment<br />
propagated along curved paths, becoming aligned with the newly forming set V joints<br />
and propagating further in this orientation.<br />
Set V apparently formed during a syn-folding stage before much bedding<br />
curvature (and thus before set III joints) accumulated in the backlimb. In this case,<br />
there are two scenarios that could lead to a rotation in local principal stress directions<br />
allowing new joints to form at 075°. Both scenarios are linked to the development <strong>of</strong><br />
the thumb, a secondary fold on the backlimb <strong>of</strong> SMA with a fold axis rotated 20° –30°<br />
clockwise from that <strong>of</strong> the main fold. In the first scenario, a clockwise reorientation <strong>of</strong><br />
the remote greatest compressive stress (σ1) could have occurred. A clockwise rotation<br />
<strong>of</strong> the maximum contraction during the Laramide is supported by a study <strong>of</strong> the<br />
118
N<br />
10 cm<br />
N<br />
set V<br />
(b)<br />
(a)<br />
set III<br />
set II<br />
10 cm<br />
Figure 3.16. Field photograph and interpretation <strong>of</strong> set II and set V joints that grew<br />
together. In most cases, set V joints truncate against set II joints, but as seen at<br />
location (a) above, some set V joints grew through gaps in echelon set II joints. The<br />
sigmoidal shape <strong>of</strong> the segment at location (b) records a rotation in the σ1 direction.<br />
The part <strong>of</strong> the segment shown in bold formed first as a set II joint. As the σ1 direction<br />
rotated, both tips <strong>of</strong> this original segment propagated along a curved path, realigning<br />
with a σ1 direction parallel to the average set V joint strike.<br />
119
kinematic history <strong>of</strong> the Rocky Mountain foreland that is based on existing structural,<br />
paleomagnetic, and stress data (Bird, 1998). This rotation would have decreased the<br />
potential for slip along the main SMA fault, while at the same time enhancing the<br />
potential for slip along faults <strong>of</strong> a more north-south orientation, such as the one<br />
proposed to exist beneath the thumb (Savage and Cooke, 2004). Slip along such a fault<br />
would lead to the uplift <strong>of</strong> the thumb and, if tensile stresses exceeded rock strength, a<br />
set <strong>of</strong> joints aligned with the direction <strong>of</strong> σ1. In the second scenario, the remote σ1<br />
could have remained in the same orientation. As some <strong>of</strong> the applied remote load was<br />
relieved by oblique slip along the fault beneath the thumb, the thumb fold developed,<br />
and the potential for further slip along the main fault decreased. Formation <strong>of</strong> set V<br />
fractures would then be linked to local perturbations in the stress field caused by the<br />
interaction <strong>of</strong> the faults beneath the folds, pre-existing heterogeneities, bending <strong>of</strong><br />
bedding within the thumb, or any other mechanism by which the local stress field is<br />
perturbed.<br />
For either principal stress rotation scenario, we must justify the presence <strong>of</strong> set V<br />
in the forelimb, where the paucity <strong>of</strong> set II has been attributed to elevated compressive<br />
stresses in the hanging wall <strong>of</strong> the thrust fault beneath SMA as slip accrued during<br />
early folding (Bellahsen et al., 2006b). The state <strong>of</strong> stress in the forelimb must have<br />
differed during formation <strong>of</strong> the two fracture sets. In both scenarios for the formation<br />
<strong>of</strong> set V fractures discussed above, the decrease in activity along the main thrust fault<br />
and the accompanying relaxation in compressive stresses near the tip <strong>of</strong> that fault, is<br />
consistent with the development <strong>of</strong> set V in the forelimb.<br />
Stress field constraints<br />
Field observations at SMA constrain the stress state throughout the fold at the<br />
time <strong>of</strong> fracture reactivation. As illustrated through the failure analyses carried out<br />
within this section, the presence or absence <strong>of</strong> shear along specific fracture sets<br />
provides estimates <strong>of</strong> local principal stress magnitudes. The direction(s) <strong>of</strong> shearing<br />
along fracture sets constrains the orientation <strong>of</strong> the local principal stresses.<br />
120
Constraints on spatial variation in stress orientation: conjugate shearing<br />
Conjugate shearing along set II and V joints places constraints on the direction<br />
<strong>of</strong> the local principal stresses during joint reactivation, assuming that the recorded slip<br />
occurred concurrently. In the second backlimb domain, at site 22 in the Tensleep<br />
sandstone, set V, with an average local strike <strong>of</strong> 080°, has sheared in a left lateral<br />
sense (Fig. 3.17a, 3.17b). Set II, composed <strong>of</strong> joints that are less pronounced than<br />
those <strong>of</strong> set V, has an average strike <strong>of</strong> 050° and has sheared in a right lateral sense<br />
(Fig. 3.17a, 3.17b). Although joint orientations within sets II and V are dispersed (Fig.<br />
3.17c), a distinct cut<strong>of</strong>f for shearing direction is observed. Fractures <strong>of</strong> strike direction<br />
066° and less shear in a right-lateral sense; fractures <strong>of</strong> strike direction 078° and<br />
greater shear in a left-lateral sense. Assuming that σ2 is parallel to the intersection <strong>of</strong><br />
sets II and V, then the conjugate slip along these fracture sets constrains the σ1<br />
direction during shearing to an orientation within this twelve degree range (Fig. 3.18).<br />
Spatial variation in stress orientation: opposite senses <strong>of</strong> shearing<br />
Where two sub-parallel joints within close proximity to one another are sheared in<br />
opposite directions, the local stress direction may be constrained. Data from the<br />
backlimb suggest that opposite senses <strong>of</strong> shearing are a result <strong>of</strong> temporal, rather than<br />
spatial, variations in the stress field. Opposite senses <strong>of</strong> shearing along approximately<br />
parallel joints are observed at site 8 within set II and at sites 127, 128, and 130 within<br />
set V. Although the joints initiated and slipped within folding stages where spatial<br />
heterogeneities in the stress field due to bedding plane slip and faulting were present<br />
(Fig. 3.15d, 3.15e), sub-parallel fractures would be expected to shear with a similar<br />
sense. The proximity <strong>of</strong> these features suggests that the shearing is not spatially<br />
dependent: at site 130, the oppositely sheared set V fractures are decimeters apart (Fig.<br />
3.11a). Instead, we suggest that the joint set has been subjected to a temporal stress<br />
field rotation in which the σ1 direction varied around the mean strike direction (Fig.<br />
3.19).<br />
To analyze this interpretation, we refer to frictional faulting theory (Coulomb,<br />
1773; Anderson, 1951) as applied to pre-existing fractures (Jaeger, 1958). Assuming<br />
that σ1 (maximum compressive stress) and σ3 are in the horizontal plane and the<br />
121
NNW SSE NNW SSE<br />
(a)<br />
1 m (b)<br />
050 o<br />
010 o<br />
150 o<br />
092 o<br />
075 o<br />
045 o<br />
1 m<br />
(c)<br />
N<br />
measured<br />
N<br />
set V<br />
set II<br />
unfolded<br />
Figure 3.17. Fractures at backlimb site 22 in the Tensleep sandstone. (a) Field<br />
photograph and (b) line interpretation <strong>of</strong> sheared fractures at the site. (c) Stereonets<br />
<strong>of</strong> poles to fractures as observed in the field and unfolded.<br />
122
4<br />
5<br />
Figure 3.18. Spatial constraints on local principal stress directions. Gray areas<br />
represent different shearing domains. Tick marks represent σ1 directions as<br />
constrained by shearing observations. Joints would form parallel to the orientations <strong>of</strong><br />
these tick marks.<br />
(a)<br />
(b)<br />
(c)<br />
Figure 3.19. Conceptual depiction <strong>of</strong> how opposite shearing may be resolved along<br />
parallel joints as a result <strong>of</strong> a temporal rotation in the remote stress field. Black arrows<br />
represent the maximum compression direction. (a) Joints form parallel to the<br />
maximum compression direction. (b) The maximum compression direction rotates<br />
slightly clockwise, causing fractures with low friction to shear left-laterally. (c) The<br />
maximum compression direction rotates slightly counter-clockwise from the joint strike<br />
direction, causing other fractures to shear right-laterally.<br />
3<br />
123<br />
2<br />
6<br />
1<br />
N
intermediate principal stress (σ2) is contained in the vertical plane <strong>of</strong> the fracture,<br />
sliding depends upon both the angle β that the normal to the surface makes with σ1<br />
and on the magnitudes <strong>of</strong> σ1 and σ3. An analysis following Jaeger (1959) and Jaeger<br />
and Cook (1979), provides the combinations <strong>of</strong> angle β and horizontal stress values<br />
that lead to frictional slip along pre-existing joints.<br />
The Coulomb criterion for frictional sliding on a pre-existing weakness is<br />
| σ +<br />
(1)<br />
s | = S o µσ n<br />
where σs is the shear stress resolved on the fracture, So is cohesion, µ is the coefficient<br />
<strong>of</strong> static friction, and σn is the resolved normal stress. σs and σn are related to the<br />
horizontal principal stresses as follows:<br />
1<br />
1<br />
σ n = ( σ 1 + σ 3 ) + ( σ 1 − σ 3 ) cos 2β<br />
(2)<br />
2<br />
2<br />
1<br />
σ ( σ 1 σ 3 ) sin 2β<br />
2<br />
− − = s (3)<br />
where β is the angle between the normal to the fracture and the direction <strong>of</strong> σ1. The<br />
angles β1 and β2 define the range <strong>of</strong> orientations within which sliding will occur for<br />
given principal stress magnitudes, friction, and cohesion:<br />
−1<br />
⎧⎡⎛<br />
1<br />
⎞ 1 ⎤ ⎫<br />
β1 = π + φ − sin ⎨⎢⎜<br />
( σ 1 + σ 3)<br />
+ S o cotφ<br />
⎟ / ( σ 1 − σ ) ⎥ sinφ<br />
⎬ (5)<br />
⎩⎣⎝<br />
2<br />
⎠ 2 ⎦ ⎭<br />
2 3<br />
−1<br />
⎧⎡⎛<br />
1<br />
⎞ 1 ⎤ ⎫<br />
β 2 = φ + sin ⎨⎢⎜<br />
( σ 1 + σ 3)<br />
+ S o cotφ<br />
⎟ / ( σ 1 −σ<br />
) ⎥ sinφ<br />
⎬ (6)<br />
⎩⎣⎝<br />
2<br />
⎠ 2 ⎦ ⎭<br />
2 3<br />
where φ is the angle <strong>of</strong> friction. We assume that the variation around the σ1 direction<br />
that led to reactivation <strong>of</strong> the joints occurred during the same period <strong>of</strong> deformation<br />
within which the joints initiated. It is thus unlikely that cementation <strong>of</strong> the joint walls<br />
had occurred before reactivation. Assuming that the joint walls were bare (i.e. no vein<br />
fill), we set So = 0. As determined by laboratory experiments investigating friction<br />
along bare joint surfaces (Jaeger, 1958), we use φ = 30 o .<br />
To assess these equations for the case <strong>of</strong> oppositely sheared joints at SMA,<br />
constraints must be placed on the possible principal stress magnitudes. Assuming a<br />
124
density <strong>of</strong> 2700 kg/m 3 for sedimentary rock and a depth <strong>of</strong> 2200 m, representing the<br />
depth <strong>of</strong> the Tensleep Fm. during Laramide time, the layer within which we find<br />
oppositely sheared joints would have been subjected to a vertical stress <strong>of</strong> 58 MPa. For<br />
the reactivation observed along set II and set V joints to occur, the state <strong>of</strong> stress must<br />
be a strike-slip faulting regime where the vertical stress is the intermediate principal<br />
stress (σ2). Appropriate values for the horizontal principal stresses, as determined by<br />
in situ stress measurements (McGarr and Gay, 1978; Brace and Kohlstedt, 1980) and<br />
consideration <strong>of</strong> the strength <strong>of</strong> the crust (see Moos and Zoback, 1990; Zoback et al.,<br />
2003), range from 0.6σv to 2.2σv.<br />
To assess these limited ranges <strong>of</strong> σ1 and σ3, we set σ1 at 127 MPa, (2.2σv), we<br />
allow σ3 to vary over the range 34 MPa to 58 MPa (0.6σv to σv), and we solve<br />
equations (5) and (6) for β1 and β2. Figure 3.20a plots the critical angles for slip along<br />
joints for the specified range <strong>of</strong> principal stress ratios: the gray area represents<br />
conditions under which the pre-existing joint would slip, whereas the white area<br />
represents those in which the stress state is insufficient for slip. This concept is readily<br />
visualized on a Mohr diagram (Fig. 3.20b). For σ1 and σ3, (say σ1 =127 MPa and σ3<br />
=37 MPa) for example, intersections with the failure envelope occur at angles<br />
2(β1=48 o ) and 2(β2=72 o ) as measured from σ1 (dashed lines, Fig. 3.20b). The geometry<br />
<strong>of</strong> a joint with respect to σ1 and σ3 for these two critical angles is shown in figure<br />
3.20c. Slip will occur for all angles between β1 and β2 (θ in Fig. 3.20c), as indicated by<br />
the gray area in figure 3.20b. For σ1 =127 MPa, σ1/σ3 = 3 represents the limiting case<br />
for frictional slip. Slip occurs only at β1 = β2 = 60 o , as indicated by the tangency <strong>of</strong> the<br />
Mohr circle to the failure envelope at 2β1=2β2 from σ1 (Fig. 3.20b). When σ1 =127<br />
MPa smaller stress ratios will not cause reactivation <strong>of</strong> the joints.<br />
Results for the above analysis when revisited including pore pressure at a hydrostatic<br />
gradient <strong>of</strong> 10 MPa/km are shown in figures 3.20d,e,f. A plot <strong>of</strong> the ratio <strong>of</strong> the<br />
maximum and minimum principal stresses, again where σ1 = 127 MPa and σ3 ranges<br />
over 34 MPa to 58 MPa, versus the angle β indicates that when pore pressure is<br />
accounted for, the stress ratio for the limiting case <strong>of</strong> slip is lowered to ~2.2. Sliding<br />
125
(a)<br />
Angle β (degrees)<br />
(b)<br />
(c)<br />
75<br />
70<br />
65<br />
60<br />
55<br />
50<br />
45<br />
2 2.<br />
|σs|<br />
β1 β2 β1 = 48 o<br />
β = 72 2 o<br />
σ1 /σ3 = 3.4<br />
2 2. 4 2. 6 2. 8<br />
σ1/σ3 3 3. 2 3. 4 3. 6<br />
critical case: σ 1 /σ 3 = 3<br />
σ 1 /σ 3 = 3.4<br />
joint<br />
β2 σ3 β<br />
σ 1<br />
3<br />
β 2<br />
β 1<br />
n<br />
θ<br />
β<br />
σ 2<br />
1<br />
2β 1<br />
2β 1 = 2β 2<br />
β<br />
σ 1<br />
1<br />
2β 2<br />
σ n<br />
(d)<br />
90<br />
Angle β (degrees)<br />
(e)<br />
(f)<br />
80<br />
70<br />
60<br />
50<br />
40<br />
30<br />
2 2.2 2.4 2.6 2.8<br />
σ1/σ3 3 3.2 3.4 3.6<br />
|σs*|<br />
β1 β2 β1 = 36 o<br />
σ1 /σ3 = 3.4<br />
β 2 = 84 o<br />
joint<br />
σ 3 β 2<br />
2β 2<br />
critical case:σ 1 /σ 3 = 2.2<br />
σ 1 /σ 3 = 3.4<br />
β1 σ3 2β 1<br />
2β 1 = 2β 2<br />
Figure 3.20. Analysis <strong>of</strong> principal stress directions and magnitudes for oppositely<br />
sheared joints <strong>of</strong> the same set. For the case <strong>of</strong> σ1 = 127 MPa and σ3 ranging from 34<br />
MPa to 58 MPa, the β1 and β2 values (representing the angle between the normal to<br />
the joint and the σ1 direction) at which pre-existing joints will slip are represented by<br />
the gray envelopes in (a), representing the dry case and (d), where hydrostatic pore<br />
pressure is included. (b) and (e) are Mohr circle depictions for the respective cases.<br />
The solid line in each figure represents the critical angle (2β1 = 2 β2) at which slip will<br />
occur. The dotted lines bound the 2β values <strong>of</strong> pre-existing joints that would slip<br />
within a stress state where σ1 = 127 MPa and σ1 /σ3 = 3.4. (c) and (f) depict the<br />
geometry <strong>of</strong> the σ1 directions with respect to the joint surface and the joint normal for<br />
the β values representing the boundaries <strong>of</strong> the gray zones in (b) and (e). All preexisting<br />
joints formed at angles represented by this zone, marked by the angles θ in<br />
(b) and (e) would slip under the given stress conditions.<br />
126<br />
β 2<br />
β 1<br />
n<br />
θ<br />
β<br />
σ 2<br />
1<br />
β<br />
σ 1<br />
1<br />
σ n *
occurs when the normal to the joint and σ1 form an angle <strong>of</strong> 60 o . Numerous<br />
combinations <strong>of</strong> σ1/σ3 and β result in slip, as shown by the gray area in figure 3.20d.<br />
About 95% <strong>of</strong> set II and set V joints show no evidence for slip in the areas where<br />
opposite senses <strong>of</strong> shearing were found. One may conclude that the state <strong>of</strong> stress was<br />
at the frictional sliding limit for the weakest members only, while the majority <strong>of</strong> set II<br />
joints at site 8 and set V joints at sites 127, 128, and 130 remained locked. Therefore<br />
the combinations <strong>of</strong> stress states and β values situated along the boundary <strong>of</strong> the gray<br />
envelope (Fig. 3.20a, 3.20d) are most appropriate. Because we interpret the opposite<br />
senses <strong>of</strong> shearing to result from minor variation <strong>of</strong> σ1 around the strike direction <strong>of</strong><br />
the joints, the β2 curve defines the minimum critical slip angle for each state <strong>of</strong> stress.<br />
We calculate the relative magnitudes <strong>of</strong> the regional principal strains relating to<br />
the principal stresses at the critical point <strong>of</strong> failure for β2 = 85 o , 80 o , 75 o , and 70 o .<br />
Values for σ3 are calculated from the corresponding principal stress ratios (Fig. 3.20d)<br />
using σ1 = 127 MPa. Representative strains (ε1, ε3) for these principal stresses are then<br />
calculated from Hooke’s law for the isotropic elastic medium:<br />
+ ν ν<br />
ε ij = σ ij − σ kkδ<br />
ij<br />
E E<br />
1<br />
Although Laramide strains were clearly beyond the elastic limit, we postulate<br />
that the relative magnitudes <strong>of</strong> elastic strains calculated from principal stress values<br />
are representative <strong>of</strong> discrete deformation events such as an episode <strong>of</strong> slip along the<br />
faults beneath SMA. Elastic strains then provide reasonable boundary conditions for<br />
mechanical models attempting to relate stress, strain, and displacement fields at SMA<br />
during such events. Figure 3.21 plots the fracture parallel (ε1) and fracture<br />
perpendicular (ε3) strains corresponding to specific values <strong>of</strong> σ3 for four different βs at<br />
the critical limit when σ1 = 127 MPa. Plotted combinations <strong>of</strong> (ε1, ε3) that correspond<br />
to the same σ3 value and the same β value represent strain configurations that are<br />
plausible for inducing reactivation along set II and V joints as seen in the field.<br />
The above analysis indicates that a variation <strong>of</strong> principal stress directions by as<br />
little as a few degrees could result in shearing along joints. We conclude that<br />
observations <strong>of</strong> opposite senses <strong>of</strong> shear along sub-parallel joints indicate that the<br />
127<br />
(7)
strike <strong>of</strong> the joints is a reasonable average σ1 direction. Because opposite senses have<br />
been observed along set II in domain three and set V in domain five, we posit that σ1<br />
varied around 045° in domain three and around 080° in domain five (Fig. 3.18) during<br />
the time period in which the joints slipped. In the case that set V formed due to a<br />
clockwise rotation in the remote σ1 direction, set II would have reactivated during an<br />
earlier stage <strong>of</strong> folding than set V (Fig. 3.15). In the case that set V formed due to local<br />
principal stress rotations, set II and V reactivation could have occurred in separate<br />
locations concurrently.<br />
Constraints on spatial variation in stress field magnitude: set I fractures<br />
Here we investigate shearing along pre-existing set I fractures in the Tensleep<br />
sandstone <strong>of</strong> the limbs and the formation <strong>of</strong> new set III joints in the Madison limestone<br />
<strong>of</strong> the hinge. This analysis involves comparing sliding along pre-existing fractures to<br />
tensile failure <strong>of</strong> intact rock. The majority <strong>of</strong> hinge observations were made within the<br />
Madison limestone, which is locally dolomitized (Sonnenfeld, 1997). Representative<br />
values for cohesion and angle <strong>of</strong> internal friction for dolomitized limestone are 17<br />
MPa and 53 o , respectively (Kahraman et al., 2006). We also consider the failure<br />
envelope for intact sandstone to demonstrate states <strong>of</strong> stress that are inconsistent with<br />
field observations within the Tensleep Fm. Representative values for cohesion and<br />
angle <strong>of</strong> internal friction for sandstone are 28 MPa and 26 o , respectively (Jaeger and<br />
Cook, 1979).<br />
For the backlimb, the cases where set I reactivated while set II was forming and<br />
while set V was forming are compared in figures 3.22a and 3.22b. In the former case,<br />
σ1 was oriented at 045 o and the angle between the normal to set I and the direction <strong>of</strong><br />
σ1 was 025 o (Fig. 3.22a). In the latter case, σ1 was oriented at 075 o and the angle<br />
between the normal to set I and the direction <strong>of</strong> σ1 was 065 o (Fig. 3.22b). The<br />
configuration <strong>of</strong> the stress states in figures 3.22a and 3.22b represent the onset <strong>of</strong><br />
sliding along set I fractures, given specific values <strong>of</strong> the maximum shear stress (radius<br />
<strong>of</strong> the Mohr circle; ½(σ1 - σ3)) and the mean stress (center <strong>of</strong> the Mohr circle; ½ (σ1 +<br />
σ3)). Sliding occurs where the line at an angle <strong>of</strong> 2β from σ1 intersects the failure<br />
envelope for sliding along a bare fracture at (σn ,σs). The stress state for the case when<br />
128
% strain<br />
1.2<br />
1.0<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
0<br />
σ 3 ’/σ 1 ’ = 3.63; α = 85 o<br />
σ 3 ’/σ 1 ’ = 2.89; α = 80 o<br />
σ 3 ’/σ 1 ’ = 2.54; α = 75 o<br />
σ 3 ’/σ 1 ’ = 2.34; α = 70 o<br />
ε 1 : fracture parallel<br />
ε 3 : fracture perpendicular<br />
-0.2<br />
30 35 40 45 50 55 60<br />
σ 3 (MPa)<br />
Figure 3.21. Plot showing possible remote strain boundary conditions derived from<br />
frictional faulting theory applied to observations <strong>of</strong> reactivated joints. The strains<br />
above are calculated for the case where σ1 = 127 MPa and account for hydrostatic<br />
pore pressure.<br />
129
σ1 was oriented at 075 o was more favorable for invoking sliding along set I fractures<br />
than the case when σ1 was oriented at 045 o .<br />
In the hinge, when set III fractures formed, σ1 was oriented at 135 o , parallel to<br />
the strike <strong>of</strong> the joint set. The normal to set I fractures formed an angle β <strong>of</strong> 065 o with<br />
σ1. If set I fractures were not cemented, sliding would have occurred along set I<br />
fractures before failure <strong>of</strong> the intact rock for any stress state. This concept is<br />
represented conceptually by the Mohr circle in figure 3.22c. The point (σn, σs) on the<br />
Mohr circle (at angle 2β from σ1) representing sliding along set I intersects with the<br />
failure envelope for bare fracture surfaces before reaching the point <strong>of</strong> tensile failure<br />
for the dolomitic limestone represented by S0 dls /2. Because the failure envelope for<br />
bare fracture surfaces has a y-intercept <strong>of</strong> 0, slip along set I fractures would occur<br />
before set III fractures formed for any stress state. If set I had been infilled, then the<br />
failure envelope shifts to represent the cohesion and the angle <strong>of</strong> internal friction <strong>of</strong><br />
the infilled material (Jaeger, 1958).<br />
Thin sections <strong>of</strong> set I fractures in the hinge and backlimb indicate the possibility<br />
<strong>of</strong> a multi-stage evolution in the backlimb. In the hinge (Fig. 3.23a), set I fractures are<br />
marked by a zone <strong>of</strong> fine grained calcite cement. In the backlimb (Fig. 3.23b), fine<br />
grained calcite cement lines the contact between the host rock and larger grained<br />
calcite cement. Comparison <strong>of</strong> the two thin sections suggests that set I fractures in the<br />
backlimb were subjected to a second stage <strong>of</strong> deformation not recorded by set I<br />
Figure 3.22 (opposite page). Mohr circles investigating slip along set I fractures for<br />
(a) backlimb positions in sandstone where the local σ1 is oriented at 045 o ; (b)<br />
backlimb positions in sandstone where the local σ1 is oriented at 075 o ; and (c) hinge<br />
positions in dolomitized limestone where the local σ1 is oriented at 135 o . (d) Mohr<br />
circle depiction <strong>of</strong> how the failure envelope <strong>of</strong> the fracture fill may be constrained by<br />
field observations. The a marks the point <strong>of</strong> tensile failure <strong>of</strong> the dolomitic limestone<br />
and the b marks the point <strong>of</strong> failure <strong>of</strong> the fracture fill. (e) Mohr circle depiction <strong>of</strong> how<br />
the addition <strong>of</strong> a bending stress affects the state <strong>of</strong> stress. As the bending stress<br />
increases from stage t1 to t5, the initial σ1 becomes more tensile. Between stages t3<br />
and t4, the principal stress directions have rotated 90 o . Additional increments <strong>of</strong><br />
bending stress move the stress state toward tensile failure, which is shown at stage<br />
t5. In this figure, fi is the coefficient <strong>of</strong> internal friction, fs is the coefficient <strong>of</strong> sliding<br />
friction, S0 is cohesion, bf = bare fracture, ss = sandstone, dls = dolomitic limestone,<br />
fill = infilled material.<br />
130
(a)<br />
(c)<br />
(e)<br />
S 0 ss<br />
S 0 ss /2<br />
S 0 dls<br />
S 0 fill<br />
S 0 dls<br />
σ 3 f<br />
|σ s|<br />
σ 3<br />
S 0 dls /2<br />
|σ s|<br />
|σ s|<br />
t5 t4 t 3<br />
σ 1 f σ 3 i<br />
σ 3<br />
2β<br />
(σ n , σ s )<br />
σ 1<br />
dls<br />
(σ n , σ s )<br />
dls<br />
t 2<br />
2β<br />
t 1<br />
σ 1<br />
σn 50<br />
(b)<br />
S 0 ss<br />
S 0 ss /2<br />
|σ s|<br />
ss ss<br />
σ n<br />
50<br />
σ 1 i<br />
131<br />
(d)<br />
S 0 fill<br />
S 0 dls<br />
σ 3<br />
(σ n , σ s )<br />
2β<br />
σ1<br />
φ i ss=26 0 ; φ s dls=53 0 ; φ s bf=30 0 ; φ s fill=28 0<br />
S 0 ss = 28 MPa; S 0 dls = 17 MPa<br />
S 0 bf = 0 MPa; S 0 fill = 18 MPa<br />
σ n<br />
S 0 ss<br />
b<br />
a<br />
σ3 |σ s |<br />
dls<br />
σ1<br />
lithology failure envelope<br />
bare fracture failure envelope<br />
fracture fill failure envelope<br />
σn 50<br />
ss<br />
σn 50
fractures in the hinge. The fracture filling was broken during a later stage <strong>of</strong><br />
deformation, and opening provided space for the crystallization <strong>of</strong> the larger calcite<br />
grains (Fig. 3.23b). It is plausible that set I fractures, thought to have formed during<br />
the Sevier orogeny (Bellahsen et al., 2006a), had been infilled by the time <strong>of</strong> the<br />
Laramide orogeny. In this case, the cohesion and angle <strong>of</strong> internal friction <strong>of</strong> the fine<br />
grained calcite cement would determine the stress conditions under which slip along<br />
set I fractures occurs.<br />
Perhaps using a limestone failure envelope for calcite fracture fill would be<br />
appropriate. However, as a literature search reveals, the frictional properties <strong>of</strong><br />
limestone vary over a large range. For example, two references alone provide a range<br />
for the angle <strong>of</strong> internal friction <strong>of</strong> 27.9 o to 46.9 o and a range for cohesion <strong>of</strong> 15 MPa<br />
to 105 MPa for limestone (Handin, 1969; Kahraman et al., 2006). In figure 22d, we<br />
plot selected frictional properties (φ = 30 o , S0 = 18 MPa) that are consistent with the<br />
deformation observed at SMA. For set III fractures to form before reactivation <strong>of</strong> set I<br />
fractures, the stress state must reach the point <strong>of</strong> tensile failure (point a, Fig. 3.22d) <strong>of</strong><br />
the intact rock before the calcite fails. For set I fractures to slip in the backlimb, the<br />
stress state must reach the point where the infill material fails (point b, Fig. 3.22d)<br />
before the intact sandstone fails.<br />
In the Laramide tectonic setting within which SMA developed, for set III joints<br />
to form parallel to the hinge, the bending-related stress would have to be large enough<br />
so that the most tensile stress direction rotates by 90°. Assuming that the bending-<br />
related stress affects only the fold perpendicular stress magnitude, we consider the<br />
process through which the bending stress alters the stress state (Fig. 3.22e). Given an<br />
initial stress state, generated by the onset <strong>of</strong> fold perpendicular contraction, σ1 is<br />
oriented at 045°. With an increase in fold amplitude, a tensile bending-related stress is<br />
introduced and acts to decrease the magnitude <strong>of</strong> σ1 (stages t1 through t3, Fig. 3.22e).<br />
At the point when the bending-related stress reaches a magnitude greater than the fold<br />
perpendicular tectonic σ1 magnitude, the σ1 direction rotates 90° and the<br />
initialσ3 magnitude becomes the new σ1 magnitude (represented by stage t3 to t4, Fig.<br />
3.22e). As the fold continues to amplify, σ3 becomes more tensile. At the point where<br />
the magnitude <strong>of</strong> σ3 equals the tensile strength <strong>of</strong> the limestone, set III joints form.<br />
132
(a)<br />
(b)<br />
Figure 3.23. Thin section <strong>of</strong> set I fracture in the (a) hinge at site 41 and (b) backlimb<br />
at site 23. The backlimb fracture indicates an additional phase <strong>of</strong> deformation.<br />
133
Through this analysis, it becomes clear that the state <strong>of</strong> stress in the backlimb leading<br />
to the reactivation <strong>of</strong> set I fractures would have a greater mean stress magnitude and a<br />
greater maximum shear stress than the state <strong>of</strong> stress in the hinge, where a bending-<br />
related stress exists.<br />
Discussion<br />
Kinematics <strong>of</strong> shearing and folding<br />
Most examples <strong>of</strong> fracture reactivation recorded during field work at SMA are<br />
kinematically consistent. All observed strike-slip reactivation along set I is left-lateral<br />
(Fig. 3.7). The geometry <strong>of</strong> set I fractures subjected to contraction in an orientation <strong>of</strong><br />
045° or 075° suggests that, should the shear stress resolved along the fracture plane<br />
overcome the frictional resistance, slip would occur in a left-lateral sense (Fig. 3.24b,<br />
3.24c). Set II, striking 045°, would be expected to slip in a right-lateral sense with the<br />
clockwise reorientation <strong>of</strong> the local σ1 responsible for the initiation <strong>of</strong> set V joints<br />
(Fig. 3.24c). Indeed, at twenty-two <strong>of</strong> the twenty-five sites where reactivation <strong>of</strong> set II<br />
joints has been noted, right-lateral motion has been identified (Fig. 3.7). At six <strong>of</strong><br />
these sites, set II joints have a left-lateral sense <strong>of</strong> shear. Here we suggest that these<br />
joints reactivated in response to a local stress perturbation that deflected σ1 counter<br />
clockwise prior to the clockwise rotation that resulted in the development <strong>of</strong> set V.<br />
Implications for the mechanics <strong>of</strong> fracturing within a thrust fault related fold<br />
The asymmetry with respect to the regional tectonic stress field <strong>of</strong> both the<br />
formation (Fig. 3.5) and reactivation (Fig. 3.7) <strong>of</strong> fracture sets at SMA highlights an<br />
important concept for the mechanics <strong>of</strong> fracturing in a thrust fault related fold: the<br />
influence <strong>of</strong> the underlying faults. In the forelimb, the major fracture sets developed at<br />
measurement sites vary along the length <strong>of</strong> the fold (Fig. 3.5a). Additionally,<br />
subdomains within which set II and set V exhibit consistent senses <strong>of</strong> shear are not<br />
readily apparent (Fig. 3.7). Conversely, in the backlimb distinct trends are apparent in<br />
the formation <strong>of</strong> fractures: for instance the occurrence <strong>of</strong> sets IV and V are both<br />
localized in the thumb area (Fig. 3.5b). Trends also are observed in the reactivation <strong>of</strong><br />
joints (Fig. 3.14) related to structural position.<br />
134
(a)<br />
(b)<br />
(c)<br />
N<br />
Figure 3.24. Schematic diagram illustrating the kinematics <strong>of</strong> shearing <strong>of</strong> fracture<br />
sets at SMA. Black arrows represent σ1 directions. (a) Outcrop prior to Laramide<br />
orogeny with set I fractures developed at 110 o . (b) At onset <strong>of</strong> Laramide orogeny,<br />
joints form at 045 o . Small amounts <strong>of</strong> left-lateral shear may be resolved along set I<br />
fractures. (c) Local principal stress directions rotate clockwise. Joints form at 075 o .<br />
Left-lateral shear is resolved along set I fractures and right-lateral shear is resolved<br />
along set II fractures.<br />
135
In a pure buckle fold, the expected fracture pattern in the backlimb and forelimb<br />
is symmetric about the hinge (e.g. Dietrich, 1970). Had SMA developed as a buckle<br />
fold with forelimb and backlimb bedding dips becoming asymmetric with increasing<br />
deformation, one would expect the fracture pattern in the forelimb to resemble a<br />
progression <strong>of</strong> the fracture pattern in the backlimb. The development <strong>of</strong> small <strong>of</strong>fset<br />
thrust faults along the pre-existing set I fractures in the forelimb can be viewed as an<br />
example <strong>of</strong> this progression. However, the formation and reactivation <strong>of</strong> the set II and<br />
V fractures, which developed during the uplift <strong>of</strong> the fold, is not consistent in the<br />
forelimb and the backlimb. This observation leads to the conclusion that consideration<br />
<strong>of</strong> stress perturbations related to curvature and layer parallel contraction is insufficient<br />
for prediction <strong>of</strong> the fracture pattern developed within this thrust fault related fold. The<br />
underlying fault(s) apparently generate significant perturbations in the stress state<br />
prevailing throughout the fold that differ between the forelimb and backlimb and must<br />
be accounted for to understand the fracture patterns.<br />
Acknowledgements<br />
We thank Yukiyasu Fujii, Ashley Griffith, Ole Kaven, Ian Mynatt, and Chris<br />
Wilson for field assistance. This study was supported by the National Science<br />
Foundation Collaboration in Mathematical Geosciences Program Grant No. EAR-<br />
04177521 and the <strong>Stanford</strong> Rock Fracture Project.<br />
References<br />
Allmendinger, R. W., 1998, Inverse and forward numerical modeling <strong>of</strong> trishear faultpropagation<br />
folds: Tectonics, v. 17, p. 640-656.<br />
Anderson, E. M., 1951, The dynamics <strong>of</strong> faulting and dyke formation, with<br />
applications to Britain: Edinburgh, Oliver & Boyd, 206 p.<br />
Bellahsen, N., P. Fiore, and D. D. Pollard, 2006a, The role <strong>of</strong> fractures in the structural<br />
interpretation <strong>of</strong> Sheep Mountain anticline, Wyoming: Journal <strong>of</strong> Structural<br />
Geology, v. 28, p. 850-867.<br />
Bellahsen, N., P. E. Fiore, and D. D. Pollard, 2006b, From spatial variation <strong>of</strong> fracture<br />
patterns to fold kinematics: A geomechanical approach: Geophysical Research<br />
Letters, v. 33, doi:10.1029/2005GL024189.<br />
136
Bergbauer, S., and D. D. Pollard, 2004, A new conceptual fold-fracture model<br />
including prefolding joints, based on field data from the Emigrant Gap<br />
anticline, Wyoming: Geological Society <strong>of</strong> America Bulletin, v. 116, p. 294-<br />
307.<br />
Bird, P., 1998, Kinematic history <strong>of</strong> the Laramide orogeny in latitudes 35°-49°N,<br />
western United States: Tectonics, v. 17, p. 780-801.<br />
Bourne, S. J., and E. J. M. Willemse, 2001, Elastic stress control on the pattern <strong>of</strong><br />
tensile fracturing around a small fault network at Nash Point, UK: Journal <strong>of</strong><br />
Structural Geology, v. 23, p. 1753-1770.<br />
Brace, W. F., and D. L. Kohlstedt, 1980, Limits on lithospheric stress imposed by<br />
laboratory experiments: JGR. Journal <strong>of</strong> Geophysical Research. B, v. 85, p.<br />
6248-6252.<br />
Coulomb, C. A., 1773, Sur une application des regles de Maximis et Minimis a<br />
quelques problems de statique relatifs a l'Architecture: Acad. Roy. Des<br />
<strong>Sciences</strong> Memoires de math. et de Physique par Divers Servants, v. 7, p. 343-<br />
382.<br />
Cruikshank, K. M., G. Zhao, and A. M. Johnson, 1991, Analysis <strong>of</strong> minor fractures<br />
associated with joints and faulted joints: Journal <strong>of</strong> Structural Geology, v. 13,<br />
p. 865-886.<br />
Davatzes, N. C., and A. Aydin, 2005, Distribution and nature <strong>of</strong> fault architecture in a<br />
layered sandstone and shale sequence; an example from the Moab Fault, Utah:<br />
AAPG memoir, v. 85, p. 153-180.<br />
Dieterich, J. H., 1970, Computer experiments on mechanics <strong>of</strong> finite amplitude folds:<br />
Canadian journal <strong>of</strong> earth sciences, v. 7, p. 467-476.<br />
Fischer, M. P., and M. S. Wilkerson, 2000, Predicting the orientation <strong>of</strong> joints from<br />
fold shape: Results <strong>of</strong> pseudo-three-dimensional modeling and curvature<br />
analysis: Geology, v. 28, p. 15-18.<br />
Gries, R., 1983, Oil and gas prospection beneath Precambrian <strong>of</strong> foreland thrust plates<br />
in Rocky Mountains: American Association <strong>of</strong> Petroleum Geologists Bulletin,<br />
v. 67, p. 1-28.<br />
Griggs, D., and J. Handin, 1960, Observations on fracture and a hypothesis <strong>of</strong><br />
earthquakes: Geological Society <strong>of</strong> America Memoir, v. 79, p. 347-364.<br />
Handin, J., 1969, On the Coulomb-Mohr failure criterion: Journal <strong>of</strong> Geophysical<br />
Research, v. 74, no. 22, p. 5343-5348.<br />
137
Jaeger, J. C., 1959, The frictional properties <strong>of</strong> joints in rock: Ge<strong>of</strong>isica pura applica,<br />
v. 43, p. 148-158.<br />
Jaeger, J. C., and N. G. W. Cook, 1979, Fundamentals <strong>of</strong> Rock Mechanics: London,<br />
Chapman and Hall, 593 p.<br />
Kahraman, S., H. Altun, B. S. Tezekici, and M. Fener, 2006, Sawability prediction <strong>of</strong><br />
carbonate rocks from shear strength parameters using artificial neural<br />
networks: International Journal <strong>of</strong> Rock Mechanics and Mining <strong>Sciences</strong>, v.<br />
43, p. 157-164.<br />
Kattenhorn, S. A., A. Aydin, and D. D. Pollard, 2000, Joints at high angles to normal<br />
fault strike: an explanation using 3-D numerical models <strong>of</strong> fault-perturbed<br />
stress fields: Journal <strong>of</strong> Structural Geology, v. 22, p. 1-23.<br />
Maerten, L., Gillespie, P., Daniel, J.-M., 2006, 3-D geomechanical modeling for<br />
constraint <strong>of</strong> subseismic fault simulation: American Association <strong>of</strong> Petroleum<br />
Geologists, v. 90, p. 1337-1358.<br />
Maerten, L., P. Gillespie, and D. D. Pollard, 2002, Effects <strong>of</strong> local stress perturbation<br />
on secondary fault development: Journal <strong>of</strong> Structural Geology, v. 24, p. 145-<br />
153.<br />
McGarr, A., and N. C. Gay, 1978, State <strong>of</strong> stress in the earth's crust: Annual Review<br />
<strong>of</strong> <strong>Earth</strong> and Planetary <strong>Sciences</strong>, v. 6, p. 405-436.<br />
Moos, D., and M. D. Zoback, 1990, Utilization <strong>of</strong> observations <strong>of</strong> well bore failure to<br />
constrain the orientation and magnitude <strong>of</strong> crustal stresses: application to<br />
Continental Deep Sea Drilling Project and Ocean Drilling Program boreholes:<br />
Journal <strong>of</strong> Geophysical Research, v. 95, p. 9305-9325.<br />
Myers, R., and A. Aydin, 2004, The evolution <strong>of</strong> faults formed by shearing across<br />
joint zones in sandstone: Journal <strong>of</strong> Structural Geology, v. 26, p. 947-966.<br />
Peacock, D. C. P., 2001, The temporal relationship between joints and faults: Journal<br />
<strong>of</strong> Structural Geology, v. 23, p. 329-341.<br />
Pollard, D. D., and P. Segall, 1987, Theoretical displacements and stresses near<br />
fractures in rock: with applications to faults, joints, veins, dikes, and solution<br />
surfaces, in B. K. Atkinson, ed., Fracture Mechanics <strong>of</strong> Rock: London,<br />
Academic Press Inc., p. 277-349.<br />
Renshaw, C. E., and D. D. Pollard, 1994, Numerical simulation <strong>of</strong> fracture set<br />
formation: A fracture mechanics model consistent with experimental<br />
observations: Journal <strong>of</strong> Geophysical Research, v. 99, p. 9,359-9,372.<br />
138
Robbins, S. L., and J. A. Grow, 1992, Isostatic residual gravity mapping <strong>of</strong> Wyoming:<br />
Geological Survey circular, p. 65-66.<br />
Sassi, W., and J. L. Faure, 1996, Role <strong>of</strong> faults and layer interfaces on the spatial<br />
variation <strong>of</strong> stress regimes in basins; inferences from numerical modelling:<br />
Tectonophysics, v. 266, p. 101-119.<br />
Savage, H., and M. L. Cooke, 2004, The effect <strong>of</strong> non-parallel fault interaction on fold<br />
patterns: Journal <strong>of</strong> Structural Geology, v. 26, p. 905-917.<br />
Segall, P., and D. D. Pollard, 1983, Nucleation and growth <strong>of</strong> strike-slip faults in<br />
granite: Journal <strong>of</strong> Geophysical Research, v. 88, p. 555-568.<br />
Silliphant, L., 2002, The state <strong>of</strong> stress in the limb <strong>of</strong> the Split Mountain Anticline,<br />
Utah; constraints placed by transected joints: Journal <strong>of</strong> structural geology, v.<br />
24, p. 155-172.<br />
Sonnenfeld, M., 1996, An integrated sequence stratigraphic approach to reservoir<br />
characterization <strong>of</strong> the Lower Mississippian Madison Limestone, emphasizing<br />
Elk Basin Field, Bighorn Basin, Wyoming and Montana: PhD thesis thesis,<br />
Colorado <strong>School</strong> <strong>of</strong> Mines, Golden, CO.<br />
Stearns, D. W., 1968, Certain aspects <strong>of</strong> fractures in naturally deformed rocks, in R. E.<br />
Riecker, ed., Rock mechanics seminar: Bedford, Terrestrial <strong>Sciences</strong><br />
Laboratory, p. 97-118.<br />
Stone, D. S., 1993, Basement-involved thrust-generated folds as seismically imaged in<br />
the subsurface <strong>of</strong> the central Rocky Mountain foreland: Laramide basement<br />
deformation in the Rocky Mountain Foreland <strong>of</strong> the Western United Sates, v.<br />
Special Paper 280: Boulder, Colorado, Geological Society <strong>of</strong> America.<br />
Stone, D. S., 2004, Rio thrusting, multi-stage migration, and formation <strong>of</strong> vertically<br />
segregated Paleozoic oil pools at Torchlight Field on the Greybull Platform<br />
(Eastern Bighorn Basin): implications for exploration: The Mountain<br />
Geologist, v. 41, p. 119-138.<br />
Thomas, L., 1965, Sedimentation and structural development <strong>of</strong> Big Horn Basin:<br />
Bulletin <strong>of</strong> the American Association <strong>of</strong> Petroleum Geologists, v. 49, p. 1867-<br />
1877.<br />
Wennberg, O. P., Azizzadeh M., Aqrawi A.A.M., Blanc, E., Brockbank, P., Lyslo,<br />
K.B., Pickard, N., Salem, L.D., and T. Svånå, 2007, The Khaviz Anticline - an<br />
Outcrop Analogue to Giant Fractured Asmari Formation Reservoirs in SW-<br />
Iran, in Lonegran, L., Jolly, R.J.H., Sanderson, D.J. and K. Rawnsley, eds.,<br />
139
Fractured Reservoirs: Geological Society, London, Special Publication 270, p.<br />
21-39.<br />
Wilkins, S. J., M. R. Gross, M. Wacker, Y. Eyal, and T. Engelder, 2001, Faulted<br />
joints: kinematics, displacement-length scacling relations and criteria for their<br />
identification: Journal <strong>of</strong> Structural Geology, v. 23, p. 315-327.<br />
Willemse, E. J. M., and D. D. Pollard, 1998, On the orientation and patterns <strong>of</strong> wing<br />
cracks and solution surfaces at the tips <strong>of</strong> a sliding flaw or fault: Journal <strong>of</strong><br />
Geophysical Research, v. 103, p. 2427-2438.<br />
Zoback, M. D., C. A. Barton, M. Brudy, D. Castillo, B. Grollimund, D. Moos, P.<br />
Peska, C. Ward, and D. Wiprut, 2003, Determination <strong>of</strong> stress orientation and<br />
magnitude in deep wells: International journal <strong>of</strong> rock mechanics and mining<br />
sciences, v. 40, p. 1049-1076.<br />
140
Chapter 4<br />
Curvature and fracturing based on GPS data collected at Sheep<br />
Mountain Anticline, WY<br />
Abstract<br />
We investigate the curvature-fracture relationship at Sheep Mountain Anticline<br />
by coupling fracture mapping with the analysis <strong>of</strong> high precision GPS positions.<br />
Carrier-phase post-processing techniques <strong>of</strong> spatial data collected across patches <strong>of</strong><br />
bedding surfaces results in a high resolution dataset. Differential geometry tools form<br />
the basis for curvature analysis, allowing for a quantitative understanding <strong>of</strong> the<br />
shapes <strong>of</strong> these surfaces. Comparison <strong>of</strong> principal curvature magnitudes with fracture<br />
measurements indicates that greater curvature correlates with greater spherical<br />
variance <strong>of</strong> fracture sets. Fracture intensities, however, seem to correlate only loosely<br />
with curvature, as fracturing mechanisms other than curvature <strong>of</strong> bedding must be<br />
taken into account.<br />
Introduction<br />
Outcrop scale brittle structures such as small faults, joints, and sheared joints,<br />
form within folding sedimentary rock. These structures represent a second order <strong>of</strong><br />
deformation, developing as localized deformation features within more brittle<br />
lithologies and relieving local stress perturbations as the deforming strata bend into<br />
various shapes. As small-scale structural heterogeneities, faults, joints, and sheared<br />
joints affect the flow properties <strong>of</strong> reservoirs and aquifers. They represent<br />
discontinuities in the permeability <strong>of</strong> the rock volume that disrupt both the vertical and<br />
lateral transport <strong>of</strong> fluids. Accurate characterization <strong>of</strong> these structures within<br />
reservoirs or aquifers is sought for economic purposes.<br />
Sedimentary horizons and major faults can be satisfactorily imaged in seismic<br />
reflection data (e.g. Fiore et al., in press; Kattenhorn and Pollard, 2001; Maerten et al.,<br />
2000; Needham et al., 1996; Mansfield and Cartwright, 1994). Identifying so-called<br />
subseismic fractures (with length scales ≤ 20 - 30 m), however, proves to be<br />
problematic. The secondary structures on which this paper focuses fall into this<br />
141
category, being typically below seismic resolution. Direct observation <strong>of</strong> the patterns<br />
in which they form is unfeasible, except within boreholes, where spatial coverage is<br />
limited. New methods for predicting fracture patterns from available subsurface data<br />
would play a crucial role in the development <strong>of</strong> hydrocarbon reservoirs and<br />
groundwater aquifers.<br />
Many previous studies have hypothesized a relationship between fracture<br />
location, orientation, and spatial density and structural position across a fold (e.g.<br />
Woodring et al., 1940; Harris et al., 1960; Stearns, 1968; Narr, 1991; Cooper, 1992).<br />
In recent years, curvature analysis quantifying properties <strong>of</strong> fold geometry has been<br />
emphasized as a means <strong>of</strong> predicting fracture patterns within folds (e.g. Schultz-Ela<br />
and Yeh, 1992; Lisle, 1994; Fischer and Wilkerson, 2000; Hennings et al., 2000).<br />
Studies have implemented curvature analysis in various ways. Fischer and Wilkerson<br />
(2000) relate fracture orientation to minimum curvature trajectories; Lisle (1994),<br />
Robinson (1997), and Hennings et al. (2000) correlate joint occurrence and density<br />
with Gaussian curvature magnitudes. These studies rely on an assortment <strong>of</strong> curvature<br />
calculation methods, some <strong>of</strong> which present approximated values <strong>of</strong> surface curvature<br />
(e.g. Murray, 1968; Ekman, 1988; Ivanov, 1989; Schultz-Ela and Yeh, 1992; Lisle,<br />
1994; Lisle and Robinson, 1995; Nothard et al., 1996; Stewart and Podolski, 1998;<br />
Johnson and Johnson, 2000; Roberts, 2001). Recently, Bergbauer and Pollard (2003)<br />
have presented a method <strong>of</strong> surface curvature calculation that is derived from<br />
differential geometry.<br />
We investigate the relationship between curvature and fracturing at Sheep<br />
Mountain anticline (SMA) by comparing the magnitudes <strong>of</strong> the principal curvatures,<br />
derived from differential geometry calculations, <strong>of</strong> small patches <strong>of</strong> bedding surfaces<br />
with the intensities and orientations <strong>of</strong> fractures measured across these surfaces.<br />
Geological Setting<br />
SMA is located on the northeast flank <strong>of</strong> the Bighorn Basin, just west <strong>of</strong> the<br />
Bighorn Mountains. It is a basement-cored thrust fault related fold that formed in<br />
response to Laramide tectonics. The fold trends northwest-southeast and is cut by the<br />
Bighorn River approximately perpendicular to this trend (Fig. 4.1). The study area<br />
142
consists <strong>of</strong> the portion <strong>of</strong> the anticline that lies to the northwest <strong>of</strong> the river cut, as well<br />
as the area immediately southeast <strong>of</strong> the river cut and includes sedimentary rocks<br />
ranging in age from Lower Carboniferous to Permian (Fig. 4.1). The oldest rocks are<br />
<strong>of</strong> the Mississippian Madison Fm., a massive limestone that has been dolomitized<br />
throughout much <strong>of</strong> the study area (Pranter et al., 2004; Sonnenfeld, 1996). The<br />
Madison Fm. is exposed in the canyon where the Bighorn River dissects Sheep<br />
Mountain and in the hinge <strong>of</strong> the anticline where younger layers have been eroded.<br />
The Pennsylvanian Amsden Fm. sits above a karst surface at the top <strong>of</strong> the Madison<br />
Fm. and is comprised <strong>of</strong> a basal sandstone unit, a middle silty shale unit, and an upper<br />
unit <strong>of</strong> interbedded limestone and dolomite (Ladd, 1979; Hennier, 1984). The Amsden<br />
Fm. crops out primarily in the hinge <strong>of</strong> the fold. Above the Amsden Fm., the<br />
Pennsylvanian Tensleep Fm. consists predominantly <strong>of</strong> sandstone that is interlayered<br />
with thin beds <strong>of</strong> dolomite and shale. The Tensleep Fm. forms large pavements in the<br />
backlimb and forelimb <strong>of</strong> Sheep Mountain. Limited Tensleep outcrops are found in the<br />
hinge <strong>of</strong> the fold near the northwestern nose. The youngest formation in the study area<br />
is the Permian Phosphoria Fm., composed <strong>of</strong> interbedded siltstones and shales that are<br />
overlain by a massive limestone. This limestone forms the flatirons along the steep<br />
forelimb <strong>of</strong> the fold, the folded pavements over the northwest nose, and the small<br />
pavements at the base <strong>of</strong> the backlimb slopes. For this study, we focus on the<br />
Phosphoria Fm. because it forms fairly continuous pavements both in areas <strong>of</strong><br />
significant curvature (i.e. the hinge) and apparently planar areas (i.e. base <strong>of</strong> forelimb<br />
and backlimb dipslopes).<br />
Methodology<br />
GPS data collection<br />
To collect the three-dimensional spatial data analyzed in this study, we used<br />
differential GPS technology with a two receiver set up. A Trimble TM Pro XRS<br />
receiver served as a stationary base station and a Trimble TM Pro XL receiver with a<br />
pole mounted antenna served as a rover. For two <strong>of</strong> the pavements considered in this<br />
study, we walked across the bedding surfaces with the rover system, but the remaining<br />
five pavements were too steep. For these, the rover was kept stationary at distances<br />
143
N<br />
108°12'<br />
Thumb fold<br />
Quaternary<br />
Cretaceous<br />
Jurassic<br />
Triassi c<br />
108°10'<br />
Permian (Phosphoria Fm)<br />
Carboniferous (Pennsylvanian, Tensleep Fm )<br />
Carboniferous (Pennsylvanian, Amsden Fm)<br />
Carboniferous (Mississippian, Madison Fm)<br />
108°08'<br />
Bighorn River<br />
44°38'<br />
108°06'<br />
Anticlinal axis Synclinal axis 1 km<br />
Figure 4.1. Geological map <strong>of</strong> SMA. The Bighorn River dissects the fold<br />
approximately perpendicular to the fold trend. This study focuses on deformation <strong>of</strong><br />
the Permian Phophoria limestone. From Bellahsen et al., 2006a. After Rioux, 1994.<br />
144<br />
108°04'<br />
44°36'<br />
108°02'<br />
44°34'
etween 5 and 20 meters and <strong>of</strong>fsets to positions on the bedding surfaces were<br />
recorded with a LaserCraft TM Contour XLRic laser range finder.<br />
For all pavements considered in this study, data were collected and post-<br />
processed using the carrier-phase (L1) signal, which has a much higher frequency than<br />
the more common code signal (C/A, pseudo random code; Kaplan, 1996). The higher<br />
frequency <strong>of</strong> the carrier signal enables greater precision and accuracy <strong>of</strong> measurements<br />
by orders <strong>of</strong> magnitude (Kaplan, 1996). The collection <strong>of</strong> precise GPS data sets is thus<br />
feasible on an academic budget.<br />
To determine the effect <strong>of</strong> various post-processing techniques on collected GPS<br />
data, we ran a test case at a biological preserve in <strong>Stanford</strong>, CA. An area <strong>of</strong> noticeable<br />
curvature and <strong>of</strong> comparable size to pavements intended for analysis in Wyoming was<br />
selected at the preserve. Three-dimensional spatial data were collected at<br />
approximately regular intervals and then were post-processed by four different<br />
methods. To investigate the difference between correcting GPS positions with an on-<br />
site base station versus a distant base station, we post-processed the collected positions<br />
with data from both a base station we had set up at the preserve and a community base<br />
station 28 km away at Pigeon Point, CA. To investigate the difference between<br />
correcting GPS positions with code data versus carrier-phase data, we post-processed<br />
both the code data and the carrier-phase data that we had collected with the roving<br />
GPS receiver. The resulting corrected data sets are represented by black dots in figures<br />
4.2a – 4.2d. Basic surfaces (MATLAB’s triangle based linear interpolation) have been<br />
fitted to these points and contoured at a 2 ft interval for comparison to a digital<br />
elevation model <strong>of</strong> the preserve with a resolution <strong>of</strong> 2 ft (Fig. 4.2e). Our results<br />
indicate that for post-processing code data, an on-site base station provides more<br />
accurate measurements than a base station 28 km away. More notable is the accuracy<br />
<strong>of</strong> carrier-phase post-processing. The contours in figure 4.2e are reproduced in figures<br />
4.2c and 4.2d.<br />
The decision to set up a base station at Sheep Mountain rather than using a<br />
community base station was based on the desire to collect large amounts <strong>of</strong> high<br />
quality data. When post-processing using carrier-phase data, a position solution is<br />
generated at the rate <strong>of</strong> the least common multiple <strong>of</strong> the base and rover logging<br />
145
(a)<br />
Y (m)<br />
(c)<br />
Y (m)<br />
50<br />
40<br />
30<br />
20<br />
10<br />
0<br />
0 10 20 30<br />
X (m)<br />
40 50 60<br />
50<br />
40<br />
30<br />
20<br />
10<br />
Code: on−site base<br />
Carrier: on−site base<br />
0<br />
0 10 20 30<br />
X (m)<br />
40 50 60<br />
(e)<br />
Z (ft)<br />
Z (ft)<br />
25<br />
20<br />
15<br />
10<br />
5<br />
20<br />
15<br />
10<br />
5<br />
Y (m)<br />
Y (m)<br />
50<br />
40<br />
30<br />
20<br />
10<br />
Code: PPT1<br />
0<br />
0 10 20 30<br />
X (m)<br />
40 50 60<br />
50<br />
40<br />
30<br />
20<br />
10<br />
Collected data on DEM (2 ft countours)<br />
Carrier: PPT1<br />
0<br />
0 10 20 30<br />
X (m)<br />
40 50 60<br />
Figure 4.2. Results <strong>of</strong> testing various DGPS post-processing methods. GPS data are<br />
post-processed using (a) code data with an on-site base station; (b) code data with a<br />
TrimbleTM referenced base station located 28 km from the field site; (c) carrier-phase<br />
data with an on-site base station; (d) with a Trimble TM referenced base station located<br />
28 km from the field site. Surfaces have been gridded from the respective postprocessed<br />
data. Elevation is shown in feet so that contours, plotted in black and<br />
spaced at two foot intervals, can be compared with the DEM contours shown in (e).<br />
(e) Collected data are shown in black. Green lines represent a 2 foot resolution DEM<br />
<strong>of</strong> the ground surface. The black polygon represents the area that is gridded in (a) -<br />
(d).<br />
(b)<br />
(d)<br />
146<br />
Z (ft)<br />
Z (ft)<br />
20<br />
15<br />
10<br />
5<br />
20<br />
15<br />
10<br />
5
intervals. Most community base stations have a five second logging interval at<br />
minimum. With five to ten position readings per location required to ensure a<br />
measurement <strong>of</strong> reasonable precision, setting up a base station with a one second<br />
logging rate allowed us to collect data much more efficiently. Additionally, the ability<br />
<strong>of</strong> the post-processing method to synchronize the signals collected by the base station<br />
and rover is inversely proportional to the baseline distance. The nearest base station to<br />
Sheep Mountain is 180 km away, much beyond the 30 km maximum baseline distance<br />
that is required for high precision post-processing (TSC1 Asset Surveyor Operation<br />
Manual).<br />
For this project, we are characterizing the shapes <strong>of</strong> individual patches <strong>of</strong><br />
bedding surfaces. Therefore, we require high relative accuracy and precision <strong>of</strong> points<br />
within a single surface, but not high global accuracy (positioning <strong>of</strong> surfaces within a<br />
global reference frame). Moving the location <strong>of</strong> the base station for each characterized<br />
surface therefore provides the best quality data for these purposes. The base station<br />
typically remained within 500 m <strong>of</strong> a characterized surface. The longest baseline from<br />
the base station to the rover was 1.8 km.<br />
GPS data filtering<br />
To ensure that the appropriate features are analyzed during the curvature<br />
calculation, two steps are taken. During the collection phase, to prevent aliasing<br />
effects, the pavement is sampled at a scale that is smaller than the scale <strong>of</strong> features<br />
being studied. During the data processing phase, small scale undulations that are not<br />
related to the phenomenon being considered (i.e. folding) are removed using the<br />
spectral analysis technique described by Bergbauer and Pollard (2003). Through this<br />
technique, the data are transformed from the spatial to the frequency domain and<br />
decomposed into a series <strong>of</strong> trigonometric functions <strong>of</strong> varying amplitude, wavelength,<br />
and phase (Davis, 1986; Bracewell, 2000). We then specify a maximum frequency<br />
threshold so that any data <strong>of</strong> higher frequency (shorter wavelength) than this threshold<br />
value are discarded. This spectral analysis technique provides the opportunity to<br />
control the wavelength content <strong>of</strong> the dataset and focus on the scale <strong>of</strong> folding that is<br />
<strong>of</strong> interest (e.g. Stewart and Wynn, 2000).<br />
147
Curvature calculation<br />
The curvature calculation in this study is derived from concepts and equations <strong>of</strong><br />
differential geometry presented in Bergbauer and Pollard (2003). The shape <strong>of</strong> non-<br />
planar surfaces can be completely described using the First and Second Fundamental<br />
Forms (Struik, 1961). These quantities relate to the arc length in various directions<br />
through a point on a surface and the shape <strong>of</strong> the surface near that point (Bergbauer<br />
and Pollard, 2003; Pollard and Fletcher, 2005). The ratio <strong>of</strong> the Second to the First<br />
Fundamental Form, both <strong>of</strong> which are invariants, defines the shape <strong>of</strong> the surface, also<br />
referred to as the normal curvature (Struik, 1961). Normal curvature at a point varies<br />
with orientation and the extreme values are termed the principal curvatures, κ1 and κ2.<br />
Respectively, these are the maximum and minimum curvature values and they occur<br />
along orthogonal curves in the surface.<br />
Fracture data collection<br />
Fracture orientation data were collected across each <strong>of</strong> the selected pavements.<br />
Mode <strong>of</strong> deformation (opening or shearing), evidence for reactivation, and spacing<br />
also were recorded. Intensity measurements were obtained perpendicular to the strike<br />
<strong>of</strong> the fracture set under consideration and parallel to bedding. Bed thicknesses were<br />
recorded at each site.<br />
Fracture data analysis<br />
Fisher analysis is used to determine the dispersion in orientation <strong>of</strong> fractures<br />
within a given set. This method is based on the assumption <strong>of</strong> circular symmetry<br />
around a point maximum (Fisher, 1953) and has been described by Ramsay (1967),<br />
Cheeney (1983), and Fisher et al. (1987). Each fracture measurement is first converted<br />
into a direction vector (i.e. pole to the plane). The maximum direction, or mean pole,<br />
<strong>of</strong> the fracture set is calculated as the sum <strong>of</strong> all direction vectors. The magnitude <strong>of</strong><br />
the resultant vector, R, is a measure <strong>of</strong> the dispersion <strong>of</strong> the data. In an ideal case,<br />
where all measurements are exactly the same, R is equal to N, the number <strong>of</strong><br />
measurements. Increasing discrepancy between R and N indicates increasing<br />
148
dispersion <strong>of</strong> measurements and greater error in calculating the maximum. The error in<br />
the maximum can be quantified in three additional ways: precision, k, is defined as:<br />
spherical variance, v, is defined as:<br />
and a confidence cone, which can be calculated as :<br />
k = (N-1)/(N-R); (1)<br />
v = (N-R)/N; (2)<br />
cos (αcl) = 1 – (N-R)*(a-1)/R (3)<br />
where cl is the confidence level, a = P 1/(1-N) and P = (1 – cl). Commonly, a 95%<br />
confidence cone is reported, and P for this case is equal to 0.05. A collection <strong>of</strong><br />
fracture measurements approaches the ideal cluster where all direction vectors equal<br />
the mean direction vector when R approaches N, k approaches infinity, v approaches<br />
0, and α95 approaches 0°.<br />
Field data<br />
GPS data<br />
Three-dimensional spatial data were collected across six pavements (Fig. 4.3).<br />
These pavements were chosen for their locations on the fold in various structural<br />
positions (backlimb, hinge, forelimb) and for their noticeable shape differences.<br />
Pavement GPS5 is in the backlimb; GPS6 and GPS7 are in the hinge; GPS14, GPS15,<br />
and GPS16 are in the forelimb. Figure 4.3 shows the location <strong>of</strong> the pavements, the<br />
collected data points, and preliminary meshes through these points that are color coded<br />
for elevation. These help to visualize the dimensions and shape <strong>of</strong> the pavements. The<br />
forelimb pavements are the most limited in area, due to erosion <strong>of</strong> the steeply dipping<br />
strata. The smallest pavement characterized is GPS15 which has dimensions <strong>of</strong><br />
approximately six meters long by a few meters wide. The largest pavement is GPS6<br />
which has dimensions <strong>of</strong> approximately 15 meters by 10 meters.<br />
For data collected with the two receiver setup and the moving rover (GPS6 and<br />
GPS7), precision is approximately 10 cm horizontally and 5 cm vertically. Data for<br />
GPS5, GPS14, GPS15, and GPS16 were collected with the laser range finder, which<br />
adds an additional uncertainty on the order <strong>of</strong> +/- 0.1 m (LaserCraft TM specification<br />
sheet).<br />
149
Elevation (meters)<br />
1274<br />
1272<br />
1270<br />
1268<br />
1266<br />
10<br />
Y (meters)<br />
5<br />
Elevation (meters)<br />
0<br />
1310<br />
1305<br />
1300<br />
1295<br />
10<br />
Y (meters)<br />
5<br />
GPS5<br />
0<br />
GPS6<br />
0<br />
5<br />
10<br />
X (meters)<br />
1272<br />
1271<br />
1270<br />
1269<br />
−4 0 2 4<br />
X (meters)<br />
6 8<br />
1304<br />
1302<br />
1300<br />
1298<br />
Elevation (meters)<br />
15<br />
1320<br />
1315<br />
1310<br />
0<br />
5<br />
Y (meters)<br />
10<br />
Elevation (meters)<br />
GPS7<br />
15<br />
1324<br />
1322<br />
1320<br />
1318<br />
1316<br />
0<br />
20<br />
Y (meters)<br />
GPS14<br />
5<br />
15<br />
10<br />
10<br />
1318<br />
1316<br />
1314<br />
1312<br />
1310<br />
5<br />
X (meters)<br />
0<br />
2<br />
4<br />
6<br />
8<br />
10<br />
1324<br />
12<br />
1322<br />
1320<br />
1318<br />
1316<br />
1314<br />
Figure 4.3. Digital Orthophoto Quarter Quadrangles (DOQQs) <strong>of</strong> the northwestern<br />
part <strong>of</strong> Sheep Mountain anticline showing the locations <strong>of</strong> pavements across which<br />
GPS data were collected and meshes generated from the post-processed data.<br />
Meshes are color coded for elevation and provide information on the aerial extent <strong>of</strong><br />
the mapped pavements. DOQQs downloaded from http://wgiac.state.wy.us/.<br />
0<br />
150<br />
X (meters)<br />
Elevation (meters)<br />
1324<br />
1322<br />
1320<br />
1318<br />
0<br />
1<br />
Y (meters)<br />
2<br />
3<br />
4<br />
GPS15<br />
5<br />
6<br />
4<br />
2<br />
X (meters)<br />
Elevation (meters)<br />
1260<br />
1250<br />
1240<br />
0<br />
1 km<br />
1322<br />
1321<br />
1320<br />
1319<br />
1318<br />
1317<br />
0<br />
2<br />
Y (meters)<br />
4<br />
6<br />
GPS16<br />
8<br />
10<br />
12<br />
6<br />
4<br />
X (meters)<br />
2<br />
0<br />
1256<br />
1254<br />
1252<br />
1250<br />
1248<br />
1246<br />
1244
Fracture data<br />
Fracture sets with average strikes <strong>of</strong>: 020°, 045°, 065°, 080°, 135°, and 170° are<br />
present within the collected data at the surveyed sites. Many <strong>of</strong> these sets have been<br />
documented in previous Sheep Mountain fracture studies (Bellahsen et al., 2006a,<br />
2006b; Fiore et al., in prep), with their relative times <strong>of</strong> formation determined based on<br />
abutting relationships in the backlimb. The 045° is the hinge perpendicular set II <strong>of</strong><br />
Bellahsen et al (2006a, 2006b), which initiated during early folding in response to fold<br />
perpendicular Laramide contraction. The 135° set is the hinge parallel set III <strong>of</strong><br />
Bellahsen et al. (2006a) that could have formed at any time during folding. Fractures<br />
striking 135° are localized in the hinge, but also are found in specific locations in the<br />
backlimb and are hypothesized to be related to areas where layer curvature exists. The<br />
080° set is set V <strong>of</strong> Fiore et al. (in prep) that formed in response to a rotation in the<br />
local most tensile stress direction due to either a change in the regional contraction<br />
direction or the influence <strong>of</strong> a secondary fault developing beneath the backlimb and<br />
forming the thumb fold (Fig. 4.1). The 020° fractures comprise a minor set<br />
documented by Bellahsen et al. (2006a). Based on abutting relationships, 020°<br />
fractures are younger than 045° and 080° fractures and older than at least some <strong>of</strong> the<br />
135° fractures, although most 020° and 135° intersections are cross-cutting. The 170°<br />
fractures were identified by Bellahsen et al. (2006a) as a minor set. Although they are<br />
formed primarily in the forelimb, these 170° fractures also are found at the backlimb<br />
and hinge sites included in this study. Abutting relationships indicate that the 170° set<br />
is younger than the 080° set. Based on their preferential formation in specific<br />
structural locations (forelimb, nose), we suggest that this 170° fracture set is folding<br />
related.<br />
By assuming that fractures striking 045° and 170° are fold related and<br />
determining through the examination <strong>of</strong> abutting relationships that these two fracture<br />
sets are the oldest and youngest sets present at the surveyed pavements, we have made<br />
the case that all <strong>of</strong> the fracture sets included in this study formed during folding. The<br />
majority <strong>of</strong> fracture timing relationships were worked out in the backlimb, where<br />
abutments are consistent. In other structural positions, however, timing relationships<br />
are more uncertain. Opposite abutments exist within the pavements in the hinge and<br />
151
measured<br />
measured<br />
measured<br />
GPS5<br />
N = 94<br />
GPS6<br />
N = 55<br />
GPS7<br />
N = 45<br />
unfolded<br />
unfolded<br />
unfolded<br />
Fracture Sets<br />
020 0<br />
045 0<br />
065 0<br />
080 0<br />
135 0<br />
180 0<br />
bedding<br />
measured<br />
measured<br />
GPS14<br />
N = 75<br />
GPS15<br />
N = 39<br />
GPS16<br />
N = 59<br />
unfolded<br />
unfolded<br />
measured unfolded<br />
Figure 4.4. Fracture orientation data collected at each pavement. Lower hemisphere<br />
stereonets show the orientations <strong>of</strong> poles to fractures as observed in the field<br />
(measured) and relative to horizontal bedding (unfolded). Specific fracture sets were<br />
defined in the field based on orientation, mode <strong>of</strong> deformation, and abutting relations.<br />
The average strike direction <strong>of</strong> each fracture set is listed in the figure legend, next to<br />
the corresponding symbol that has been used to plot the poles for that set. Contours<br />
are plotted at an interval <strong>of</strong> two and highlight the clustering <strong>of</strong> poles.<br />
152
forelimb. We suggest that rather than the formation <strong>of</strong> each fracture set being confined<br />
to specific periods <strong>of</strong> folding, infilling <strong>of</strong> previously formed fracture sets (e.g.<br />
Bergbauer and Pollard, 2004) occurred throughout folding in the hinge and forelimb as<br />
a result <strong>of</strong> anisotropy within the rock generated by the presence <strong>of</strong> previously formed<br />
fractures.<br />
For this study, the fracture characteristics we focus on are orientation relative to<br />
horizontal bedding and intensity. All <strong>of</strong> the fracture sets included in this study dip<br />
approximately perpendicular to bedding, suggesting that all fracture sets initiated prior<br />
to significant rotation <strong>of</strong> forelimb beds. Unfolding observed fracture measurements<br />
clarifies which fracture sets in the steeply dipping forelimb are equivalent to sets<br />
observed in the more shallowly dipping backlimb and hinge. Observing the<br />
orientations <strong>of</strong> fractures relative to horizontal bedding thus provides the opportunity to<br />
study the differences in characteristics <strong>of</strong> sets developed in different structural<br />
positions. In the essentially uniformly dipping beds <strong>of</strong> the forelimb and the backlimb,<br />
the unfolding process does not affect the statistics <strong>of</strong> the fracture orientations, as all<br />
fractures are rotated the same amount. In the hinge, unfolding the hinge parallel<br />
curvature related fracture set (135°) tightens the clustering. Curvature related fractures<br />
form parallel to the fold hinge and perpendicular to bedding. As mapped in the field,<br />
set 135° fractures thus have a larger dispersion in orientation than as considered<br />
relative to horizontal bedding. We tested the 080° set that formed obliquely to the<br />
hinge at GPS7 and found that the spherical variance <strong>of</strong> the set as measured in the field<br />
(0.094) is slightly more than as unfolded (0.091). We suggest that this small difference<br />
(0.003) is due to the fact that bedding dip at GPS7 varies by 5° at most. The surveyed<br />
pavements are not expansive enough to generate large bedding dip related apparent<br />
orientation dispersion; the calculated dispersion is mostly (97% in the tested case) real.<br />
Nonetheless, we unfold fracture measurements before performing Fisher analysis.<br />
Stereonets in figure 4.4 show the distribution <strong>of</strong> poles to fractures for each <strong>of</strong> the<br />
study sites. The data are presented both as observed and unrotated so that bedding is<br />
horizontal. Symbols represent fractures <strong>of</strong> specific sets. Contours within the stereonets<br />
indicate where clustering <strong>of</strong> poles occurs. Rather than being interpreted from<br />
stereonets, distinct fracture sets were noted in the field (Fig. 4.5). Thus, despite a<br />
153
(a) GPS5 (b) GPS6<br />
NW SE<br />
(c) GPS7<br />
N<br />
149 o<br />
(e)GPS15<br />
067 o<br />
052 o<br />
087 o<br />
159 o<br />
140 o<br />
089 o<br />
026 o<br />
072 o<br />
1 m<br />
1 m<br />
10 cm<br />
S<br />
SE<br />
070 o<br />
(d) GPS14<br />
SE<br />
010 o<br />
(f) GPS16<br />
SE NW SE<br />
NW<br />
0.5 m<br />
Figure 4.5. Fracture sets present at pavements: (a) GPS5; (b) GPS6, sets with<br />
average strikes <strong>of</strong> 040 o and 174 o also are present at this site; (c) GPS7, sets with<br />
average strikes <strong>of</strong> 023 o and 172 o also are present at this site; (d) GPS14; (e) GPS15,<br />
a minor fracture set striking 180 o also is present at this site; (f) GPS16. Clusters in<br />
figure 4.4 were broken apart based on these field observations. (b) and (c) are cross<br />
sectional views <strong>of</strong> fractures in relatively flat bedding planes. (a), (d), (e), and (f) are<br />
photographs <strong>of</strong> bedding surfaces.<br />
154<br />
060 o<br />
127 o<br />
150 o<br />
062 o<br />
179 o<br />
166 o<br />
10 cm<br />
081 o<br />
0.5 m<br />
10 cm<br />
NW<br />
NW
GPS 5<br />
GPS 6<br />
GPS 7<br />
GPS 8<br />
Mean Plane n R v k 95%<br />
026°/87° 7 6.85 0.141 38.86 9.8°<br />
052°/89° 12 11.83 0.076 65.58 22.8°<br />
087°/83° 35 32.56 0.042 13.93 6.7°<br />
140°/83° 10 9.88 0.095 63.15 6.1°<br />
159°/ 83° 19 18.75 0.042 72.87 4.0°<br />
040°/89° 10 7.95 0.117 4.39 26.1°<br />
070°/83° 15 9.05 0.354 2.35 32.5°<br />
150°/84° 10 5.22 0.348 2.11 47.9°<br />
174°/ 84° 10 9.78 0.087 41.02 7.6°<br />
023°/ 79° 8 5.94 0.152 3.40 35.5°<br />
072°/86° 13 10.91 0.091 5.73 19.0°<br />
149°/75° 7 2.96 0.507 1.48 83.4°<br />
172°/83° 8 3.99 0.431 1.74 62.5°<br />
029°/ 81° 10 9.85 0.094 58.71 6.4°<br />
093°/87° 52 47.17 0.075 10.56 6.4°<br />
129°/82° 40 39.34 0.009 59.23 3.0°<br />
178°/86° 38 37.05 0.001 38.75 3.8°<br />
GPS 14<br />
010°/ 88° 14 13.87 0.067 102.2 4.0°<br />
062°/88° 12 11.96 0.087 268.7 2.7°<br />
081°/89° 17 16.82 0.051 89.09 3.8°<br />
166°/87° 29 28.66 0.023 81.45 3.0°<br />
GPS 15<br />
067°/83° 15 17.64 0.038 47.68 5.1°<br />
089°/86° 18 13.63 0.049 35.59 6.8°<br />
GPS 16<br />
060°/87° 41 32.81 0.180 4.89 11.3°<br />
179°/89° 12 11.73 0.066 40.03 6.9°<br />
Table 4.1. Fisher statistics as calculated for each <strong>of</strong> the fracture sets measured at<br />
individual pavements. The mean fracture plane, number <strong>of</strong> measurements (n),<br />
magnitude <strong>of</strong> the resultant vector (R), spherical variance (v), precision (k), and 95%<br />
confidence cone (95%) are tabulated.<br />
155
cluster on a stereonet with one maximum that seems to represent a single fracture set,<br />
in some cases two sets within the cluster have been recorded (e.g. sets 140° and 159°<br />
at GPS5, Fig. 4.4a, Fig. 4.5a).<br />
Results <strong>of</strong> a Fisher analysis for each <strong>of</strong> the fracture sets are listed in Table 4.1.<br />
We consider values <strong>of</strong> spherical variance to compare the dispersion <strong>of</strong> specific sets in<br />
different structural locations. The 020° set exists at one site in each position: GPS5 in<br />
the backlimb, GPS7 in the hinge, and GPS14 in the forelimb. Spherical variance is<br />
lowest at GPS14 and highest at GPS7. The 045° set has a lower spherical variance at<br />
GPS5 in the backlimb than at GPS6 in the hinge. The 080° set has comparable<br />
spherical variance values at backlimb and forelimb sites GPS5, GPS14, and GPS15; it<br />
has higher values at hinge sites GPS6 and GPS7. Although no fractures <strong>of</strong> the set with<br />
an average strike <strong>of</strong> 135° have been recorded in forelimb sites, the spherical variance<br />
<strong>of</strong> this set at backlimb site GPS5 is much less than that at either hinge site. The<br />
spherical variance for the 170° set at GPS5 is intermediate to the values at forelimb<br />
sites GPS14 and GPS16. All three <strong>of</strong> these values are less than the spherical variance<br />
<strong>of</strong> the 170° set at hinge sites GPS6 and GPS7.<br />
Fracture intensities for the six distinct fracture sets are represented by bar graphs<br />
in figure 4.6. Average thickness <strong>of</strong> the bedding at each pavement is also documented<br />
in figure 4.6. We do not normalize the intensities to bed thickness because all<br />
thicknesses are similar. Values plotted are normalized to ten meters so that we may<br />
compare measurements made at all locations. Highest intensities occur in the<br />
Phosphoria pavements that are in the hinge: GPS6 and GPS7. Lowest intensities occur<br />
in the backlimb Phosphoria pavement GPS5. Forelimb intensities are intermediary.<br />
Intensity <strong>of</strong> the fracture set with an average strike <strong>of</strong> 080° is approximately<br />
consistent between the hinge and the forelimb, with values at GPS6 and GPS15<br />
similar and values at GPS7 and GPS14 similar. The intensity <strong>of</strong> the same 080° set at<br />
site GPS5 in the backlimb is much lower. In the backlimb at GPS5 and the forelimb at<br />
GPS16, the intensities <strong>of</strong> the 135° set are similar. The 135° set is more intense at both<br />
hinge locations. Where the 170° set exists in the hinge at GPS7, it is three times more<br />
intense than at GPS14. The other two forelimb sites and the backlimb site GPS5 have<br />
intensities <strong>of</strong> the 170° set that are less than that at GPS14. In the backlimb, no fracture<br />
156
N / 10 m<br />
20<br />
0<br />
GPS5<br />
t = 0.35 m<br />
159° 140° 087° 052° 026°<br />
N / 10 m<br />
100<br />
80<br />
60<br />
40<br />
20<br />
0<br />
GPS6<br />
t = 0.40 m<br />
150°<br />
070°<br />
N / 10 m<br />
100<br />
80<br />
60<br />
40<br />
20<br />
0<br />
GPS7<br />
t = 0.40 m<br />
172° 149° 072°<br />
N / 10 m<br />
100<br />
80<br />
60<br />
40<br />
20<br />
0<br />
GPS14<br />
t = 0.30 m<br />
166° 081° 062° 010°<br />
GPS15<br />
t = 0.45 m<br />
100<br />
N / 10 m<br />
80<br />
60<br />
40<br />
20<br />
0<br />
River cut<br />
067° 089°<br />
N / 10 m<br />
020 0 080 0<br />
045 0<br />
065 0<br />
60<br />
40<br />
20<br />
0<br />
GPS16<br />
t = 0.40 m<br />
179° 127° 060°<br />
Figure 4.6. Three-dimensional sketch <strong>of</strong> Sheep Mountain with bar graphs showing<br />
fracture intensities <strong>of</strong> the major fracture sets at each study site. Intensities have been<br />
normalized to show the number <strong>of</strong> fractures per ten meters. To facilitate comparison<br />
<strong>of</strong> fracture intensities among sites, symbols are plotted beneath the bar graph to<br />
indicate which sets have been determined to be equivalent (based on orientation,<br />
mode <strong>of</strong> deformation, abutting relations) at different sites. An average bed thickness<br />
for each pavement is reported.<br />
157<br />
135 0<br />
180 0
set has an intensity more than two fractures per meter. In the hinge, all fracture sets<br />
have intensities greater than six fractures per meter. In the forelimb, the intensity <strong>of</strong><br />
fracturing varies from set to set, and even within the same set. The 065° set, for<br />
instance, varies from less than one fracture per meter at GPS14 to approximately two<br />
fractures per meter at GPS 15 to approximately six fractures per meter at GPS16. At<br />
each <strong>of</strong> the three forelimb sites, a different fracture set is dominant.<br />
Curvature analysis<br />
We begin the curvature analysis by removing an average plane through the data.<br />
This process effectively removes the dip <strong>of</strong> the dataset, allowing one to better compare<br />
the relative elevations <strong>of</strong> the collected data points (Fig. 4.7). The relative elevations<br />
color coded in figures 4.7a, 4.7d, 4.7e, and 4.7f are very noisy, indicating that there are<br />
no consistent elevation trends within the data. Conversely, red swaths present in<br />
figures 4.7b and 4.7c represent maxima and suggests the presence <strong>of</strong> anticlinal<br />
curvatures. Application <strong>of</strong> curvature analysis to the datasets in their current state<br />
would highlight the small scale undulations visible in figure 4.7. These undulations are<br />
most likely a result <strong>of</strong> slight spatial differences in erosion or the error included in the<br />
data collection method and do not reflect the natural shape <strong>of</strong> the bedding surface. To<br />
remove these artifacts from the datasets and thus capture folding on the appropriate<br />
scale, we followed the spectral analysis technique <strong>of</strong> Bergbauer and Pollard (2003).<br />
Application <strong>of</strong> a smoothing factor that removes oscillations <strong>of</strong> wavelength 13 meters<br />
and below discards the high frequency content <strong>of</strong> the datasets. The smoothed surfaces<br />
are shown in figure 4.8. The lack <strong>of</strong> contours in figures 4.8a, 4.8d, 4.8e, and 4.8f<br />
indicates that the surface elevations vary by less than 0.1 meters and are thus<br />
approximately planar.<br />
The maximum and minimum principal curvatures, κ and κ2, were calculated for<br />
the area surrounding each grid node <strong>of</strong> the smoothed surfaces. The extreme values <strong>of</strong><br />
κ and κ2 for each surface are listed in table 4.2, which indicates that GPS5, GPS14,<br />
GPS15, and GPS16 have very small curvatures, with extreme values ranging from<br />
0.00034 m -1 to 0.001 m -1 . The spectral analysis filtering algorithm removed all <strong>of</strong> the<br />
noise from the original surfaces (Fig. 4.7), producing smoothed surfaces (Fig. 4.8)<br />
158
κ1<br />
κ2<br />
GPS5 0.0086 -0.0082<br />
GPS6 0.0399 -0.0442<br />
GPS7 0.0466 -0.0340<br />
GPS8 0.0376 -0.0344<br />
GPS14 0.0010 -0.0010<br />
GPS15 0.00041 -0.00034<br />
GPS16 0.0034 -0.0038<br />
Table 4.2. Extreme values <strong>of</strong> the maximum principal normal curvature (κ1) and<br />
minimum principal normal curvature (κ2) calculated across each pavement.<br />
159
meters<br />
meters<br />
meters<br />
meters<br />
meters<br />
(a) GPS5 (b) GPS6<br />
5<br />
4<br />
3<br />
2<br />
1<br />
0<br />
0 2 4 6 8 10<br />
meters<br />
(c) GPS7<br />
6<br />
5<br />
4<br />
3<br />
2<br />
1<br />
0<br />
0 5 10<br />
meters<br />
15 20<br />
(d) GPS14<br />
1.5<br />
1<br />
0.5<br />
0<br />
0<br />
(e) GPS15<br />
2.5<br />
2<br />
1.5<br />
1<br />
0.5<br />
12<br />
25<br />
relative elevation (m)<br />
0.8<br />
0.4<br />
0<br />
−0.4<br />
−0.8<br />
relative elevation (m)<br />
meters<br />
14<br />
12<br />
10<br />
8<br />
6<br />
4<br />
2<br />
0<br />
0 2 4 6 8<br />
meters<br />
1 2 3 4 5 6 7 8 9 10 11<br />
meters<br />
0<br />
0 1 2 3 4 5<br />
meters<br />
(f) GPS16<br />
4<br />
3<br />
2<br />
1<br />
0<br />
0 2 4 6<br />
meters<br />
8 10<br />
6<br />
0.4<br />
0.2<br />
0<br />
−0.2<br />
−0.4<br />
−0.6<br />
Figure 4.7. Relative elevations across surfaces constructed from unfiltered GPS data<br />
at pavements (a) GPS5; (b) GPS6; (c) GPS7; (d) GPS14; (e) GPS15; (f) GPS16.<br />
relative<br />
elevation (m)<br />
0.2<br />
0.1<br />
0<br />
-0.1<br />
-0.2<br />
160<br />
12<br />
0.6<br />
0.4<br />
0.2<br />
0<br />
-0.2<br />
-0.4<br />
relative<br />
elevation (m)<br />
0. 5<br />
0<br />
−0. 5<br />
relative<br />
elevation (m)<br />
10<br />
0.3<br />
0.2<br />
0.1<br />
0<br />
−0.1<br />
−0.2<br />
−0.3<br />
−0.4<br />
−0.5<br />
relative elevation (m)
meters<br />
meters<br />
meters<br />
meters<br />
meters<br />
(a) GPS5 (b) GPS6<br />
5<br />
4<br />
3<br />
2<br />
1<br />
0<br />
0 2 4 6 8 10<br />
meters<br />
(c) GPS7<br />
6<br />
5<br />
4<br />
3<br />
2<br />
1<br />
0<br />
0 5 10<br />
meters<br />
15 20<br />
(d) GPS14<br />
1.5<br />
1<br />
0.5<br />
0<br />
0<br />
(e) GPS15<br />
2.5<br />
2<br />
1.5<br />
1<br />
0.5<br />
12<br />
meters<br />
0<br />
0 2 4 6 8<br />
meters<br />
1 2 3 4 5 6 7 8 9 10 11<br />
meters<br />
0<br />
0 1 2 3 4 5<br />
meters<br />
(f) GPS16<br />
4<br />
3<br />
2<br />
1<br />
0<br />
0 2 4 6<br />
meters<br />
8 10<br />
6<br />
Relative Elevation (m)<br />
−1 −0. 5 0 0. 5 1<br />
Figure 4.8. Smoothed relative elevations across surfaces constructed from filtered<br />
GPS data collected at pavements (a) GPS5; (b) GPS6; (c) GPS7; (d) GPS14; (e)<br />
GPS15; (f) GPS16. Contour interval is 0.1.<br />
161<br />
25<br />
14<br />
12<br />
10<br />
8<br />
6<br />
4<br />
2<br />
12<br />
10
meters<br />
meters<br />
meters<br />
(a) GPS6 - κ 1<br />
14<br />
12<br />
10<br />
8<br />
6<br />
4<br />
2<br />
0<br />
0 2 4 6 8<br />
meters<br />
(c) GPS7 - κ 1<br />
6<br />
5<br />
4<br />
3<br />
2<br />
1<br />
10<br />
meters<br />
(b) GPS6 - κ 2<br />
14<br />
12<br />
10<br />
8<br />
6<br />
4<br />
2<br />
Curvature (m -1 )<br />
0<br />
0 2 4 6 8<br />
meters<br />
0<br />
0 5 10 15 20<br />
meters<br />
(d) GPS7 - κ 2<br />
6<br />
5<br />
4<br />
3<br />
2<br />
1<br />
0<br />
0 5 10<br />
meters<br />
15 20<br />
−0.02 −0.01 0 0.01 0.02 0.03 0.04<br />
Figure 4.9. Plots <strong>of</strong> maximum (κ1) and minimum (κ2) normal curvature values across<br />
surfaces for which magnitudes are greater than a threshold value <strong>of</strong> 0.005 m-1. The<br />
corresponding directions <strong>of</strong> κ1 and κ2 are represented by black tick marks. (a) κ1<br />
values and directions across GPS6; (b) κ2 values and directions across GPS6; (c) κ1<br />
values and directions across GPS7; (d) κ2 values and directions across GPS7.<br />
162<br />
25<br />
25<br />
10
with curvatures that are negligible, <strong>of</strong> magnitude less than the value <strong>of</strong> 0.005 m that<br />
we designate as the curvature threshold. When we apply the threshold value, GPS6<br />
and GPS7 are the only two pavements that have significant curvatures. The values and<br />
directions <strong>of</strong> κ and κ across these surfaces are plotted in figure 4.9 with a normalized<br />
colorbar so that magnitudes <strong>of</strong> curvature can be compared between the datasets.<br />
Discussion<br />
2<br />
Curvature analyses<br />
In the maximum and minimum principal curvature plots (Fig. 4.9), warm colors<br />
represent anticlinal folding and cool colors represent synclinal folding. GPS6 and<br />
GPS7 are very near to the hingeline <strong>of</strong> the fold (Fig. 4.4). To the naked eye, these<br />
surfaces appear to have distinct curvatures (Fig. 4.10a). Analysis confirms the<br />
existence <strong>of</strong> this curvature (Fig. 4.9). As expected, GPS7, which is closer to the<br />
hingeline, has higher magnitudes <strong>of</strong> curvature than GPS6. The curvature analysis for<br />
GPS6 highlights that the surface has two directions <strong>of</strong> curvature, one parallel to the<br />
hinge <strong>of</strong> the fold and one perpendicular to the hinge <strong>of</strong> the fold. This phenomenon is<br />
noticeable in field photos as well (Fig. 4.10a). GPS6 is located in the nose <strong>of</strong> the fold,<br />
where bedding strike rotates, and so the existence <strong>of</strong> a hinge parallel component <strong>of</strong><br />
curvature at this location is not surprising. Localized flexures <strong>of</strong> bedding surfaces also<br />
are found in the nose. The curvature analysis for GPS7 reflects one instance <strong>of</strong> this<br />
localized flexure. In figure 4.9c, the left edge <strong>of</strong> the data set represents the area closest<br />
to the hinge. A traverse from left to right across this plot approximates the dip<br />
azimuth. In the curvature plot, the existence <strong>of</strong> anticlinal curvature across the majority<br />
<strong>of</strong> the pavement is apparent, but an area <strong>of</strong> synclinal curvature exists at extreme down<br />
dip locations. This synclinal curvature also is noticeable in field photos (Fig. 4.10b).<br />
Relating curvature analysis to fracture measurements<br />
The most noticeable correlation between curvature and fracturing relates to<br />
fracture orientation. In figure 4.12, we plot spherical variance for the fracture sets<br />
mapped in this study. Large spherical variances occur only at sites GPS6 and GPS7,<br />
the two pavements <strong>of</strong> notable curvature. Thus, in pavements that have higher<br />
163<br />
-1
(a)<br />
(b)<br />
synclinal area<br />
anticlinal area<br />
hinge<br />
parallel<br />
folding<br />
hinge perpendicular<br />
folding<br />
Figure 4.10. Photographs <strong>of</strong> the pavements at (a) GPS6 and (b) GPS7. The black<br />
line outlines the approximate area <strong>of</strong> surveying. In (a), two directions <strong>of</strong> curvature are<br />
apparent, one parallel to the hinge and one perpendicular to the hinge. In (b), both<br />
anticlinal and synclinal curvature are apparent in a direction parallel to the hinge. In<br />
the photo, shading highlights the faces <strong>of</strong> fractures striking ~080 o .<br />
164<br />
1 m<br />
1 m
Spherical Variance<br />
0.5 020 o set<br />
0.25<br />
0<br />
0.5 045 o set<br />
0.25<br />
0<br />
0.5 065 o set<br />
0.25<br />
0<br />
0.5 080 o set<br />
0.25<br />
0<br />
0.5 135 o set<br />
0.25<br />
0<br />
0.5 170 o set<br />
0.25<br />
0<br />
GPS15 GPS14 GPS16 GPS5 GPS6 GPS7<br />
Figure 4.11. Spherical variance for the fracture sets mapped at study sites.<br />
Pavements are plotted on the x-axis in the order <strong>of</strong> increasing curvature magnitudes.<br />
165
curvature values, the clustering <strong>of</strong> distinct fracture sets is less pronounced than in<br />
pavements <strong>of</strong> lower curvature values.<br />
We look at minimum normal curvature (κ2) trajectories to determine if fracturing<br />
was enhanced by folding in the direction perpendicular to the maximum curvature. At<br />
pavement GPS6, κ1 is parallel to the hinge. Thus, curvature related fractures would be<br />
expected to form in the dip direction (Fig. 4.9b), which ranges from 065 o to 080 o . Both<br />
the intensity (Fig. 4.6) and the spherical variance (Table 4.1) <strong>of</strong> the fracture set <strong>of</strong><br />
average strike 070 o are large. We pointed out previously, however, that two directions<br />
<strong>of</strong> curvature are present at this pavement (Fig. 4.10a). Fracturing may thus be expected<br />
in the direction perpendicular to this set, formed at a strike <strong>of</strong> ~ 160 o . The spherical<br />
variance and intensities <strong>of</strong> a set striking 150 o at GPS6 are also large. At GPS7, κ2 is<br />
parallel to the hinge (Fig. 4.9d). GPS7 is at a location in the hinge where the plunging<br />
northwestern nose controls the local strike direction, which varies between 077 o and<br />
100 o . Curvature related fractures would thus be expected to form parallel to this<br />
direction. Although the spherical variance and intensity <strong>of</strong> the 072 o set is great<br />
compared to sets at pavements GPS5, GPS14, GPS15, and GPS16, the values <strong>of</strong><br />
spherical variance for the 149 o and 172 o sets at GPS7 are greater. The intensity <strong>of</strong> the<br />
149 o set is slightly less than that <strong>of</strong> the 072 o set and the 172 o set is much more intense.<br />
Fracture statistics at GPS6 and GPS7 suggest that, if fracturing in the hinge is due<br />
primarily to curvature, sets in addition to the fracture set that forms in the minimum<br />
curvature direction due to outer arc extension <strong>of</strong> a flexed bedding surface<br />
(Timoshenko, 1934) are affected by folding.<br />
Fracture intensities may correlate loosely with curvature. The highest intensity <strong>of</strong><br />
fracturing and the highest values <strong>of</strong> curvature are found at GPS6 and GPS7 from the<br />
hinge (Fig. 4.6). Lowest intensities are found at GPS5 in the backlimb. Where the<br />
lowest curvature magnitudes exist at GPS14, GPS15, and GPS16, however, high<br />
intensity <strong>of</strong> fracturing has been recorded. Fracturing in the forelimb is not related to<br />
present day curvature. It is most likely not related to paleo-curvatures (i.e. migration<br />
<strong>of</strong> forelimb beds through the hinge) either, as characteristics <strong>of</strong> fracturing in the hinge<br />
and forelimb are very different. Spherical divergences <strong>of</strong> all fracture sets in the<br />
forelimb are small (Table 4.1), and the hinge parallel fracture set striking 135 o is<br />
166
sparse; whereas in the hinge, large spherical divergences are found and the 135 o<br />
fracture set is intensely formed. We believe the fractures in the forelimb formed due to<br />
some mechanism other than bedding flexure. Noting that the fracture sets developed in<br />
the forelimb, as well as the most intensely formed set, vary from site to site, we<br />
suggest that fracturing has been affected by some local mechanism <strong>of</strong> deformation.<br />
The correlation between curvature and intensity <strong>of</strong> fracturing is not necessarily direct.<br />
Conclusions<br />
GPS collection and post-processing methods have allowed us to acquire very<br />
precise three-dimensional surface data <strong>of</strong> pavements within the Phosphoria Formation<br />
at Sheep Mountain. Curvature analyses <strong>of</strong>, and fracture measurements across, these<br />
surfaces indicate that greater curvature correlates with greater variance in fracture<br />
orientation. Greater fracture intensities may loosely correlate with curvature, however<br />
structural position <strong>of</strong> the fold must be taken into account.<br />
Acknowledgements<br />
This project is funded by the <strong>Stanford</strong> Rock Fracture Project and the National<br />
Science Foundation Collaboration in Mathematical Geosciences Program Grant No.<br />
EAR-04177521. We thank Ashley Griffith, Ole Kaven, Ian Mynatt, and Chris Wilson<br />
for help in collecting field data. Trevor Hebert from Jasper Ridge Biological Preserve<br />
provided crucial GPS support.<br />
References<br />
Bellahsen, N., P. Fiore, and D. D. Pollard, 2006a, The role <strong>of</strong> fractures in the structural<br />
interpretation <strong>of</strong> Sheep Mountain anticline, Wyoming: Journal <strong>of</strong> Structural<br />
Geology, v. 28, p. 850-867.<br />
Bellahsen, N., P. E. Fiore, and D. D. Pollard, 2006b, From spatial variation <strong>of</strong> fracture<br />
patterns to fold kinematics: A geomechanical approach: Geophysical Research<br />
Letters, v. 33, doi:10.1029/2005GL024189.<br />
Bergbauer, S., and D. D. Pollard, 2003, How to calculate curvatures <strong>of</strong> geological<br />
surfaces: Journal <strong>of</strong> Structural Geology, v. 25, p. 277-289.<br />
167
Bergbauer, S., and D. D. Pollard, 2004, A new conceptual fold-fracture model<br />
including prefolding joints, based on the Emigrant Gap anticline, WY:<br />
Geological Society <strong>of</strong> America Bulletin, v. 116, p. 294-307.<br />
Bracewell, R. N., 2000, The Fourier transform and its applications: Boston, McGraw-<br />
Hill, 616 p.<br />
Cheeney, R. F., 1983, Statistical methods in geology: London, George Allen &<br />
Unwin, 169 p.<br />
Cooper, M., 1992, The analysis <strong>of</strong> fracture systems in subsurface thrust structures<br />
from the Foothills <strong>of</strong> the Canadian Rockies: in McClay, K.R., ed., Thrust<br />
Tectonics: Chapman and Hall, London, p. 391-405.<br />
Davis, J. C., 1986, Statistics and data analysis in geology: New York, Wiley, 646 p.<br />
Ekman, M., 1988, Gaussian curvature <strong>of</strong> postglacial rebound and the discovery <strong>of</strong><br />
caves created by minor earthquakes in Fennoscandia: Geophysica, v. 24, p. 47-<br />
56.<br />
Fiore, P. E., D. D. Pollard, B. R. Currin, and D. M. Miner, in press, Mechanical and<br />
stratigraphic constraints on the evolution <strong>of</strong> faulting at Elk Hills, CA: AAPG<br />
Bulletin.<br />
Fischer, M. P., and M. S. Wilkerson, 2000, Predicting the orientation <strong>of</strong> joints from<br />
fold shape: Results <strong>of</strong> pseudo-three-dimensional modeling and curvature<br />
analysis: Geology, v. 28, no. 1, p. 15-18.<br />
Fisher, R. S., 1953, Dispersion on a sphere: Proceedings <strong>of</strong> the Royal Society <strong>of</strong><br />
London, v. A 217, p. 295-305.<br />
Fisher, N. I., T. L. Lewis, and B. J. Embleton, 1987, Statistical analysis <strong>of</strong> spherical<br />
data: Cambridge, Cambridge <strong>University</strong> Press, 329 p.<br />
Harris, J. F., G. L. Taylor, J. L. Walper, 1960, Relation <strong>of</strong> deformational fractures in<br />
sedimentary rocks to regional and local structure: American Association <strong>of</strong><br />
Petroleum Geologists Bulletin, v. 44, no. 12, p. 1853-1873.<br />
Hennier, J., 1984, Structural analysis <strong>of</strong> the Sheep Mountain anticline, Bighorn Basin,<br />
Wyoming: Unpublished MS thesis thesis, Texas A&M <strong>University</strong>, 119 p.<br />
Hennings, P. H., J. E. Olson, and L. B. Thompson, 2000, Combining outcrop data and<br />
three dimensional structural models to characterize fractured reservoirs: an<br />
example from Wyoming: American Association <strong>of</strong> Petroleum Geologists<br />
Bulletin, v. 84, p. 830-849.<br />
168
Ivanov, S. S., 1989, Effect <strong>of</strong> changes in curvature <strong>of</strong> the surface <strong>of</strong> the oceanic<br />
lithosphere on its stress state: Oceanology, v. 29, p. 465-468.<br />
Johnson, K. M., and A. A. Johnson, 2000, Localization <strong>of</strong> layer-parallel faults in San<br />
Rafael swell, Utah and other monoclinal folds: Journal <strong>of</strong> Structural Geology,<br />
v. 22, p. 1455-1468.<br />
Kaplan, E. D., 1996, Understanding GPS Principles and Applications, Artech House,<br />
Boston, 554 p.<br />
Kattenhorn, S. A., and D. D. Pollard, 2001, Integrating 3-D seismic data, field analogs,<br />
and mechanical models in the analysis <strong>of</strong> segmented normal faults in the<br />
Wytch Farm oil field, Southern England, United Kingdom: American<br />
Association <strong>of</strong> Petroleum Geologists Bulletin, v. 85, no. 7, p. 1183-1210.<br />
Ladd, R. E., 1979, The geology <strong>of</strong> Sheep Canyon Quadrangle: Wyoming. PhD<br />
dissertation. Ames, Iowa State <strong>University</strong>, 124p.<br />
Lisle, R. J., 1994, Detection <strong>of</strong> abnormal strains in structures using Gaussian curvature<br />
analysis: American Association <strong>of</strong> Petroleum Geologists Bulletin, v. 78, p.<br />
1811-1819.<br />
Lisle, R. J., and J. M. Robinson, 1995, The Mohr circle for curvature and its<br />
application to fold description: Journal <strong>of</strong> Structural Geology, v. 17, p. 739-<br />
750.<br />
Maerten, L., Gillespie, P., and D. D. Pollard, 2002, Effects <strong>of</strong> local stress perturbation<br />
on secondary fault development: Journal <strong>of</strong> Structural Geology, v. 24, p. 145-<br />
153.<br />
Mansfield, C. S., and J. A. Cartwright, 1994, High resolution fault displacement<br />
mapping from three-dimensional seismic data; evidence for dip linkage during<br />
fault growth: Journal <strong>of</strong> Structural Geology, v. 18, p. 249-263.<br />
Murray, G. H., 1968, Quantitative fracture study-Sanish Pool, McKenzie County,<br />
North Dakota: American Association <strong>of</strong> Petroleum Geologists Bulletin, v. 52,<br />
p. 57-65.<br />
Narr, W., 1991, Fracture density in the deep subsurface: Techniques with application<br />
to Point Arguello Oil Field: American Association <strong>of</strong> Petroleum Geologists<br />
Bulletin, v. 75, p. 1300-1323.<br />
Needham, D. T., G. Yielding, and B. Freeman, 1996, Analysis <strong>of</strong> fault geometry and<br />
displacement patterns: Geological Society Special Publications, v. 99, p. 189-<br />
199.<br />
169
Northard, S., D. McKenzie, J. Haines, and J. Jackson, 1996, Gaussian curvature and<br />
the relationship between the shape and deformation <strong>of</strong> the Tonga slab:<br />
Geophysical Journal International, v. 127, p. 311-327.<br />
Pollard, D. D., and R. C. Fletcher, 2005, Fundamentals <strong>of</strong> Structural Geology.<br />
Cambridge <strong>University</strong> Press, New York, 500p.<br />
Pranter, M. J., C. B. Hirstius, and D. A. Budd, 2005, Scales <strong>of</strong> lateral petrophysical<br />
heterogeneity in dolomite lith<strong>of</strong>acies as determined from outcrop analogs;<br />
implications for 3-D reservoir modeling: AAPG bulletin, v. 89, p. 645-662.<br />
Ramsay, J. G., 1967, Folding and fracturing <strong>of</strong> rocks: New York, McGraw-Hill, 568 p.<br />
Roberts, A., 2001, Curvature attributes and their application to 3D interpreted<br />
horizons: First Break, v. 19, no. 2, p. 85-100.<br />
Robinson, J. M., 1997, Prediction <strong>of</strong> fracturing in reservoirs from an analysis <strong>of</strong><br />
curvature <strong>of</strong> folded surfaces: <strong>University</strong> <strong>of</strong> Wales, 256 p.<br />
Schultz-Ela, D. D., and Y. Yeh, 1992, Predicting fracture permeability from bed<br />
curvature: 33rd U.S. Symposium on Rock Mechanics, p. 579-589.<br />
Sonnenfeld, M., 1996, An integrated sequence stratigraphic approach to reservoir<br />
characterization <strong>of</strong> the Lower Mississippian Madison Limestone, emphasizing<br />
Elk Basin Field, Bighorn Basin, Wyoming and Montana: PhD thesis, Colorado<br />
<strong>School</strong> <strong>of</strong> Mines, Golden, CO.<br />
Stearns, D. W., 1968, Certain aspects <strong>of</strong> fractures in naturally deformed rocks, in<br />
Riecker, R. E., ed., Rock mechanics seminar: Bedford, Terrestrial <strong>Sciences</strong><br />
Laboratory, p. 97-118.<br />
Stewart, S. A., and R. Podolski, 1998, Curvature analysis <strong>of</strong> gridded surfaces, in<br />
Coward, M. P., Daltaban, T. S., Johnson, H., ed., Structural Geology in<br />
Reservoir Characterization, London Geological Society, Special Publication, p.<br />
133-147.<br />
Struik, D. J., 1961, Lectures on classical differential geometry, Addison-Wesley Series<br />
in Mathematics: London, Addison-Wesley Publishing Company, Inc., 231 p.<br />
Timoshenko, S., 1934, Theory <strong>of</strong> Elasticity: New York, McGraw-Hill, 416 p.<br />
Woodring, W. P., R. B. Stewart, and R. W. Richards, 1940, Geology <strong>of</strong> the Kettleman<br />
Hills oil field, California; stratigraphy, paleontology, and structure.<br />
170
Appendix 1<br />
Tectonic Shortening Style in the Southern San Joaquin Valley,<br />
Revisited<br />
Abstract<br />
Pure shear and simple shear kinematic analyses are used to determine and assess<br />
the geological and geophysical implications <strong>of</strong> a suggested 32° − 48° Quaternary<br />
(since 0.78 Ma) rotation <strong>of</strong> the Elk Hills anticline within a zone that is 40 km wide and<br />
bounded to the west by the San Andreas Fault. Pure shear analysis reveals that a 32°<br />
rotation <strong>of</strong> the Elk Hills anticline would have involved a 45% fault perpendicular<br />
shortening <strong>of</strong> the shear zone. Simple shear analysis reveals that the Elk Hills anticline<br />
would have evolved from a domal structure. No geological evidence in support <strong>of</strong><br />
either <strong>of</strong> these phenomena exists at Elk Hills. Further calculations indicate that the<br />
suggested magnitude <strong>of</strong> rotation within a simple shear zone would account for 6.2<br />
cm/yr <strong>of</strong> relative plate motion between the Pacific and North American plates. When<br />
this value is added to the measured long term San Andreas slip rate, a relative plate<br />
motion is calculated that is, at a minimum, 70% more than the value derived from<br />
Euler pole angular velocities. In light <strong>of</strong> these inconsistencies, we find the suggested<br />
rotation <strong>of</strong> Elk Hills is unlikely.<br />
Mechanical models consider the end member cases <strong>of</strong> thrusting and strike-slip<br />
related wrenching for the development <strong>of</strong> the Elk Hills anticline. Model results<br />
highlight the inconsistency between suggested wrench evolution <strong>of</strong> Elk Hills and<br />
existing geological evidence. Forward elastic models driven by strike-slip along the<br />
San Andreas Fault alone cannot reproduce the vertical displacements mapped within<br />
seismic data and visualized within structure contour maps. Additional consideration <strong>of</strong><br />
the shapes <strong>of</strong> the faults imaged within the seismic reflection volume at Elk Hills<br />
indicates that the shortening within the southwestern San Joaquin Valley has been<br />
more consistent with thrust rather than wrench tectonics during the growth <strong>of</strong> the<br />
anticline.<br />
171
Introduction<br />
Literature published over the latter half <strong>of</strong> the past century chronicles the debate<br />
over the mechanism by which folds lining the western side <strong>of</strong> the southern San<br />
Joaquin Valley (Fig. A1.1) have developed. At the introduction <strong>of</strong> wrench tectonics in<br />
1956, the southwestern San Joaquin Valley was noted as a location in which the<br />
average orientation <strong>of</strong> anticlines is compatible with one <strong>of</strong> several orientations at<br />
which wrench related anticlines were hypothesized to develop (Moody and Hill,<br />
1956). This wrench faulting mechanism <strong>of</strong> formation for the San Joaquin Valley<br />
anticlines gained momentum in the 1970s (Wilcox et al., 1973; Harding, 1974, 1976).<br />
Seismic activity in the following decade at New Idria in 1982 (M=5.5), Coalinga in<br />
1983 (M=6.5) and Kettleman Hills North Dome in 1985 (M=6.1), led to the revelation<br />
that present day slip occurs on thrust faults that strike subparallel to the San Andreas<br />
Fault (Wentworth et al., 1984; Namson and Davis, 1988); and to the reclassification <strong>of</strong><br />
these structures as thrust related (Mount and Suppe, 1987; Zoback et al., 1987). A later<br />
study focused on Elk Hills attempted to reconcile the previous wrench and thrust<br />
interpretations for the San Joaquin Valley anticlines, suggesting that anticlines farther<br />
from the San Andreas Fault, such as Coalinga, Kettleman Hills, and Lost Hills<br />
deformed according to thrust tectonics, while those closer to the San Andreas Fault,<br />
such as Elk Hills deformed according to wrench tectonics (Nicholson, 1990). This<br />
structural study adopted the positive flower structure model described by Lowell<br />
(1972; Fig. A1.2) to explain the existence <strong>of</strong> two echelon anticlines at Elk Hills. Five<br />
years later, a study investigating the structure, stratigraphy, and tectonics <strong>of</strong> the Great<br />
Valley based on well log correlations and gravity anomalies provided further support<br />
for the thrust formation interpretation for the anticlines in the San Joaquin Valley<br />
including Elk Hills (Imperato, 1995). Additional investigation <strong>of</strong> the structures<br />
including analysis <strong>of</strong> paleomagnetic data (White, 1987) led to the suggestion that the<br />
opposing theories <strong>of</strong> wrench and thrust deformation may be compatible within the San<br />
Joaquin Valley if viewed as temporally distinct processes (Miller, 1998). The<br />
proposition resulting from this investigation was that the folds within the southwestern<br />
San Joaquin Valley formed initially with trends oblique to the San Andreas Fault and<br />
subsequently were rotated to their subparallel orientations, with deformation style<br />
172
36 0 00’<br />
Diablo Range<br />
New Idria<br />
Coalinga<br />
Coalinga<br />
120 0 00’<br />
San Andreas Fault<br />
N<br />
Kettleman Hills<br />
Temblor Range<br />
0 mile 20<br />
0 km 30<br />
120 0 00’<br />
San Joaquin<br />
Valley<br />
Lost Hills<br />
Elk Hills<br />
Buena Vista<br />
119 0 00’<br />
Taft<br />
Midway Sunset<br />
Sierra Nevada Range<br />
Bakersfield<br />
San Emigdio Mtns<br />
119 0 00’<br />
Figure A1.1. Location <strong>of</strong> the Elk Hills, Lost Hills, Kettleman Dome, Coalinga, and<br />
New Idria anticlines within the southwestern San Joaquin Valley.<br />
173<br />
36 0 00’<br />
35 0 00’
29R<br />
NWS<br />
31S<br />
Figure A1.2. Schematic model <strong>of</strong> a compressional flower structure applied to Elk<br />
Hills. Anticlines 29R, 31S, and the Northwest Stevens (NWS) are labeled in red.<br />
Modified from Lowell (1972) according to the explanation <strong>of</strong> Nicholson (1990).<br />
174
transitioning from wrench-related shearing to fault-perpendicular shortening (Miller,<br />
1998).<br />
This hypothesis introduced by Miller (1998) resulted from an attempt to<br />
reconcile: (1) the obliquity <strong>of</strong> San Joaquin Valley anticlines to the San Andreas Fault<br />
and their en echelon formation; (2) the existence <strong>of</strong> paleomagnetic data from the<br />
flanks <strong>of</strong> anticlines in the San Joaquin Valley (White, 1987) and unpublished isochore<br />
maps over Lost Hills (Julander, 1992), both <strong>of</strong> which suggest a clockwise rotation <strong>of</strong><br />
the structures; and (3) recent earthquakes suggesting present day slip in a direction<br />
perpendicular to the San Andreas Fault (Eaton et al., 1983; Wentworth et al., 1984;<br />
Namson and Davis, 1988; Ekstrom et al., 1992). Although the paleomagnetic data<br />
appear to be robust (McWilliams, 2004, pers. comm.), we are cautious in accepting<br />
these data. For non-cylindrical folds such as Elk Hills, apparent rotations are <strong>of</strong>ten<br />
introduced into paleomagnetic data because a simple bedding correction does not<br />
correctly restore the geometry (Stewart, 1995; Pueyo et al., 2003). We look to shearing<br />
calculations to determine if the suggested magnitude <strong>of</strong> rotation is consistent with<br />
existing geological and geophysical data for the San Joaquin Valley.<br />
In this paper, we first review White’s study (1987), describing the existing Elk<br />
Hills paleomagnetic data. We then introduce Miller’s shear zone hypothesis (1998) in<br />
further detail. Using kinematic equations, we quantify the amount <strong>of</strong> deformation<br />
accompanying the suggested 32° <strong>of</strong> rotation at Elk Hills through both pure and simple<br />
shearing. Finally, we discuss the implications <strong>of</strong> the calculated shearing related<br />
deformation, and we assess the likelihood <strong>of</strong> the faults and folds at Elk Hills initiating<br />
within a wrench tectonic environment in the absence <strong>of</strong> a rotation.<br />
Previous Work<br />
White gathered twenty one samples from surface outcrops <strong>of</strong> the Pleistocene<br />
Tulare formation (3.4 Ma) on the northern flank <strong>of</strong> the 31S anticline at Elk Hills and<br />
analyzed them for remanent magnetism. The resulting data indicated that a secondary<br />
normal magnetic field overprinted a primary reversed magnetic field. Based on the<br />
magnetic reversal chart (Harland et al., 1990), this secondary normal remanence was<br />
inferred to have been acquired during the Bruhnes chron, (0.78 Ma to the present). The<br />
orientation <strong>of</strong> the secondary remanent field was expected to mimic the orientation <strong>of</strong><br />
175
the present axial dipole field (PADF). The mean inclination <strong>of</strong> the Elk Hills samples<br />
was measured at 52.3°, only a few degrees from the PADF inclination <strong>of</strong> 55°. The<br />
mean declination <strong>of</strong> the Elk Hills samples was measured at 48° +/− 11°, far from the<br />
PADF declination <strong>of</strong> 0°. Due to this disparity, White (1987) suggested that a<br />
clockwise rotation <strong>of</strong> 48° <strong>of</strong> the Elk Hills anticline occurred sometime after the<br />
secondary remanent field was locked in. If the secondary field had been acquired more<br />
recently, during the present-day field that has a declination <strong>of</strong> 16°, then the rotation <strong>of</strong><br />
Elk Hills would have been only 32°. This study, later cited as evidence for the<br />
shearing related rotation <strong>of</strong> anticlines along the western margin <strong>of</strong> the southern San<br />
Joaquin Valley (Miller, 1998), indicates that sometime over the past 0.78 Ma, Elk<br />
Hills has rotated at least 32° clockwise.<br />
Although Miller (1998) developed his rotation hypothesis based on<br />
paleomagnetic data and other geological and geophysical data collected at the<br />
Kettleman Hills and Lost Hills anticlines that are northwest <strong>of</strong> Elk Hills, he<br />
acknowledges that a clockwise rotation <strong>of</strong> 35° at Elk Hills (based on the findings <strong>of</strong><br />
White, 1987) is also consistent with his hypothesis. Miller (1998) suggests that the<br />
anticlines <strong>of</strong> the southwestern San Joaquin Valley have rotated within a broad shear<br />
zone that is bounded to the west by the San Andreas Fault. The rotation <strong>of</strong> the<br />
anticlines was driven by early right-lateral simple shearing and later shortening<br />
perpendicular to the shear zone, which is characterized as pure shear. Miller states that<br />
the relative importance <strong>of</strong> simple shear versus pure shear cannot be defined due to the<br />
lack <strong>of</strong> quantification <strong>of</strong> extension parallel to the fold hinges along the shear zone. He<br />
acknowledges that if the suggested rotations were produced by simple shear alone, the<br />
associated hinge parallel extension would far exceed that inferred from the folds<br />
themselves, and concludes that pure shear is likely the dominant mechanism for<br />
rotation. Application <strong>of</strong> Miller’s hypothesis to Elk Hills would suggest that the<br />
anticline has undergone 32° - 48° <strong>of</strong> clockwise rotation from an initial orientation <strong>of</strong><br />
(at least) 62° to the San Andreas Fault.<br />
176
Shearing Calculations<br />
The application <strong>of</strong> either a pure shear or simple shear model to a crustal scale<br />
zone at shallow depths requires idealizations that may not be justified. These<br />
kinematic models are used to describe the distributed deformation <strong>of</strong> ductile materials<br />
that flow in response to deviatoric stress (Ramsay and Graham, 1970; Ramsay, 1980;<br />
Robin and Cruden, 1994; Treagus and Lan, 2003). Seismic data (e.g. Medwedeff and<br />
Suppe, 1986; Namson and Davis, 1988; Bloch et al., 1993; Guz<strong>of</strong>ski and Shaw, 2004)<br />
and field studies carried out both east <strong>of</strong> the San Andreas Fault (e.g. Dholakia et al.,<br />
1998; Woodring et al., 1940) and along the coast <strong>of</strong> California (e.g. Belfield et al.,<br />
1983; Hickman and Dunham, 1992; Gross, 1993) portray a shallow crust that is<br />
riddled with faults and fractures, characteristic <strong>of</strong> a brittle response to the applied<br />
stress. Additionally, strength <strong>of</strong> the crust versus depth plots indicate that the brittle-<br />
ductile transition is at approximately 12 km depth (Sibson, 1983). For reference, the<br />
deepest unit considered in the present study is at an average depth <strong>of</strong> 4 km, above<br />
which ductile flow would not be expected. A second questionable idealization is that<br />
the deformation within the broad shear zone is homogeneous. The presence <strong>of</strong> the<br />
prominent folds themselves within the zone east <strong>of</strong> the San Andreas Fault<br />
demonstrates that the deformation is heterogeneous. This has been pointed out and<br />
modeled for other transpressional regimes throughout the world (e.g. Robin and<br />
Cruden, 1994). Plate boundaries, such as the San Andreas Fault in California, the Najd<br />
Fault System in Saudi Arabia, and the North Anatolian Fault in Turkey, are systems <strong>of</strong><br />
subparallel vertical strike-slip faults formed in response to shearing motion <strong>of</strong> one<br />
plate with respect to the other. Neither existing seismic data nor digital elevation maps<br />
indicate the presence <strong>of</strong> large scale vertical strike-slip faults in the zone containing Elk<br />
Hills, Lost Hills, Kettleman Hills, Coalinga, and New Idria.<br />
Acknowledging the oversimplifications <strong>of</strong> the combined pure shear and simple<br />
shear model presented by Miller (1998), we evaluate this model using data from Elk<br />
Hills. We consider the present day geometry <strong>of</strong> Elk Hills and work backwards in time,<br />
calculating how many degrees <strong>of</strong> clockwise rotation may have occurred over the past<br />
0.78 Ma through pure shear alone. We then attribute the remaining rotation to simple<br />
shearing and assess the amount <strong>of</strong> hinge parallel elongation and hinge perpendicular<br />
177
shortening. We also consider the implications that this amount <strong>of</strong> rotation has for the<br />
relative plate motion <strong>of</strong> the North American plate with respect to the Pacific plate. The<br />
western extent <strong>of</strong> the proposed shear zone is taken as the San Andreas Fault (Miller,<br />
1998), and the eastern extent is postulated to lie just beyond the northeastern flanks <strong>of</strong><br />
the New Idria, Coalinga, Kettleman Hills, Lost Hills, and Elk Hills anticlines. The<br />
minimum width <strong>of</strong> a zone that just encompasses these structures is 40 km.<br />
Pure Shear<br />
Bloch et al. (1993) have estimated a 16% contraction in the western San Joaquin<br />
Valley in an orientation perpendicular to the San Andreas Fault since 2.5 Ma.<br />
Assuming a constant strain rate, this indicates that a shortening perpendicular to the<br />
zone <strong>of</strong> approximately 5% has occurred over the past 0.78 Ma. We take this as a<br />
maximum value <strong>of</strong> shortening, as Miller suggests that a period <strong>of</strong> simple shear<br />
occurred, initiating the rotation <strong>of</strong> the anticlines, prior to the current regime <strong>of</strong> pure<br />
shear. We consider two-dimensional pure shear (Ramsay, 1967) in the horizontal<br />
plane (no extension in the vertical direction) to determine the amount <strong>of</strong> rotation <strong>of</strong> a<br />
material line that is presently oriented at 30° to the San Andreas Fault, the orientation<br />
<strong>of</strong> the hinge <strong>of</strong> the Elk Hills anticline. For a 5% shortening across the zone, we have<br />
the squares <strong>of</strong> principal stretches λ 1 = 0.908 and λ 2 = 1.103. The angle <strong>of</strong> rotation<br />
(θrot) is found from (Ramsay 1967, p.67):<br />
⎛ λ ⎞<br />
2<br />
1<br />
tanθ i tanθ<br />
f<br />
λ ⎟<br />
2<br />
⎟ =<br />
⎜<br />
⎝<br />
Using a θf <strong>of</strong> 60° and a θi <strong>of</strong> 57.5°, we calculate a θrot <strong>of</strong> 2.5°. Given the estimate <strong>of</strong><br />
shortening across the zone, less than 10% <strong>of</strong> the rotation can be accounted for by pure<br />
shear: a shortening <strong>of</strong> 45% would be necessary to rotate Elk Hills 32°. This shortening<br />
would reduce the width <strong>of</strong> the zone from 73 km initially to 40 km post rotation.<br />
Simple Shear<br />
We calculate the simple shear strain, principal stretches, and orientations <strong>of</strong> the<br />
principal stretches for a rotation <strong>of</strong> both 32° and 48° to assess the range <strong>of</strong> rotation<br />
178<br />
⎠<br />
1<br />
() 1
suggested by White (1987). The value <strong>of</strong> the homogeneous simple shear strain (γ)<br />
involved in the rotation can be calculated by exploiting the relationship (Ramsay 1967,<br />
p.88) between the initial angle (α = 62° to 78°) and the final angle (α’ = 30°) that the<br />
Elk Hills anticline makes with the San Andreas Fault:<br />
γ = cot α’ – cot α (2)<br />
For a 32° rotation, we calculate a simple shear strain value <strong>of</strong> 1.20. For a 48° rotation,<br />
this value is 1.52. With these estimates <strong>of</strong> shear strain, the magnitudes <strong>of</strong> the squares<br />
<strong>of</strong> the principal stretches <strong>of</strong> the strain ellipses for the two end member cases are 3.12<br />
(λ1) and 0.32 (λ2) for the low end and 4.04 (λ1) and 0.25 (λ2) for the high end, as given<br />
by (Ramsay 1967, p.85):<br />
2 ( γ + 4)<br />
1 2<br />
2<br />
γ + 2 ± γ<br />
λ 1 , λ2<br />
=<br />
(3)<br />
2<br />
The range <strong>of</strong> maximum principal stretches (Smax) is thus 1.77 – 2.02. The orientation<br />
<strong>of</strong> the line <strong>of</strong> maximum stretch for each <strong>of</strong> the end member cases is (Ramsay, 1967):<br />
−1<br />
⎛ γ ⎞<br />
θ = tan ⎜<br />
⎟<br />
⎜<br />
⎟<br />
(4)<br />
2<br />
⎝ 1+<br />
γ − 1 λ1<br />
⎠<br />
For a 32° rotation, we calculate an orientation <strong>of</strong> 29.5°, for a 48° rotation, an<br />
orientation <strong>of</strong> 26.4°.<br />
The respective elongation and shortening <strong>of</strong> material lines parallel to and<br />
perpendicular to the fold hinge may be deduced from the value <strong>of</strong> shearing. For<br />
example, a material line originally oriented at 62° is elongated by a factor <strong>of</strong> 1.77<br />
when rotated to 30° with a value <strong>of</strong> γ = 1.20, and a material line oriented at 152° is<br />
shortened by a factor <strong>of</strong> 0.57. The entire Elk Hills field today has a dimension <strong>of</strong> 25<br />
km in the hinge parallel direction and 8 km in the hinge perpendicular direction. The<br />
values <strong>of</strong> lengthening and shortening indicate that the pre-rotational structure would<br />
have ranged from 14 km long by 14 km wide to 14 km long by 16 km wide,<br />
approximating a domal shape.<br />
Implication <strong>of</strong> Shearing-Related Rotation on Relative Plate Velocities<br />
We calculate the relative motion between the North American and Pacific plates<br />
associated with the proposed shearing from the following calculation incorporating the<br />
179
shear zone width (w), the value <strong>of</strong> the homogeneous simple shear strain (γ), and the<br />
time period <strong>of</strong> interest (t) (Ramsay, 1967):<br />
w⋅<br />
γ<br />
slip rate = (5)<br />
t<br />
Using a shear zone width <strong>of</strong> 40 km, and the suggested time period <strong>of</strong> rotation, 0.78<br />
Ma, we calculate a velocity ranging from 6.2 cm/yr to 7.8 cm/yr. The current long<br />
term slip rate on the San Andreas Fault in this area is approximately 2.3 cm/yr (Toda<br />
and Stein, 2002). Adding these estimates, we have a relative plate velocity ranging<br />
from 8.5 cm/yr to 10.1 cm/yr for the range <strong>of</strong> rotations suggested by White (1987).<br />
Discussion<br />
Analysis <strong>of</strong> shearing calculations<br />
The two-dimensional pure shear analysis <strong>of</strong> the zone east <strong>of</strong> the San Andreas<br />
Fault is an approximation at best, as there was vertical motion as evidenced by the<br />
anticlines. For homogeneous three-dimensional pure shear, uplift would be uniform<br />
across the zone and would not alter the orientation <strong>of</strong> material lines in the horizontal<br />
plane. Because volume is conserved, vertical extension would decrease the magnitude<br />
<strong>of</strong> the horizontal extension calculated for the two-dimensional plane strain case so the<br />
rotation would be less than that calculated above. The existence <strong>of</strong> the anticlines<br />
indicates that the uplift was not uniform. Structure contour maps <strong>of</strong> horizons <strong>of</strong> mid<br />
Miocene (10 Ma) age at Elk Hills and younger indicate that the maximum uplift since<br />
this time is about 2 km (Fig. A1.3a). For a constant deformation rate, we calculate an<br />
uplift <strong>of</strong> 0.16 km over the past 0.78 Ma. This value is 8% <strong>of</strong> the horizontal<br />
displacement, and is a maximum value <strong>of</strong> uplift because we took a constant vertical<br />
uplift rate yet most deformation occurred from mid Miocene through early Pliocene<br />
time (Chapter 1; Imperato, 1995). We conclude that the rotation <strong>of</strong> Elk Hills due<br />
Figure A1.3 (opposite page). (a) Structure contour map <strong>of</strong> a Middle Miocene (top<br />
McDonald) stratigraphic unit. (b) A cross section through the western part <strong>of</strong> the field<br />
running along the line A to A’ in (a). (c) A cross section through the eastern part <strong>of</strong> the<br />
field running along the line B to B’ in (a). Anticlinal crests, faults, and marker horizons<br />
are labeled.<br />
180
(b)<br />
1<br />
2<br />
3<br />
4<br />
5<br />
depth (km) 0<br />
6<br />
7<br />
8<br />
(a)<br />
35 0 16’00” 35 0 20’00”<br />
N<br />
0mile1 0 km 2<br />
0 mile 1<br />
0 km 2<br />
(c)<br />
2R<br />
29R anticline<br />
A<br />
NWS anticline<br />
5R<br />
A’<br />
3R<br />
31S anticline<br />
1R<br />
C.I. = 152 m (500 ft)<br />
B’<br />
B<br />
7<br />
6R<br />
depth (m)<br />
SW NE<br />
1<br />
2<br />
3<br />
4<br />
5<br />
depth (km) 0<br />
6<br />
7<br />
8<br />
119 0 32’00”<br />
119 0 32’00”<br />
0 mile 1<br />
0 km 2<br />
1R<br />
29R<br />
anticline<br />
5R<br />
6R<br />
119 0 26’00”<br />
119 0 26’00”<br />
A A’<br />
31S<br />
anticline<br />
3R<br />
7<br />
31S<br />
anticline<br />
2R<br />
NWS<br />
anticline<br />
B B’<br />
S N<br />
181<br />
119 0 20’00”<br />
119 0 20’00”<br />
35 0 20’00”<br />
4877<br />
4267<br />
3658<br />
3048<br />
2438<br />
1829<br />
NE<br />
MYA4-A<br />
WILHELM<br />
CALITROLEUM<br />
BASE REEF RIDGE<br />
MYA4-A<br />
WILHELM<br />
CALITROLEUM<br />
BASEREEFRIDGE<br />
McDONALD<br />
McDONALD
to pure shearing deformation was negligible and disregard it. If the shear zone<br />
hypothesis is correct, then the majority <strong>of</strong> the rotation at Elk Hills must be attributed to<br />
simple shear.<br />
If the simple shear kinematic model is a valid analog for the structural history <strong>of</strong><br />
Elk Hills, we would expect to see some signature <strong>of</strong> stretching (e.g. normal faults<br />
perpendicular to the hinge) and shortening (thrust faults parallel to the hinge). Hinge<br />
perpendicular normal faults can be seen in the seismic data, but they terminate at depth<br />
within a shale unit that separates the Miocene and older sediments from the Pliocene<br />
and younger sediments (Maher et al., 1975; unpublished seismic data, Occidental Oil<br />
and Gas). Because Miocene units are involved in the folding at Elk Hills, we would<br />
expect to see extension accommodated by normal faulting <strong>of</strong> these layers. Similarly,<br />
thrust faults parallel to the fold hinge are evident within the seismic data. However,<br />
sedimentary signatures within the seismic data show that the majority <strong>of</strong> uplift related<br />
thrusting occurred prior to Pleistocene time and therefore is not consistent with the<br />
rotation and shortening occurring in the last 0.78 my. Furthermore, mechanical models<br />
show that to generate a thrust fault related anticline with equal axes, the down dip fault<br />
dimension must be approximately twice the along strike dimension (Savage and<br />
Cooke, 2004). In the literature, field and subsurface studies documenting faults with a<br />
greater down dip dimension are noticeably lacking (e.g. Schultz and Fossen, 2002;<br />
Maerten et al., 2002; Billi et al., 2003).<br />
Next, we assess the shearing related rotation hypothesis by comparing the<br />
relative plate velocities calculated above with those derived from published values <strong>of</strong><br />
Euler pole angular velocities (DeMets et al., 1990). Following the method presented<br />
by Fowler (1990), the present day relative velocity between the North American and<br />
Pacific plates is approximately 5 cm/yr in an orientation <strong>of</strong> 139°, only a few degrees<br />
from the orientation <strong>of</strong> the San Andreas Fault, near Elk Hills. This is a high value, as<br />
recent geodetic results indicate that the Coast Ranges and the San Andreas Fault<br />
accommodate 39 ± 2 mm/yr <strong>of</strong> relative plate motion, primarily by strike-slip faulting<br />
(Argus and Gordon, 2001). Still, the estimated values <strong>of</strong> 8.5 cm/yr to 10.1 cm/yr are<br />
70% and 100% more than this maximum relative plate motion. The 2.7 cm/yr<br />
discrepancy between the relative plate motion and the long term slip rate <strong>of</strong> 2.3 cm/yr<br />
182
(a)<br />
35 0 16’00” 35 0 20’00”<br />
(b)<br />
35 0 16’00” 35 0 20’00”<br />
N<br />
0mile 1<br />
0 km 2<br />
N<br />
0mile 1<br />
0 km 2<br />
119 0 32’00”<br />
2R<br />
2R<br />
119 0 32’00”<br />
5R<br />
5R<br />
3R<br />
1R<br />
119 0 26’00”<br />
3R<br />
1R<br />
119 0 26’00”<br />
C.I. = 76 m (250 ft)<br />
7<br />
6R<br />
C.I. = 15 m (50 ft)<br />
7<br />
119 0 20’00”<br />
6R<br />
119 0 20’00”<br />
35 0 20’00”<br />
thickness<br />
(m)<br />
35 0 20’00”<br />
1524<br />
1219<br />
914<br />
610<br />
305<br />
thickness<br />
(m)<br />
Figure A1.4. Isochore maps <strong>of</strong> the intervals (a) McDonald to Base Reef Ridge and<br />
(b) Wilhelm to Mya 4-A, as interpreted within a three-dimensional volume <strong>of</strong> seismic<br />
reflection data. Fault traces are plotted and labeled with solid lines representing<br />
active faults, dashed lines representing faults along which activity has ceased, and<br />
dotted lines representing faults that have not yet begun to slip during the deposition <strong>of</strong><br />
the contoured interval.<br />
183<br />
366<br />
305<br />
244<br />
183<br />
122
(Toda, 2002) must be accounted for by deformation near the plate boundaries. If we<br />
attribute all <strong>of</strong> this deformation to the shear zone, by using equation (5) followed by<br />
equation (2), we back calculate a rotation <strong>of</strong> 9.7° over the past 0.78 Ma. The non San<br />
Andreas Fault related relative plate motion is not enough to account for the suggested<br />
rotation, thus rendering the proposed Pleistocene through Holocene rotation suggested<br />
for the Elk Hills anticline unlikely.<br />
Variation in isochore trends at Elk Hills<br />
We posit that the change in orientation <strong>of</strong> stratigraphic thinning at Elk Hills that<br />
is apparent in isochore maps can be explained based on changes in the activity <strong>of</strong><br />
faults that have been interpreted from seismic reflection data. In figure A1.4, we<br />
present an isochore map for the oldest (Fig. A1.4a) and youngest (Fig. A1.4b)<br />
stratigraphic intervals included in the Elk Hills study (Chapter 1). For the older<br />
interval, the activity <strong>of</strong> the 7 fault has a distinct east-west trending influence on the<br />
isochore map in the eastern part <strong>of</strong> the field (Fig. A1.4a). At the time <strong>of</strong> deposition <strong>of</strong><br />
the younger interval, activity along the 7 fault had ceased, and the east-west trend<br />
became diffuse, giving way to the more northwest-southeast directed trend (Fig.<br />
A1.4b). One may imagine that Lost Hills, an anticline located less than 50 km<br />
northwest <strong>of</strong> Elk Hills, evolved in response to a similarly complex four-dimensional<br />
fault geometry. Thus, the reported change in the orientation <strong>of</strong> thinning over the fold<br />
(Julander, 1992) does not necessarily implicate a rotation <strong>of</strong> the fold axis; it could also<br />
be a result <strong>of</strong> changes in fault activity.<br />
Analysis <strong>of</strong> a wrenching growth mechanism at Elk Hills<br />
Having determined that large rotations <strong>of</strong> anticlines within the San Joaquin<br />
Valley are unlikely, we investigate a slightly different wrench faulting mechanism for<br />
the formation <strong>of</strong> Elk Hills wherein the majority <strong>of</strong> the Elk Hills faults formed<br />
subparallel to a master strike-slip fault driving the deformation, and thus would not<br />
rotate appreciably with slip along the master fault. In the literature, faults in this<br />
geometry have been classified as a “flower structure” (Lowell, 1972). We assess the<br />
validity <strong>of</strong> this wrench faulting model as applied to Elk Hills in light <strong>of</strong> the available<br />
184
geological and geophysical data as well as mechanical considerations. The classic<br />
model <strong>of</strong> a compressional flower structure, presented by Lowell (1972, Fig. A1.2),<br />
consists <strong>of</strong> subparallel concave downward thrust faults that converge at depth into a<br />
deep-seated strike slip fault trending in the same orientation. Anticlines develop above<br />
the fault system at an oblique angle to the strike <strong>of</strong> the faults. In this model, the<br />
initiation <strong>of</strong> thrust faults and the subsequent anticlines is attributed to a component <strong>of</strong><br />
compression acting in a direction perpendicular to the faults. The maximum horizontal<br />
compression for this model is assumed to be essentially parallel to the strike <strong>of</strong> the<br />
deep strike-slip fault, however, driving predominantly horizontal motion.<br />
Some inconsistencies arise when applying this flower structure model to Elk<br />
Hills. The concave downward geometry <strong>of</strong> the thrust faults is not supported by the<br />
seismic reflection data. All interpretations <strong>of</strong> the western part <strong>of</strong> the volume suggest<br />
that the major faults are concave upward, steep in the shallow section and soling out<br />
with depth (Fig. A1.3b, A1.3c). Additionally, 3D representations <strong>of</strong> interpretations <strong>of</strong><br />
the faults and deformed stratigraphic horizons reveal that the faults (1R, 2R, 3R, and<br />
5R) and anticlines (29R and 31S) at Elk Hills are subparallel features (Fig. A1.3a). A<br />
final inconsistency lays in the suggested direction <strong>of</strong> slip along the deep seated fault.<br />
The model is suspect as it suggests the development <strong>of</strong> left-lateral slip within and at a<br />
very low angle (25°) to the broader right-lateral domain <strong>of</strong> the San Andreas Fault<br />
system. Thus, the data cast doubt on the interpretation <strong>of</strong> Elk Hills as a flower<br />
structure.<br />
Carrying this investigation one step further, we test the mechanical consequences<br />
<strong>of</strong> applying a flower structure model to Elk Hills. We import a fault geometry<br />
developed with the flower structure model as a basis for interpretation into an elastic<br />
boundary element code. In the shallow layers <strong>of</strong> the seismic volume, this fault<br />
geometry is similar to the fault geometry used in the previously described models. At<br />
depth, however, where the seismic data are obscure, we take the liberty <strong>of</strong> interpreting<br />
a different fault geometry. In this flower structure model, the faults, although still<br />
concave upward, converge at depth into a deep strike slip fault. A left-lateral<br />
displacement discontinuity is applied along the deep-seated fault as a driving<br />
mechanism for slip along the shallower Elk Hills faults. These shallower faults are<br />
185
designated as shear traction free surfaces, which permits them to slip freely in both<br />
dip-slip and strike-slip motion, and they are restricted to only in-plane motion. The<br />
objective <strong>of</strong> this model is to apply the suggested strike-slip motion to the deep-seated<br />
fault and to assess if such motion is capable <strong>of</strong> generating the slip along the more<br />
shallow thrust faults and generating the deformation <strong>of</strong> stratigraphic horizons as<br />
imaged within the seismic data. The results <strong>of</strong> this model are shown in figure A1.5, a<br />
map view representation <strong>of</strong> the vertical displacement field resulting from a single<br />
increment <strong>of</strong> deformation at a stratigraphic level comparable to the level <strong>of</strong> a Late<br />
Pliocene horizon. Uplift does occur at the central part <strong>of</strong> Elk Hills. The general trends<br />
<strong>of</strong> the 29R and 31S anticlines are not apparent. The flower structure model thus proves<br />
to be inconsistent with both the interpretation <strong>of</strong> the shallow seismic data and the<br />
mechanical models.<br />
Conversely, the thrust fault related model is supported by the mechanical models<br />
(Chapter 1) and the seismic data as well as the regional geology. Most significantly,<br />
the ability <strong>of</strong> the mechanical models to approximately reproduce the deformation<br />
observed within the seismic data set (Chapter 1) supports the idea that the western part<br />
<strong>of</strong> the Elk Hills is a thrust related structure. Additional support is garnered from the<br />
fact that evidence exists within the seismic data set for the presence <strong>of</strong> concave<br />
upward faults with dips that shallow at depth. Consideration <strong>of</strong> the regional geology<br />
also supports the model <strong>of</strong> Elk Hills as a thrust related feature. The world stress map<br />
(Zoback, 1992) compiled from a collection <strong>of</strong> earthquake focal mechanisms, wellbore<br />
breakout and drilling induced fracture analyses, in-situ stress measurements, and fault<br />
slip analyses, indicates that the regional maximum horizontal compressional stress is<br />
oriented northeast – southwest. This orientation is consistent with faults and anticlines<br />
oriented perpendicular to this orientation, with strikes trending northwest – southeast,<br />
and is indeed the orientation <strong>of</strong> the maximum strain direction that was applied as a<br />
remote boundary condition in our modeling efforts.<br />
Conclusions<br />
The absence <strong>of</strong> geological and geophysical evidence for features that would<br />
develop in response to large amounts <strong>of</strong> pure shear or simple shear deformation in the<br />
186
35 0 16’00” 35 0 20’00”<br />
0<br />
N<br />
km 2<br />
119 0 32’00”<br />
119 0 26’00”<br />
normalized displacement<br />
119 0 20’00”<br />
Figure A1.5. Model results <strong>of</strong> a mechanical test <strong>of</strong> a suggested strike-slip driven<br />
deformation at Elk Hills wherein the shallow Elk Hills faults and two deep seated leftlateral<br />
strike-slip faults form a compressional flower structure. The inset is a threedimensional<br />
view with the geometry <strong>of</strong> the hypothetical deep vertical strike-slip faults<br />
drawn in dashed lines. Model results are shown as a normalized vertical<br />
displacement field with a contour interval <strong>of</strong> 0.1.<br />
187<br />
35 0 20’00”<br />
35 0 16’00”
southwestern San Joaquin Valley indicates that a suggested 32° − 48° rotation <strong>of</strong> the<br />
Elk Hills anticline cannot be accounted for. Geometrical and mechanical investigation<br />
<strong>of</strong> a wrench faulting scenario for Elk Hills in the absence <strong>of</strong> any rotation also proves to<br />
be incompatible with available data. In light <strong>of</strong> these inconsistencies, we find that the<br />
shortening within the southwestern San Joaquin Valley has been more consistent with<br />
compressional rather than wrench tectonics during the growth <strong>of</strong> the Elk Hills<br />
anticline.<br />
Acknowledgements<br />
This project was supported by funds from the <strong>Stanford</strong> Rock Fracture Project.<br />
The ideas presented in this manuscript benefited from discussions with Don Miller and<br />
Mike McWilliams.<br />
References<br />
Argus, D. F., and R. G. Gordon, 2001, Present tectonic motion across the Coast<br />
Ranges and San Andreas fault system in Central California: Geological Society<br />
<strong>of</strong> America Bulletin, v. 113, p. 1580-1592.<br />
Belfield, W. C., J. Helwig, P. R. LaPointe, and W. K. Dahleen, 1983, Monterey<br />
fractured reservoir, Santa Barbara Channel, California: AAPG Bulletin, v. 67,<br />
p. 421-422.<br />
Billi, A., F. Salvini, and F. Storti, 2003, The damage zone - fault core transition in<br />
carbonate rocks: implications for fault growth, structure and permeability:<br />
Journal <strong>of</strong> Structural Geology, v. 25, p. 1779-1794.<br />
Bloch, R. B., R. Von Huene, P. E. Hart, and C. M. Wentworth, 1993, Style and<br />
magnitude <strong>of</strong> tectonic shortening normal to the San Andreas fault across<br />
Pyramid Hills and Kettleman Hills South Dome, California: Geological<br />
Society <strong>of</strong> America Bulletin, v. 105, p. 464-478.<br />
DeMets, C., R. G. Gordon, D. F. Argus, and S. Stein, 1990, Current plate motions:<br />
Geophysical Journal International, v. 101, p. 425-478.<br />
Dholakia, S. K., A. Aydin, D. D. Pollard, and M. D. Zoback, 1998, Fault-controlled<br />
hydrocarbon Pathways in the Monterey formation, California: American<br />
Association <strong>of</strong> Petroleum Geologists Bulletin, v. 82, p. 1551-1574.<br />
188
Eaton, J. P., Cockerham, R., and F. Lester, 1983, Study <strong>of</strong> the May 2, 1983, Coalinga<br />
earthquake and its aftershocks, based on the USGS seismic network in<br />
northern California, in Bennet, J. H., and Sherburne, R. W., eds., The 1983<br />
Coalinga, California earthquakes, California Division <strong>of</strong> Mines and Geology,<br />
Special Publication 66, p. 261-272.<br />
Ekstrom, G., R. S. Stein, J. P. Eaton, and D. Eberhart-Phillips, 1992, Seismicity and<br />
geometry <strong>of</strong> a 110-km-long blind thrust fault; 1. The 1985 Kettleman Hills,<br />
California, earthquake: Journal <strong>of</strong> Geophysical Research, v. 97, p. 4843-4864.<br />
Fowler, C. M. R., 1990, The Solid <strong>Earth</strong>: an introduction to global geophysics:<br />
Cambridge, Cambridge <strong>University</strong> Press.<br />
Gross, M. R., 1993, The origin and spacing <strong>of</strong> cross joints: examples from the<br />
Monterey Formation, Santa Barbara coastline, California: Journal <strong>of</strong> Structural<br />
Geology, v. 15, p. 737-751.<br />
Guz<strong>of</strong>ski, C. A., and J. H. Shaw, 2004, Coalinga anticline, San Joaquin basin,<br />
California, USA, in J. H. Shaw, Connors, C., and Suppe, J., ed., Seismic<br />
interpretation <strong>of</strong> contractional fault-related folds: An AAPG seismic atlas,<br />
AAPG Special Publication.<br />
Harding, T. P., 1974, Petroleum traps associated with wrench faults: American<br />
Association <strong>of</strong> Petroleum Geologists Bulletin, v. 58, p. 1290-1304.<br />
Harding, T. P., 1976, Tectonic significance and hydrocarbon trapping consequences <strong>of</strong><br />
sequential folding synchronous with San Andreas faulting, San Joaquin Valley,<br />
California: American Association <strong>of</strong> Petroleum Geologists Bulletin, v. 60, p.<br />
356-378.<br />
Harland, W. B., R. L. Armstrong, A. V. Cox, L. E. Craig, A. G. Smith, and D. G.<br />
Smitt, 1990, A geologic time scale, 1989: Cambridge <strong>University</strong> Press.<br />
Hickman, R. G., and J. B. Dunham, 1992, Controls on the development <strong>of</strong> fractured<br />
reservoirs in the Monterey Formation <strong>of</strong> Central California, in R. M. Larsen,<br />
Brekke, H., Larsen, B. T., Talleraas, E., ed., Structural and tectonic modelling<br />
and its application to petroleum geology, proceedings, v. 1, Norwegian<br />
Petroleum Society (NPF) Special Publication, p. 343-353.<br />
Imperato, D. P., 1995, Studies <strong>of</strong> the Stratigraphy and Structure <strong>of</strong> the Great Valley <strong>of</strong><br />
California and Implications for Plate Tectonics: PhD dissertation, <strong>University</strong> <strong>of</strong><br />
California at Santa Barbara, Santa Barbara, California, 271 p.<br />
Julander, D. R., 1992, Implications from a study <strong>of</strong> the timing <strong>of</strong> oil entrapment in<br />
Monterey siliceous shales, Lost Hills, San Joaquin Valley, California:<br />
Geological Society <strong>of</strong> America, Abstracts with Programs, v. 24, p. 308-309.<br />
189
Lowell, J. D., 1972, Spitzenbergen Tertiary Orogenic Belt and the Spitzenbergen<br />
Fracture Zone: Geological Society <strong>of</strong> America Bulletin, v. 83, p. 3091-3102.<br />
Maerten, L., P. Gillespie, and D. D. Pollard, 2002, Effects <strong>of</strong> local stress perturbation<br />
on secondary fault development: Journal <strong>of</strong> Structural Geology, v. 24, p. 145-<br />
153.<br />
Maher, J. C., R. D. Carter, and R. J. Lantz, 1975, Petroleum geology <strong>of</strong> Naval<br />
Petroleum Reserve No. 1, Elk Hills, Kern County, California, p. 109.<br />
Medwedeff, D. A., and J. Suppe, 1986, Kinematics, timing, and rates <strong>of</strong> folding and<br />
faulting from syntectonic sediment geometry: AGU 1986 fall meeting, EOS,<br />
Transactions, American Geophysical Union, v. 67, p. 1223.<br />
Miller, D. D., 1998, Distributed shear, rotation, and partitioned strain along the San<br />
Andreas fault, central California: Geology, v. 26, p. 867-870.<br />
Moody, J. D., and M. J. Hill, 1956, Wrench-fault tectonics: Geological Society <strong>of</strong><br />
America Bulletin, v. 67, p. 1207-1246.<br />
Mount, V. S., and J. Suppe, 1987, State <strong>of</strong> stress near the San Andreas fault:<br />
Implications for wrench tectonics: Geology, v. 15.<br />
Namson, J. S., and T. L. Davis, 1988, Seismically active fold and thrust belt in the San<br />
Joaquin Valley, central California: Geological Society <strong>of</strong> America Bulletin, v.<br />
100, p. 257-273.<br />
Nicholson, G. E., 1990, Structural overview <strong>of</strong> Elk Hills: in Kuespert, J. G. and Reid,<br />
S. A., eds., Structure, stratigraphy and hydrocarbon occurrences <strong>of</strong> the San<br />
Joaquin Basin, California: Field Trip Guidebook - Pacific Section, Society <strong>of</strong><br />
Economic Paleontologists and Mineralogists, v. 64, p. 133-140.<br />
Pueyo, E. L., Pares, J. M., Millan, H., and A. Pocovi, 2003,Conical folds and apparent<br />
rotations in paleomagnetism (a case study in the Southern Pyrenees):<br />
Tectonophysics, v. 362, p. 345-366.<br />
Ramsay, J. G., 1967, Folding and fracturing <strong>of</strong> rocks: New York, McGraw-Hill, 568 p.<br />
Ramsay, J. G., 1980, The crack-seal mechanism <strong>of</strong> rock deformation: Nature, v. 284,<br />
p. 135-139.<br />
Ramsay, J. G., and R. H. Graham, 1970, Strain Variation in Shear Belts: Canadian<br />
Journal <strong>of</strong> <strong>Earth</strong> Science, v. v. 7, p. 786-813.<br />
190
Robin, P. Y. F., and A. R. Cruden, 1994, Strain and Vorticity Patterns in Ideally<br />
Ductile Transpression Zones: Journal <strong>of</strong> Structural Geology, v. v. 16, p. 447-<br />
466.<br />
Savage, H., and M. L. Cooke, 2004, The effect <strong>of</strong> non-parallel fault interaction on fold<br />
patterns: Journal <strong>of</strong> Structural Geology, v. 26, p. 905-917.<br />
Schultz, R. A., and H. Fossen, 2002, Displacement-length scaling in three dimensions;<br />
the importance <strong>of</strong> aspect ratio and application to deformation bands: Journal <strong>of</strong><br />
Structural Geology, v. 24, p. 1389-1411.<br />
Sibson, R. H., 1983, Continental fault structure and the shallow earthquake source:<br />
Journal <strong>of</strong> the Geological Society <strong>of</strong> London, v. 140, p. 741-767.<br />
Stewart, S. A., 1995, Paleomagnetic analysis <strong>of</strong> plunging fold structures: errors and a<br />
simple fold test: <strong>Earth</strong> and Planetary Science Letters, v. 130, p. 57-67.<br />
Toda, S., and R. S. Stein, 2002, Response <strong>of</strong> the San Andreas Fault to the 1983<br />
Coalinga-Nunez earthquakes; an application <strong>of</strong> interaction-based probabilities<br />
for Parkfield: Journal <strong>of</strong> Geophysical Research, v. 107, p. 16 pp.<br />
Treagus, S. H., and L. Lan, 2003, Simple shear <strong>of</strong> deformable square objects: Journal<br />
<strong>of</strong> Structural Geology, v. 25, p. 1993-2003.<br />
Wentworth, C. M., M. C. Blake, Jr., D. L. Jones, A. W. Walter, and M. D. Zoback,<br />
1984, Tectonic wedging associated with emplacement <strong>of</strong> the Franciscan<br />
assemblage, California Coast Ranges: Franciscan geology <strong>of</strong> northern<br />
California, p. 163-173.<br />
White, R. E., 1987, Paleomagnetism <strong>of</strong> the Tulare Formation from cores and surface<br />
exposures west-central and southwestern San Joaquin Valley, California, Long<br />
Beach State <strong>University</strong>, Long Beach, California, 272 p.<br />
Wilcox, R. E., T. P. Harding, and D. R. Seely, 1973, Basic wrench tectonics:<br />
American Association <strong>of</strong> Petroleum Geologists Bulletin, v. 57, p. 74-96.<br />
Woodring, W. P., R. B. Stewart, and R. W. Richards, 1940, Geology <strong>of</strong> the Kettleman<br />
Hills oil field, California; stratigraphy, paleontology, and structure, U. S.<br />
Geological Survey Pr<strong>of</strong>essional Paper, p. 170.<br />
Zoback, M. D., M. L. Zoback, V. S. Mount, J. Suppe, J. P. Eaton, J. H. Healy, D.<br />
Oppenheimer, P. Reasenberg, L. M. Jones, C. B. Raleigh, I. G. Wong, O.<br />
Scotti, and C. M. Wentworth, 1987, New evidence on the state <strong>of</strong> stress <strong>of</strong> the<br />
San Andreas fault system: Science, v. 238, p. 1105-1111.<br />
Zoback, M. L., 1992, First- and second-order patterns <strong>of</strong> stress in the lithosphere: The<br />
World Stress Map project: Journal <strong>of</strong> Geophysical Research, v. 97, p. 11,703-<br />
11,728.<br />
191
192
Appendix 2<br />
THE ROCK FRACTURE PROJECT FIELD TRIP<br />
Sheep Mountain Anticline, WY<br />
by<br />
Patricia E. Fiore<br />
Nicolas Bellahsen<br />
David D. Pollard<br />
2006<br />
June 15 - 16, 2006<br />
193
Introduction<br />
Sheep Mountain anticline (SMA) is a Laramide, basement cored fold located<br />
along the eastern flank <strong>of</strong> the Bighorn basin, which trends NW/SE and is bounded to<br />
the east by the Bighorn Mountains, to the south by the Owl Creek Mountains, and to<br />
the west by the Absaroka and Beartooth Mountains (Figure A2.1).<br />
Sheep<br />
Mountain<br />
anticline<br />
44°<br />
43°<br />
45°<br />
110°<br />
Absaroka Mnts<br />
WIND RIVER<br />
RANGE<br />
109°<br />
BIG<br />
HORN<br />
WIND RIVER<br />
BASIN<br />
BASIN<br />
Owl Creek Mnts<br />
108°<br />
Big Horn Mnts<br />
107°<br />
100 km<br />
POWDER<br />
Casper Arch<br />
RIVER<br />
BASIN<br />
Figure A2.1. Tectonic map <strong>of</strong> Wyoming showing the location <strong>of</strong> Sheep Mountain<br />
anticline. From Bellahsen et al., 2006a.<br />
Themes:<br />
Fracture characterization at the outcrop<br />
This field trip emphasizes the importance <strong>of</strong> a full fracture characterization<br />
which begins at the outcrop. A well constrained fracture history combines fracture<br />
orientations (strike and dip relative to bedding) with all other fracture characteristics<br />
observable in outcrop, including surface textures, filling, geometry, displacement<br />
discontinuity, and abutting relations. An understanding <strong>of</strong> the mode <strong>of</strong> deformation <strong>of</strong><br />
a tectonic fracture set (opening, closing, shearing), along with its time <strong>of</strong> formation<br />
relative to other fracture sets, greatly enhances the ability to determine the causal<br />
mechanism.<br />
194
Fracture characterization over the fold<br />
During this field trip we will consider different scales <strong>of</strong> deformation. Although<br />
most <strong>of</strong> the field trip stops focus on outcrop observations <strong>of</strong> fractures, the outcrop<br />
stops are in different structural locations on the fold and therefore can be combined to<br />
understand the larger scale structure. Variations in three fracture sets, the spatial<br />
density <strong>of</strong> fractures in a given set, the type <strong>of</strong> fillings, and the reactivation by shearing<br />
<strong>of</strong> originally opening fractures all contribute to the interpretation <strong>of</strong> the folding.<br />
Fold-thrust fault relationships based on fracture patterns<br />
Field work on the fractures has helped constrain the kinematics <strong>of</strong> folding at<br />
Sheep Mountain and relationships to the underlying thrust fault. We will investigate<br />
how the location and geometry <strong>of</strong> a blind thrust fault can be deduced, with respect to<br />
the position <strong>of</strong> the fold limbs, based on spatial variations in fracture patterns.<br />
Tectonic history revealed by fracture patterns<br />
Systematic fracture sets may form in response to either remote regional stresses<br />
or local deformation events, such as folding and faulting. The fracture pattern at a<br />
specific field location will reflect the tectonic history <strong>of</strong> the site but may not record all<br />
such events. Interpretation <strong>of</strong> the fracture pattern at Sheep Mountain will be put in the<br />
context <strong>of</strong> regional orogenic events, their maximum compression direction, and their<br />
timing. This study helps to determine the causal mechanisms <strong>of</strong> some fracture sets.<br />
195
Field Trip Stops:<br />
First Day<br />
Stop 1: Geology <strong>of</strong> the greater region<br />
Stop 2: Fold shape<br />
Stop 3: Fracture introduction, nose fractures<br />
Second Day<br />
Stop 4: Backlimb fractures<br />
Stop 5: Backlimb fractures and shearing<br />
Stop 6a & 6b: Backlimb fractures and shearing, influence <strong>of</strong> thumb<br />
Stop 7: Forelimb and hinge fractures<br />
Stop 8: Fracturing synthesis<br />
N<br />
108°10'<br />
1<br />
2<br />
BACKLIMB<br />
HINGE<br />
4<br />
5b<br />
44°39'<br />
FORELIMB<br />
5a<br />
3a<br />
3b<br />
108°10'<br />
44°38'<br />
1 km<br />
Figure A2.2. Digital Orthophoto Quarter Quadrangles <strong>of</strong> the NW part <strong>of</strong> SMA.<br />
Locations <strong>of</strong> stops in the Tensleep sandstone are shown in red; stops in the<br />
Phosphoria limestone are shown in yellow.<br />
196<br />
108°08'<br />
44°37
N<br />
108°12'<br />
Quaternary<br />
Cretaceous<br />
Jurassic<br />
Triassic<br />
108°10'<br />
Permian (Phosphoria Fm)<br />
Carboniferous (Pennsylvanian, Tensleep Fm)<br />
Carboniferous (Pennsylvanian, Amsden Fm)<br />
Carboniferous (Mississipian, Madison Fm)<br />
Anticlinal axis Synclinal axis<br />
108°08'<br />
44°38'<br />
108°06'<br />
1 km<br />
108°04'<br />
44°36'<br />
Figure A2.3. Geological map <strong>of</strong> Sheep Mountain anticline after Rioux, 1994. Fracture<br />
measurements discussed during this field trip have been made in the Phosphoria,<br />
Tensleep, Amsden, and Madison formations. Additional measurements have been<br />
made in the Jurassic Gypsum Springs and Sundance Formations (Savage, 2003).<br />
Due to outcrop quality and access considerations, work to date has been focused on<br />
the part <strong>of</strong> the anticline that lies to the NW <strong>of</strong> the river cut.<br />
197
44°39’0”N<br />
44°36’0”N<br />
108°12’0”W 108°9’0”W<br />
108°12’0”W 108°9’0”W<br />
Figure A2.4. Structural map <strong>of</strong> the NW part <strong>of</strong> Sheep Mountain anticline. Black<br />
symbols are data from Hennier (1984), white symbols and formation contacts (slightly<br />
modified from previous interpretations) are interpreted from remote surface mapping.<br />
From Banerjee and Mitra, [AAPG Bulletin. AAPG@2004. Reprinted by permission <strong>of</strong><br />
the AAPG whose permission is required for further use.]<br />
198<br />
44°39’0”N 44°36’0”N
DAY 1<br />
Thursday, June 15 th<br />
Arrive in Billings, MT and leave via rental SUVs at 1:00 PM. Drive to Sheep<br />
Mountain anticline via 212S to 310S.<br />
Just before mile marker 223 on 310S, take 1 st left past Lane 16 ½, cut through Alkali<br />
anticline (Fig. A2.5). At 1 st intersection, take a left to head to the NE. At second<br />
intersection, stay straight, driving toward the SE (do not take a left). Cut across the<br />
plunging nose <strong>of</strong> Sheep Mountain anticline and park to the NW <strong>of</strong> where the structure<br />
rises.<br />
Figure A2.5. Road map (yellow line) to the nose <strong>of</strong> Sheep Mt. anticline from highway<br />
310 through Alkali anticline (trend drawn in black on map).<br />
Figure A2.6. Day 1 stops at the nose <strong>of</strong> Sheep Mt. anticline. Park on the NW side <strong>of</strong><br />
the fold near the nose, just north <strong>of</strong> the fence. Walk (dotted yellow line) through the<br />
Chugwater up the nose <strong>of</strong> the fold.<br />
199
Stop 1: Geology <strong>of</strong> the greater region<br />
NW nose<br />
30 minutes walking (Fig. A2.6)<br />
3:30 PM – 4:30 PM<br />
Waypoint (UTM zone 12N): 4947765 N<br />
0722336 E<br />
elev. = 1370 m<br />
Objectives<br />
Discuss the tectonic setting <strong>of</strong> the Laramide orogeny<br />
Discuss the structural style <strong>of</strong> the Laramide orogeny<br />
Introduce stratigraphy <strong>of</strong> the Bighorn Basin<br />
Point out the surrounding structures<br />
Discuss previous structural interpretations <strong>of</strong> Sheep Mountain<br />
Key Points<br />
SMA is a Laramide fault related fold that exposes Paleozoic sediments within<br />
its core.<br />
The Sheep Mountain fault is a 3 rd order structure: Bighorn Mts. eastern frontal<br />
thrust, Rio thrust, SMA thrust.<br />
A secondary fold exists on the backlimb <strong>of</strong> SMA.<br />
Tectonic setting <strong>of</strong> Laramide Orogeny<br />
Sheep Mountain formed during the Laramide orogeny, which occurred during<br />
late Cretaceous through early Tertiary time, from about 80 Ma to 40 Ma, and produced<br />
folds trending both NW-SE and east-west. These varying structural orientations have<br />
sparked debate about the orientation and possible temporal variation <strong>of</strong> the tectonic<br />
stresses <strong>of</strong> the orogeny. A common interpretation is <strong>of</strong> a constant NE-trending<br />
compression throughout Laramide time (Dickinson and Snyder, 1978; Engebretson et<br />
al., 1985; Bird, 1998; Bird, 2002).<br />
Laramide tectonism is attributed to subduction <strong>of</strong> the Farallon plate beneath the<br />
North American plate at an abnormally shallow angle (Fig. A2.7). One line <strong>of</strong><br />
evidence for shallow subduction is the lack <strong>of</strong> Laramide age volcanism in the Rocky<br />
Mountain foreland. A younger analog has been identified in the Andean foreland<br />
Sierras Pampeanas (Sales, 1968; Coney, 1976; Jordan et al., 1983; Fielding and<br />
Jordan, 1988).<br />
200
(a)<br />
(b)<br />
Figure A2.7. Two types <strong>of</strong> arc orogens displaying two modes <strong>of</strong> subduction: (a)<br />
steep and (b) shallow plate descent. Modified after Barazangi and Isacks (1976) and<br />
Megard and Philip (1976). From Dickinson and Snyder (1978).<br />
201
Structural styles <strong>of</strong> Laramide folds and thrust faults<br />
Laramide folds are classified as “thick-skinned” structures, indicating the role <strong>of</strong><br />
basement blocks in the deformation. Various theories presented since the 1940s as to<br />
how basement involved structures develop have generated controversy over the<br />
relative importance <strong>of</strong> vertical uplift (forced folds/drape folds) versus horizontal<br />
contraction (thrust-fault related folds). Blackstone (1940) and Berg (1962) were the<br />
first proponents <strong>of</strong> the thrust-fault related Laramide deformation with their structural<br />
interpretations <strong>of</strong> specific Rocky Mountain folds (Fig. A2.8). In the 1970s,<br />
interpretations shifted toward vertical deformation with interpretations <strong>of</strong> steep to<br />
subvertical fault zones and unfolded basement that deformed by brittle fracture only<br />
(Fig. A2.9; Stearns, 1971, 1978; Stearns and Weinberg, 1975; Stearns and Stearns,<br />
1978), a concept that had been introduced earlier by Thom (1923, 1952) and Prucha et<br />
al. (1965). In the late 1970s, high quality seismic reflection pr<strong>of</strong>iles across the Rocky<br />
Mountain foreland provided ground truth for the controversy. These data, revealing<br />
thrust fault geometries that place PreCambrian basement over Paleozoic sediments,<br />
emphasized the importance <strong>of</strong> horizontal contraction (Smithson et al., 1978, 1979).<br />
Figure A2.8. Thrust fault interpretation <strong>of</strong> the Golden Thrust in Jefferson County,<br />
Colorado. From Berg, 1962. [AAPG Bulletin. AAPG@1962. Reprinted by permission<br />
<strong>of</strong> the AAPG whose permission is required for further use.]<br />
202
Figure A2.9. Drape fold interpretation <strong>of</strong> Rattlesnake Mountain near Cody, Wyoming.<br />
From Stearns, 1971.<br />
Although modern data have cast doubt on the vertical uplift theory for Laramide<br />
deformation, the issue <strong>of</strong> how basement deforms remains controversial. Some studies<br />
have suggested how cover rocks may fold in the absence <strong>of</strong> folded basement (Erslev,<br />
1986; Spang and Evans, 1988; Narr and Suppe, 1994), while other studies have<br />
suggested mechanisms by which basement may fold due to slip along foliation planes<br />
(Schmidt and Garihan, 1983; Miller and Lageson, 1990; Schmidt et al., 1993), or slip<br />
along closely spaced fractures (Spang et al., 1985; Spang and Evans 1988; Garcia and<br />
Davis, 2004). Although the exact mechanism for basement folding at Sheep Mountain<br />
has not been identified, during this field trip, we will make the case for folding <strong>of</strong> the<br />
basement beneath the anticline.<br />
203
Stratigraphy <strong>of</strong> the Bighorn Basin<br />
During the Paleozoic and Mesozoic, the Bighorn basin filled with approximately<br />
3000 m <strong>of</strong> interbedded shales, sandstones, and limestones (Fig. A2.10; Thomas, 1965;<br />
Ladd, 1979). These sediments lie on top <strong>of</strong> PreCambrian basement.<br />
At Sheep Mountain, the oldest exposed formation is the Lower Carboniferous<br />
Madison Limestone, which is about 200m thick and is topped by a paleokarst surface.<br />
The Madison Formation is unconformably overlain by the Upper Carboniferous<br />
Amsden Formation. The base <strong>of</strong> the Amsden Formation is marked by a crossbedded,<br />
light gray fine-grained quartz arenite (Ladd, 1979). The remainder <strong>of</strong> the Formation<br />
consists <strong>of</strong> thick siltstones, sandstones, shales and carbonates (Fig. A2.11, Fig. A2.12).<br />
Above the Amsden Formation, the Tensleep Formation (also Upper Carboniferous in<br />
age) is composed <strong>of</strong> interbedded thin sandstones, shales, and carbonates in its lower<br />
part and thicker beds <strong>of</strong> crossbedded quartz arenite in its upper part. Above the<br />
Carboniferous section is the Phosphoria Formation, Permian in age. The lower beds <strong>of</strong><br />
the Phosphoria Fm. are predominantly siltstones and shales, with a thin interbedded<br />
gypsum layer (Ladd, 1979). Higher in section, the Phosphoria Formation is composed<br />
<strong>of</strong> thick carbonates (biolithite, micrite and biosparite). Due to minor Ancestral Rocky<br />
Mountains uplift, the Tensleep and Phosphoria Formations are thinned at Sheep<br />
Mountain (Simmons and Scholle, 1990). Above these units, the base <strong>of</strong> the Mesozoic<br />
rocks is defined by the Triassic Chugwater Formation, distinctive due to its red color.<br />
The overlying sediments are composed <strong>of</strong> sandstones and shales that have been eroded<br />
from the Sheep Mountain ediface.<br />
Our studies at Sheep Mountain have focused on fracturing <strong>of</strong> the Madison,<br />
Tensleep, Amsden and Phosphoria Formations. These formations range from<br />
Mississippian to Permian in age and were deposited approximately 330 Ma – 250 Ma<br />
(Fig. A2.12). During the field trip, we will investigate the role that lithology plays in<br />
fracturing.<br />
204
K<br />
J<br />
TR<br />
P<br />
P<br />
M<br />
D<br />
O<br />
C<br />
pC<br />
Mesa Verde<br />
Cody<br />
Frontier<br />
Mowry<br />
Thermopolis<br />
Cloverly<br />
Morrison<br />
Sundance<br />
Gypsum Springs<br />
Chugwater<br />
Phosphoria<br />
Tensleep<br />
Amsden<br />
Madison<br />
Jefferson -<br />
Three Forks<br />
Bighorn<br />
Gallatin<br />
Gros Ventre<br />
Flathead<br />
Granite<br />
Shale<br />
Sandstone<br />
Limestone<br />
Dolomite<br />
Gypsum<br />
Granite<br />
Figure A2.10. Stratigraphic column for the Bighorn Basin. After Hennier, 1984.<br />
205
Amsden<br />
Tensleep<br />
Phosphoria<br />
Chugwater<br />
Gypsum Springs<br />
Sundance<br />
Morrison<br />
Thermopolis<br />
Cloverly<br />
Figure A2.11. Photograph <strong>of</strong> the NW nose <strong>of</strong> Sheep Mountain. The stratigraphic<br />
layers that we will drive through, walk over, and investigate in outcrop on this field trip<br />
are labeled.<br />
Perimian Trias<br />
Carb.<br />
(Penn.)<br />
Carboniferous (Miss.)<br />
250 Ma<br />
292 Ma<br />
320 Ma<br />
Chugwater<br />
174m<br />
Phosphoria<br />
68m<br />
Tens<br />
29m<br />
Ams<br />
35m<br />
Madison<br />
230m<br />
Frontier<br />
Mowry<br />
Figure A2.12. Stratigraphic column for Sheep Mountain. The formations in which<br />
fracture measurements were made are shown in this column. From Bellahsen et al.,<br />
2006a.<br />
206
Structures surrounding Sheep Mountain<br />
The view from the NW nose <strong>of</strong> Sheep Mountain reveals a complicated<br />
geometrical pattern <strong>of</strong> folds (Fig. A2.13; Fig. A2.14). To the east-southeast, Crystal<br />
Creek Anticline has a meandering fold trend. To the northeast, a small syncline flanks<br />
the forelimb <strong>of</strong> Sheep Mountain. Beyond this syncline, Spence Dome, an actively<br />
producing oil field, has a domal shape that is oblong in the NNW-SSE direction.<br />
Further to the northeast, Little Sheep Mountain Anticline trends subparallel to Sheep<br />
Mountain. Along the trend <strong>of</strong> Sheep Mountain, to the NW, Rose Dome is oblong in<br />
the NW-SE direction. The intersection <strong>of</strong> this Rose Dome trend with the Spence Dome<br />
and Sheep Mountain trends produces a complicated geometry just northeast <strong>of</strong> the<br />
plunging nose <strong>of</strong> Sheep Mountain. To the northwest, Goose Egg Anticline and Alkali<br />
Anticline lie along a NW-SE trend, subparallel to Sheep Mountain. It has been<br />
proposed that these anticlines initiated as distinct folds and grew together (Savage,<br />
2003).<br />
Figure A2.13. Geological map for the area surrounding Sheep Mountain. Fold hinge<br />
lines are plotted and labeled. Modified from Rioux, 1994. From Savage, 2003.<br />
207
¹<br />
0 2.5 5 10 15 20<br />
Km<br />
Figure A2.14. Color Infra Red digital orthoquad quadrangle photos (CIR DOQQs) <strong>of</strong> the Bighorn area with the hinge<br />
lines <strong>of</strong> major folds shown in white. DOQQs downloaded from http://wgiac.state.wy.us/.<br />
Sheep Mt.<br />
Anticline<br />
Alkali<br />
Anticline<br />
Crystal Creek<br />
Anticline<br />
208<br />
Spence<br />
Dome<br />
GooseEgg<br />
Anticline<br />
Rose<br />
Dome<br />
Little<br />
Sheep Mt.<br />
Anticline<br />
Big Horn Mountains
In a recent study investigating fold and fault interactions in three dimensions,<br />
Savage (2003) inferred the geometry <strong>of</strong> the blind thrust faults that formed these<br />
Laramide features from the shapes <strong>of</strong> the folds as mapped in the field. Incorporating<br />
the faults into elastic boundary element models and simulating the deformation <strong>of</strong> the<br />
area (Fig. A2.15), Savage concluded that slip along faults oriented obliquely to one<br />
another could have produced the pattern <strong>of</strong> folds seen in the Sheep Mountain area with<br />
one direction <strong>of</strong> tectonic contraction.<br />
Figure A2.15. Synthetic structure contour map for the region surrounding Sheep<br />
Mountain with a 2 m contour interval (From Savage, 2003). Orientations <strong>of</strong> faults<br />
included in the model are plotted. The shape <strong>of</strong> the folds represented in this structure<br />
contour map are similar to those seen in figures A2.13 and A2.14.<br />
209
The same study investigated strain energy density (Fig. A2.16a; Fig. A2.16b)<br />
and Navier-Coulomb stress (Fig. A2.16c; Fig. A2.16d) to determine whether the NW-<br />
SE trending faults could have caused stress perturbations on faults oblique to the<br />
direction <strong>of</strong> Laramide contraction that brought them closer to failure. An interesting<br />
result, having implications for the structural interpretation <strong>of</strong> Sheep Mountain, is that<br />
both the strain energy density and the Navier-Coulomb stress plots show highs in the<br />
area to the southwest <strong>of</strong> Sheep Mountain Anticline (Fig. A2.16). This is the suggested<br />
location <strong>of</strong> the blind Rio thrust fault (Stone, 1993).<br />
The Rio thrust fault is a backthrust <strong>of</strong> the major southwest dipping thrust fault<br />
that bounds the eastern edge <strong>of</strong> the Bighorn Mountains and is responsible for their<br />
uplift (Fig. A2.17; Stone, 1993). Sheep Mountain Anticline lies in the hanging wall <strong>of</strong><br />
the Rio thrust fault, and although current interpretations <strong>of</strong> the relationship between<br />
the Rio thrust fault and the SMA thrust fault conflict (Fig. A2.21-A2.23), the Sheep<br />
Mountain fault is most likely a backthrust <strong>of</strong> the Rio thrust fault.<br />
210
(a) (b)<br />
0.0 1.2 2.5 3.8 5.0<br />
MPa<br />
(c) (d)<br />
-40 0 40<br />
MPa<br />
Figure A2.16. (a) Strain energy density for a four fault model; (b) strain energy<br />
density for a seven fault model; (c) Navier-Coulomb stress for a four fault model; (d)<br />
Navier-Coulomb stress for a seven fault model. Areas <strong>of</strong> high strain energy density<br />
and high Navier-Coulomb stress suggest the presence <strong>of</strong> faults missing from the<br />
models and/or fault propagation tendency. From Savage, 2003.<br />
211
(a)<br />
(b)<br />
Bighorn Basin<br />
Sheep Mt.<br />
Rio<br />
Thrust<br />
SMA<br />
Thrust<br />
Bighorn Mts.<br />
Western Thrust<br />
Bighorn<br />
Mountains<br />
Bighorn Mts.<br />
Eastern Thrust<br />
N<br />
10km<br />
Figure A2.17. (a) Color infra-red DOQQs <strong>of</strong> the Bighorn Mt. and Bighorn Basin area.<br />
Quadrangles downloaded from http://wgiac.state.wy.us/. Dashed red lines trace the<br />
surface projections <strong>of</strong> major thrust faults. Yellow line shows the location <strong>of</strong> the crosssection<br />
in (b). (b) Schematic cross section through the Bighorn Basin and Bighorn<br />
Mountains. The SMA thrust can be considered a 3 rd order structure. It is a backthrust<br />
<strong>of</strong> the Rio thrust fault, which is in turn a backthrust <strong>of</strong> the Bighorn Mts. Eastern Thrust.<br />
212
Structural interpretations for Sheep Mountain anticline<br />
The first structural interpretations <strong>of</strong> Sheep Mountain anticline to consider the<br />
geometry <strong>of</strong> faults in the subsurface (Fig. A2.18; Fig. A2.19; Fig. A2.20; Hennier and<br />
Spang, 1983; Forster et al., 1996; Brown 1984) were based primarily on surficial<br />
mapping <strong>of</strong> bedding contacts and attitudes (Rioux, 1958; Hennier and Spang, 1983),<br />
along with stratigraphic picks from exploration wells. The studies conclude that the<br />
steep forelimb <strong>of</strong> the anticline is due to a southwest dipping thrust fault. To reconcile<br />
this northeast thrusting direction with the southwest thrusting direction <strong>of</strong> a deeper<br />
fault, suggested by Gries (1983) in light <strong>of</strong> unpublished seismic data and later named<br />
the Rio thrust fault by Stone (1993), these studies proposed that the fault causing the<br />
uplift <strong>of</strong> Sheep Mountain is a backthrust <strong>of</strong> the Rio thrust (Fig. A2.17; Fig. A2.21).<br />
Figure A2.18. SW–NE trending cross section through Sheep Mountain anticline from<br />
Hennier and Spang, 1983. Bedding dips and formation contacts are constrained by<br />
surface mapping and geologic markers from exploration wells. Hennier and Spang<br />
postulate a relatively undeformed basement with multiple thrust planes in an overall<br />
wedge shaped geometry to generate folding in the overlying sediments.<br />
213
Figure A2.19. SW-NE trending cross-section through Sheep Mountain anticline from<br />
Forster et al., 1996. Bedding dips and formation contacts are constrained by surface<br />
mapping and geologic markers from exploration wells. A wedge shaped fault zone is<br />
hypothesized as the mechanism by which overlying strata fold.<br />
Figure A2.20. SW-NE trending cross-section through Sheep Mountain anticline from<br />
Brown, 1984. Geological constraints are not given, but are most likely surface dips<br />
and formation markers from wells. Brown (1984) proposes substantial basement<br />
folding and a wedge shaped fault zone beneath the forelimb <strong>of</strong> Sheep Mountain.<br />
[AAPG Continuing Education Courses. AAPG@1984. Reprinted by permission <strong>of</strong> the<br />
AAPG whose permission is required for further use.]<br />
214
Figure A2.21. SW-NE trending cross-section from the Bighorn Basin through the<br />
Bighorn Mountains from Forster et al., 1996 showing the fault beneath Sheep<br />
Mountain as a backthrust <strong>of</strong> the Rio Fault. Bedding dips and formation contacts are<br />
constrained by surface mapping and geologic markers from exploration wells.<br />
Basement is slightly folded in the cross-section, but there is still a wedge shaped fault<br />
zone hypothesized as the mechanism by which overlying strata fold.<br />
Figure A2.22. SW-NE trending cross-section through Sheep Mountain anticline from<br />
Stanton and Erslev, 2002. Geological constraints are surface dips, formation markers<br />
from wells, and three 2D seismic pr<strong>of</strong>iles. Stanton and Erslev propose a moderately<br />
folded basement. Their kinematic modeling suggests that the Rio thrust fault slipped<br />
after slip along the fault beneath Sheep Mountain Anticline had already uplifted the<br />
fold.<br />
215
A later study reinvestigated the fault geometry (Stanton and Erslev, 2004) with<br />
the aid <strong>of</strong> additional subsurface data in the form <strong>of</strong> two seismic reflection pr<strong>of</strong>iles<br />
perpendicular to, and one pr<strong>of</strong>ile parallel to, the trend <strong>of</strong> Sheep Mountain. Stanton and<br />
Erslev (2004) built a 3D geometric model <strong>of</strong> the structure at Sheep Mountain and then<br />
kinematically restored 2D cross sections and 3D stratigraphic surfaces taken from the<br />
geometric model, using line length balancing and inclined shear unfolding techniques.<br />
Based on these restorations, they suggest that the southwest dipping fault formed prior<br />
to the Rio thrust, being cut and <strong>of</strong>fset as the Rio thrust began to slip (Fig. A2.22).<br />
These restorations suggest the existence <strong>of</strong> a fault surface (the lower part <strong>of</strong> the<br />
southwest dipping fault) that is not supported by any currently available subsurface<br />
data (Don Stone, pers. communication).<br />
An additional structural geometry has been suggested for Sheep Mountain based<br />
on geologic interpretations further to the south, at the Torchlight Field (Don Stone,<br />
pers. commun.; Fig. A2.23; Fig. A2.24; Stone, 2004). At the Torchlight Field, the<br />
geochemistry <strong>of</strong> oil pools at various depths within the fold suggests that these pools<br />
were segmented during fold growth (Stone, 2004). As a result, Stone has proposed a<br />
structural growth history whereby the Rio thrust and the Torchlight thrust, which can<br />
be likened to the southwest dipping fault beneath Sheep Mountain, propagated<br />
simultaneously. In this structural interpretation, the two faults do not intersect or abut<br />
one another (Fig. A2.23).<br />
216
Figure A2.23 (opposite page). SW-NE trending cross-section through the Torchlight<br />
Field showing the coeval Rio and Torchlight thrust faults. From Stone, 2004. [The<br />
Mountain Geologist. RMAG@2004. Reprinted by permission <strong>of</strong> the RMAG whose<br />
permission is required for further use.]<br />
T<br />
56<br />
N<br />
T<br />
55<br />
N<br />
T<br />
54<br />
N<br />
T<br />
53<br />
N<br />
T<br />
52<br />
N<br />
43°<br />
45°<br />
44°<br />
110°<br />
Absaroka Mnts<br />
WIND RIVER<br />
RANGE<br />
R95W<br />
RIO<br />
N<br />
BIG<br />
HORN<br />
WIND RIVER<br />
BASIN<br />
108°15’<br />
BASIN<br />
Owl Creek Mnts<br />
109°<br />
108°<br />
100 km<br />
THRUST<br />
Big Horn Mnts<br />
R94W R93W R92W<br />
Sheep MountainAnticline<br />
POWDER<br />
Casper Arch<br />
107°<br />
RIVER<br />
BASIN<br />
RIO<br />
THRUST<br />
A<br />
BighornRiver<br />
BASIN<br />
BIGHORN<br />
MOUNTAINS<br />
A‘<br />
basement<br />
involved<br />
thrusts<br />
Paleozoic<br />
anticlines<br />
5 mi<br />
8km<br />
SCALE<br />
Torchlight Field<br />
MANDERSON<br />
Figure A2.24. Tectonic map <strong>of</strong> the northeastern edge <strong>of</strong> the Bighorn Basin showing<br />
the location <strong>of</strong> Sheep Mountain anticline in red. The inset shows the location, within<br />
Wyoming, <strong>of</strong> the area shown in the figure. Solid black lines represent the axes <strong>of</strong><br />
Paleozoic anticlines, and dashed black lines represent the related thrust faults. The<br />
curvilinear, segmented thick dashed black line represents the projected trace <strong>of</strong> the<br />
Rio thrust fault. Green dashed line A-A’ shows the location <strong>of</strong> the seismic pr<strong>of</strong>ile<br />
through the Torchlight Field. Modified from Stone, 2004.<br />
217<br />
44°45’<br />
44°30’
A recently published geomechanical study (Savage and Cooke, 2004) used a<br />
heuristic approach to infer the fault geometry responsible for generating the splay fold,<br />
termed “the thumb” (Savage and Cooke, 2004), along the southwestern backlimb <strong>of</strong><br />
SMA (Fig. A2.25). Following Hennier and Spang (1984), Savage and Cooke (2004)<br />
assumed that the main Sheep Mountain fold is underlain by a primary fault and that a<br />
secondary fault underlies the thumb. They used a boundary element code to forward<br />
model for the vertical displacement fields resulting from a series <strong>of</strong> models within<br />
which the primary fault was held constant in length, depth, dip, and aspect ratio and<br />
the secondary fault varied systematically in these parameters, as well as in distance<br />
from the main fault (Fig. A2.26). The study also considered the influence <strong>of</strong> fault<br />
interaction and differing principal contraction directions on fold shape. Model results,<br />
some <strong>of</strong> which are presented in Figure A2.27, indicate that best estimates for the<br />
geometry <strong>of</strong> the secondary fault are: 30% <strong>of</strong> the length <strong>of</strong> the main fault; shallower<br />
depth than the main fault; 20° clockwise from the main fault, 45° dip; not connected to<br />
the main fault.<br />
Figure A2. 25. Structure contour map <strong>of</strong> SMA (from Andrews et al., 1944) with gray<br />
arrow showing the location <strong>of</strong> the thumb structure that has been interpreted by<br />
Hennier and Spang (1984) to overly a splay fault that branches from the major fault<br />
underlying SMA. [Reprinted from Journal <strong>of</strong> Structural Geology, v. 26., Savage, H.<br />
and M. L. Cooke, The effect <strong>of</strong> non-parallel fault interaction on fold patterns, p. 905-<br />
917, Copyright 2004, with permission from Elsevier].<br />
218
Figure A2.26. Model set-up. The geometry <strong>of</strong> the primary fault is held constant in<br />
length, depth, dip, and aspect ratio. The secondary fault varies in (A) size, distance<br />
from the primary fault, orientation, and (B) depth. [Reprinted from Journal <strong>of</strong> Structural<br />
Geology, v. 26., Savage, H. and M. L. Cooke, The effect <strong>of</strong> non-parallel fault<br />
interaction on fold patterns, p. 905-917, Copyright 2004, with permission from<br />
Elsevier].<br />
219
Figure A2.27. Surface fold patterns for models within which secondary fold size and<br />
depth were varied. Thick gray lines show traces <strong>of</strong> the upper tip <strong>of</strong> the faults. Contour<br />
interval is 2 m. The dip and orientation <strong>of</strong> the secondary fault is held constant at 60°<br />
and 20° respectively. The gray polygon outlines the synthetic structure contour maps<br />
that depict multiple fold patterns whereas synthetic structure contour maps outside<br />
the gray polygon depict isolated folds. From Savage and Cooke, 2004. [Reprinted<br />
from Journal <strong>of</strong> Structural Geology, v. 26., Savage, H. and M. L. Cooke, The effect <strong>of</strong><br />
non-parallel fault interaction on fold patterns, p. 905-917, Copyright 2004, with<br />
permission from Elsevier].<br />
220
44°30’<br />
44°45’<br />
Reprocessing <strong>of</strong> ten seismic lines acquired in the early 1980s is underway.<br />
Figure A2.28 shows the locations <strong>of</strong> these lines. We hope to better understand the<br />
geometry <strong>of</strong> the Sheep Mountain fault and the Rio thrust fault. Initial results place<br />
constraints on the depth to the Sheep Mountain fault and its angle <strong>of</strong> dip. The Rio<br />
thrust fault is more difficult to constrain, but specific unfaulted sedimentary layers<br />
provide a minimum constraint on the depth to the Rio thrust fault.<br />
108°22’30”<br />
BH-6<br />
108°22’30”<br />
41-82<br />
2 km<br />
17-81<br />
19-81<br />
12-81<br />
11-81<br />
44-82<br />
108°00’<br />
108°00’<br />
Figure A2.28. DEM <strong>of</strong> the western Bighorn Basin showing the location <strong>of</strong> 10 seismic<br />
lines that are being investigated for thrust fault geometry.<br />
14-81<br />
221<br />
TE-103<br />
13-81<br />
44°45’<br />
44°30’
Stop 2: Fold shape<br />
5 minutes walking (Fig. A2.6)<br />
4:35 PM – 4:45 PM<br />
Waypoint (UTM zone 12N): 4947765 N<br />
0722336 E<br />
elev. = 1370 m<br />
Objectives<br />
Discuss fold shape<br />
Discuss location <strong>of</strong> hinge<br />
Key Points<br />
The fold shape changes from being tight and kink-like in the NW to being<br />
more rounded toward the SE.<br />
The hinge is not coincident with the topographic high, but instead lies to the<br />
NE.<br />
The shape <strong>of</strong> Sheep Mountain anticline changes along the fold axis. Near the<br />
northern termination, the fold pr<strong>of</strong>ile is very tight (Twiss and Moores, 1992, p.228;<br />
Fig. A2.29a). Toward the south, the asymmetry increases while the fold hinge<br />
becomes rounder (Fig. A2.29b).<br />
(a) (b)<br />
Figure A2.29. The hinge <strong>of</strong> SMA changes along strike from being tighter in the NW<br />
(a) to rounder in the SE (b). (a) View to the southeast. (b) View to the west.<br />
222
The hinge <strong>of</strong> Sheep Mountain anticline lies to the northeast side <strong>of</strong> the<br />
topographic high (Fig. A2.30). The highest parts <strong>of</strong> SMA are within the backlimb <strong>of</strong><br />
the fold.<br />
Figure A2.30. The hinge <strong>of</strong> SMA is not coincident with the topographic high.<br />
Resistant beds within the Phosphoria (yellow) and Tensleep (red) are correlated from<br />
the backlimb through the hinge (where they are eroded) and to the forelimb with<br />
dotted lines. View to the SE.<br />
223
Stop 3: Fracture introduction; nose fractures<br />
NW nose – site 2<br />
5 minutes walking (Fig. A2.6)<br />
4:45 PM – 5:45 PM<br />
Waypoint (UTM zone 12N): 4947359 N<br />
0722823 E<br />
elev. = 1423 m<br />
Objectives<br />
Review previous fracture studies for Sheep Mountain<br />
Discuss methods <strong>of</strong> fracture characterization<br />
Present fracture interpretation for the site and the nose introducing the two<br />
main systematic fracture sets<br />
Key Points<br />
Previous fracture studies date back to the 1960s and are archaic.<br />
Current SMA fracture studies include a complete outcrop characterization:<br />
fracture orientations (strike and dip relative to bedding), surface<br />
textures, filling, displacement discontinuity, and abutting relations.<br />
Two systematic fracture sets are observable in the nose <strong>of</strong> SMA. The strike <strong>of</strong><br />
the fractures within these sets rotates clockwise toward the NW<br />
termination <strong>of</strong> the fold.<br />
Previous fracture studies at Sheep Mountain<br />
Two fracture studies at Sheep Mountain were conducted during the 1960s:<br />
Harris et al. (1960) and Johnson et al. (1965). Both studies relied primarily on field<br />
observations <strong>of</strong> fracture orientations and measures <strong>of</strong> spacing or frequency.<br />
Recognizing that many factors influence the occurrence and concentration <strong>of</strong><br />
fractures on a fold, Harris et al. (1960) developed a method to correct for variations in<br />
lithology and bed thickness. After documenting the number <strong>of</strong> fractures per square<br />
yard at various stations, the researchers calculated proportionality constants to<br />
normalize measurements made within beds <strong>of</strong> different lithologic units and<br />
thicknesses to a datum bed and thus better understand how structural position<br />
influences fracturing. The collected data are displayed on (a) a fracture pattern map<br />
(Fig. A2.31) that shows the trends <strong>of</strong> the deformational fracture sets and their field<br />
intensities at locations on a structure contour map and (b) an iso-fracture map that<br />
shows the concentration <strong>of</strong> fractures relative to a datum bed (Fig. A2.32).<br />
224
Harris et al. (1960) found that thinner beds are more susceptible to fracturing<br />
than thicker beds and ductile units have poorer developed and more widely spaced<br />
fractures than brittle units. Based on strike directions, they determined that one main<br />
fracture set is present on each flank <strong>of</strong> Sheep Mountain and that these fracture sets are<br />
both present at the plunging noses <strong>of</strong> the fold. These two systematic (planar, parallel,<br />
repetitious) fracture sets were interpreted to be conjugate sets “<strong>of</strong> compressional<br />
deformational origin” and “related to shear stresses”.<br />
Figure A2.31. Fracture pattern map from Harris et al., 1960 showing the strike<br />
directions and observed densities <strong>of</strong> the major fracture sets at Sheep Mountain<br />
superposed on a structure contour map. [AAPG Bulletin. AAPG@1960. Reprinted by<br />
permission <strong>of</strong> the AAPG whose permission is required for further use.]<br />
225
A critique <strong>of</strong> this study in light <strong>of</strong> present day characterization techniques<br />
presents points for improvement. (1) In correcting fracture measurements to a datum<br />
bed, fracture saturation (Bai and Pollard, 1999; Wu and Pollard, 1995) is assumed. (2)<br />
Diagnostic evidence for the interpretation <strong>of</strong> the main fractures sets as being related to<br />
shear stresses (see Pollard and Aydin, 1988) was not published. (3) Fracture<br />
orientations were not rotated to remove the effect <strong>of</strong> bedding orientation. (4) The<br />
relative age relationships <strong>of</strong> the fracture sets, which could have strengthened or<br />
invalidated the interpretation that the two sets at SMA formed during the same<br />
deformational event, were not deduced from field observations.<br />
Figure A2.32. Iso-fracture map from Harris et al., 1960 showing the relative intensity<br />
<strong>of</strong> fracturing in the Sheep Mountain area as corrected to a datum bed. [AAPG<br />
Bulletin. AAPG@1960. Reprinted by permission <strong>of</strong> the AAPG whose permission is<br />
required for further use.]<br />
226
Johnson et al. (1965) studied fracture geometries within two formations <strong>of</strong><br />
significantly different ages, the Pennsylvanian Tensleep Fm. and the Lower<br />
Cretaceous Cloverly Fm., in the Bighorn Basin. The study was designed to test the<br />
hypothesis that differences between the fracture patterns within the two lithologies<br />
would suggest that a Permo-Triassic orogeny had occurred in the Bighorn Basin.<br />
Fracture strike, dip, length and frequency were noted at several study sites.<br />
Four fracture sets were documented (Fig. A2.33) in both lithologies, prompting<br />
the conclusion that pre-existing heterogeneities are an important factor during the<br />
development <strong>of</strong> fractures, despite the age relation between the fracturing beds and the<br />
previous orogenies. Based on orientation data, Johnson et al. (1965) suggest the<br />
mechanism by which each fracture set formed. East-west and north-south trending sets<br />
were suggested to be “shear-joints” developed at acute angles to the fold axes. A 105º<br />
to 155º trending set was interpreted as tension-joints developed parallel to fold axes.<br />
Together with a 025º to 065º trending set, this 105º to 155º trending set was also<br />
interpreted as “release tension-joints” developed either perpendicular or parallel to the<br />
fold axis.<br />
Again, a critique <strong>of</strong> this study in light <strong>of</strong> present day characterization techniques<br />
provides points for improvement. (1) Rather than being documented in the field, the<br />
modes <strong>of</strong> deformation <strong>of</strong> these fracture sets were suggested based on angular<br />
relationships between fracture sets and fold axes. (2) In the northeastern section <strong>of</strong> the<br />
study area, fold axes are north-south, and the north-south and east-west fracture sets<br />
are still observed. The interpretation <strong>of</strong> these as shear-joints formed at acute angles to<br />
the fold axes breaks down. (3) Fracture measurements were not unfolded. (4) Regional<br />
studies or measurements in flat lying areas were not looked at to delineate regional<br />
fracture sets from folding related fracture sets.<br />
227
Figure A2.33. Joint frequencies presented in rose diagrams at selected study sites.<br />
The spatial locations <strong>of</strong> these sites are plotted with respect to structural axes. From<br />
Johnson et al., 1965.<br />
228
Methods <strong>of</strong> fracture characterization<br />
At Sheep Mountain, fracture characterization <strong>of</strong> systematic fractures at the<br />
outcrop included recording orientation relative to bedding, size, and spacing (Fig.<br />
A2.34); and noting evidence for opening or shearing mode in the form <strong>of</strong> fillings, tail<br />
cracks, tensile gashes, etc. (Fig. A2.35a). Fracture mode was also investigated at the<br />
microscale (Fig. A2.35b). Chronological relationships based on abutting relations<br />
among the fracture sets were noted and documented by mapping on field photos (Fig.<br />
A2.36).<br />
(a) (b)<br />
Figure A2.34. Characterizing fracture orientations. (a) Fracture orientations and<br />
orientation <strong>of</strong> bedding were recorded. (b) Fracture measurements were then plotted<br />
on stereonets and rotated to derive their orientations relative to horizontal bedding.<br />
Densities <strong>of</strong> clusters <strong>of</strong> poles to fractures, shown in shades <strong>of</strong> pink, helped to<br />
determine the orientations <strong>of</strong> distinct fracture sets, represented by black great circles.<br />
Figure A2.35. Characterizing mode <strong>of</strong> deformation. (a) Field evidence for sheared<br />
fractures includes the presence <strong>of</strong> tail cracks. (b) Thin section evidence for jointing<br />
includes the absence <strong>of</strong> the products <strong>of</strong> shearing such as crushed grains, planar<br />
fabrics, and slickenlines.<br />
229
Figure A2.36. Characterizing abutting relationships. (a) Field photograph <strong>of</strong> a<br />
pavement with two fracture sets. (b) Interpretation <strong>of</strong> abutting relationships between<br />
fracture sets.<br />
230
Fracture interpretation<br />
Site 2 - Tensleep sandstone<br />
Nose Hinge<br />
Figure A2.37. Field photograph showing the fracture pattern in a sandstone<br />
pavement <strong>of</strong> the Tensleep Fm. at site 2 in the nose hinge.<br />
At the site 2 sandstone pavement (Fig. A2.37), we will introduce many aspects<br />
<strong>of</strong> the Sheep Mountain fracture characterization study. First, different sets can be<br />
distinguished based on orientation (strike and dip) and mode <strong>of</strong> deformation (Fig.<br />
A2.38; Fig. A2.39, Fig. A2.40). Where shearing indicators exist in the field, we will<br />
determine if all fractures <strong>of</strong> the given orientation have slipped in the same direction.<br />
We will look at abutting relationships to see if consistent age relationships can be<br />
determined (Fig. A2.39, Fig. A2.40), and we will notice the spacing between fractures<br />
<strong>of</strong> each set. These techniques will be used over the course <strong>of</strong> the field trip to<br />
characterize fracture patterns seen in outcrop at Sheep Mountain.<br />
The major systematic fracture sets present at site 2 are the 045º and the 135º sets<br />
(Figure 38). Respectively, they are called Set II and Set III.<br />
Figure A2.38. Polar stereonets left to right are present day fracture poles, pre-folding<br />
fracture poles, and great circles for the mean orientation <strong>of</strong> each set. Poles to<br />
bedding are gray dots.<br />
231
N<br />
10 cm<br />
Figure A2.39. Field photo and line drawing from site 2 showing interpreted fracture<br />
sets and abutting relationships. Note that the 135º fractures have a range <strong>of</strong><br />
orientations. Here, 135º, 010º, and 080º abut against 045º. Some geometries within<br />
this outcrop might suggest that the 010º fracture set are tail cracks related to left<br />
lateral shear along 045º fractures. We will determine if other kinematic evidence for<br />
this idea is present at the outcrop.<br />
N<br />
10 cm<br />
Figure A2.40. Field photo and line drawing from site 2 showing interpreted fracture<br />
sets and abutting relationships. Here, 135º fractures abut against 080º more than<br />
080º abut against 135º. Geometries in this photo might suggest that the 080º fracture<br />
set is related to right lateral shear along 045º fractures. We will determine if other<br />
kinematic evidence for this idea is present at the outcrop.<br />
232<br />
045º<br />
N<br />
10 cm<br />
080º<br />
135º<br />
010º<br />
045º<br />
080º<br />
135º<br />
N<br />
10 cm
Fracture characterization in the nose<br />
The fold nose is defined as the area NW <strong>of</strong> the position in the backlimb where<br />
bedding strike has rotated to 150° from the typical value <strong>of</strong> 135°. In the nose, fracture<br />
data were collected primarily from limestones within the Phosphoria Formation<br />
because the Tensleep Formation crops out in limited locations.<br />
Close to the nose hinge, in the Tensleep Fm, the fractures consist <strong>of</strong> two main<br />
joint sets trending 045° (Set II) and 135° (Set III) (Fig. A2.38). From abutting<br />
relationships, the Set II joints predate Set III joints (Fig. A2.39; Fig. A2.40). In the<br />
nose hinge, we also observe two main fracture sets (Figure 41) in both Tensleep (Fig.<br />
A2.42) and Phosphoria (Fig. A2.43) outcrops. One set is NE-trending and composed<br />
<strong>of</strong> joints. Another set is SE-trending and also composed <strong>of</strong> joints. The chronology is<br />
difficult to determine (Fig. A2.42) as the abutting relationships are not entirely<br />
consistent. However, based on strike and mode <strong>of</strong> deformation, we suggest that theses<br />
two joint sets are similar to Set II and Set III described throughout the fold that we will<br />
see later during the field trip.<br />
Throughout the nose, as mentioned above, we observe that the NE-trending Set<br />
II joints vary in orientation from 045° to 070° toward the northwest (Fig. A2.41).<br />
Fractures trend 045°at sites 2, 26, 53, and 60 and 070° at all but one <strong>of</strong> the remaining<br />
sites. The SE-trending Set III joints also vary in orientation throughout the nose, but to<br />
the largest extent within the nose backlimb (Fig. A2.41). They trend 135° at sites 60,<br />
61, and 62, and trend 160° at sites 64, 65, and 66. In the nose hinge, these SE-trending<br />
joints maintain an average orientation <strong>of</strong> 140° at all sites except site 57 (Fig. A2.41).<br />
233
Jurassic<br />
Trias<br />
Permian (Phospphoria Fm)<br />
Carboniferous<br />
(Pennsylvanien, Tensleep Fm)<br />
Carboniferous<br />
(Pennsylvanian, Amsden Fm)<br />
Carboniferous<br />
(Mississipian, Madison Fm)<br />
Anticlinal axis<br />
Hinge<br />
site 66<br />
N<br />
site 65<br />
N<br />
46<br />
50<br />
site 57<br />
site 64<br />
N<br />
N<br />
Backlimb<br />
N<br />
37<br />
250 m<br />
site 56<br />
site 63<br />
N<br />
N<br />
site 67<br />
site 55<br />
57<br />
66 56<br />
55 67<br />
65 68<br />
26<br />
64<br />
54<br />
63 53<br />
62<br />
N<br />
N<br />
61<br />
60<br />
2<br />
site 68<br />
site 54<br />
Forelimb<br />
site 26<br />
site 53<br />
site 02<br />
site 62 site 61 site 60<br />
Figure A2.41. Geologic map from Rioux (1994) <strong>of</strong> the nose <strong>of</strong> Sheep Mountain<br />
anticline with the nose fracture measurement sites and the corresponding rose<br />
diagrams for measurement sites in the backlimb <strong>of</strong> the nose. Red lines show the<br />
average strike <strong>of</strong> Set II fractures and blue lines show the average strike <strong>of</strong> Set III<br />
fractures. Note that the orientations <strong>of</strong> these fracture sets rotate clockwise as we<br />
progress to the northwest. From Bellahsen et al., 2006a.<br />
234<br />
54<br />
52<br />
46<br />
N<br />
58<br />
56<br />
36<br />
N<br />
N<br />
N<br />
31<br />
53<br />
57<br />
N<br />
N<br />
N<br />
N<br />
31<br />
78<br />
61<br />
79
Figure A2.42. Fracture pattern in the hinge <strong>of</strong> the fold nose. (a) Field photograph<br />
showing the fracture pattern in the sandstone <strong>of</strong> the Tensleep Fm. at site 2. (b) Line<br />
drawing <strong>of</strong> the outcrop in (a) showing that Set III (135°) terminate at Set II (045°)<br />
fractures more times than Set II fractures terminate at Set III fractures. Stereonets<br />
show poles to fractures as measured in the field, poles to fractures relative to<br />
horizontal bedding, and great circles representing the average orientation <strong>of</strong> each<br />
fracture set. From Bellahsen et al., 2006a.<br />
235
Figure A2.43. Fracture pattern in the backlimb <strong>of</strong> the fold nose. (a) Field photograph<br />
showing the fracture pattern in the limestone <strong>of</strong> the Phosphoria Fm. at site 2. (b) Line<br />
drawing <strong>of</strong> the outcrop in (a) showing that the chronology <strong>of</strong> fracture Set II (045°) and<br />
Set III (135°) is hard to determine from abutting relationships at this location.<br />
Stereonets show poles to fractures as measured in the field, poles to fractures<br />
relative to horizontal bedding, and great circles representing the average orientation<br />
<strong>of</strong> each fracture set, respectively. From Bellahsen et al., in press.<br />
236
DAY 2<br />
Friday, June 16 th<br />
310<br />
Spence Oilfield Rd<br />
Stop 4<br />
Stop 7<br />
Stop 5<br />
Stop 6<br />
Stop 8<br />
Ribbon Canyon Rd<br />
WyoBen<br />
Lunch<br />
CR 26<br />
From Greybull<br />
Figure A2.44. Google <strong>Earth</strong> image showing roads near Sheep Mountain and<br />
directions to Day 2 stops. Light blue dashed line marks the driving route to stop 4.<br />
Yellow dashed line marks the driving route to stops 5 - 8. Red hachured lines mark<br />
walking routes to field trip stops.<br />
237
Stop 4: Backlimb fractures<br />
Site 8 – Tensleep sandstone<br />
Backlimb<br />
30 minutes driving from Greybull<br />
walk up Gypsum Springs mound to the west <strong>of</strong> the road (5 min.), view site 8<br />
8:30 AM – 9:15 AM<br />
Waypoint (UTM zone 12N): 4947765 N<br />
0722336 E<br />
elev. = 1370 m<br />
Objectives<br />
Discuss fracture characterization at site<br />
Discuss kinematic indicators at site<br />
Discuss fracture characterization in the backlimb<br />
Key Points<br />
In the backlimb, four systematic fracture sets are observed: 110°, 045°,<br />
135°, and 110°V.<br />
At site 8, hackle marks and tail cracks are observed along Set II fractures<br />
indicating both opening and shearing modes <strong>of</strong> deformation.<br />
Figure A2.45. Photo showing location <strong>of</strong> vantage point for stop 4. Note the Tensleep<br />
pavement on the fold at the horizon.<br />
238
Overview<br />
At stop 3, we will walk up onto the Gypsum Springs mound to the west <strong>of</strong> the<br />
fold to discuss fracturing in a backlimb pavement <strong>of</strong> Tensleep sandstone that is visible<br />
from the road (Fig. A2.45). The noticeable lineaments are due to weathering along the<br />
two main fracture sets that are orthogonal to one another. The weathering gives the<br />
surface a pronounced hummocky nature (Fig. A2.46, Fig. A2.47). Strike and dip<br />
measurements relative to horizontal bedding (Fig. A2.47c) indicate that there are four<br />
major fracture sets at this site. Three are perpendicular to bedding and trend 110° (Set<br />
I), 045° (Set II), and 135° (Set III). A fourth set is oblique to bedding and trends 110°<br />
(Set IV). Two minor fracture sets are also present at this site.<br />
Set I<br />
Set II<br />
Figure A2.46. Photo showing the hummocky nature <strong>of</strong> site 8 pavement. The two<br />
noticeable fracture sets trend 110° (Set I) and 045° (Set II).<br />
239
Figure A2.47. (a) Field photo <strong>of</strong> Tensleep sandstone pavement<br />
<strong>of</strong> site 8. (b) Line drawing <strong>of</strong> outcrop in (a) that shows Set II fractures<br />
(strike <strong>of</strong> 045°) terminating at Set I fractures (strike <strong>of</strong><br />
110°). (c) Stereonets for fractures measured at pavement in (a).<br />
From left to right, the stereonets show the poles to fractures as<br />
oriented in the field today, poles as oriented when bedding is<br />
restored to horizontal, and great circles representing the major<br />
fracture sets at the outcrop as oriented when bedding is<br />
restored to horizontal. From Bellahsen et al., 2006a.<br />
Nb planes 116<br />
(c)<br />
N<br />
N<br />
N<br />
3 m<br />
Set I<br />
Set II<br />
240<br />
(b)<br />
(a)<br />
NW SE
Kinematic Indicators<br />
Investigation <strong>of</strong> Set II fractures (trending 045°) at site 8 provides evidence for<br />
the kinematic history <strong>of</strong> the fractures. Hackle visible in outcrop (Fig. A2.48) indicate<br />
that Set II fractures formed as joints, with an opening mode <strong>of</strong> deformation. Shearing<br />
indicators (Fig. A2.49) suggest that some Set II fractures have sheared in a left-lateral<br />
sense.<br />
1 m<br />
Figure A2.48. Concentric rib marks and hackle on the surface <strong>of</strong> a fracture a few<br />
meters in size trending at 045°. Hackle such as these provide field evidence<br />
supporting an opening mode <strong>of</strong> formation for the 045° fracture set (Pollard and Aydin,<br />
1988).<br />
Figure A2.49. Splay cracks suggest left-lateral shearing has occurred along this<br />
submeter scale Set II fracture.<br />
241
Fracture characterization in the backlimb<br />
Figure A2.50. Aerial photo <strong>of</strong> the backlimb <strong>of</strong> SMA. View to the North.<br />
Four systematic fracture sets are found at locations in the backlimb. Three are<br />
bed perpendicular and trend 110° (Set I), 045° (Set II), and 135° (Set III). A fourth set<br />
is oblique to bedding and trends 110° (Set IV) (Fig. A2.51; Fig. A2.52). A description<br />
<strong>of</strong> each set, as observed both in outcrop and in thin section, follows.<br />
Bed perpendicular fractures trending 110° are 10-20 m long as compared to a<br />
height <strong>of</strong> a few meters (equivalent to mechanical layer thickness). The fracture traces<br />
are linear and their spacing varies from 1 to 3 m (Fig. A2.47). Their deformation mode<br />
is difficult to determine in the field. They resemble joints at some sites and at other<br />
sites they resemble deformation bands or display evidence <strong>of</strong> left lateral shear.<br />
Microscopically, the fillings <strong>of</strong> Set I fractures are characterized by a decrease <strong>of</strong> grain<br />
size, a decrease <strong>of</strong> porosity, and an increase in amount <strong>of</strong> calcite cement as compared<br />
to the host rock (Fig. A2.53).<br />
Set II fractures trend 045° and are bed perpendicular. Set II fractures terminate<br />
against Set I fractures (Fig. A2.47) and, as a result, are only 2 to 5 m in length. Their<br />
traces are linear and their spacing is approximately 1 meter. In most locations, they are<br />
interpreted as opening mode. As seen in thin section, the fillings typically consist <strong>of</strong><br />
large calcite crystals without evidence <strong>of</strong> grain fracturing or crushing, which supports<br />
242
a dilational origin (Fig. A2.54). Some instances where left-lateral shearing occurred<br />
along Set II fractures has been documented (Fig. A2.49).<br />
Set III fractures have a more restricted occurrence than Sets I and II (Fig.<br />
A2.52). They trend 135°, are bed perpendicular, and contain a coarse calcite mineral<br />
filling (Fig. A2.55) that is indicative <strong>of</strong> opening mode. The length <strong>of</strong> these fractures is<br />
on the order <strong>of</strong> a few meters. Set III fractures terminate against both Set I and Set II<br />
fractures.<br />
Set IV fractures trend 110° and are parallel to Set I fractures, but are vertical and<br />
therefore oblique rather than perpendicular to bedding (Fig. A2.57). Abutting<br />
relationships are difficult to establish because these fractures have been observed<br />
mainly in cross-section. These fractures are several meters long with an approximate<br />
spacing <strong>of</strong> one meter. Most Set IV fractures are open, and lack evidence <strong>of</strong> shearing.<br />
Microstructural examination shows that the preserved calcite filling is distinct from<br />
that in Set II and Set III fractures (Fig. A2.56). Matrix grains at the walls <strong>of</strong> Set IV<br />
fractures are crushed and display a preferred elongation direction, suggesting a two<br />
phase deformation: a shearing event followed by an opening vein-filling event.<br />
Figure A2.51. A typical backlimb stereonet showing the orientations <strong>of</strong> the four main<br />
fracture sets found in this structural location at SMA. Set I fractures (110°) are in<br />
green, Set II fractures (045°) are in blue, Set III fractures (135°) are in yellow, and Set<br />
IV fractures (110°V) are in purple.<br />
243
Site 7-8<br />
N<br />
Site 18<br />
N<br />
40<br />
N<br />
20<br />
108°10'<br />
Site 25<br />
N<br />
Site 72<br />
N<br />
Site 77a<br />
N<br />
38<br />
15<br />
40<br />
7-8<br />
Site 71<br />
N<br />
Site 80<br />
N<br />
Site 84<br />
N<br />
26<br />
24<br />
07<br />
37<br />
25<br />
Site 78<br />
N<br />
Site 22<br />
N<br />
08<br />
26<br />
Site 07<br />
N<br />
25<br />
23<br />
36<br />
44°39'<br />
18 18<br />
Site 08<br />
N<br />
71 17<br />
72<br />
Site 81<br />
N<br />
Site 76<br />
N<br />
35<br />
16<br />
116<br />
Site 23<br />
N<br />
108°09'<br />
01<br />
80 78<br />
15<br />
81<br />
22<br />
22<br />
Site 77b<br />
N<br />
32<br />
77<br />
76<br />
30<br />
Site 85<br />
N<br />
19<br />
84<br />
25<br />
86<br />
85<br />
20<br />
Site 18<br />
N<br />
51<br />
Site 17<br />
N<br />
83<br />
Site 83<br />
N<br />
21<br />
29<br />
42<br />
59<br />
Site 16<br />
N<br />
Site 01<br />
N<br />
44<br />
Site 15<br />
N<br />
74<br />
1 km<br />
Site 59<br />
N<br />
48<br />
37<br />
Site 22<br />
N<br />
139<br />
73<br />
52<br />
Fracture Sets<br />
Site 74<br />
N<br />
Site 19<br />
N<br />
36<br />
44<br />
Set I<br />
Set II<br />
Set III<br />
Set IV<br />
minor set<br />
47<br />
Site 20<br />
N<br />
108°08'<br />
Site 21<br />
N<br />
44<br />
Site 73<br />
N<br />
63<br />
Site 52<br />
N<br />
Figure A2.52. Backlimb fracture measurements. Phosphoria sites are labeled with<br />
yellow numbers and dots with the corresponding stereonets to the lower left <strong>of</strong> the<br />
DOQQ. Tensleep sites are labeled in red numbers and dots with the corresponding<br />
stereonets to the upper right <strong>of</strong> the DOQQ. Great circles are color coded: Set I is<br />
green, Set II is blue, Set III is yellow, and Set IV is purple. Other sets present at<br />
measurement sites that are not one <strong>of</strong> the four main fracture sets are shown in gray.<br />
244<br />
44°37'<br />
35<br />
35
0.5 mm<br />
Figure A2.53. Microscopic detail <strong>of</strong> a Set I (110°) fracture in the Tensleep Fm.<br />
sandstone <strong>of</strong> the backlimb. The fracture is characterized by a zone with less porosity,<br />
smaller quartz grains and a greater amount <strong>of</strong> calcite cement as compared to the host<br />
rock. These fractures are suggestive <strong>of</strong> shearing as in a deformation band. From<br />
Bellahsen et al., 2006a.<br />
Figure A2.54. Microscopic detail <strong>of</strong> a Set II (045°) fracture in the Tensleep Fm.<br />
sandstone <strong>of</strong> the backlimb. The fracture is characterized by distinct fracture walls and<br />
a large-crystal calcite filling, suggestive <strong>of</strong> opening. From Bellahsen et al., 2006a.<br />
245
Figure A2.55. Microscopic detail <strong>of</strong> a Set III (135°) fracture in the Tensleep Fm.<br />
sandstone <strong>of</strong> the backlimb. The fracture is characterized by distinct fracture walls and<br />
a large-crystal calcite filling, suggestive <strong>of</strong> opening. From Bellahsen et al., 2006a.<br />
Figure A2.56. Microscopic detail <strong>of</strong> a Set IV (110°, vertical) fracture in the Tensleep<br />
Fm. sandstone <strong>of</strong> the backlimb. The fracture is characterized by distinct fracture walls<br />
and a large-crystal calcite filling and also has very fine grains along the fracture walls,<br />
suggestive <strong>of</strong> shearing followed by opening. From Bellahsen et al., 2006a.<br />
246
NE SW<br />
1 m<br />
Figure A2.57. Vertical Set IV fractures in the backlimb to the NW <strong>of</strong> stop 5 at site 23<br />
in the Tensleep Fm. From Bellahsen et al., 2006a.<br />
247
Stop 5: Backlimb fractures and shearing <strong>of</strong> Set I<br />
Site 72 – Phosphoria limestone<br />
Backlimb<br />
5 minutes driving from previous stop; 10 minutes walking<br />
9:30 – 10:00<br />
Waypoint (UTM zone 12N): 4945401 N<br />
0724268 E<br />
elev. = 1310 m<br />
Objectives<br />
Observe and discuss shearing indicators at the outcrop.<br />
Key Points<br />
Field evidence for shearing <strong>of</strong> fractures exists in the form <strong>of</strong> tail cracks.<br />
Tail cracks indicate a left-lateral sense <strong>of</strong> shear along Set I fractures.<br />
045°<br />
020°<br />
090°<br />
Figure A2.58. Site 72 pavement at stop 5. Five systematic fracture sets are found at<br />
this outcrop. The nominal strike direction <strong>of</strong> each set is labeled in the photo: 020°,<br />
045°, 090°, 110°, and 170°<br />
170°<br />
248<br />
110°
Shearing <strong>of</strong> Set I fractures in the backlimb<br />
Shearing along Set I fractures has been noted in the backlimb. Tail cracks along<br />
isolated small fractures provide the most convincing evidence for shear (Figures 59 –<br />
62). At site 72, we also see shear along fractures that measure several meters long or<br />
more (Figure 63). These tail cracks have an average strike <strong>of</strong> 080°. All recorded tail<br />
cracks indicate a left-lateral sense <strong>of</strong> shearing.<br />
N<br />
Figure A2.59. Set I fractures in the backlimb at site 72 that have sheared in a leftlateral<br />
sense.<br />
249<br />
N
N<br />
10 cm<br />
N<br />
10 cm<br />
Figure A2.60. Set I fracture in the backlimb at site 72 that has sheared in a leftlateral<br />
sense.<br />
N<br />
10 cm<br />
Figure A2.61. Set I fracture in the backlimb at site 72 that has sheared in a leftlateral<br />
sense.<br />
250<br />
N<br />
10 cm
W E<br />
Figure A2.62. Set I fractures in the backlimb at site 74 that have sheared in a leftlateral<br />
sense. As in this photo, set I fractures that have sheared are <strong>of</strong>ten found in<br />
close proximity to set I fractures that have not sheared.<br />
251
080°<br />
110°<br />
Figure A2.63. Set I fractures on the order <strong>of</strong> several meters in the backlimb at site 72<br />
that have sheared in a left-lateral sense.<br />
252
Stop 6: Backlimb fractures<br />
Site 81 – Phosphoria limestone; Site 22 – Tensleep sandstone (same wash)<br />
Backlimb<br />
10 minutes driving from previous stop<br />
15 minutes walking<br />
10:30 AM – 11:30 AM<br />
Waypoint (UTM zone 12N): 4944638 N<br />
0724648 E<br />
elev. = 1293 m<br />
Objectives<br />
Discuss fracture characterization at site<br />
Point out shearing seen in outcrop<br />
Discuss the role <strong>of</strong> the thumb in local variation <strong>of</strong> fracture pattern<br />
Key Points<br />
110° vertical fractures are present in the Phosphoria pavement at this site.<br />
Conjugate shearing along fractures striking 045° and 080° in the Tensleep<br />
pavement constrains the stress field during shearing.<br />
a<br />
Figure A2.64. Photograph <strong>of</strong> stop 6 sites. We will investigate fracturing in the<br />
Phosphoria limestone, the pavements marked in yellow in the foreground <strong>of</strong> this<br />
photo, as well as in the Tensleep sandstone, the pavement marked in red visible at<br />
the back <strong>of</strong> the wash seen in this photo.<br />
253<br />
b<br />
a
Fracture characterization<br />
This stop is a drainage wash where we will walk through a cross section <strong>of</strong><br />
Phosphoria limestone outcrop and visit a Tensleep sandstone pavement that is exposed<br />
in the wash (Figure 64). The four typical backlimb fracture sets are observed at this<br />
stop (Figure 65, 66, 67). After removal <strong>of</strong> bedding dips, three <strong>of</strong> these sets strike 110°,<br />
045°, 135° respectively and are perpendicular to bedding, whereas one set strikes 110°<br />
and is nearly vertical (not perpendicular to bedding). An additional set, striking 070°<br />
and dipping perpendicular to bedding is also observed at this site (Figure 67).<br />
An 070° fracture set is observed at this site and is interpreted as being similar to<br />
Set II. As seen in Figure 38, stop 6 is located on the thumb structure. The trend <strong>of</strong> the<br />
thumb is rotated 20° clockwise from the trend <strong>of</strong> the main fold, and we believe this<br />
change in fold orientation affects the secondary structures that form. This will be<br />
discussed with reference to mechanical models.<br />
Phosphoria<br />
Site 81<br />
(a) (b)<br />
N<br />
32<br />
Fracture Sets<br />
Set I<br />
Set II<br />
Set III<br />
Set IV<br />
075°<br />
Tensleep<br />
Site 22<br />
Figure A2.65. Stereonets for the (a) Phosphoria and (b) Tensleep pavements. Set II<br />
(045°) fractures are relatively sparse at the outcrops (Fig. A2.66; Figs. A2.68-A2.71).<br />
A set striking 070° to 080° is also present. In both pavements, set I (110°) fractures<br />
are sparse (Fig. A2.66; Figs. A2.68- A2.72).<br />
254<br />
N<br />
80
Phosphoria characterization:<br />
N<br />
1 m<br />
135°<br />
045°<br />
070°<br />
Figure A2.66. Photograph and line interpretation <strong>of</strong> fracturing <strong>of</strong> the Phosphoria<br />
pavement at stop 6.<br />
110°<br />
(a) (b)<br />
110°V<br />
110°<br />
110°V<br />
110°V<br />
Figure A2.67. Vertical set IV fractures in the backlimb at site 81 in the Phosphoria<br />
Fm. (a) Field photograph <strong>of</strong> a cross-sectional view <strong>of</strong> the pavement. (b) Line drawing<br />
interpretation <strong>of</strong> fractures <strong>of</strong> set I and set IV. (c) Set I and set IV fractures together in<br />
a tilted pavement. Set IV fractures have formed with the same strike as set I, but they<br />
are vertical in tilted bedding, dipping obliquely to the bedding interfaces, whereas Set<br />
I fractures are bed perpendicular. (a), (b), and (c) show set IV fractures nucleating at<br />
the terminations <strong>of</strong> set I fractures, providing evidence for the influence <strong>of</strong> set I<br />
fractures on the formation <strong>of</strong> set IV fractures.<br />
255<br />
110°<br />
110°V<br />
110°<br />
110°<br />
110°V<br />
(c)
Tensleep characterization:<br />
N S<br />
1 m<br />
N S<br />
1 m<br />
Figures: A2.69<br />
A2.70<br />
Figure A2.74<br />
Figure A2.71<br />
Figure A2.68. (a) Photo <strong>of</strong> the majority <strong>of</strong> the stop 6 Tensleep pavement. (b) Line<br />
interpretation <strong>of</strong> fractures. Boxes show the locations <strong>of</strong> following smaller scale<br />
interpretations.<br />
256
(a) (b)<br />
080°<br />
Figure A2.69. (a) Field photo <strong>of</strong> pavement at site 22 in the Tensleep sandstone. (b)<br />
Line drawing <strong>of</strong> fractures in (a) which, based on abutting relations, is broken down<br />
into stages <strong>of</strong> formation in figure A2.70.<br />
(a) (b)<br />
(c)<br />
140°<br />
N<br />
140°<br />
080°<br />
Figure A2.70. Interpretation <strong>of</strong> stages <strong>of</strong> fracture growth for pavement in figure<br />
A2.69 based on abutting relations. (a) Development <strong>of</strong> 140° fracture. (b) 080°<br />
fractures form, in some places stopping against 140° fractures. (c) 020° fractures<br />
form, abutting both 140° and 080° fractures.<br />
257<br />
N<br />
140°<br />
080°<br />
140°<br />
080°<br />
020°<br />
N<br />
020°<br />
N
Shearing at site<br />
In the Tensleep sandstone, tail cracks are found on two fracture sets (Figure 71,<br />
72, 73). The first set, with an average strike <strong>of</strong> 080°, has sheared in a left lateral sense<br />
(Figure 72, 74, 75). The second set, composed <strong>of</strong> fractures that are less pronounced<br />
than those <strong>of</strong> the 080° set, has an average strike <strong>of</strong> 050° and has sheared in a right<br />
lateral sense (Figure 73; Figure 76). The conjugate shearing <strong>of</strong> these fracture sets<br />
constrains the maximum compressive stress direction during the episode <strong>of</strong><br />
deformation that the shearing represents.<br />
(a) (b)<br />
Figure A2.71. (a) Field photograph and (b) interpretation <strong>of</strong> fracturing at site 22 in a<br />
section <strong>of</strong> the Tensleep pavement outlined in figure A2.68. Note opposite sense <strong>of</strong><br />
shearing along the 075° - 095° fracture set (left lateral) and the 045° - 065° fracture<br />
set (right lateral).<br />
258
Figure A2.72. Field photograph <strong>of</strong> a sheared fracture at site 22. A fracture <strong>of</strong> strike<br />
095° has been sheared in a left lateral sense.<br />
Figure A2.73. Field photograph and line drawing <strong>of</strong> a sheared fracture at site 22. A<br />
fracture <strong>of</strong> strike 060° has been sheared in a right lateral sense. In the field, this<br />
fracture is within a meter <strong>of</strong> the fracture in figure A2.72.<br />
259
(a) (b)<br />
(c) (d) (e)<br />
N<br />
080°<br />
N<br />
080°<br />
Figure A2.74. (a) Field photograph and (b) interpretation <strong>of</strong> a sheared 080° fracture<br />
at site 22. (c) The fracture formed (d) and was sheared in a left lateral sense<br />
producing low angle splays. (e) 020° fractures formed, abutting both the 080° fracture<br />
and its related splay cracks. In some cases the 020° fractures may be secondary<br />
higher angle splay cracks <strong>of</strong>f <strong>of</strong> the primary splay cracks.<br />
260<br />
N<br />
080°<br />
N<br />
080°<br />
020°<br />
020°
Figure A2.75. Field photo and interpretation <strong>of</strong> left lateral shear along a 070°<br />
fracture. In this photo, mineralization can be seen both along the main fracture, where<br />
it is outlined by light gray lines, and along the traces <strong>of</strong> some <strong>of</strong> the splay cracks.<br />
261
20 cm<br />
N<br />
20 cm<br />
Figure A2.76. Field photograph and interpretation <strong>of</strong> sheared 075° fractures, drawn<br />
in red, found in the backlimb at site 15, indicating that the shearing seen at site 22<br />
occurs at other locations on the fold. Motion along these features is right lateral.<br />
262
An <strong>of</strong>fset fracture provides evidence for bedding plane slip at site 22 (Figure 77).<br />
The <strong>of</strong>fset is on the order <strong>of</strong> centimeters, indicating that since the 168° fracture<br />
developed, bedding plane slip has not been a huge factor in deformation <strong>of</strong> the<br />
backlimb. The bedding plane motion, top to the northeast, is consistent with the<br />
kinematics <strong>of</strong> folding.<br />
NE<br />
5 cm<br />
Figure A2.77. Field photograph and interpretation <strong>of</strong> bedding plane slip at site 22.<br />
Offset <strong>of</strong> this 168° fracture is on the order <strong>of</strong> centimeters and motion is top to the<br />
northeast.<br />
263<br />
NE<br />
5 cm
Role <strong>of</strong> thumb in fracture variation<br />
In the backlimb, a fracture set trending 070° is observed in several locations<br />
(Figure 78), one being the Tensleep pavement <strong>of</strong> site 22. Noticing that most <strong>of</strong> the<br />
070° fractures are found near the thumb area, we hypothesize that the development <strong>of</strong><br />
these fractures is related to the influence <strong>of</strong> active faulting during the time <strong>of</strong><br />
formation <strong>of</strong> the thumb structure.<br />
N<br />
pole densities<br />
28<br />
26<br />
24<br />
22<br />
20<br />
18<br />
16<br />
14<br />
12<br />
10<br />
8<br />
6<br />
4<br />
2<br />
E<br />
fracture sets<br />
110<br />
045<br />
135<br />
110V<br />
070<br />
Site 08<br />
Site 18<br />
N<br />
112, 19<br />
44, 0<br />
Site 23<br />
N<br />
Site 82<br />
N<br />
08<br />
64, 0<br />
95, 33<br />
23<br />
44°39'<br />
Site 16<br />
N<br />
18<br />
Site 15<br />
N<br />
228, 59<br />
16<br />
82<br />
129, 52<br />
15<br />
108°09'<br />
22<br />
N<br />
01<br />
Site 01<br />
19<br />
37, 0<br />
20<br />
Site 22<br />
N<br />
32, 6<br />
21<br />
44°38'<br />
1 km<br />
Site 19<br />
N<br />
149, 33<br />
Site 20<br />
N<br />
110, 32<br />
108°08'<br />
Site 21<br />
N<br />
Figure A2.78. Backlimb fracture data. Red great circles highlight a set <strong>of</strong> fractures<br />
striking 080°. This set displays left lateral shearing in the thumb area. No consistent<br />
sense <strong>of</strong> shearing can be determined further to the NW. Great circles are color coded<br />
to show the main orientation <strong>of</strong> each fracture set. The densities <strong>of</strong> poles to each<br />
fracture set are shown in shades <strong>of</strong> pink. Numbers to the lower right <strong>of</strong> each<br />
stereonet indicate the total number <strong>of</strong> fracture measurements followed by the number<br />
<strong>of</strong> fractures <strong>of</strong> the 080° set for that site.<br />
264<br />
44°37'<br />
59, 0
We adopt a fault geometry from a previous study by Savage and Cooke (JSG,<br />
2004), introducing a fault beneath the thumb, and run a mechanical model with the<br />
boundary conditions shown in Figure 80. Assuming the 080° fractures initially formed<br />
as tensile cracks, we observe the least compressive principal stress magnitude and the<br />
maximum compressive principal stress direction (Figure 81) to consider their possible<br />
spatial distribution.<br />
In the area where the thumb structure joins the main fold, the formation <strong>of</strong> a<br />
fracture set trending 080° may be explained by investigating the stress field<br />
perturbation resulting from the interaction <strong>of</strong> the main fault with the thumb fault. The<br />
shearing we see on these fractures may be a result <strong>of</strong> subsequent uplift and folding.<br />
Ongoing field work is carefully documenting the presence and sense <strong>of</strong> slip along the<br />
080° fracture set along the length <strong>of</strong> the fold. The existence <strong>of</strong> this fracture set further<br />
to the NW cannot be explained by this stress analysis.<br />
Figure A2.79. Field photo and interpretation <strong>of</strong> left lateral shear along 080° fractures.<br />
At the bottom <strong>of</strong> this photo a second fracture is sheared.<br />
265
horizontal<br />
observation<br />
grid<br />
contraction<br />
(-)<br />
thumb<br />
thrust<br />
fault<br />
main<br />
thrust<br />
fault<br />
gravity<br />
extension<br />
(+)<br />
Figure A2.80. Model setup. Projections <strong>of</strong> the two faults (geometry per Savage and<br />
Cooke, 2004) are shown in dashed lines on the horizontal observation grid. The faults<br />
are specified to be shear traction free and the fault walls are restricted from opening<br />
or interpenetrating. A contraction is applied perpendicular to, and a small extension<br />
parallel to, the main fault. Stress perturbations are observed across the horizontal<br />
observation grid (Fig. A2.81).<br />
(a)<br />
Figure A2.81. (a) Large scale and (b) inset model results showing the least<br />
compressive principal stress magnitude, an index for fracturing intensity, and the<br />
most compressive principal stress direction, the direction in which tensile cracks are<br />
expected to form. Solid black lines represent the projection <strong>of</strong> the faults to the<br />
horizontal observation grid. Dotted yellow lines represent the location <strong>of</strong> the primary<br />
and secondary fold hinges. Although faulting related stress perturbations in the thumb<br />
area are compressive, the orientation <strong>of</strong> the stress trajectories are consistent with the<br />
080° fracture set. These fractures would have required elevated pore pressure to<br />
form under this stress state.<br />
266<br />
(b)
Lunch<br />
Along highway 20 at rest stop next to Greybull Airport<br />
30 minutes driving from previous stop<br />
12:00 PM – 12:45 PM<br />
Stop 7: Forelimb and hinge fractures<br />
Site 12 – Tensleep sandstone<br />
Forelimb<br />
45 minutes driving from lunch stop<br />
30 minutes walking<br />
2:00 PM – 4:00 PM<br />
Waypoint (UTM zone 12N): 4946412 N<br />
0724547 E<br />
elev. = 1327 m<br />
Objectives<br />
Discuss fracture characterization in the forelimb<br />
Discuss shearing <strong>of</strong> set I fractures in the forelimb<br />
Discuss bedding plane slip in the forelimb<br />
Site specific observations and interpretations <strong>of</strong> orientations<br />
REGROUP<br />
Discuss fracture characterization in the hinge<br />
Discuss shearing in the hinge<br />
Key Points<br />
In the forelimb, slickenlines indicate that set I fractures have been reactivated<br />
in shear.<br />
In the forelimb, set II fractures are sparse.<br />
In the hinge, there is little evidence for shear along set I fractures. Set III<br />
fractures have a wide range <strong>of</strong> strike directions.<br />
Figure A2.82. Photo <strong>of</strong> the forelimb <strong>of</strong> SMA. View to the SSW. Note the near vertical<br />
bedding dips.<br />
267
Fracture characterization in the forelimb<br />
In the forelimb, bedding dips are very steep, varying from 40° to 90° to the<br />
northeast (Fig. A2.82). We observe one systematic fracture set within the Tensleep<br />
sandstone, trending 110° (Fig. A2.83, sites 10 to 14 and 29 to 32; Fig. A2.84).<br />
Additionally, non-systematic sets are locally developed (striking primarily 070° and<br />
180°, Fig. A2.83) and are interpreted to reflect more local rather than fold-scale or<br />
regional deformation.<br />
N<br />
Site 58<br />
N<br />
72<br />
108°10'<br />
Site 12<br />
N<br />
21<br />
Site 11<br />
N<br />
29<br />
15<br />
Site 10<br />
N<br />
Site 29<br />
N<br />
58<br />
30<br />
14<br />
36<br />
35<br />
44°39'<br />
13<br />
Site 33<br />
N<br />
Site 30<br />
N<br />
22<br />
12<br />
12<br />
108°09'<br />
Site 70<br />
N<br />
16<br />
Site 14<br />
N<br />
10<br />
11<br />
11<br />
Site 13<br />
N<br />
35<br />
44°38'<br />
10<br />
10<br />
Fracture Sets<br />
31<br />
33<br />
32<br />
Set I<br />
Set II<br />
Set III<br />
Set IV<br />
minor set<br />
Site 69<br />
N<br />
Figure A2.83. Forelimb fracture measurements. Phosphoria sites are shown with<br />
yellow dots and numbers with the corresponding stereonets to the lower left <strong>of</strong> the<br />
DOQQ. Tensleep sites are shown with red dots and numbers with the corresponding<br />
stereonets to the upper right <strong>of</strong> the DOQQ. Great circles are color coded: set I is<br />
green, set II is blue, set III is yellow, and set IV is purple. Other sets present at<br />
measurement sites that are not one <strong>of</strong> the four main fracture sets are shown in gray.<br />
268<br />
63<br />
Site 11<br />
N<br />
24<br />
Site 12<br />
N<br />
101<br />
Site 31<br />
N<br />
39<br />
Site 10<br />
N<br />
37<br />
Site 32<br />
N<br />
56<br />
37<br />
108°08'<br />
70<br />
69<br />
44°37
a)<br />
S N<br />
Nb planes 94<br />
SE<br />
b)<br />
Nb planes35<br />
N<br />
N<br />
N<br />
Figure A2.84. Field photographs <strong>of</strong> fracture patterns on a tilted bedding surface<br />
taken at forelimb sites (a) 12 and (b) 32. Note the abundance and small spacing <strong>of</strong><br />
set I fractures (striking 110°). Numerous fractures <strong>of</strong> different orientation can be<br />
observed but are non-systematic. Stereonets show poles to fractures as measured in<br />
the field, poles to fractures relative to horizontal bedding, and great circles<br />
representing the average orientation <strong>of</strong> each fracture set, respectively. From<br />
Bellahsen et al., 2006a.<br />
N<br />
269<br />
set I<br />
set I<br />
N<br />
N<br />
1 m<br />
1 m<br />
NW
Set I fractures are linear and several meters long (Fig. A2.84). Their spacing is<br />
on the order <strong>of</strong> a few tens <strong>of</strong> cm. In the forelimb, their mode <strong>of</strong> deformation is difficult<br />
to determine, as different fractures within the set exhibit characteristics <strong>of</strong> either joint<br />
or shear band morphology. In some cases, the fractures are open with or without<br />
mineral fill, and in other cases, they have small positive relief. This latter attribute may<br />
be related to either cementing (for the case <strong>of</strong> joints or dilational bands) or tighter<br />
packing <strong>of</strong> grains within the fracture (for the case <strong>of</strong> deformation bands). At the<br />
microscale, the fractures are defined by zones that contain smaller quartz grains with<br />
more angular shapes, poorer sorting, less porosity, and smaller calcite cement crystals<br />
than the surrounding rock (Fig. A2.85). These features are characteristic <strong>of</strong><br />
deformation bands (Aydin, 1978; Antonellini et al. 1995), and we interpret set I<br />
fractures to be such brittle structures. Offset indicating a thrust sense <strong>of</strong> shearing was<br />
obvious in the field.<br />
zone <strong>of</strong> def.<br />
0.5 mm<br />
Figure A2.85. Microscopic detail <strong>of</strong> a set I fracture in the forelimb from site 13. This<br />
fracture strikes 110° and dips perpendicular to bedding. In the deformed zone, there<br />
is less porosity than in the surrounding matrix. There are also more angular quartz<br />
grains, that are, for the most part, smaller in size than those within the matrix. There<br />
is also a larger amount <strong>of</strong> calcite cement within the deformed zone. From Bellahsen<br />
et al., 2006a.<br />
270
Shearing (reactivation) <strong>of</strong> Set I fractures in the forelimb<br />
Bed-normal reverse faults that strike 110° and dip 30° south are present along<br />
the forelimb at sites 11, 13, 14, and 30 to 32 (Fig. A2.83). The faults are oblique to the<br />
fold axis and the Laramide regional compression. The oblique striations noticeable<br />
along the fault planes indicate oblique slip, consistent with the resolution <strong>of</strong> shear<br />
stress from the NE directed compression onto these planes (Fig. A2.86).<br />
SE NW<br />
a)<br />
d)<br />
SE<br />
c)<br />
S 0<br />
N<br />
Nb planes34<br />
1 m<br />
N<br />
b)<br />
N<br />
10 cm<br />
N<br />
NW<br />
10 cm<br />
Figure A2.86. Reactivated set I fractures in the forelimb at site 13. (a) Field<br />
photograph <strong>of</strong> set I (110°) small reverse faults within the sandstone <strong>of</strong> the Tensleep<br />
Fm. at site 13 that cut a bedding surface. (b) Cross sectional view <strong>of</strong> the photograph<br />
in (a) showing <strong>of</strong>fset bedding. (c) Close up <strong>of</strong> one fault. The slip decreases toward<br />
fault tips. (d) Striation data (thin arrows on the fault planes) that indicate an oblique<br />
reverse slip along the faults. The large arrows represent the inferred direction <strong>of</strong><br />
compression that is compatible with the striations. Stereonets show poles to fractures<br />
as measured in the field, poles to fractures relative to horizontal bedding, and great<br />
circles representing the average orientation <strong>of</strong> each fracture set, respectively. From<br />
Bellahsen et al., 2006a.<br />
271
Bedding plane slip in the forelimb<br />
In the forelimb, tail cracks emanating from bedding surfaces (Fig. A2.87),<br />
polished undersides <strong>of</strong> bedding surfaces (Fig. A2.88), and slickenlines on bedding<br />
surfaces (Fig. A2.89) provide evidence for bedding plane slip. All recorded kinematic<br />
indicators suggest that upper beds have sheared to the southwest, up and over lower<br />
beds. This motion is consistent with the slip direction predicted by flexural slip folding<br />
(Fig. A2.90). Bedding plane slip appears to be <strong>of</strong> greater significance in the forelimb<br />
than in the backlimb, where the only direct evidence that has been found is a single<br />
fracture <strong>of</strong>fset on the order <strong>of</strong> centimeters (Fig. A2.77). Greater bed parallel slip in the<br />
forelimb, where beds dip 40° to 90°, than in the backlimb, where beds dip 10° and<br />
40°, is consistent with flexural folding theory, as regions <strong>of</strong> greater dip have greater<br />
slip than areas <strong>of</strong> lesser dip (Fig. A2.90).<br />
(a)<br />
Figure A2.87. (a) Splay cracks between bedding surfaces at site 13 in the forelimb<br />
provide evidence for bedding plane slip. Yellow lines highlight splay cracks; red<br />
arrows show the interpreted direction <strong>of</strong> motion. (b) Splay cracks between bedding<br />
surfaces at site 12 in the forelimb. Inset interpretation shows the orientation <strong>of</strong> a<br />
bedding plane and related splays and the direction <strong>of</strong> shearing.<br />
272<br />
(b)
Figure A2.88. Polished undersides <strong>of</strong> bedding planes in the forelimb, as the one in<br />
this photo from site 12, provide evidence for bedding plane slip as a mechanism <strong>of</strong><br />
folding at SMA.<br />
(a)<br />
10 cm<br />
Figure A2.89. (a) Bed parallel slickenlines found in the canyon between the beds<br />
marked by the yellow x in figure A2.91, but on the opposite side <strong>of</strong> the river. (b)<br />
Closer view <strong>of</strong> the slickenlines in (a) with kinematic indicators interpreted. The rough<br />
edges <strong>of</strong> the slickenlines indicate that the shearing motion was top up. The motion<br />
was almost purely along the dip direction.<br />
273<br />
(b)<br />
3 cm
Figure A2.90. Conceptual model <strong>of</strong> flexural slip folding in a multilayer showing<br />
relative displacement on layer surfaces. Layers on the convex side <strong>of</strong> a surface slip<br />
toward the hinge line relative to those on the concave side. The shear sense reverses<br />
across the hinge line. The lines on the surface <strong>of</strong> the layer indicate the orientation <strong>of</strong><br />
slickenside lineations, and their lengths, along with the lengths <strong>of</strong> the arrows<br />
representing slip between layers, indicate relative amounts <strong>of</strong> slip. Note that where<br />
dip is greater, relative motion is greater. From Twiss and Moores, 1992, p. 246.<br />
E W<br />
Figure A2.91. Cross section through Sheep Mountain provided by the river cut. Red<br />
arrows show the interpreted direction <strong>of</strong> bedding plane slip. Kinematic indicators<br />
within the forelimb at SMA have provided evidence for upper beds shearing to the<br />
southwest and up over lower beds. This motion is consistent with flexural slip folding<br />
(Fig. A2.90). The yellow X marks the location across the river that corresponds to the<br />
beds between which the slickenlines in figure A2.89 were found.<br />
274<br />
X
Fracture characterization at site<br />
At site 12 in the forelimb, we will look at fracturing within three different<br />
lithologies (Fig. A2.93): the Tensleep sandstone (Figs. A2.94 – A2.97), a limey<br />
sandstone at the top <strong>of</strong> the Tensleep Fm. (Figure 98, 99), and the Phosphoria limestone<br />
(Figs. A2.100, A2.101). North-south and east-west striking fracture sets are present in<br />
all three lithologies (Fig. A2.95, A2.99, A2.101). A set striking 110° is present in the<br />
sandstone and the limey sandstone, but it not widely seen in the Phosphoria at this site.<br />
This lack <strong>of</strong> 110° measurements could be because the Phosphoria bed in which<br />
fractures were measured is highly eroded and weathered at site 12. The 110° are found<br />
elsewhere in the forelimb in the Phosphoria Fm. (Fig. A2.100).<br />
Figure A2.92. Photo the forelimb <strong>of</strong> SMA. The red X marks the location <strong>of</strong> site 12.<br />
275<br />
X
Phosphoria<br />
Tensleep<br />
Limey<br />
Layer<br />
Amsden<br />
Madison<br />
Figure A2.93. Photograph <strong>of</strong> the southwest side <strong>of</strong> the wash at site 12. We will<br />
investigate fracturing within the Tensleep sandstone, a limey sandstone layer, and<br />
the Phosphoria limestone.<br />
Tensleep characterization:<br />
Figure A2.94. Photograph <strong>of</strong> the Tensleep pavement at site 12. A closer view is<br />
shown in figure A2.96.<br />
276
N<br />
N = 136<br />
+16S<br />
+14S<br />
+12S<br />
+10S<br />
+8S<br />
+6S<br />
+4S<br />
+2S<br />
E<br />
N<br />
N = 136<br />
N<br />
N = 136<br />
Figure A2.95. Stereonets <strong>of</strong> fracture measurements made in the Tensleep Fm. at<br />
site 12 showing: (a) poles and density <strong>of</strong> fractures as measured in the field, (b) poles<br />
and density <strong>of</strong> fractures relative to horizontal bedding, and (c) great circles<br />
representing the average orientation <strong>of</strong> each fracture set.<br />
SE<br />
1 m<br />
110°<br />
Figure A2.96. Photograph <strong>of</strong> the Tensleep Fm. at the top <strong>of</strong> the southeast side <strong>of</strong> the<br />
wash at site 12. The dominant fracture set strikes 110°. Slickenlines indicate that the<br />
set is comprised <strong>of</strong> small thrust faults.<br />
277<br />
NW
10 cm<br />
Figure A2.97. (a) Field photograph <strong>of</strong> slickenlines along two echelon fractures in the<br />
Tensleep sandstone trending 110°. (b) A closer view <strong>of</strong> the section outlined by the red<br />
box in (a). The rough edges <strong>of</strong> the slickenlines indicate that the lower fault surface (no<br />
longer present at the outcrop) slid obliquely into the photo in the down dip direction.<br />
The fractures are thus small thrust faults.<br />
278
Limey Layer characterization:<br />
SE NW<br />
Figure A2.98. Field photograph <strong>of</strong> a section <strong>of</strong> the limey layer that sits on top <strong>of</strong> the<br />
Tensleep sandstone. The two main fracture sets are indicated in red. One set trends<br />
110° and is most likely comprised <strong>of</strong> small thrust faults (note shadows beneath the<br />
fractures in the photo above). Slickenlines or other kinematic indicators have not<br />
been found in the field. The second set is a north-south trending set. The age<br />
relationship between these fracture sets can not be deduced from field evidence.<br />
N<br />
N = 23<br />
+10S<br />
+8S<br />
+6S<br />
+4S<br />
+2S<br />
E<br />
Figure A2.99. Stereonets <strong>of</strong> fracture measurements made in the limey sandstone<br />
just above the Tensleep Fm. at site 12 showing: (a) poles and density <strong>of</strong> fractures as<br />
measured in the field, (b) poles and density <strong>of</strong> fractures relative to horizontal bedding,<br />
and (c) great circles representing the average orientation <strong>of</strong> each fracture set.<br />
N<br />
279<br />
180°<br />
110°<br />
N = 23<br />
1 m<br />
N<br />
N = 23
Phosphoria characterization:<br />
SE<br />
1 m<br />
110°<br />
Figure A2.100. Phosphoria flat-iron southeast <strong>of</strong> site 11 (Fig. A2.83) in which the<br />
major fracture set strikes at 110°. This pavement is noticeable from the road along<br />
which we will park to get to site 12.<br />
N<br />
N = 39<br />
+24S<br />
+22S<br />
+20S<br />
+18S<br />
+16S<br />
+14S<br />
+12S<br />
+10S<br />
+8S<br />
+6S<br />
+4S<br />
+2S<br />
E<br />
N<br />
Figure A2.101. Stereonets <strong>of</strong> fracture measurements made in the Phosphoria Fm. at<br />
site 12 showing: (a) poles and density <strong>of</strong> fractures as measured in the field, (b) poles<br />
and density <strong>of</strong> fractures relative to horizontal bedding, and (c) great circles<br />
representing the average orientation <strong>of</strong> each fracture set.<br />
280<br />
N = 39<br />
N<br />
NW<br />
N = 39
Fracture characterization in the hinge<br />
Figure A2.102. Photo <strong>of</strong> the hinge (dashed line) <strong>of</strong> SMA. View to the west. Dotted<br />
line traces the line <strong>of</strong> maximum curvature. Note that the crest <strong>of</strong> SMA lies to the SW<br />
<strong>of</strong> the hinge.<br />
In the hinge, fracture measurements were made in the Amsden Fm. sandstone<br />
beds. We observed three sets <strong>of</strong> fractures with orientations: 110°, 045°, 135° (Fig.<br />
A2.103).<br />
Set I fractures (trending 110°) are bed-normal. They are less numerous in the<br />
hinge than in the limbs, and their spacing is greater. In thin section (Fig. A2.104a),<br />
these fractures are marked by reduced grain size and porosity as compared to the host<br />
rock, similar to the set I fractures in the forelimb (Fig. A2.85). The alignment <strong>of</strong><br />
elongate grains seen in thin section (Fig. A2.104a) may be indicative <strong>of</strong> shearing<br />
during deformation. As can be noted from figure A2.103, this set is not visible at<br />
many locations.<br />
281
Site 39<br />
N<br />
Site 40<br />
N<br />
62<br />
42<br />
N<br />
108°10'<br />
Site 41<br />
N<br />
Site 43<br />
N<br />
53<br />
12<br />
Site 45<br />
N<br />
37<br />
38<br />
39<br />
40 42<br />
7 41<br />
43<br />
Site 44<br />
N<br />
49<br />
26<br />
Site 46<br />
N<br />
Site 51<br />
N<br />
26<br />
19<br />
Site 37<br />
N<br />
44°39'<br />
4425<br />
Site 50<br />
N<br />
Site 47<br />
N<br />
38<br />
21<br />
45<br />
24<br />
Site 5<br />
N<br />
Site 38<br />
N<br />
Site 42<br />
N<br />
Site 48<br />
N<br />
31<br />
108°09'<br />
49<br />
35<br />
36<br />
Site 25<br />
N<br />
Site 49<br />
N<br />
46<br />
43<br />
40<br />
51<br />
Site 4b1<br />
N<br />
Site 3h<br />
N<br />
50<br />
16<br />
23<br />
44°38'<br />
1 km<br />
Site 4b2<br />
N<br />
Site 3i<br />
N<br />
49<br />
19<br />
23<br />
Site 4e<br />
N<br />
Site 3j<br />
N<br />
Fracture Sets<br />
94<br />
15<br />
108°08'<br />
Set I<br />
Set II<br />
Set III<br />
Set IV<br />
minor set<br />
Site 6b<br />
N<br />
Site 6a<br />
N<br />
47, 48<br />
3j<br />
3h3i<br />
5<br />
4b<br />
4e<br />
6<br />
Figure A2.103. Hinge fracture measurements. Amsden sites are shown with white<br />
dots and numbers with the corresponding stereonets to the lower left <strong>of</strong> the DOQQ.<br />
Madison sites are shown in red with the corresponding stereonets to the upper right<br />
<strong>of</strong> the DOQQ. Great circles are color coded: Set I is green, set II is blue, set III is<br />
yellow, and set IV is purple. Other sets present at measurement sites that are not one<br />
<strong>of</strong> the four main fracture sets are shown in gray.<br />
282<br />
48<br />
44°37'<br />
26
Set II fractures trend 045°, are bed-normal, and have a coarse calcite fill (Fig.<br />
A2.104b) similar to that seen in the backlimb (Fig. A2.54). These fractures are joints,<br />
with lengths <strong>of</strong> a few meters and 1 meter spacing.<br />
Set III fractures trend 135° (parallel to the fold axis), are bed-normal. Set III<br />
fractures abut set II fractures in the hinge and thus postdate set II (Fig. A2.105). Set II<br />
fractures abut set I fractures in the backlimb, so we infer that set III fractures also<br />
postdate set I fractures.<br />
a)<br />
b)<br />
0.5 mm<br />
0.5 mm<br />
Figure A2.104. (a) Microstructure <strong>of</strong> a set I (110°) fracture in the sandstone <strong>of</strong> the<br />
Amsden Fm. in the hinge at site 44. The fracture is composed <strong>of</strong> crushed matrix<br />
grains surrounded by quartz cement. (b) Microstructure <strong>of</strong> a set II (045°) fracture in<br />
the sandstone <strong>of</strong> the Amsden Fm. in the hinge at site 41. The fracture has distinct<br />
walls and is filled with large crystals <strong>of</strong> calcite cement. From Bellahsen et al., 2006a.<br />
283
a)<br />
Nb planes42<br />
b)<br />
N<br />
N N<br />
10 cm<br />
Set II<br />
N<br />
Set III<br />
Figure A2.105. Fracture pattern in the hinge. (a) Field photograph showing the<br />
abutting relationships between set II (045°) and set III (135°) at site 39 in the<br />
sandstone <strong>of</strong> the Amsden Fm. (b) Line drawing <strong>of</strong> the outcrop in (a) showing that 8 <strong>of</strong><br />
13 set III fractures terminate at set II fractures. Stereonets show poles to fractures as<br />
measured in the field, poles to fractures relative to horizontal bedding, and great<br />
circles representing the average orientation <strong>of</strong> each fracture set, respectively. From<br />
Bellahsen et al., 2006a.<br />
284
Shearing in the hinge<br />
In the hinge, we find no conclusive evidence for shearing <strong>of</strong> set I fractures.<br />
Often, the set III fractures have a wide dispersion in strike direction (Fig. A2.106). We<br />
believe that in the hinge, the stress field is such that tensile fracturing is more<br />
favorable than shearing <strong>of</strong> previously formed fractures (Bourne and Willemse, 2001).<br />
In extreme cases, we see very intensive fracturing (Fig. A2.107), a phenomenon that is<br />
seen only in the hinge. This supports our hypothesis that tensile fracturing plays a<br />
much greater role in folding related deformation in the hinge than shearing does.<br />
Site 53 N<br />
Site 54 N<br />
50° 60°<br />
78<br />
53<br />
Site 55<br />
N<br />
60° 60°<br />
56<br />
Site 56<br />
Figure A2.106. Stereonets from sites 53-56 in the hinge <strong>of</strong> the nose showing a wide<br />
dispersion (50° to 60° spread) in the strike <strong>of</strong> joints that are subparallel to the trend <strong>of</strong><br />
the fold.<br />
Figure A2.107. Field photograph taken in the Madison Fm. just southwest <strong>of</strong> the river<br />
cut showing very intense fracturing. Pencil points northwest. The major fracture set<br />
noticeable in the photo strikes subparallel to the hinge.<br />
285<br />
N<br />
46
Stop 8: Fracture synthesis<br />
Site 10<br />
Backlimb<br />
10 minutes driving from previous stop<br />
15 minutes walking<br />
4:30 PM – 5:30 PM<br />
Waypoint (UTM zone 12N): 4945503 N<br />
0726382 E<br />
elev. = 1187 m<br />
Objectives<br />
Discuss stages <strong>of</strong> fracturing<br />
Discuss constraints on kinematics <strong>of</strong> folding<br />
Discuss spatial variations in fracture sets and how they may be understood<br />
Discuss the role <strong>of</strong> shearing along set I fractures in folding<br />
Key Points<br />
Four stages <strong>of</strong> fracturing have been interpreted from the fracture pattern at<br />
SMA.<br />
Sheep Mountain formed with a fixed hinge style <strong>of</strong> folding.<br />
Mechanical considerations help to explain variations in fracture sets.<br />
During folding, the pre-existing set I fractures sheared in a left lateral sense in<br />
the backlimb, were <strong>of</strong>fset in thrust motion in the forelimb, and had<br />
relatively little role in the deformation in the hinge.<br />
Figure A2.108. Photograph <strong>of</strong> site 10, where we will synthesize the fracture data<br />
observed over the past day and a half. The Madison Fm. is folded on the horizon in<br />
this photo, while pavements <strong>of</strong> the Amsden, Tensleep, and Phosphoria are in the<br />
foreground.<br />
286
Site 07<br />
N<br />
Site 08<br />
N<br />
36<br />
116<br />
N<br />
Site 23<br />
N<br />
86<br />
Fracture Sets<br />
108°10'<br />
Set I<br />
Set II<br />
Set III<br />
Set IV<br />
minor set<br />
Site 18<br />
N<br />
40<br />
51<br />
Site 40<br />
N<br />
62<br />
41<br />
07<br />
Site 17<br />
N<br />
Site 15<br />
N<br />
Site 41<br />
N<br />
30<br />
14<br />
43<br />
44<br />
08<br />
Site 43<br />
N<br />
12<br />
Site 16<br />
42 N<br />
139<br />
23<br />
44°39'<br />
Site 22<br />
N<br />
13<br />
18<br />
44<br />
Site 30<br />
N<br />
45<br />
36<br />
Site 01<br />
N<br />
Site 14<br />
22 N<br />
Site 44<br />
N<br />
53<br />
12<br />
17<br />
16<br />
15<br />
108°10'<br />
22<br />
37<br />
01<br />
Site 13<br />
N<br />
63<br />
Site 45<br />
26<br />
N<br />
11<br />
46<br />
19<br />
Site 19<br />
N<br />
20<br />
51<br />
47<br />
Site 12<br />
35 N<br />
Site 46<br />
49 N<br />
50<br />
21<br />
Site 11<br />
N<br />
101<br />
Site 50<br />
N<br />
19<br />
44°38'<br />
1 km<br />
Site 20 Site 21<br />
N<br />
N<br />
44<br />
10<br />
Site 10<br />
N<br />
24<br />
Site 51<br />
24<br />
N<br />
31<br />
32<br />
52<br />
63<br />
47, 48<br />
26<br />
108°08'<br />
Site 52<br />
N<br />
Site 31<br />
N<br />
37<br />
Site 47<br />
N<br />
69<br />
35<br />
44°37'<br />
Site 32<br />
39 N<br />
Site 48<br />
38 N<br />
Figure A2.109. DOQQ showing location <strong>of</strong> Tensleep and Amsden measurement<br />
sites in the backlimb (green dots and numbers), hinge (yellow dots and numbers),<br />
and forelimb (magenta dots and numbers) and the related stereonets. Backlimb<br />
stereonets are to the lower left <strong>of</strong> the DOQQ, hinge stereonets are to the upper right<br />
<strong>of</strong> the DOQQ, and forelimb stereonets are to the upper right <strong>of</strong> the hinge stereonets.<br />
Great circles are color coded: set I is green, set II is blue, set III is yellow, and set IV<br />
is purple. Other sets present at measurement sites that are not one <strong>of</strong> the four main<br />
fracture sets are shown in gray.<br />
287<br />
49<br />
37<br />
Site 69<br />
N<br />
56
Stages <strong>of</strong> fracturing<br />
Pre-existing fractures<br />
Set I fractures are observed in most <strong>of</strong> the locations across the fold (Fig. A2.109)<br />
and are systematically perpendicular to bedding. The exact nature <strong>of</strong> these fractures<br />
remains uncertain because we do not know if they initiated in a shearing mode (e.g. as<br />
deformation bands) or in an opening mode (as joints) and subsequently were sheared.<br />
Fracture set I is oblique to the fold, striking approximately 25° counterclockwise<br />
from the fold axis. Additionally, abutting relationships indicate that set I predates all<br />
other fracture sets. Thus, we interpret set I as the oldest set and as having initiated<br />
prior to the Laramide orogeny. A similar interpretation was made by Silliphant et al.<br />
(2002) at Split Mountain in Utah and Hennings et al. (2000) at Oil Mountain in<br />
Wyoming, where a fracture set <strong>of</strong> similar strike (WNW-trending) was present at<br />
nearby locations where bed dips are approximately horizontal, as well as in each<br />
position <strong>of</strong> the fold after rotation <strong>of</strong> the bedding to horizontal.<br />
If the set I fractures formed as shear fractures, they would have formed oblique<br />
to the direction <strong>of</strong> greatest compression. Taking an estimated 30° angle, the tectonic<br />
compression would have been in a direction <strong>of</strong> either 080° or 140°. If they formed as<br />
joints, they would be associated with a 110° directed compression. Further study is<br />
needed to constrain the nature and origin <strong>of</strong> this fracture set, but this is not crucial for<br />
constraining the fold growth as we view set I as having formed before folding and as<br />
having been rotated with bedding during folding.<br />
Early Laramide compression: onset <strong>of</strong> faulting and folding<br />
Set II joints strike parallel to the NE-SW direction <strong>of</strong> Laramide compression<br />
(Dickinson and Snyder, 1978; Engebretson et al., 1985; Bird, 2002) and are<br />
perpendicular to bedding. We showed using abutting relations at some localities that<br />
set II joints predate the fold-parallel hinge-restricted set III joints. Thus, we interpret<br />
the set II joints as having formed in response to early Laramide compression, prior to<br />
significant development <strong>of</strong> the fold (Fig. A2.110).<br />
288
Joints initiating parallel to an early compressive event are documented in the<br />
literature (Engelder and Geiser, 1980; Engelder et al., 1997). Joints with the same<br />
orientation as set II are found in several locations in proximity to Sheep Mountain: at<br />
Garland and Little Sand Draw in the southeast Bighorn basin (Garfield et al., 1992), at<br />
Teapot Dome in Wyoming (Allison, 1983; Cooper et al., 1998) and in the southeast<br />
Bighorn basin near the Tensleep fault (Allison, 1983), confirming their regional status.<br />
At Sheep Mountain, we find set II joints in the backlimb, the hinge, and the nose.<br />
Fractures <strong>of</strong> this set are notably absent in the forelimb (Fig. A2.109), however,<br />
suggesting that an early structure, most likely the incipient fold or the underlying<br />
thrust fault, may have influenced their formation (Fig. A2.110).<br />
Fold growth: intermediate stage<br />
In the hinge, joints striking parallel to the fold axis and dipping perpendicular to<br />
bedding are classified as fracture set III. Their geometry and spatial location indicates<br />
that they formed due to the curvature <strong>of</strong> bedding layers. This set could have formed at<br />
any time during folding. Set III joints also are found in the fold nose. In the backlimb<br />
<strong>of</strong> the nose, the joint strike changes along the fold from 135° to 160° (Fig. A2.41).<br />
This change roughly coincides with the change in fold limb orientation, as the strike <strong>of</strong><br />
the layers changes from 130° to 150°, south to north (Fig. A2.4). The layers in this<br />
area are curved and this bending can explain the rotation <strong>of</strong> the Set III joints. In the<br />
nose hinge zone, set III is the main joint set, where it most likely initiated due to layer<br />
bending.<br />
Fold growth: late stage<br />
During the late stage <strong>of</strong> fold growth, the fracture patterns in the hinge and in the<br />
nose did not change, although some fold-parallel joints may have continued to form.<br />
In the limbs, however, new fractures initiated and others were reactivated (Fig.<br />
A2.110).<br />
289
In the forelimb, we observe small thrust faults with oblique slip (Figs. A2.86,<br />
A2.110). Given the geometric similarities to set I fractures, these structures are<br />
interpreted as reactivated set I fractures. They are reverse faults that dip approximately<br />
30° from the horizontal, perpendicular to bedding. Thus, we infer that the reactivation<br />
occurred late in the fold evolution. Incorporated into this interpretation is the<br />
assumption that the set I fractures rotated passively with the strata and were<br />
reactivated when their dip reached a value low enough to allow a thrust <strong>of</strong>fset along<br />
them. This mechanism implies a horizontal greatest compressive stress striking<br />
perpendicular to the fold and a vertical least compressive stress.<br />
In the backlimb, we observed a second late fracture set, set IV, which is<br />
composed <strong>of</strong> vertical joints striking 110° (Figs. A2.57, A2.109 and A2.110). They are<br />
interpreted as late due to their vertical dip that is oblique to bedding. We suggest that<br />
this joint set was influenced by the presence <strong>of</strong> the earlier set I fractures, because they<br />
strike oblique to the fold axis and parallel to the set I fractures. Such influence by pre-<br />
existing fractures has been suggested recently in Guiton et al. (2003a, 2003b) and<br />
Bergbauer and Pollard (2004).<br />
290
c)<br />
Set I<br />
d)<br />
a)<br />
b)<br />
Set I<br />
Set III<br />
Set III<br />
Set II<br />
N E<br />
Set IV<br />
Fracture Sets<br />
Set I<br />
Set II<br />
Set III<br />
Set IV<br />
Figure A2.110. Schematic representation <strong>of</strong> the fracturing history at SMA. (a) Set I<br />
(110°) fractures form prior to the Laramide compression in horizontal beds. (b) Set II<br />
(045°) joints are initiated as early compression-parallel fractures. (c) Set III (135°)<br />
joints develop in the hinge during folding. (d) Vertical set IV (110°) joints initiate<br />
parallel to set I fractures in the backlimb, while in the forelimb, set I fractures are<br />
reactivated as reverse faults during a late stage <strong>of</strong> (or posterior to) folding. After<br />
Bellahsen et al., 2006a.<br />
291
Constraints on fold kinematics<br />
Fixed hinge<br />
At Elk Basin Anticline, a basement-cored fold in Montana and Wyoming, fold<br />
perpendicular fractures comprise only a minor fracture set, and they are interpreted as<br />
a late set formed in response to an axis-parallel stretching (Gross and Engelder, 1995;<br />
Gross et al., 1998; Fig. A2.111). A mechanism for this type <strong>of</strong> joint formation is<br />
curvature related to a doubly-plunging, non cylindrical fold geometry (Fischer and<br />
Wilkerson, 2000). For such a mechanism, rather than a regional deformation, to be an<br />
explanation for set II fractures at Sheep Mountain anticline, the present-day fold shape<br />
(quite cylindrical in its central part) would have had to have evolved from a more non-<br />
cylindrical shape. However, a perturbation in the strike <strong>of</strong> set II fractures occurs only<br />
in the present-day fold nose, and similar perturbations, which would represent<br />
previous locations <strong>of</strong> the fold nose, are not found. Therefore, we infer that the fold<br />
nose did not migrate laterally, and the early fold length was very similar to the current<br />
fold length.<br />
The localized occurence <strong>of</strong> set III joints is also consistent with a fixed-hinge<br />
model <strong>of</strong> fold evolution (Allmendinger, 1982; Fischer et al., 1992; Fisher and<br />
Anastasio, 1994; McConnell, 1994). Had the hinge migrated, we would expect to find<br />
fold-parallel joints elsewhere. The hinge is very tight, so it is unlikely that the<br />
observed hinge curvature could have been accommodated without joint formation.<br />
Figure A2.111. Figure showing that hinge perpendicular joints may open during<br />
folding due to along hinge stretching. This stretching can be the result <strong>of</strong> a doubly<br />
plunging anticline. Modified from Gross et al., 1998.<br />
292
Understanding spatial variations<br />
Set III fractures<br />
We find some fold-parallel set III joints in the backlimb (Figs. A2.109, A2.110<br />
sites 17 to 20). These joints might be related to areas where layer curvature is greater.<br />
To test this hypothesis, we computed a curvature map (Fig. A2.112) to assess the<br />
relative curvature <strong>of</strong> various fold locations. Forster et al. (1996) published a structure<br />
contour map <strong>of</strong> a reference horizon at the base <strong>of</strong> the Jurassic Sundance Fm. We<br />
assume that changes in formation thicknesses across the fold between the Upper<br />
Carboniferous Amsden Fm. and the Sundance (about 300m) are not substantial and<br />
therefore that this map can be used to study layers that are stratigraphically below the<br />
Sundance from the Amsden to the Permian Phosphoria Fm. We digitized the structure<br />
contour map and calculated the maximum curvature across the resulting three<br />
dimensional surface using gOcad, a 3D geomodeling s<strong>of</strong>tware program (Mallet, 2002).<br />
The algorithm for maximum curvature selects the prinicipal curvature with the greater<br />
absolute value and plots that curvature with its sign. Thus, positive curvature (concave<br />
upward) may be differentiated from negative curvature (concave downward). In figure<br />
A2.112, warm colors have positive curvature and mark synclinal hinges, whereas cool<br />
colors have negative curvature and mark anticlinal hinges.<br />
The darkening <strong>of</strong> the blue colors <strong>of</strong> the curvature plot toward the north along the<br />
fold axis reflects the tightening <strong>of</strong> the fold in this direction. Looking along lines<br />
perpendicular to the fold hinge, note that in the northwest, zero or near zero curvature<br />
values are reached just a short distance from the fold hinge, whereas further southeast,<br />
this distance is greater. The set III joints are more common toward the southeast, the<br />
direction in which the fold shape changes from a tight to a more rounded pr<strong>of</strong>ile (Fig.<br />
A2.112). This supports our hypothesis that there is a link between curvature and the<br />
existence <strong>of</strong> set III joints. Where the hinge is tight in the north, the limbs are<br />
approximately planar with lesser curvature and set III is confined to the hinge.<br />
293
Hinge<br />
Backlimb<br />
curvature (m -1 )<br />
x10 -3<br />
6<br />
4<br />
2<br />
0<br />
-2<br />
-4<br />
-6<br />
Hinge<br />
Subsidiary fold<br />
1 km<br />
Forelimb<br />
N<br />
Syncline<br />
Figure A2.112. Curvature map <strong>of</strong> SMA calculated from the structure contour map in<br />
Forster et al., (1996). Reds represent synclinal folding and blues represent anticlinal<br />
folding. Black contour traces the line <strong>of</strong> zero curvature. From Bellahsen et al., 2006a<br />
294
Set II fractures<br />
We consider a regional deformation as the most likely formation mechanism for<br />
set II fractures and suggest that the paucity <strong>of</strong> set II joints in the forelimb is due to a<br />
stress perturbation resulting from slip on the underlying basement thrust fault. To test<br />
this hypothesis, we use Poly3D (Thomas, 1993), a 3D BEM program based on linear<br />
elasticity, and forward model for the stress perturbation resulting from a single slip<br />
event along the underlying thrust fault. A specified remote contraction is applied<br />
perpendicular to the strike <strong>of</strong> the underlying fault to represent the prevailing tectonic<br />
deformation during early Laramide time. The model setup is illustrated in figure<br />
A2.113.<br />
vertical<br />
observation<br />
grid<br />
gravity<br />
thrust fault<br />
contraction<br />
(-)<br />
extension<br />
(+)<br />
Remote strain boundary conditions:<br />
εy = - 1%, εx = 0.1%<br />
Local fault plane boundary conditions:<br />
tx = 0, ty = 0, bz = 0<br />
Figure A2.113. Model geometry. A vertical plane perpendicular to fault strike and<br />
located at its center is designated as an observation grid. The arrows represent the<br />
remote extension and contraction. Modified from Bellahsen et al., 2006b.<br />
The model space is homogeneous, but we want to observe stresses and<br />
displacements at a level that correlates to the Tensleep sandstone in which the majority<br />
<strong>of</strong> our field measurements were taken. At Laramide time, the sediment pile on top <strong>of</strong><br />
granitic basement was approximately 3 km thick (Fig. A2.114). The vertical<br />
separation between early Laramide layers and the Tensleep Formation is<br />
approximately 2200 m (Fig. A2.114). To be able to compare model results with<br />
outcrop interpretations, we observe stresses and displacements at 2200m.<br />
295
Model results indicate that at a depth equivalent to the Tensleep, near the upper<br />
tip line in the model fault footwall, slip creates a zone <strong>of</strong> tensile stress (Fig. A2.114),<br />
while in the hanging wall, a zone <strong>of</strong> compression. To relate these perturbations to<br />
various structural positions on the fold (i.e. backlimb, hinge or forelimb), we plot the<br />
vertical displacements across the layer (Fig. A2.114a). Figure A2.114a shows the<br />
development <strong>of</strong> the early fold with the backlimb, hinge, and forelimb readily<br />
distinguishable. Correlating the location <strong>of</strong> the forelimb to the stress perturbation<br />
(black rectangle, Fig. A2.114b), we find that it coincides with the zone <strong>of</strong> enhanced<br />
compression in the fault hanging wall. In this zone, the formation <strong>of</strong> joints striking<br />
parallel to the maximum compression direction would be inhibited. In the field, we<br />
observed a similar zone in the forelimb <strong>of</strong> SMA, where joints parallel to the<br />
compression direction (set II) are sparse. If these two zones correspond to each other<br />
(Fig. A2.115), we can conclude that the forelimb was located above the fault and in<br />
the hanging wall <strong>of</strong> the fault in the early stages <strong>of</strong> the folding.<br />
(a)<br />
(b)<br />
tension<br />
(+)<br />
compression<br />
(-)<br />
vert. displ. (m)<br />
300<br />
150<br />
0<br />
0 500<br />
1000 1500 2000 2500<br />
3000 m<br />
MPa<br />
50<br />
- 150<br />
- 350<br />
- 550<br />
- 750<br />
horizontal distance<br />
296
Figure A2.114 (opposite page). (a) Vertical displacement pr<strong>of</strong>ile across the fold at the<br />
depth <strong>of</strong> the Tensleep Fm. at early Laramide time. (b) Least compressive principal<br />
stress magnitude across the observation grid. This stress component trends<br />
perpendicular to the grid and controls the formation <strong>of</strong> new joints striking parallel to<br />
the grid, the orientation <strong>of</strong> the set II fractures. A zone <strong>of</strong> enhanced compressive stress<br />
is located just behind the upper fault tip line in the hanging wall (compressive<br />
quadrant, black rectangle) at the paleodepth <strong>of</strong> the Tensleep Fm. The model space is<br />
homogeneous and the layering shown on the observation grid is solely to point out<br />
the depth <strong>of</strong> the Tensleep and the depth <strong>of</strong> the sediment-basement contact at<br />
Laramide time. Modified from Bellahsen et al., 2006b.<br />
σ 1<br />
σ 2<br />
σ 3<br />
backlimb forelimb<br />
σ 1<br />
σ 2<br />
σ 3<br />
Figure A2.115. Forward modeled effective stresses in the backlimb and forelimb can<br />
be linked to the heterogeneity in set II fracture formation observed in the field.<br />
297
This spatial constraint on the location <strong>of</strong> the forelimb relative to the thrust fault<br />
enables us to describe the folding process in more detail. In the case <strong>of</strong> SMA, the<br />
basement fault most likely formed prior to the Laramide orogeny (Fig. A2.116a)<br />
(Stanton and Erslev, 2004; Bellahsen et al., 2006a). With the onset <strong>of</strong> NE<br />
compression, the fault was reactivated (Fig. A2.116b), perturbing the stress field in its<br />
vicinity. With ongoing regional contraction, the fold developed above the fault, within<br />
the hanging wall, because the forelimb was located above the fault before folding<br />
(Figs. A2.116c, A2.116d). Seismic lines (Stanton and Erslev, 2004; Stone, personal<br />
communication) in close proximity to the fold show that the fold is above the fault, as<br />
in other basement fault-cored anticlines (Stone, 1993) and not ahead <strong>of</strong> the upper tip<br />
line, as in the forced fold model.<br />
a)<br />
Pre-existing<br />
fault<br />
cover<br />
basement<br />
c) d)<br />
b)<br />
future forelimb<br />
fixed hinge<br />
Figure A2.116. Conceptual model for basement fault-cored anticlines. a) Pre-<br />
Laramide configuration. The thrust fault is inherited. b) Onset <strong>of</strong> Laramide faulting.<br />
The basement starts deforming, as does the cover. Both are affected by the stress<br />
field perturbation resulting from the superposition <strong>of</strong> the slip related stresses and the<br />
shortening related stresses. c) Fold initiation and d) fold amplification with a fixed<br />
hinge and rotating limbs. The basement hanging wall block is internally deformed.<br />
The fault is represented as propagating through the cover. From Bellahsen et al.,<br />
2006b.<br />
298
Role <strong>of</strong> shearing <strong>of</strong> set I fractures<br />
Set I fractures played a role in the folding deformation at Sheep Mountain in<br />
both the forelimb (Figs. A2.84, A2.86, A2.97, A2.100) and the backlimb (Figs. A2.58<br />
– A2.63), but little evidence has been found to suggest that set I fractures were<br />
reactivated to relieve folding related stresses in the hinge. Instead, in the hinge, we see<br />
dispersion in the strike direction <strong>of</strong> set III hinge parallel fractures (Figs. A2.106,<br />
A2.107).<br />
In the forelimb, set I fractures were reactivated as thrust faults after having been<br />
rotated with bedding to a shallow angle (Fig. A2.117). In the backlimb, shearing <strong>of</strong> set<br />
I fractures is consistent with the kinematics <strong>of</strong> hinge perpendicular compression and<br />
folding <strong>of</strong> the anticline. The set I fractures are oriented obliquely to the inferred<br />
maximum compression direction, so left-lateral shearing results (Fig. A2.118, stage 2).<br />
In the hinge, no shearing <strong>of</strong> set I fractures has been recorded.<br />
pre-folding configuration<br />
late-folding<br />
configuration<br />
Figure A2.117. Conceptual model for development <strong>of</strong> set IR fractures in the forelimb<br />
<strong>of</strong> SMA.<br />
Perhaps this lack <strong>of</strong> shearing in the hinge, along with the recorded higher<br />
intensity <strong>of</strong> fracturing in the hinge and the disperse set III fracture orientations can<br />
help to constrain the state <strong>of</strong> stress throughout the fold. As detailed by Bourne and<br />
Willemse (2001), whether a rock will fail in tension or shear depends upon where the<br />
299
Figure A2.118. Conceptual model for left-lateral shearing <strong>of</strong> set I fractures in the<br />
backlimb and development <strong>of</strong> set III fractures in the hinge with a wide range <strong>of</strong><br />
orientations.<br />
300
Mohr Circle for the stress state intersects the failure envelope (Fig. A2.119). In the<br />
locations where we see shearing <strong>of</strong> set I fractures, we infer that the Mohr circle was<br />
closer to the shear failure portion <strong>of</strong> the envelope. This implies a relatively greater<br />
principal stress difference. In the hinge, where the highest curvature values exist, the<br />
lack <strong>of</strong> shearing related kinematic indicators suggests that the stress state was closer to<br />
the tensile failure portion <strong>of</strong> the envelope during folding. Rather than shear occurring<br />
along pre-existing fractures, new joints formed (Fig. A2.118, stage 4), and this implies<br />
a relatively lesser principal stress difference.<br />
Figure A2.119. Proximity <strong>of</strong> a stress state to brittle failure is represented by the<br />
smallest stress increment required to reach that stress state from either the shear part<br />
<strong>of</strong> the brittle failure envelope, χshear or the tensile part <strong>of</strong> the brittle failure envelope,<br />
χtensile. [Reprinted from Journal <strong>of</strong> Structural Geology, v. 23., Bourne, S. J. and E. J.<br />
M. Willemse, Elastic stress control on the pattern <strong>of</strong> tensile fracturing around a small<br />
fault network at Nash Point, UK, p. 1753-1770, Copyright 2001, with permission from<br />
Elsevier].<br />
301
References<br />
Allison, M. L., 1983, Deformation styles along the Tensleep fault, Bighorn Basin,<br />
Wyoming: Wyoming Geol. Assoc. Guidebook, v. Thirty-Fourth Annual Field<br />
Conference.<br />
Allmendinger, R., 1982, COCORP pr<strong>of</strong>iling across the Rocky Mountain Front in<br />
southern Wyoming; Part 2, Precambrian basement structure and its influence<br />
on Laramide deformation: Geological Society <strong>of</strong> America bulletin, v. 93, p.<br />
1253-1263.<br />
Andrews, D., W. Pierce, and G. Kirby, 1944, Structure contour map <strong>of</strong> the Big Horn<br />
Basin, Wyoming and Montana: U.S. Department <strong>of</strong> Interior Geological<br />
Survey.<br />
Antonellini, M. A., A. Aydin, and D. D. Pollard, 1994, Microstructure <strong>of</strong> deformation<br />
bands in porous sandstones at Arches National Park, Utah: Journal <strong>of</strong><br />
Structural Geology, v. 16, p. 941-959.<br />
Aydin, A., and A. M. Johnson, 1978, Development <strong>of</strong> faults as zones <strong>of</strong> deformation<br />
bands and as slip surfaces in sandstone: Pure & Applied Geophysics, v. 116, p.<br />
931-942.<br />
Bai, T., and D. D. Pollard, 1999, Spacing <strong>of</strong> fractures in a multilayer at fracture<br />
saturation: International Journal <strong>of</strong> Fracture, v. 100, p. L23-L28.<br />
Banerjee, S., and S. Mitra, 2004, Remote surface mapping using orthophotos and<br />
geologic maps draped over digital elevation models; application to the Sheep<br />
Mountain Anticline, Wyoming: AAPG bulletin, v. 88, p. 1227-1237.<br />
Barazangi, M., and B. L. Isacks, 1976, Spatial distribution <strong>of</strong> earthquakes and<br />
subduction <strong>of</strong> the Nazca Plate beneath South America: Geology, v. 4, p. 686-<br />
692.<br />
Bellahsen, N., P. Fiore, and D. D. Pollard, 2006a, The role <strong>of</strong> fractures in the structural<br />
interpretation <strong>of</strong> Sheep Mountain anticline, Wyoming: Journal <strong>of</strong> Structural<br />
Geology, V. 28, p. 850-867.<br />
Bellahsen, N., P. E. Fiore, and D. D. Pollard, 2006b, From spatial variation <strong>of</strong> fracture<br />
patterns to fold kinematics: A geomechanical approach: Geophysical Research<br />
Letters, v. 33, doi:10.1029/2005GL024189.<br />
Berg, R., Robert, 1962, Mountain flank thrusting in Rocky Mountain foreland,<br />
Wyoming and Colorado: American Association <strong>of</strong> Petroleum Geologists<br />
Bulletin, v. 46, p. 2019-2032.<br />
302
Bergbauer, S., and D. D. Pollard, 2004, A new conceptual fold-fracture model<br />
including prefolding joints, based on field data from the Emigrant Gap<br />
anticline, Wyoming: Geological Society <strong>of</strong> America Bulletin, v. 116.<br />
Bird, P., 1998, Kinematic history <strong>of</strong> the Laramide orogeny in latitudes 35°-49°N,<br />
western United States: Tectonics, v. 17, p. 780-801.<br />
Bird, P., 2002, Stress direction history <strong>of</strong> the Western United States and Mexico since<br />
85 May: Tectonics, v. 21, p. 14 pp.<br />
Blackstone, D. L., Jr., 1940, Structure <strong>of</strong> the Pryor Mountains, Montana: Journal <strong>of</strong><br />
Geology, v. 48, p. 590-618.<br />
Bourne, S. J., and E. J. M. Willemse, 2001, Elastic stress control on the pattern <strong>of</strong><br />
tensile fracturing around a small fault network at Nash Point, UK: Journal <strong>of</strong><br />
Structural Geology, v. 23, p. 1753-1770.<br />
Brown, W., 1984, AAPG continuing education course note series: AAPG continuing<br />
education course note series.<br />
Coney, P., 1976, Plate tectonics and the Laramide Orogeny: Special publication - New<br />
Mexico Geological Society, p. 5-10.<br />
Cooper, S., L. B. Goodwin, J. C. Lorenz, L. W. Teufel, and B. S. Hart, 1998,<br />
Geometric and genetic relationships between fractures, normal faults, and a<br />
doubly plunging anticline; Teapot Dome, Wyoming: Abstracts with programs -<br />
Geological Society <strong>of</strong> America, v. 30, p. 62.<br />
Dickinson, W. R., and W. S. Snyder, 1978, Plate tectonics <strong>of</strong> the Laramide orogeny:<br />
Geological Society <strong>of</strong> America Memoir 151, p. 355-366.<br />
Engebretson, D. C., A. Cox, and R. G. Gordon, 1985, Relative motion between<br />
oceanicand continental plates in the Pacific basin: Geological Society <strong>of</strong><br />
America Special Paper 206, 59 pp. p.<br />
Engelder, T., and P. Geiser, 1980, On the use <strong>of</strong> regional joint sets as trajectories <strong>of</strong><br />
paleostress fields during the development <strong>of</strong> the Appalachian Plateau, New<br />
York: Journal <strong>of</strong> Geophysical Research, v. 85, p. 6,319-6,341.<br />
Engelder, T., M. R. Gross, and P. Pinkerton, 1997, An analysis <strong>of</strong> joint development<br />
in thick sandstone beds <strong>of</strong> the Elk Basin Anticline, Montana-Wyoming: Rocky<br />
Mountain Association <strong>of</strong> Geologists, v. Fractured Reservoirs: Characterization<br />
and Modeling Guidebook.<br />
Erslev, E. A., 1986, Basement balancing <strong>of</strong> Rocky Mountain foreland uplifts:<br />
Geology, v. 14, p. 259-262.<br />
303
Fielding, E., and T. E. Jordan, 1988, Active deformation at the boundary between the<br />
Precordillera and Sierras Pampeanas, Argentina, and comparison with ancient<br />
Rocky Mountain deformation: Memoir.<br />
Fischer, M. P., N. B. Woodward, and M. M. Mitchell, 1992, The kinematics <strong>of</strong> breakthrust<br />
folds: Journal <strong>of</strong> structural geology, v. 14, p. 451-460.<br />
Fischer, M. P., and M. S. Wilkerson, 2000, Predicting the orientation <strong>of</strong> joints from<br />
fold shape: Results <strong>of</strong> pseudo-three-dimensional modeling and curvature<br />
analysis: Geology, v. 28, p. 15-18.<br />
Fisher, D., and D. J. Anastasio, 1994, Kinematic analysis <strong>of</strong> a large-scale leading edge<br />
fold, Lost River Range, Idaho: Journal <strong>of</strong> structural geology, v. 16, p. 337-354.<br />
Forster, A., A. P. Irmen, and C. Vondra, 1996, Structural interpretation <strong>of</strong> Sheep<br />
Mountain Anticline, Bighorn Basin, Wyoming: Wyoming Geological<br />
Association Guidebook, v. 47, p. 239-251.<br />
Garcia, P. E., and G. H. Davis, 2004, Evidence and mechanisms forvfolding <strong>of</strong><br />
granite, Sierra de Hualfin basement-cored uplift, northwest Argentina:<br />
American Association <strong>of</strong> Petroleum Geologists Bulletin, v. 88.<br />
Garfield, T. R., N. F. Hurley, and D. A. Budd, 1992, Little Sand Draw File, Big Horn<br />
Basin, Wyoming: a hybrid dual-porosity and single-porosity reservoir in the<br />
Phosphoria Formation: American Association <strong>of</strong> Petroleum Geologists<br />
Bulletin, v. 76, p. 371-391.<br />
Gries, R., 1983, Oil and gas prospection beneath Precambrian <strong>of</strong> foreland thrust plates<br />
in Rocky Mountains: American Association <strong>of</strong> Petroleum Geologists Bulletin,<br />
v. 67, p. 1-28.<br />
Gross, M. R., G. Gutierrez-Alonso, and W. L. Bartlett, 1998, Fold-related fractures in<br />
coastal outcrops <strong>of</strong> the Monterey Formation; effects <strong>of</strong> structural style,<br />
mechanical stratigraphy, and scale at Arroyo Burro Beach: Book - Pacific<br />
Section, Society <strong>of</strong> Economic Paleontologists and Mineralogists.<br />
Gross, M. R., and T. Engelder, 1995, Strain accommodated by brittle failure in<br />
adjacent units <strong>of</strong> the Monterey Formation, U.S.A.; scale effects and evidence<br />
for uniform displacement boundary conditions: Journal <strong>of</strong> Structural Geology,<br />
v. 17, p. 1303-1318.<br />
Guiton, M., Y. Leroy, and W. Sassi, 2003a, Activation <strong>of</strong> diffuse discontinuities and<br />
folding <strong>of</strong> the sedimentary layers: Journal <strong>of</strong> Geophysical Research, v. 108.<br />
Guiton, M. L. E., W. Sassi, Y. M. Leroy, and B. D. M. Gauthier, 2003b, Mechanical<br />
constraints on the chronology <strong>of</strong> fracture activation in folded Devonian<br />
304
sandstone <strong>of</strong> the western Moroccan Anti-Atlas: Journal <strong>of</strong> Structural Geology,<br />
v. 25, p. 1317-1330.<br />
Harris, J. F., G. L. Taylor, and J. L. Walper, 1960, Relation <strong>of</strong> deformational fractures<br />
in sedimentary rocks to regional and local structure: American Association <strong>of</strong><br />
Petroleum Geologists Bulletin, v. 44, p. 1853-1873.<br />
Hennier, J., Jeffrey, 1984, Structural analysis <strong>of</strong> the Sheep Mountain anticline,<br />
Bighorn Basin, Wyoming: MS thesis, Texas A&M <strong>University</strong>, 119 p.<br />
Hennier, J., and J. Spang, 1983, Mechanisms for deformation <strong>of</strong> sedimentary strata at<br />
Sheep Mountain anticline, Big Horn Basin, Wyoming: Wyoming Geological<br />
Association Guidebook, v. 34th annual field conference, p. 97-111.<br />
Hennings, P. H., J. E. Olson, and L. B. Thompson, 2000, Combining outcrop data and<br />
three dimensional structural models to characterize fractured reservoirs: an<br />
example from Wyoming: American Association <strong>of</strong> Petroleum Geologists<br />
Bulletin, v. 84, p. 830-849.<br />
Johnson, G. D., L. J. Garside, and A. J. Warner, 1965, A study <strong>of</strong> the structure and<br />
associated features <strong>of</strong> Sheep Mountain Anticline, Big Horn County, Wyoming:<br />
. Iowa Academy <strong>of</strong> Science, v. 72, p. 332-342.<br />
Jordan, T. E., B. L. Isacks, R. W. Allmendinger, J. A. Brewer, V. A. Ramos, and C. J.<br />
Ando, 1983, Andean tectonics related to geometry <strong>of</strong> subducted Nazca Plate:<br />
Geological Society <strong>of</strong> America bulletin, v. 94, p. 341-361.<br />
Ladd, R. E., 1979, The geology <strong>of</strong> Sheep Canyon Quadrangle, MS thesis, Wyoming,<br />
Iowa State <strong>University</strong>, Ames, 124 p.<br />
Mallet, J. L., 2002, Geomodelling: New York, Oxford <strong>University</strong> Press.<br />
McConnell, D., 1994, Fixed-hinge, basement-involved fault-propagation folds,<br />
Wyoming: Geological Society <strong>of</strong> America bulletin, v. 106, p. 1583-1593.<br />
Megard, F., and H. Philip, 1976, Plio-Quaternary tectono-magmatic zonation and plate<br />
tectonics in the central Andes: <strong>Earth</strong> and planetary science letters, v. 33, p.<br />
231-238.<br />
Miller, E. W., and D. R. Lageson, 1990, Laramide basement deformation in the<br />
northern Gallatin Range and southern Bridger Range, Southwest Montana:<br />
Abstracts with programs - Geological Society <strong>of</strong> America, v. 22, p. 39.<br />
Narr, W., and J. Suppe, 1994, Kinematics <strong>of</strong> basement-involved compressive<br />
structures: The American journal <strong>of</strong> science, v. 294, p. 802-860.<br />
305
Pollard, D. D., and A. Aydin, 1988, Progress in understanding jointing over the past<br />
century: Geological Society <strong>of</strong> America Bulletin, v. 100, p. 1181-1204.<br />
Prucha, J. J., J. A. Graham, and R. P. Nickelson, 1965, Basement-controlled<br />
deformation in Wyoming Province <strong>of</strong> Rocky Mountain foreland: American<br />
Association <strong>of</strong> Petroleum Geologists Bulletin, v. 49, p. 966-992.<br />
Rioux, R. L., 1958, Geology <strong>of</strong> the Spence-Kane area, Bighorn County, Wyoming,<br />
MS thesis, <strong>University</strong> <strong>of</strong> Illinois, 182 p.<br />
Rioux, R. L., 1994, Geologic map <strong>of</strong> the Sheep Mountain--Little Sheep Mountain<br />
area, Big Horn County, Wyoming. Scale 1:31,680.<br />
Sales, J. K., 1968, Crustal mechanics <strong>of</strong> Cordilleran foreland deformation; a regional<br />
and scale-model approach: The American Association <strong>of</strong> Petroleum Geologists<br />
bulletin, v. 52, p. 2016-2044.<br />
Savage, H., 2003, Three-dimensional interaction among fault-cored folds: MS thesis,<br />
UMass Amherst.<br />
Savage, H., and M. L. Cooke, 2004, The effect <strong>of</strong> non-parallel fault interaction on fold<br />
patterns: Journal <strong>of</strong> Structural Geology, v. 26, p. 905-917.<br />
Schmidt, C. J., and J. M. Garihan, 1983, Laramide tectonic development <strong>of</strong> the Rocky<br />
Mountain foreland <strong>of</strong> southwestern Montana: Field conference [and<br />
guidebook], v. 1983, p. 271-294.<br />
Schmidt, C. J., P. W. Genovese, and R. B. Chase, 1993, Role <strong>of</strong> basement fabric and<br />
cover-rock lithology on the geometry and kinematics <strong>of</strong> twelve folds in the<br />
Rocky Mountain foreland: Special papers.<br />
Silliphant, L. J., T. Engelder, and M. R. Gross, 2002, The state <strong>of</strong> stress in the limb <strong>of</strong><br />
the Split Mountain Anticline, Utah; constraints placed by transected joints:<br />
Journal <strong>of</strong> structural geology, v. 24, p. 155-172.<br />
Simmons, S. P., and P. A. Scholle, 1990, Late Paleozoic uplift and sedimentation,<br />
northeast Big Horn Basin, Wyoming: Wyoming Geological Association<br />
Guidebook, v. 41, p. 39-55.<br />
Smithson, S. B., J. A. Brewer, S. Kaufman, J. E. Oliver, and C. A. Hurich, 1979,<br />
Structure <strong>of</strong> the Laramide Wind River Uplift, Wyoming, from COCORP deep<br />
reflection data and from gravity data: Journal <strong>of</strong> geophysical research, v. 84, p.<br />
5955-5972.<br />
306
Smithson, S., J. Brewer, S. Kaufman, J. Oliver, and C. Hurich, 1978, Nature <strong>of</strong> the<br />
Wind River thrust, Wyoming, from COCORP deep-reflection data and from<br />
gravity data: Geology, v. 6, p. 648-652.<br />
Spang, J. H., and J. P. Evans, 1988, Geometrical and mechanical constraints on<br />
basement-involved thrusts in the Rocky Mountain foreland province, in C. J.<br />
Schmidt, and W. J. Perry, Jr, eds., Interaction <strong>of</strong> the Rocky Mountain foreland<br />
and the Cordilleran thrust belt, Geological Society <strong>of</strong> America Memoir 171, p.<br />
41-51.<br />
Spang, J. H., J. P. Evans, and B. Douglas, 1985, Balanced cross sections <strong>of</strong> small foldthrust<br />
structures: Mountain Geologist, v. 22, p. 41-46.<br />
Stanton, H. I., and E. A. Erslev, 2004, Sheep Mountain: backlimb tightening and<br />
sequential deformation in the Bighorn Basin, Wyoming: Wyoming Geol.<br />
Assoc. Guidebook, v. Fifty third field conference, p. 75-87.<br />
Stearns, D. W., and D. M. Weinberg, 1975, A comparison <strong>of</strong> experimentally created<br />
and naturally formed drape folds: Guidebook, Annual field conference, p. 159-<br />
166.<br />
Stearns, D. W., 1971, Mechanisms <strong>of</strong> drape folding in the Wyoming Province:<br />
Wyoming Geol. Assoc. Guidebook, 25th Annual Field Conference, p. 149-<br />
158.<br />
Stearns, D. W., 1978, Faulting and forced folding in the Rocky Mountains foreland, in<br />
V. Matthews, ed., Laramide Folding Associated With Basement Block<br />
Faulting in the Rocky Mountains Region,, Geological Society <strong>of</strong> America<br />
Memoir 151, p. 1-37.<br />
Stearns, M. T., and D. W. Stearns, 1978, Geometric analysis <strong>of</strong> multiple drape folds<br />
along the northwest Big Horn Mountain front, Wyoming, in V. Matthews, ed.,<br />
Laramide folding associated with basement faulting in the western United<br />
States: Geological Society <strong>of</strong> America Memoir 151, p. 139-156.<br />
Stone, D. S., 1993, Basement-involved thrust-generated folds as seismically imaged in<br />
the subsurface <strong>of</strong> the central Rocky Mountain foreland: Laramide basement<br />
deformation in the Rocky Mountain Foreland <strong>of</strong> the Western United Sates, v.<br />
Special Paper 280: Boulder, Colorado, Geological Society <strong>of</strong> America.<br />
Stone, D. S., 2004, Rio thrusting, multi-stage migration, and formation <strong>of</strong> vertically<br />
segregated Paleozoic oil pools at Torchlight Field on the Greybull Platform<br />
(Eastern Bighorn Basin): implications for exploration: The Mountain<br />
Geologist, v. 41, p. 119-138.<br />
307
Thom, W. T., Jr., 1923, The relation <strong>of</strong> deep-seated faults to the surface structural<br />
features <strong>of</strong> central Montana: Bulletin <strong>of</strong> the American Association <strong>of</strong><br />
Petroleum Geologists, v. 7, p. 1-13.<br />
Thom, W. T., Jr., 1952, Structural features <strong>of</strong> the Big Horn Basin rim: Wyoming<br />
Geological Association Guidebook, v. 7th annual field conference, p. 15-17.<br />
Thomas, A. L., 1993, Poly3D: a three-dimensional, polygonal element, displacement<br />
discontinuity boundary elemnt computer program with applications to<br />
fractures, faults, and cavities in the <strong>Earth</strong>'s crust.: MS thesis, <strong>Stanford</strong><br />
<strong>University</strong>.<br />
Thomas, L. E., 1965, Sedimentation and structural development <strong>of</strong> Big Horn Basin:<br />
Bulletin <strong>of</strong> the American Association <strong>of</strong> Petroleum Geologists, v. 49, p. 1867-<br />
1877.<br />
Twiss, R. J., and E. M. Moores, 1992, Structural Geology: New York, W. H. Freeman<br />
and Company, 532 p.<br />
Wu, H., and D. D. Pollard, 1995, An experimental study <strong>of</strong> the relationship between<br />
joint spacing and layer thickness: Journal <strong>of</strong> Structural Geology, v. 17, p. 887-<br />
905.<br />
308