You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
FRACTAL ANALYSIS AND THERMAL-ELASTIC MODELING OF A<br />
SUBVOLCANIC MAGMATIC BRECCIA: THE SHATTER ZONE, MOUNT<br />
DESERT ISLAND, MAINE<br />
By<br />
Samuel Ge<strong>of</strong>frey Roy<br />
B.S. <strong>University</strong> <strong>of</strong> <strong>Maine</strong>, 2008<br />
A THESIS<br />
Submitted in Partial Fulfillment <strong>of</strong> the<br />
Requirements for the Degree <strong>of</strong><br />
Master <strong>of</strong> Science<br />
(in Earth Sciences)<br />
The Graduate School<br />
The <strong>University</strong> <strong>of</strong> <strong>Maine</strong><br />
May, 2011<br />
Advisory Committee:<br />
Scott E. Johnson, Pr<strong>of</strong>essor <strong>of</strong> Earth Sciences, Advisor<br />
Christopher C. Gerbi, Assistant Pr<strong>of</strong>essor <strong>of</strong> Earth Sciences<br />
Zhihe Jin, Assistant Pr<strong>of</strong>essor <strong>of</strong> Mechanical Engineering<br />
Peter O. Koons, Pr<strong>of</strong>essor <strong>of</strong> Earth Sciences
THESIS/DISSERTATION/PROJECT<br />
ACCEPTANCE STATEMENT<br />
On behalf <strong>of</strong> the Graduate Committee for Samuel Ge<strong>of</strong>frey Roy, I<br />
affirm that this manuscript is the final accepted <strong>thesis</strong>/dissertation/project.<br />
Signatures <strong>of</strong> all committee members are on file with the Graduate School at<br />
the <strong>University</strong> <strong>of</strong> <strong>Maine</strong>, 5755 Stodder Hall, Orono <strong>Maine</strong> 04469.<br />
ii
LIBRARY RIGHTS STATEMENT<br />
In presenting this <strong>thesis</strong> in partial fulfillment <strong>of</strong> the requirements for an<br />
advanced degree at the <strong>University</strong> <strong>of</strong> <strong>Maine</strong>, I agree that the Library shall make it<br />
freely available for inspection. I further agree that permission for “fair use”<br />
copying <strong>of</strong> this <strong>thesis</strong> for scholarly purposes may be granted by the Librarian. It is<br />
understood that any copying or publication <strong>of</strong> this <strong>thesis</strong> for financial gain shall<br />
not be allowed without my written permission.<br />
Signature:<br />
Date:
FRACTAL ANALYSIS AND THERMAL-ELASTIC MODELING OF A<br />
SUBVOLCANIC MAGMATIC BRECCIA: THE SHATTER ZONE, MOUNT<br />
DESERT ISLAND, MAINE<br />
By Samuel Ge<strong>of</strong>frey Roy<br />
Thesis Advisor: Dr. Scott E. Johnson<br />
An Abstract <strong>of</strong> the Thesis Presented<br />
in Partial Fulfillment <strong>of</strong> the Requirements for the<br />
Degree <strong>of</strong> Master <strong>of</strong> Science<br />
(in Earth Sciences)<br />
May, 2011<br />
The Shatter Zone <strong>of</strong> Mount Desert Island, <strong>Maine</strong>, is a 450-1000m thick<br />
magmatic breccia that defines the perimeter <strong>of</strong> the Cadillac Mountain Intrusive<br />
Complex. The 400 Ma complex consists <strong>of</strong> gabbro-diorite sheets overlain by<br />
three different granites, the largest <strong>of</strong> which is an A-type granite emplaced at high<br />
temperature (~900 o C) and at shallow crustal depth (
emplacement <strong>of</strong> mafic magma, resulting in elastic failure <strong>of</strong> the metasedimentary<br />
and diorite wall rock and virtually instantaneous fragmentation and entrainment <strong>of</strong><br />
the clasts in hot granitic magma. The degree <strong>of</strong> brecciation is gradational, with<br />
clast supported breccias at the outer margin <strong>of</strong> the zone grading inward to<br />
granitic-matrix supported breccia, and finally into clast-free Cadillac Mountain<br />
Granite. Field observations point to an explosive breccia mechanism, and clast<br />
size distribution analysis yields fractal dimensions (D s > 3) that agree with those<br />
known to result from explosion (D s > 2.5). Field and microstructural data and<br />
observations suggest that the clast sizes and shapes <strong>of</strong> the metasedimentary<br />
host rocks reflect post-brecciation modification by partial melting and thermal<br />
fracture, while diorite dike fragments experienced little modification after the<br />
original brecciation event. Clast circularity increases with proximity to the magma<br />
reservoir, whereas clast boundary shape decreases; this implies thermal wear on<br />
clast surfaces. Numerical modeling is employed to explore the possible thermalmechanical<br />
effects on the size distribution <strong>of</strong> clasts. Instantaneous immersion is<br />
assumed for metasedimentary clasts (650°C) in a hot granitic matrix (800°C -<br />
900°C), and our thermal analysis is restricted to conductive heat transfer<br />
corrected for latent heat. The amount <strong>of</strong> clast melt is primarily dependent on the<br />
melt temperature <strong>of</strong> the clast, the matrix to clast volume ratio, and the initial<br />
magma intrusion and clast temperatures. Results show that thermal fracture and<br />
clast melt were viable secondary modification processes, and magma flow was<br />
necessary for disaggregation <strong>of</strong> melted clasts to occur. Angular clasts are highly<br />
susceptible to corner break-<strong>of</strong>f owing to large tensile stresses associated with
thermal shock. Considering the effects <strong>of</strong> these processes on clast size<br />
distribution, we conclude that the Shatter Zone formed from explosion, and latestage<br />
magma emplacement effectively altered the size and shape for many <strong>of</strong><br />
the metasedimentary clasts.
© 2011 Samuel Ge<strong>of</strong>frey Roy<br />
All Rights Reserved<br />
iii
ACKNOWLEDGEMENTS<br />
The completion <strong>of</strong> this <strong>thesis</strong> was made possible through the financial<br />
support from the National Science Foundation (EAR-0810039, EAR-0911150,<br />
and MRI-0820946), the Society <strong>of</strong> Economic Geologists, and <strong>University</strong> <strong>of</strong> <strong>Maine</strong><br />
Graduate Student Government. I thank my advisor, Scott E. Johnson, for the<br />
opportunity to work on a unique project and to allow me the freedom to pursue<br />
my own interests within the project. My research and my development as a<br />
scientist benefited greatly from discussions with my advisory committee<br />
members Peter Koons, Christopher Gerbi, and Zhihe Jin. The pr<strong>of</strong>essional<br />
attitude <strong>of</strong> my committee and the openness <strong>of</strong> discussions stemming from my<br />
research gave me the direction I needed to keep on track. I would also like to<br />
thank the Department <strong>of</strong> Earth Sciences, which has been an integral part <strong>of</strong> my<br />
life both in my undergraduate and graduate career. I am thankful for the positive<br />
support given by the faculty, staff, and my fellow graduate students. I want to<br />
thank all <strong>of</strong> my friends for the wonderful memories and experiences in and out <strong>of</strong><br />
the classroom. Most importantly, I want to thank my fiancée Teagan for putting<br />
up with my eccentricities. I couldn’t have made it this far without her love and<br />
support!<br />
iv
TABLE OF CONTENTS<br />
ACKNOWLEDGEMENTS ..................................................................................... iv<br />
LIST OF FIGURES ............................................................................................... ix<br />
LIST OF TABLES ................................................................................................. xi<br />
Chapter<br />
1. INTRODUCTION ............................................................................................. 1<br />
2. GEOLOGIC SETTING .................................................................................... 4<br />
2.1. Regional Geology: The Coastal <strong>Maine</strong> Magmatic Province ...................... 4<br />
2.2. Cadillac Mountain Intrusive Complex ........................................................ 4<br />
2.3. Bar Harbor Formation ............................................................................... 7<br />
2.4. Shatter Zone ............................................................................................. 8<br />
3. PHYSICAL DESCRIPTION OF SUBVOLCANIC SYSTEMS ........................ 10<br />
3.1. Magma Plumbing Syste<strong>ms</strong> ..................................................................... 11<br />
3.1.1. Generation and Transport <strong>of</strong> Magma ............................................. 11<br />
3.1.2. Emplacement and Growth <strong>of</strong> Magma Chambers ........................... 13<br />
3.2. Subsurface Response to Volcanic Eruption ............................................ 15<br />
3.2.1. The Mechanical Behavior <strong>of</strong> Wall Rock as a Control for<br />
Eruption Behavior: from Magma Storage to Volcanic Eruption ..... 16<br />
3.2.2. Volcanic Triggers and Chamber Rupture in a Rigid Reservoir ...... 19<br />
3.2.3. Evidence for Wall Rock Readjustment in Modern Volcanoes ........ 23<br />
v
3.3. Volcanic Energy ...................................................................................... 23<br />
3.4. Emplacement and eruptive history <strong>of</strong> the Cadillac Mountain<br />
Intrusive Complex ................................................................................... 25<br />
4. THERMAL FRAMEWORK FOR CONTACT METAMORPHISM ................... 26<br />
4.1. Characteristics <strong>of</strong> Contact Metamorphism .............................................. 26<br />
4.1.1. Conductive, Convective, and Advective Heat Transfer................... 27<br />
4.2. Contact Metamorphism in the Shatter Zone ........................................... 28<br />
4.3. Methods for Contact Metamorphic Thermal Modeling ............................ 29<br />
4.3.1. Model Setup ................................................................................... 34<br />
4.3.2. Results and Discussion .................................................................. 39<br />
4.4. Evidence for an Actively Mixing Chamber .............................................. 42<br />
5. ROCK MECHANICS AND THE FRACTAL BEHAVIOR OF ROCK ............... 44<br />
5.1. Brittle Failure <strong>of</strong> Rock ............................................................................. 45<br />
5.1.1. Basic Principles <strong>of</strong> Griffith Fracture Theory .................................... 45<br />
5.1.2. The Self-Similarity <strong>of</strong> Fracture Patterns .......................................... 48<br />
5.2. Fractal Theory ......................................................................................... 49<br />
5.3. Quantitative Methods <strong>of</strong> Breccia Classification ....................................... 51<br />
5.3.1. Clast Size Distribution .................................................................... 51<br />
5.3.2. The Fractal Dimension-Brecciation Mechanism Link for Clast<br />
Size Distribution ............................................................................. 54<br />
5.3.3. Clast Boundary Shape.................................................................... 57<br />
5.3.4. The Fractal Dimension-Brecciation Mechanism Link for Clast<br />
Boundary Shape ............................................................................. 61<br />
vi
5.3.5. Clast Circularity Analysis ................................................................ 62<br />
6. ANALYSIS AND RESULTS........................................................................... 64<br />
6.1. Field Relations in the Shatter Zone ......................................................... 65<br />
6.1.1. Gradational Characteristics ............................................................ 65<br />
6.1.1.1. Type 1 .................................................................................... 65<br />
6.1.1.2. Type 2 .................................................................................... 71<br />
6.1.1.3. Type 3 .................................................................................... 71<br />
6.2. Methods .................................................................................................. 74<br />
6.3. Data ........................................................................................................ 78<br />
6.3.1. Clast Size Distribution Data ............................................................ 78<br />
6.3.2. Clast Boundary Shape Data ........................................................... 82<br />
6.3.3. Clast Circularity Analysis Data ....................................................... 84<br />
6.3.4. Summary <strong>of</strong> Data ........................................................................... 84<br />
6.4. Discussion .............................................................................................. 86<br />
6.4.1. Bifractal Distributions for Type 1 and 2 ........................................... 86<br />
6.4.2. Differing rock types and clast modification evidence in Type 3 ...... 88<br />
7. MECHANISMS FOR SECONDARY CLAST MODIFICATION: A<br />
DISCUSSION ................................................................................................ 90<br />
7.1. Potential Mechanis<strong>ms</strong> for CSD and CBS Modification ............................ 91<br />
7.1.1. Thermal Attrition ............................................................................ 91<br />
7.2. Methods: Partial Melting <strong>of</strong> Clasts .......................................................... 92<br />
7.2.1. Model Setup and Important Parameters ........................................ 92<br />
7.2.2. Methods for Plotting Data .............................................................. 97<br />
vii
7.2.3. Applications for Dimensionless Variables ...................................... 98<br />
7.3. Clast Melt Results ................................................................................... 99<br />
7.3.1. Discussion ................................................................................... 102<br />
7.4. Thermal-Induced Fracture .................................................................... 108<br />
7.4.1. Model Setup................................................................................. 109<br />
7.4.2. Results and Discussion ............................................................... 112<br />
7.5. Final Discussion .................................................................................... 115<br />
REFERENCES ................................................................................................. 118<br />
BIOGRAPHY OF THE AUTHOR ...................................................................... 137<br />
viii
LIST OF FIGURES<br />
Figure 2.1.<br />
Figure 3.1.<br />
Figure 3.2.<br />
Figure 3.3.<br />
Figure 3.4.<br />
Figure 4.1.<br />
Bedrock map <strong>of</strong> Mount Desert Island ............................................. 5<br />
Formation <strong>of</strong> a laccolith ................................................................ 14<br />
Generalized volcanic surface discharge rates .............................. 18<br />
Two for<strong>ms</strong> <strong>of</strong> subvolcanic breccias .............................................. 21<br />
Common models for caldera collapse .......................................... 22<br />
Mineralogy <strong>of</strong> the contact metamorphosed Bar Harbor<br />
Formation ..................................................................................... 30<br />
Figure 4.2.<br />
Figure 4.3.<br />
Figure 4.4.<br />
Figure 4.5.<br />
Figure 4.6.<br />
An isograd map <strong>of</strong> the Shatter Zone ............................................ 32<br />
Geometry <strong>of</strong> the intrusion model .................................................. 37<br />
Time steps for the cooling chamber ............................................. 38<br />
A temperature versus time plot from intrusion model results ....... 40<br />
Maximum metamorphic temperature with orthogonal distance<br />
from the contact ........................................................................... 41<br />
Figure 5.1.<br />
Figure 5.2.<br />
Figure 5.3.<br />
Figure 5.4.<br />
Figure 5.5.<br />
Figure 6.1.<br />
An elliptical Griffith crack under compressive stress .................... 46<br />
A cube displaying self-similar size distribution properties ............ 50<br />
An example clast size distribution plot ......................................... 53<br />
The Koch snowflake ..................................................................... 59<br />
Euclidean distance mapping on a clast outline ............................ 60<br />
The gradient <strong>of</strong> brecciation intensity through the Shatter<br />
Zone ............................................................................................. 66<br />
Figure 6.2.<br />
Figure 6.3.<br />
Type 1 Shatter Zone .................................................................... 67<br />
Type 2 Shatter Zone .................................................................... 68<br />
ix
Figure 6.4.<br />
Figure 6.5.<br />
Type 3 Shatter Zone .................................................................... 69<br />
Centimeter-scale boudinage textures in Bar Harbor<br />
Formation ..................................................................................... 70<br />
Figure 6.6.<br />
Figure 6.7.<br />
Figure 6.8.<br />
Brecciation textures in Type 2 Shatter Zone ................................ 72<br />
Local flow textures in Type 3 Shatter Zone .................................. 73<br />
Evidence for secondary clast size, shape, and boundary<br />
modification ................................................................................. 75<br />
Figure 6.9.<br />
Figure 6.10.<br />
Figure 6.11.<br />
Figure 6.12.<br />
Figure 6.13.<br />
Figure 7.1.<br />
Figure 7.2.<br />
Figure 7.3.<br />
Figure 7.4.<br />
Figure 7.5.<br />
An outcrop grid used for fractal analysis ...................................... 77<br />
Clast size distribution data for Type 1 and 2 Shatter Zone ........... 80<br />
Clast size distribution data for Type 3 Shatter Zone .................... 81<br />
Clast boundary shape data ordered by Shatter Zone type .......... 83<br />
Circularity data ordered by Shatter Zone type .............................. 85<br />
Geometries used for thermal modeling ........................................ 93<br />
Solidus migration trend for a spherical clast ............................... 100<br />
A plot displaying clast melt over time ......................................... 101<br />
Temperature changes over time for points in a clast ................. 103<br />
The evolution <strong>of</strong> clast size distribution with progressive<br />
thermal exposure ....................................................................... 107<br />
Figure 7.6.<br />
Figure 7.7.<br />
Clast geometry used for thermal stress analysis ........................ 111<br />
Time step results for thermal stress in metasedimentary and<br />
diorite clasts ............................................................................... 113<br />
x
LIST OF TABLES<br />
Table 6.1.<br />
Table 7.1.<br />
Table 7.2.<br />
Average CSD values ..................................................................... 79<br />
Physical constants for thermal solutions ....................................... 95<br />
Physical constants for thermal-mechanical solutions .................. 110<br />
xi
Chapter 1<br />
INTRODUCTION<br />
Magma chambers are dynamic physical and chemical syste<strong>ms</strong> involving<br />
multiple processes such as mixing, mingling, convection, recharge and<br />
evacuation <strong>of</strong> magma. At deeper crustal levels, relatively high background<br />
temperatures can lead to long-term physical and chemical evolution, obscuring<br />
the spatial and temporal relations among individual magmatic events. In contrast,<br />
the sequential evolution <strong>of</strong> magmatic syste<strong>ms</strong> high in the crust at the interface<br />
between the plutonic and volcanic real<strong>ms</strong> is commonly well preserved. These<br />
subvolcanic syste<strong>ms</strong> (e.g. Johnson et al., 2002; Metcalf, 2004; Kemp et al., 2006;<br />
Marianelli et al., 2006), much like eruptive sequences, can preserve a long and<br />
varied history <strong>of</strong> instantaneous magmatic events. They typically contain a wide<br />
variety <strong>of</strong> intrusive phases (e.g. cone sheets, ring faults and dikes, and massive<br />
central intrusions) and are potentially a rich source <strong>of</strong> information about the<br />
evolution <strong>of</strong> caldera/volcano root zones and the tops <strong>of</strong> upper-crustal magma<br />
chambers. They also commonly preserve genetically related volcanic sequences<br />
on their margins. The detailed intrusive relationships in these complexes and the<br />
intimate timing relationships between the various intrusions and deformational<br />
structures are preserved in part due to rapid quenching <strong>of</strong> some units, and in part<br />
due to the sequential series <strong>of</strong> intrusions that produce a magmatic stratigraphy.<br />
These complexes provide an unusual opportunity to evaluate the evolution <strong>of</strong><br />
1
subvolcanic magmatic syste<strong>ms</strong>, the links between plutonism and volcanism, and<br />
upper-crustal magma plumbing syste<strong>ms</strong> in general.<br />
In this <strong>thesis</strong>, I describe a subvolcanic igneous system known as the<br />
Cadillac Mountain intrusive complex, emplaced at
likely explosive mechanism <strong>of</strong> breccia formation followed by modification <strong>of</strong><br />
metasedimentary clast shapes and sizes through partial melting and postbrecciation<br />
thermal fracturing. Methods from this <strong>thesis</strong> provide a new approach<br />
for the fractal analysis <strong>of</strong> breccias formed in a magmatic environment.<br />
3
Chapter 2<br />
GEOLOGIC SETTING<br />
2.1. Regional Geology: The Coastal <strong>Maine</strong> Magmatic Province<br />
The area <strong>of</strong> interest lies in the Coastal <strong>Maine</strong> Magmatic Province (Hogan<br />
and Sinha, 1989), a group <strong>of</strong> over 100 plutons <strong>of</strong> granitic through gabbroic<br />
composition located on the eastern coast <strong>of</strong> <strong>Maine</strong> with ages ranging from Late<br />
Silurian to Early Carboniferous. Plutons in this complex display a bimodal<br />
character (Chapman, 1962), with evidence for mafic and felsic magma mingling<br />
(Chapman, 1962; Wiebe, 1993). Gravity studies imply that these plutons are less<br />
than a few kilometers thick with shallow dipping floors and steep walls, underlain<br />
by mafic sheets (Sweeney, 1976; Hodge et al., 1982). These intrusions follow a<br />
NE-trend within fault-bounded continental crust that accreted onto the North<br />
American craton prior to Acadian orogenesis (Hogan and Sinha 1989, Wiebe et<br />
al. 2004). Hogan and Sinha (1989) suggested that the coastal <strong>Maine</strong> magmatic<br />
province intruded the older crust during a post-collisional, extensional rifting<br />
event related to the Acadian Orogeny (Coombs, 1994; Wiebe et al., 1997a).<br />
2.2. Cadillac Mountain Intrusive Complex<br />
The Cadillac Mountain intrusive complex <strong>of</strong> Mount Desert Island (Figure<br />
2.1) is part <strong>of</strong> the Coastal <strong>Maine</strong> Magmatic Province (Hogan and Sinha, 1989).<br />
The complex is roughly circular in map view covering an approximate area <strong>of</strong><br />
14km x 20km, and consists <strong>of</strong> the Cadillac Mountain Granite and the younger<br />
4
-68.45° -68.30° -68.15°<br />
44.40°<br />
Type 1<br />
Type 2<br />
44.35°<br />
Type 3<br />
44.30°<br />
44.25°<br />
Type 1<br />
Type 2<br />
Type 3<br />
4 km<br />
N<br />
500 m<br />
Figure 2.1. Bedrock map <strong>of</strong> Mount Desert Island. A) The Cadillac Mountain Intrusive Complex. B) The Eastern coast <strong>of</strong> the island.<br />
Blue dots represent Shatter Zone type localities.<br />
5
Somesville granite suite to the west, both <strong>of</strong> which are inferred to be underlain by<br />
composite gabbro-diorite sheets (Hodge et al., 1982; Wiebe, 1994). The entire<br />
complex dips slightly to the east, exposing the intrusive layers and their relative<br />
contact relationships. The Cranberry Island volcanic series, located in the south,<br />
features a bimodal geochemistry that correlates well with the intrusive complex,<br />
leading some authors to consider it as genetically related to the Cadillac<br />
Mountain intrusive complex (e.g. Seaman et al., 1995, 1999; Wiebe et al.,<br />
1997a). The complex was emplaced into the Ellsworth Schist, Bar Harbor<br />
Formation, and the Cranberry Island volcanic series. The Southwest Harbor<br />
Granite is a poorly studied, older unit cross-cut by the main intrusion.<br />
Several factors indicate shallow crustal emplacement <strong>of</strong> the intrusive<br />
complex, including evidence for plutonic intrusion within its own eruptive<br />
products, miarolitic textures in the upper section <strong>of</strong> the Cadillac Mountain<br />
Granite, and relatively low pressure metamorphic mineral assemblages in<br />
surrounding wall rock (Metzger, 1959; Chapman, 1962; Berry and Osberg, 1989;<br />
Seaman et al., 1995; Wiebe et al., 1997a; Seaman et al., 1999). Cadillac<br />
Mountain Granite compositions in the Quartz-Orthoclase-Albite-H 2 O system plot<br />
between 0.5-1kbar, and presence <strong>of</strong> edenitic hornblende indicates low pressure<br />
crystallization. Emplacement likely occurred at approximately 2-5km depth<br />
(Wiebe et al., 1997a; Nichols and Wiebe, 1998). Gravity data from Hodge et al.<br />
(1982) indicate a saucer-shaped floor geometry for the Cadillac Mountain Granite<br />
with a thickness <strong>of</strong> approximately 2.5km, underlain by gabbro-diorite sheets <strong>of</strong> a<br />
potentially similar thickness. Wiebe et al. (1997a) have suggested that the<br />
6
Cadillac Mountain Granite and gabbro-diorite partially mixed and formed an A-<br />
type granite, which is a dry, Fe-enriched granite typically related to anorogenic<br />
extensional tectonic processes. Thus, the A-type characteristics <strong>of</strong> the Cadillac<br />
Mountain Granite may relate more to upper crustal mixing processes rather than<br />
the original source composition.<br />
2.3. Bar Harbor Formation<br />
This study focuses on the contact between Cadillac Mountain Granite and<br />
Bar Harbor Formation on Mount Desert Island. The Bar Harbor Formation is a<br />
metasedimentary rock found in Frenchman’s Bay and in isolated segments along<br />
the eastern shore <strong>of</strong> Mount Desert Island. The majority <strong>of</strong> Bar Harbor Formation<br />
has undergone regional diagenesis followed by contact metamorphism along the<br />
perimeter <strong>of</strong> the Cadillac Mountain Granite. The unit is approximately 610m thick<br />
and stratified with dominant rock types including pelitic clays, sandstones,<br />
conglomerates, and volcanic tuff. The Bar Harbor Formation varies in modal<br />
abundance between these rock types, but generally consists <strong>of</strong> plagioclase (1-<br />
25%), quartz (2-28%), microcline (3-14%), actinolite (0-13%), lithic fragments <strong>of</strong><br />
volcanics and quartzite (9-50%), and fine granular matrix (23-52%). The matrix<br />
consists <strong>of</strong> plagioclase (10%), quartz (50%), microcline (30%), biotite (5-10%),<br />
chlorite (0-3%), and pyrite (0-3%) (mineral abundances determined by point<br />
counting, Metzger, 1959). Biotite is interstitial to the other grains and displays<br />
kinking and crushing along foliae that indicate post-crystallization deformation.<br />
7
Biotite is metamorphic in origin, and some grains show replacement by chlorite.<br />
Pyrite and magnetite are also common and are assumed to be authogenic.<br />
Metzger (1959) determined three different sediment sources that<br />
produced the observed stratified rock types within the Bar Harbor Formation. The<br />
vast majority <strong>of</strong> sediments came from Ellsworth Schist and amphibolite units that<br />
lie just below the Bar Harbor Formation. Detrital quartzite and microcline could<br />
only have come from the Ellsworth Schist as it is the only facies in which both<br />
exist in abundance. Where present, microcline is <strong>of</strong>ten heavily altered to sericite.<br />
Volcanic tuff layers were produced by the volcanic activity along the convergent<br />
boundary. The volcanic lithic shards are heavily altered and rounded, implying<br />
that they are more mature sediments from a distant source. Biotite and chlorite<br />
are an authigenic result <strong>of</strong> weak metamorphism. Beds are <strong>of</strong>ten well sorted and<br />
display micrograding, and it is believed that these sediments were deposited in a<br />
subaqueous fan (Metzger, 1979). There are no detrital biotite or muscovite<br />
grains, possibly suggesting very rapid, turbulent deposition (Metzger, 1959;<br />
Metzger and Bickford, 1972).<br />
2.4. Shatter Zone<br />
The perimeter <strong>of</strong> the Cadillac Mountain Granite is defined by the Shatter<br />
Zone, an aureole <strong>of</strong> fragmented country rock that varies in apparent thickness<br />
from 450-1000 m (Chapman, 1962; Gilman et al., 1988). The rock fragments in<br />
the eastern Shatter Zone consist <strong>of</strong>: (1) Bar Harbor Formation; (2) Devonian<br />
diorite dikes; and (3) large, relatively rare felsic volcanic xenoliths near the<br />
8
gradational contact with the CMG. Clast sizes range from millimeter to meter<br />
scale (Gilman et al., 1988). The matrix <strong>of</strong> the shatter zone appears as both a fine<br />
grained biotite leucogranite and as late stage pegmatitic quartz veins, both <strong>of</strong><br />
which differ compositionally from the dry, A-type Cadillac Mountain Granite.<br />
Average matrix grain size gradually increases toward the Cadillac Mountain<br />
Granite (Coombs, 1994; Wiebe et al., 1997a). The Shatter Zone is related to this<br />
intrusive complex, and the primary focus <strong>of</strong> this <strong>thesis</strong> is to determine the<br />
conditions <strong>of</strong> wall rock fragmentation, and how the deformation event was related<br />
to volcanic activity.<br />
9
Chapter 3<br />
PHYSICAL DESCRIPTION OF SUBVOLCANIC SYSTEMS<br />
A rarely described and intricately formed feature <strong>of</strong> volcanism, subvolcanic<br />
syste<strong>ms</strong> can yield a great deal <strong>of</strong> information about the link between deeper<br />
magma plumbing syste<strong>ms</strong> and upper crustal volcanic regions. Exposures <strong>of</strong><br />
these syste<strong>ms</strong> are uncommon because they occur at a depth between magma<br />
reservoir and volcanic edifice, providing only a small window into the processes<br />
that occur between the two. Subvolcanic syste<strong>ms</strong> can hold a wealth <strong>of</strong><br />
information on the evolution <strong>of</strong> calderas, volcanic root zones, and the upper<br />
sections <strong>of</strong> reservoirs because they can contain intrusive phases such as cone<br />
sheets, ring faults and dikes, and massive central intrusions produced during<br />
active volcanism. The evolution <strong>of</strong> the subvolcanic magmatic system is recorded<br />
by these features due in part to the rapid quenching <strong>of</strong> some units and the<br />
inherent sequential series <strong>of</strong> intrusive behavior (Lipman, 1984; Johnson, 1999).<br />
Below I review the mechanis<strong>ms</strong> behind magma generation, segregation,<br />
transport, emplacement, and volcanic eruption. Deformation features recorded in<br />
the subvolcanic system are also reviewed, and I discuss how volcanic energy is<br />
translated into deformation features, and how they relate to modern examples<br />
and the Shatter Zone.<br />
10
3.1. Magma Plumbing Syste<strong>ms</strong><br />
3.1.1. Generation and Transport <strong>of</strong> Magma<br />
The development <strong>of</strong> magma plumbing syste<strong>ms</strong> and the geometry <strong>of</strong><br />
igneous intrusions remains a major focus for many researchers who attempt to<br />
determine their correlation to tectonism and the evolution <strong>of</strong> the lithosphere (e.g.<br />
Clague, 1987; Bons et al., 2003a, 2003b; Hayashi and Morita, 2003; Jellinek and<br />
DePaolo, 2003; Bartley et al., 2006; Marianelli et al., 2006; Bohrson, 2007;<br />
Lipman, 2007; Cruden, 2008; Dietyl and Koyi, 2008). Igneous complexes form by<br />
the processes <strong>of</strong> magma generation, segregation, ascent, and emplacement. In<br />
order to relate the magma plumbing syste<strong>ms</strong> to volcanism, the generation and<br />
transport <strong>of</strong> magma through the lithosphere must first be explained. I focus this<br />
discussion on a continental-oceanic convergent tectonic margin.<br />
In a continental-oceanic convergent margin, subduction <strong>of</strong> the oceanic<br />
plate initiates mantle flow. Heat advection from flow in the mantle wedge can<br />
lead to melt in the asthenosphere, the subducting oceanic plate, and in the<br />
overlying lithosphere. Dehydration reactions in the subducting oceanic slab<br />
release water into the mantle wedge, reducing the solidus temperature <strong>of</strong><br />
peridotite and allowing for partial melt in the asthenosphere (e.g. Manea et al.,<br />
2005; Johnson and Jin, 2009). Lithospheric melt occurs from crustal thinning<br />
produced by thermal advection from mantle wedge flow. Further heating <strong>of</strong> the<br />
lithosphere reduces its viscosity, and extensional deformation occurs between<br />
the stationary continental interior and the retreating hinge <strong>of</strong> the subducting slab<br />
(e.g. Billen and Gurnis, 2001, Billen, 2008). The sharper thermal gradient in the<br />
11
thinned lithosphere allows for partial melt. The partially melted lithosphere<br />
becomes weakened and allows segregation and transport <strong>of</strong> the melt fraction<br />
(e.g., Petford et al., 2000; Jackson et al., 2003; Bergantz and Barboza, 2005;<br />
Aizawa et al., 2006). Asthenospheric melt occurs directly below the volcanic front<br />
<strong>of</strong> the convergent margin, while lithospheric melting occurs below back-arc<br />
extensional basins. Melts from both sources can undergo significant crystal<br />
fractionation, producing chemically evolved magmas (e.g. Johnson and Jin,<br />
2009).<br />
The density anomaly produced by lithospheric melting provides a<br />
buoyancy potential for the generated magma, which then rises upward into the<br />
lithosphere. The dominant mechanism <strong>of</strong> magma transport is debatable.<br />
Traditionally, diapirism was used to explain the mass transport <strong>of</strong> large igneous<br />
bodies. This explanation is flawed for upper crustal emplacement because the<br />
driving force <strong>of</strong> buoyancy cannot surpass the strength <strong>of</strong> brittle upper crustal<br />
rock. Also, the large amounts <strong>of</strong> thermal energy spent on weakening the wall<br />
rock to allow ascension reduces the potential magma transport distance before<br />
solidification (Clemens and Mawer, 1992; Petford et al., 2000; Aizawa et al.,<br />
2006). Diapirism may be plausible in the lower lithosphere where wall rock can<br />
deform under viscous strain to accommodate ascent <strong>of</strong> large magmatic bodies<br />
(Weinberg and Podladchikov, 1994), but magma transport by dike propagation is<br />
thought to be the dominant mechanism for transport through much <strong>of</strong> the mid to<br />
upper lithosphere (e.g., Gudmundsson et al., 1999; Accocella et al., 2006;<br />
Johnson and Jin, 2009).<br />
12
3.1.2. Emplacement and Growth <strong>of</strong> Magma Chambers<br />
A buoyant, mobile dike will propagate upwards, normal to the pressure<br />
and density gradients that exist in the host rock. Propagation is assisted by<br />
magma reservoir overpressure if the dike remains connected to the reservoir<br />
(Rubin, 1995a; McLeod and Tait, 1999; Apuani and Corazzato, 2009; Johnson<br />
and Jin, 2009). Propagation will continue as long as overpressure in the dike can<br />
overcome the fracture toughness <strong>of</strong> the wall rock (Rubin, 1995b, Dahm, 2000).<br />
Dike propagation halts when 1) the dike tip freezes, 2) overpressure in the dike<br />
body reduces to a subcritical level, 3) the dike intersects a pre-existing sill or<br />
chamber, 4) the dike tip arrests on contact with a stiffer boundary, 5) the dike<br />
reaches a level <strong>of</strong> neutral buoyancy, or 6) tectonic stress unloading reduces dike<br />
overpressure (Chen et al., in press). An unhindered dike will propagate vertically<br />
beyond the level <strong>of</strong> neutral buoyancy until it rapidly reduces speed, arrests, and<br />
begins to grow laterally (Aizawa et al., 2006; Chen et al., in press).<br />
Reservoir formation at shallow (
A<br />
B<br />
C<br />
Figure 3.1. Formation <strong>of</strong> a laccolith. A) Dike arrest near the level <strong>of</strong> neutral<br />
buoyancy leads to lateral expansion <strong>of</strong> intruding magma. B) As the sill expands,<br />
volumetric expansion is accommodated by lateral expansion and vertical uplift.<br />
C) A tabular pluton for<strong>ms</strong>. A minor amount <strong>of</strong> volume expansion is<br />
accommodated by floor subsidence. Overpressure within the chamber leads to<br />
vertical dike formation, which may intersect the surface.<br />
14
pluton margins (Johnson et al., 2001, 2003, 2004; Gerbi et al., 2004; Aizawa et<br />
al., 2006). However, wall rock shortening can only account for 25-40% <strong>of</strong> a<br />
magma chamber’s volume, so other processes must provide additional volume<br />
for chamber expansion (Paterson and Fowler, 1993; Johnson et al., 1999).<br />
There has been much discussion on the topic <strong>of</strong> volume accomodation by<br />
stoping (e.g. Clarke et al., 1998; Glazner & Bartley, 2006; Clark & Erdman, 2008;<br />
Glazner & Bartley, 2008; Paterson et al., 2008; Yoshinobu & Barnes, 2008),<br />
assimilation (melt and mixture) <strong>of</strong> crust (e.g. Beard & Ragland, 2005; Clarke,<br />
2007), visco-elastic deformation <strong>of</strong> host rock (e.g. Cruden & McCaffrey, 2001;<br />
Jellinek and DePaolo, 2003; Cruden, 2005; Dietyl & Koyi, 2008; Paterson &<br />
Farris, 2008) and dike propagation and sill accretion (e.g. Baer, 1987; Pinel &<br />
Jaupart, 2004; Bartley et al., 2006; Michel et al., 2008). All <strong>of</strong> these processes<br />
allow progressive growth <strong>of</strong> a shallow intrusive complex.<br />
The continued uplift from progressive shallow intrusion magma<br />
emplacement is <strong>of</strong>ten observed as a precursor for eventual magma reservoir<br />
overpressure and rupture, wall rock failure, and caldera collapse. The<br />
subvolcanic system is the zone between the ruptured magma reservoir and the<br />
collapsed volcanic edifice, and it is here that the intrusive history <strong>of</strong> the volcanic<br />
event is stored (Johnson et al., 2002).<br />
3.2. Subsurface Response to Volcanic Eruption<br />
Many geologists have studied the linkage between magma chambers and<br />
volcanism through subvolcanic wall rock deformation (Lipman, 1984; Lipman,<br />
15
1997; Branney and Kokelaar, 1998; Johnson et al., 1999; Aizawa et al., 2006;<br />
Acocella, 2007; Kawakami et al., 2007; Saito et al., 2007) and still others with the<br />
aid <strong>of</strong> lithological, geochemical, and geochronological associations (Metcalf,<br />
2004; Marianelli et al., 2006; Bachmann et al., 2007; Bohrson, 2007). Although<br />
the surface manifestations <strong>of</strong> volcanism are easily witnessed during volcanic<br />
eruptions, study <strong>of</strong> the physical processes that occur below the surface at the<br />
level <strong>of</strong> the erupting magma reservoir is more difficult (Bachmann et al., 2007;<br />
Gottsman & Battaglia, 2008). The study <strong>of</strong> magma reservoir walls is important<br />
because they record devolatilization, cooling, magma recharge, or other<br />
processes integral to volcanic stability through deformation patterns that can be<br />
observed at the surface for eroded volcanic syste<strong>ms</strong>, such as the Shatter Zone,<br />
or through geophysical methods such as seismology for active syste<strong>ms</strong>.<br />
3.2.1. The Mechanical Behavior <strong>of</strong> Wall Rock as a Control for<br />
Eruption Behavior: from Magma Storage to Volcanic Eruption<br />
Volcanic eruptions result from the rupture <strong>of</strong> a magmatic feeder reservoir.<br />
An overpressure above the lithostatic value is necessary to start an eruption, and<br />
this overpressure is controlled by the mechanical behavior <strong>of</strong> the reservoir walls.<br />
The conditions <strong>of</strong> magma flow are dependent on the viscosity <strong>of</strong> the migrating<br />
magma (Scandone, 1996). Chamber growth and pressurization is partially<br />
compensated through viscoelastic deformation <strong>of</strong> wall rock because <strong>of</strong> the<br />
amount <strong>of</strong> heat introduced by the intrusion and the duration (10 5 -10 6 years)<br />
required for a volcanic feeder reservoir to develop (Jellinek and DePaolo, 2003).<br />
16
The potential for volcanic eruption is dependent on the critical rate <strong>of</strong> reservoir<br />
pressurization by magma replenishment. If the rate <strong>of</strong> reservoir pressurization is<br />
lower than the critical level defined by the visco-elastic strength <strong>of</strong> the wall rock,<br />
volume expansion is accommodated by viscous deformation and magma is<br />
stored in the reservoir. Magma storage is controlled by a viscous regime. If the<br />
rate <strong>of</strong> pressure increase exceeds the critical level, the reservoir walls are<br />
compromised by elastic failure, a conduit for<strong>ms</strong> (Barnett and Lorig, 2007), and<br />
volcanic eruption commences. Volcanic eruption is controlled by an elastic<br />
regime (Jellinek and DePaolo, 2003, Scandura et al., 2007, 2008).<br />
Much like viscous regime magma reservoir growth, elastic regime volcanic<br />
eruption is controlled by the mechanical behavior <strong>of</strong> the reservoir walls. There<br />
are two possible end-member responses depedent on the rigidity <strong>of</strong> wall rock: the<br />
“elastic reservoir”, where elastic energy stored in a non-rigid wall rock is<br />
immediately released by the formation <strong>of</strong> a conduit to the surface, and the “rigid<br />
reservoir model”, where the elastic strength <strong>of</strong> rigid wall rock is surpassed by<br />
pressure changes in the reservoir, leading to brecciation (Wadge, 1981;<br />
Scandone, 1996). Elastic, non-rigid behavior <strong>of</strong> wall rock can be seen in some<br />
basaltic eruptions where there is a rapid and effusive initial peak in magma<br />
discharge that slowly reduces over time (Figure 3.2). Rigid reservoir behavior is<br />
reflected in felsic eruptions, where magma cannot be “squeezed out” elastically,<br />
but as a conduit for<strong>ms</strong> to the surface, pressure release in the chamber causes<br />
volatiles to volumetrically expand, leading to explosive eruption. Peak magma<br />
discharge occurs later on, when a conduit is well developed and the abundant<br />
17
Effusive-Type Eruption<br />
max<br />
10 0 - 10 3<br />
m 3 /sec<br />
Magma Discharge Rate<br />
time (days-months)<br />
Explosive-Type Eruption<br />
max<br />
10 3 - 10 6<br />
m 3 /sec<br />
Magma Discharge Rate<br />
time (hours-days)<br />
Figure 3.2. Generalized volcanic surface discharge rates. Two possible<br />
endmembers are displayed. Elastic reservoir walls depressurize with effusivestyle<br />
surface discharge that tapers <strong>of</strong>f as time progresses. Magma is “squeezed”<br />
out <strong>of</strong> the chamber by elastic energy stored in the reservoir walls. Rigid<br />
reservoirs experience peak explosive-style eruption after a conduit for<strong>ms</strong>. Rapid<br />
pressure fluctuations in the reservoir cause elastic failure <strong>of</strong> the wall rock. The<br />
reservoir walls cannot elastically compensate for pressure fluctuations produced<br />
by the volumetric expansion and discharge <strong>of</strong> volatiles.<br />
18
volatiles within the chamber are free to exsolve and volumetrically expand.<br />
Viscous, felsic magmas produce explosive eruptions because, with a limited<br />
ability to accommodate expanding gases, exsolved volatiles must force their way<br />
through. (Scandone, 1996; Scandone and Giacomelli, 2001; Scandone et al.,<br />
2007). The explosive nature <strong>of</strong> a rigid reservoir eventually leads to severe wall<br />
rock fragmentation and caldera collapse (Fisher, 1960; Acocella, 2007).<br />
3.2.2. Volcanic Triggers and Chamber Rupture in a Rigid Reservoir<br />
Overpressure may be triggered by sudden exsolution <strong>of</strong> a volatile phase,<br />
intrusion/replenishment <strong>of</strong> new magma or volatiles into the chamber, or<br />
weakening <strong>of</strong> the wall rock by tectonism or the development <strong>of</strong> fluid-filled cracks<br />
along the reservoir walls (Scandone, 1996, Macias et al., 2003; Davis et al.,<br />
2007; Dziak et al., 2007). The trigger effectively unloads the retaining lithostatic<br />
pressure on the reservoir, causing rapid and violent expansion <strong>of</strong> volatiles<br />
(Mader et al., 1994; Gardner, 1999; Scandone & Giacomelli, 2001; Gonnermann<br />
& Manga, 2007; Grosfils, 2007; Gernon et al., 2008). The differential stresses<br />
produced by volumetric expansion are directed at the wall rock, which must<br />
readjust itself either elastically or through brittle failure. I now explore the<br />
readjustment <strong>of</strong> wall rock by fragmentation, as this model appears most<br />
applicable for the development <strong>of</strong> a Shatter Zone.<br />
The differential stresses produced by pressure fluctuations in the chamber<br />
are enough to explosively fracture the wall rock (Legros and Kelfoun, 2000,<br />
Macias et al., 2003). Driven by volume expansion in the reservoir, volatile-rich<br />
19
magma quickly intrudes the developed fractures (Scandone, 1996; Oliver et al.,<br />
2006). These perimeters <strong>of</strong> fragmented rock can be large, such as in the Shatter<br />
Zone (Figure 3.3). For shallow intrusions, interaction between relatively hot<br />
magmatic volatiles and cool ground water can lead to continuous<br />
phreatomagmatic explosions inside the wall rock (Wohletz, 1986; Lorenz and<br />
Kurszlaukis, 2007).<br />
Additionally, caldera collapse is caused by the progressive fracture<br />
weakening <strong>of</strong> the reservoir ro<strong>of</strong> in the region <strong>of</strong> local uplift (Lipman, 1984;<br />
Branney and Kokelaar, 1994). Fractures act as channels for volatile rich magma<br />
to escape to the surface, and as the chamber continues to lose volume, the<br />
weakened ro<strong>of</strong> material begins to subside into the collapsing chamber. There are<br />
many models that attempt to explain these observed subsidence patterns (Figure<br />
3.4, Lipman, 1997; Cole et al., 2005; Acocella, 2007). Shear breccias form by<br />
abrasion in large ring faults that develop along the perimeter <strong>of</strong> the subsiding<br />
caldera (Lipman, 1984; Johnson et al., 1999). Where these ring faults form is<br />
dependent on the subsidence pattern <strong>of</strong> caldera collapse. For example, pistonstyle<br />
collapse would produce a concentric ring <strong>of</strong> abrasive breccia material, while<br />
a piecemeal-style collapse produces many shear breccias throughout the entire<br />
subvolcanic complex. Although formed in the same system, explosive and<br />
caldera collapse breccias are fundamentally different. This will be further<br />
explained in chapter 5.<br />
20
A<br />
B<br />
Figure 3.3. Two for<strong>ms</strong> <strong>of</strong> subvolcanic breccias. A) A subvolcanic explosion in a<br />
magma reservoir. Pressure fluctuations cause brittle failure in wall rock, with the<br />
greatest intensity <strong>of</strong> brecciation adjacent to the reservoir interface. B) Shear<br />
along the ring faults <strong>of</strong> a collapsing caldera produces a breccia with a preferred<br />
fabric parallel to the sense <strong>of</strong> shear. Clasts from the ring fault are transported<br />
downward into the sides <strong>of</strong> the magma reservoir.<br />
21
Piston<br />
Downsag<br />
Piecemeal<br />
Funnel<br />
Trap-Door<br />
Figure 3.4. Common models for caldera collapse. Piston collapse: caldera<br />
subsidence occurs by a single, coherent, piston-shaped body <strong>of</strong> ro<strong>of</strong> rock.<br />
Piecemeal: the ro<strong>of</strong> rock subsides by incrementally stoped blocks that fall into the<br />
chamber. Trap-door: an asymmetric pluton, or wall rock with heterogeneous<br />
strength distribution breaks and causes subsidence on one side <strong>of</strong> the caldera.<br />
Downsag: a pluton that is too small or deep to reach the surface may<br />
depressurize passively, causing ro<strong>of</strong> rock subsidence. Funnel: a small or deep<br />
pluton creates a skinny surface conduit, forming a small caldera. The first three<br />
models produce ring faults during caldera collapse, which result in rings <strong>of</strong><br />
brecciated wall rock around the collapsed caldera (modified from Lipman, 1997).<br />
22
3.2.3. Evidence for Wall Rock Readjustment in Modern Volcanoes<br />
In active volcanic regions, seismic activity at subvolcanic depths<br />
represents reservoir wall readjustment from rock fragmentation and settling<br />
(Scandone, 1996). During the May 1980 eruption <strong>of</strong> Mount St. Helens, seismic<br />
activity generally increased to a maximum that coincided with peak pyroclastic<br />
flow at the surface (Shemeta and Weaver, 1986; Barker and Malone, 1991). The<br />
depth <strong>of</strong> seismic activity was noted to begin at shallow levels, then to increase in<br />
abundance at both shallow and deeper levels. The seismic activity is interpreted<br />
to represent the fracture and readjustment <strong>of</strong> wall rock caused by the<br />
mobilization <strong>of</strong> magma during the formation and widening <strong>of</strong> a conduit, then the<br />
fracture <strong>of</strong> wall rock bordering the reservoir during maximum magma discharge.<br />
Seismic activity subsided proportionately to reduced surface discharge until a<br />
final decrease in activity, approximately a day after the start <strong>of</strong> the eruption<br />
(Shemeta and Weaver, 1986; Carey, 1991; Caruso et al., 2006). Geologists<br />
observed similar behavior for the Mount Pinatubo eruption in 1991 (Rutherford<br />
and Devine, 1991).<br />
3.3. Volcanic Energy<br />
The size <strong>of</strong> the volcanic eruption depends on the amount <strong>of</strong> energy<br />
contained in the volcanic system. The release <strong>of</strong> volcanic energy can take<br />
several modes, including the kinetic energy <strong>of</strong> surface ejecta, the potential<br />
energy <strong>of</strong> the rising magma column and dissolved gases, seismic energy passing<br />
through rock, water (tsunamis), or air (shockwaves), kinetic energy <strong>of</strong> rock<br />
23
fragmentation, and thermal energy held in the reservoir. For subvolcanic study,<br />
only three relative partitions <strong>of</strong> energy need to be considered: thermal energy,<br />
the kinetic energy converted into wall rock fracture and fragmentation, and the<br />
remainder <strong>of</strong> the energy budget partitioned into surface mechanis<strong>ms</strong> (Hedervari<br />
1963, Shimozuru 1968, Heffington 1982).<br />
The thermal energy contained within the volcanic system is at least an<br />
order <strong>of</strong> magnitude greater than all <strong>of</strong> the other energy for<strong>ms</strong>, and it can even be<br />
three or four orders <strong>of</strong> magnitude greater depending on the magma composition<br />
(Heffington, 1982). The study <strong>of</strong> thermal energy in volcanism can reveal<br />
information about the overall energy <strong>of</strong> the system. As mentioned previously,<br />
contact metamorphism is a product <strong>of</strong> the thermal presence <strong>of</strong> the magma<br />
reservoir, but this can also lead to partial melt, viscous deformation, and thermal<br />
fracture <strong>of</strong> wall rock as well. The Shatter Zone shows evidence for all <strong>of</strong> this, and<br />
it will be discussed in detail in Chapter 4 (contact metamorphism) and Chapter 7<br />
(outcrop-scale thermal-mechanical modeling).<br />
Subvolcanic kinetic energy causes wall rock fragmentation through<br />
reservoir explosion, caldera subsidence and wall rock abrasion along a ring fault,<br />
or as a more passive result <strong>of</strong> chamber expansion by stoping (Lipman, 1997;<br />
Scandone and Giacomelli, 2001). The Shatter Zone is intensely fractured, and to<br />
better understand its development I examine brecciation mechanism that may<br />
have produced such a damage aureole in Chapter 5.<br />
24
3.4. Emplacement and eruptive history <strong>of</strong> the Cadillac Mountain Intrusive<br />
Complex<br />
The Cadillac Mountain Granite formed by crustal thinning in an<br />
extensional terrane (Wiebe et al., 1997a). The intrusive complex provides a<br />
record <strong>of</strong> episodic basaltic magma injection before, during, and after<br />
emplacement and crystallization <strong>of</strong> the granitic pluton. Injection sequences are<br />
recorded in the gabbro-diorite-granite sheets at the base <strong>of</strong> the complex. Wiebe<br />
(1994) hypothesized that the formation <strong>of</strong> the Cadillac Mountain Granite pluton<br />
enhanced the potential to attract and trap basaltic dikes at the base <strong>of</strong> the<br />
chamber. Continuous replenishment <strong>of</strong> the reservoir extended the life <strong>of</strong> the<br />
pluton, and the steady addition <strong>of</strong> thermal energy drove convection (Chapman,<br />
1962). Based on the prevalence <strong>of</strong> enclaves throughout the Cadillac Mountain<br />
Granite, there was some amount <strong>of</strong> granitic and basaltic mixing during<br />
convection (Wiebe et al., 1997b). The continued addition <strong>of</strong> thermal energy and<br />
volumetric expansion by basaltic replenishment were also the likeliest triggers for<br />
reservoir overpressurization and subsequent volcanic eruption (e.g. Wiebe, 1994;<br />
Seaman et al., 1999; Annen and Sparks, 2002).<br />
25
Chapter 4<br />
THERMAL FRAMEWORK FOR CONTACT METAMORPHISM<br />
To fully understand the development <strong>of</strong> the Shatter Zone, it is first<br />
necessary to determine the characteristics <strong>of</strong> contact metamorphism within the<br />
unit. In this chapter, I discuss how thermal energy drives metamorphism along<br />
the contact between the Cadillac Mountain Granite and Bar Harbor Formation,<br />
and how modeling and isograd data can potentially tell us about the condition <strong>of</strong><br />
the wall rock before the formation <strong>of</strong> the Shatter Zone. Important constraints are<br />
discussed in order to develop a useful model for intrusive thermal behavior. I use<br />
a conductive heat transfer-based, instantaneous single intrusion model. Although<br />
the model is a simplified version <strong>of</strong> the intrusion complex, it provides endmember<br />
results for the true thickness <strong>of</strong> the metamorphic zones, the dominant<br />
heat transfer mode, and the effect <strong>of</strong> extended chamber activity and wall rock<br />
brecciation on contact metamorphism. I find that the model is a good first order<br />
approximation for contact metamorphism in the Shatter Zone, but convective<br />
heat transfer, extended pluton activity, and wall rock brecciation are all important<br />
factors that have been ignored here.<br />
4.1. Characteristics <strong>of</strong> Contact Metamorphism<br />
Contact metamorphism involves a balance <strong>of</strong> heat transfer (Bergantz,<br />
1991; Labotka, 1991): as the wall rock heats up from contact, the intrusion must<br />
cool down by a proportional amount. Contact metamorphism is limited to a<br />
26
elatively thin aureole surrounding an igneous intrusion. There are significant<br />
changes in metamorphic grade through the aureole, and in many cases it is<br />
possible to track the entire prograde metamorphic gradient within a single rock<br />
unit (Kerrick, 1991). The highest grade metamorphic facies is found adjacent to<br />
the intrusive contact and peak metamorphic temperature decreases outward.<br />
The effect pressure has on contact metamorphism is dependent on the depth <strong>of</strong><br />
the intruding heat source (Furlong et al., 1991). At shallow depths, temperature is<br />
the driving force <strong>of</strong> metamorphism and the contact aureole is typically well<br />
contrasted to the host material, which may be unmetamorphosed. For deep<br />
pluton aureoles, it is more difficult to distinguish the aureole from the already<br />
regionally metamorphosed rocks (Kerrick, 1991). The size <strong>of</strong> the aureole<br />
correlates positively to the size <strong>of</strong> the intrusion, therefore it directly relates to the<br />
heat source reserve (Kerrick, 1991).<br />
4.1.1. Conductive, Convective, and Advective Heat Transfer<br />
Heat transfer from pluton to wall rock can be dominantly driven by<br />
conduction and by convection and/or advection. The rate <strong>of</strong> conductive heat<br />
transfer is a function <strong>of</strong> the thermal diffusivity <strong>of</strong> the wall rock, while convective<br />
and advective heating rate is a function <strong>of</strong> the velocity <strong>of</strong> a flowing body, such as<br />
groundwater or magmatic flow (Turcotte and Schubert, 1982). Convection is a<br />
buoyancy driven process caused by the heating <strong>of</strong> a mobile fluid, and implies a<br />
circulating flow path <strong>of</strong> fluids driven by a heat source. Advection applies to an<br />
open system where fluids are permanently driven <strong>of</strong>f by the heat source. In<br />
27
contrast, conduction is heat transfer through a non-flowing material (Stuwe,<br />
2002). It is important to determine which mode <strong>of</strong> heat transfer is dominant<br />
because their fundamental differences produce different aureole characteristics<br />
and different timing for peak metamorphism.<br />
Wall rock permeability and the availability <strong>of</strong> fluids are the two major<br />
factors that determine the degree to which conduction or convection may<br />
dominate in a system. The aureoles <strong>of</strong> intrusions emplaced at shallow crustal<br />
levels are generally dominated by convection, due to the availability <strong>of</strong><br />
substantial fluid volumes and the higher permeability <strong>of</strong> upper crustal rock<br />
(Johnson et al., 2011). There has been significant work done, especially from<br />
studies in porphyry ore deposits, to determine the probability <strong>of</strong> hydrothermal<br />
flow as a dominant mechanism for wall rock metamorphism (Cathles, 1977;<br />
Norton and Knight, 1977; Norton and Taylor; 1979; Parmentier and Schedl, 1981;<br />
Johnson and Norton, 1985; Hanson and Barton, 1989; Cook et al., 1997). At<br />
greater depths (below ~8-10km), the role <strong>of</strong> fluid convection becomes<br />
overshadowed by conduction due to reduced fluid availability and permeability<br />
(Walther, 1990). At these depths, conduction can be a rate controlling factor if<br />
there are no developed fractures that allow direct transfer <strong>of</strong> magmatic volatiles<br />
into the wall rock (Furlong et al., 1991).<br />
4.2. Contact Metamorphism in the Shatter Zone<br />
Bar Harbor Formation clasts within the Shatter Zone exhibit metamorphic<br />
textures which indicate an increase in thermal influence relative to the intrusive<br />
28
contact (Figure 4.1). The metamorphic intensity increases from the biotite-chlorite<br />
assemblage found in the undeformed Bar Harbor Formation to the cordieritegarnet<br />
assemblage that dominates most <strong>of</strong> the Shatter Zone, finally increasing<br />
grade to orthopyroxene-cordierite hornfels facies proximal to the Cadillac<br />
Mountain Granite contact. Isograds (Figure 4.2) were determined by a set <strong>of</strong> 11<br />
samples taken along a traverse <strong>of</strong> the Shatter Zone. The samples from this<br />
traverse represent all known facies within the contact metamorphic aureole. Most<br />
mineral identification was done optically and some with electron microprobe.<br />
4.3. Methods for Contact Metamorphic Thermal Modeling<br />
Many attempts have been made to calculate the cooling history <strong>of</strong> igneous<br />
intrusions. The problem is described as a volume <strong>of</strong> magma with known shape<br />
and initial temperature that intrudes the wall rocks with known temperature, and<br />
the subsequent variation in thermal gradient caused by the contact is to be<br />
calculated (Jaeger, 1961, 1964; Hart, 1964; Parmentier and Schedl, 1981; Attoh<br />
and van der Meulen, 1984; Hanson and Barton, 1989; Bowers, 1990; Annen and<br />
Sparks, 2006; Johnson et al., 2011).<br />
Conduction models can serve as a baseline observation to better<br />
constrain some first order variables, including the dominant mode <strong>of</strong> heat<br />
transfer. For example, if the thermal gradient produced by the model does not<br />
match the isograds identified in the field, it could be that convection and/or<br />
advection played a large part in heat distribution. If isograd and model data<br />
match well, heat transfer was more likely dominated by conductive heat transfer<br />
29
A<br />
B<br />
Grt<br />
C<br />
Grt<br />
D<br />
Crd<br />
Crd<br />
E<br />
1 mm<br />
F<br />
Crd<br />
Crd<br />
Crd<br />
Bt<br />
1 mm<br />
Figure 4.1. Mineralogy <strong>of</strong> the contact metamorphosed Bar Harbor Formation. A)<br />
Biotite in a metapelite layer 1000m in map distance from the reservoir contact. B)<br />
and C) are garnets found in a sample 950m from the contact. D) and E) are<br />
examples <strong>of</strong> abundant cordierite within 950m <strong>of</strong> the contact, <strong>of</strong>ten with<br />
groundmass inclusions displaying growth stages. F) Cordierite porphyroblasts<br />
found 450m from the contact, with biotite ri<strong>ms</strong>.<br />
30
G<br />
H<br />
Opx<br />
Opx<br />
I<br />
J<br />
Opx<br />
K<br />
1 mm<br />
L<br />
Granite<br />
Matrix<br />
Diorite<br />
Clast<br />
Opx<br />
1 mm 1 mm<br />
Figure 4.1. Continued. G) Pyroxene begins to appear 450m from the intrusive<br />
contact, and becomes more prevalent H) within meters <strong>of</strong> the contact, shown in<br />
plane light and I) crossed polars. J) The groundmass <strong>of</strong> the Bar Harbor<br />
Formation near the contact displays abundant ilmenite grains. The rim <strong>of</strong> a diorite<br />
clast K) in plane light and L) with crossed polars.<br />
31
!<br />
!<br />
!<br />
!<br />
Biotite Zone<br />
Garnet Zone<br />
!<br />
!<br />
!<br />
Cordierite Zone<br />
!<br />
Pyroxene Zone<br />
500 m<br />
N<br />
Figure 4.2. An isograd map <strong>of</strong> the Shatter Zone. Isograd data comes from 11 samples collected in a transect <strong>of</strong> the<br />
northeastern Shatter Zone. Most <strong>of</strong> the metamorphic aureole is contained within the Shatter Zone.<br />
32
(Furlong et al., 1991; Johnson et al., 2011). These discrepancies can give<br />
information about the balance between convection and conduction, and may lead<br />
to a conclusion on the dominant mode <strong>of</strong> heat transfer. One may also consider<br />
the dynamic heat input from incremental pluton emplacement, chamber<br />
convection, and recharge events (e.g. Hanson and Barton, 1989; Bergantz,<br />
1991; Pignotta et al., 2010), which would all effectively elevate the maximum<br />
temperature achieved in the wall rock and drastically change the spatial range <strong>of</strong><br />
metamorphism (e.g. Turcotte and Schubert, 1982; Furlong et al., 1991; Stuwe,<br />
2002). Regardless, it is most beneficial to use conduction modeling for initial<br />
observations because 1) dependent variables for conduction are easily<br />
constrained, 2) using conduction modeling will give an end-member constraint on<br />
the rate <strong>of</strong> heating and possible isograd trends, and 3) it provides a simple yet<br />
realistic thermal behavior for a contact metamorphic zone (Bergantz, 1991).<br />
For precise modeling, where a solution is required near the contact<br />
between magma reservoir and wall rock, it is beneficial to correct for latent heat<br />
<strong>of</strong> fusion for the crystallizing magma body (e.g. Jaeger, 1961). A crystallizing<br />
granite can produce 400kJ Kg -1 °K -1 before the solidus is reached (e.g. Burnham<br />
and Nekvasil, 1986; Furlong et al., 1991). Additionally, endothermic metamorphic<br />
reactions, such as dehydration in pelites, can absorb 60 to 110kJ mol -1<br />
<strong>of</strong><br />
released H 2 O or CO 2 , depending on the particular reaction (e.g. Furlong et al.,<br />
1991). Applications <strong>of</strong> these components are discussed below and in Chapter 7.<br />
33
4.3.1. Model Setup<br />
The model is used to produce a maximum temperature gradient with<br />
distance into the metamorphosed zone, and to compare these results with<br />
observed isograd data. This comparison will allow us to constrain the thermal<br />
evolution <strong>of</strong> the Cadillac Mountain intrusive complex and surrounding wall rock.<br />
The thermal evolution <strong>of</strong> the wall rock surrounding the intrusion was solved<br />
numerically by use <strong>of</strong> COMSOL Multiphysics (www.co<strong>ms</strong>ol.com), a finite element<br />
program equipped with a conductive heat transfer module. Behavior <strong>of</strong> the<br />
thermal conductive system is dependent on the thermal conductivity, specific<br />
heat, and density <strong>of</strong> the intrusion and wall rock as well as latent heat <strong>of</strong> fusion for<br />
the crystallizing intrusion, endothermic metamorphic reactions in the wall rock<br />
that consume heat energy, the initial intrusion temperature, and the initial wall<br />
rock temperature during emplacement (Jaeger, 1961; Johnson et al., 2011).<br />
It must be noted that the Cadillac Mountain intrusive complex was<br />
emplaced around 2-5km depth, so the wall-rock thermal evolution was probably<br />
affected by convective flow <strong>of</strong> water (e.g Walther, 1990; Johnson et al., 2011).<br />
Also, the duration <strong>of</strong> intrusion activity plays an important role in determining<br />
maximum temperature for contact metamorphism. Multiple dike-fed<br />
emplacements are common for shallow intrusives, and the gabbro-diorite sheets<br />
that form the base <strong>of</strong> the Cadillac Mountain intrusive complex are evidence for<br />
this type <strong>of</strong> activity (Jellinek and DePaolo 2003, Glazner et al. 2004, Cruden<br />
2005, Bartley et al. 2006, Lipman 2007, Walker et al. 2007, Michel et al. 2008,<br />
Miller 2008). Plutons reinvigorate with the continued introduction <strong>of</strong> magma,<br />
34
causing contact aureoles to become wider and achieve higher peak metamorphic<br />
temperatures over far longer timescales compared to those with a single intrusive<br />
sequence (Hanson and Barton, 1989). The model is limited by assuming a single<br />
instantaneous intrusion in a conduction dominated system, but the results will<br />
provide a foundation for future studies with more realistic constraints (e.g., Attoh<br />
and van der Muellen, 1984).<br />
For the conduction dominated model, I assume that the Bar Harbor<br />
Formation was metamorphosed before wall-rock brecciation and there was a<br />
single, instantaneous intrusion event that was allowed to thermally equilibrate<br />
with the wall rock. Latent heat correction was included during magma<br />
solidification within the range <strong>of</strong> 700-800°C, producing 400kJ kg -1 °K -1 <strong>of</strong> extra<br />
heat energy (see Chapter 7 for a more detailed explanation on how latent heat <strong>of</strong><br />
crystallization is calculated). I disregard the expenditure <strong>of</strong> heat energy by<br />
endothermic metamorphic reactions, which can account for 60-110 kJ per mole<br />
<strong>of</strong> H 2 O or CO 2 released from a dehydrating pelite (Furlong et al., 1991). Intrusion<br />
geometry plays a major role in the resulting spatial distribution <strong>of</strong> the thermal<br />
gradient. The rate <strong>of</strong> conduction is entirely dependent on the material’s thermal<br />
diffusivity and the thermal gradient, but an object with high surface area to<br />
volume ratio is more exposed to the diffusive contact, allowing much faster heat<br />
transfer (Jaeger, 1961). It is important that the model geometry closely<br />
approximates that <strong>of</strong> the real intrusive system. Therefore, I produce a 3<br />
dimensional model by digitally tracing the Cadillac Mountain Granite in map view,<br />
simplifying the geometry for use in COMSOL, and extruding it 2km into z space<br />
35
to make a “hockey puck” style geometry (figure 4.3). The gabbro-diorite unit is<br />
added to the base and is given the same shape and thickness <strong>of</strong> 1km. Model<br />
boundaries must be placed at a substantial distance from the region <strong>of</strong> interest<br />
so as to not interfere with the heat transfer model. Therefore, the outer model<br />
boundaries lie 100 km away from the pluton center and are thermally insulated.<br />
The interface between the intrusion and the country rock is open and allows for<br />
free conductive heat transfer. A tetragonal mesh is used, with a fine boundary<br />
mesh located at the intrusive contact for increased resolution <strong>of</strong> the thermal<br />
evolution adjacent to the heat source.<br />
Initial wall rock temperature is 150°C at an emplacement depth <strong>of</strong> 5km<br />
based on a typical upper crustal geotherm <strong>of</strong> 30°C/km. I am concerned with the<br />
lateral evolution <strong>of</strong> the thermal gradient, so there is no need to calculate the local<br />
geothermal gradient for this model. The intrusion temperature was approximately<br />
900°C, higher than average for a granitic magma (Wiebe, 1997). The gabbro<br />
diorite sheet is given an initial temperature <strong>of</strong> 1200°C. The thermal diffusivity ( )<br />
<strong>of</strong> Bar Harbor Formation is set at 1.30E-6 m 2 /s calculated from<br />
(4.1)<br />
Where is thermal conductivity, is density, and is specific heat. Thermal<br />
diffusivities for Cadillac Mountain Granite and gabbro are given values <strong>of</strong>1.34E-6<br />
m 2 /s and 1.01E-6 m 2 /s, respectively. A series <strong>of</strong> 300 time steps are taken from<br />
time = 0s to time = 1E14s, producing solutions for the evolving thermal gradient<br />
nearly up to a point <strong>of</strong> thermal equilibrium (Figure 4.4).<br />
36
A<br />
B<br />
C<br />
D<br />
Figure 4.3. Geometry <strong>of</strong> the intrusion model. A) A view <strong>of</strong> the entire model, with<br />
wall rock boundaries located 100km away from the reservoir’s center. B) A<br />
closeup <strong>of</strong> the Cadillac Mountain Granite reservoir geometry in map view and C)<br />
displaying the “hockey puck” style extrusion into 3 dimensions, with the basal<br />
gabbro-diorite unit in green. D) The mesh used to solve the conductive heat<br />
transfer equation, with the greatest node frequency near the contact between the<br />
reservoir and the wall rock to obtain the most accurate results in the zone <strong>of</strong><br />
interest.<br />
37
t = 0s<br />
t = 1E11<br />
t = 1E12s<br />
t = 1E13s<br />
t = 1E15s<br />
Figure 4.4. Time steps for the cooling chamber. Time steps show temperature<br />
distributions in x-y and x-z space.<br />
38
4.3.2. Results and Discussion<br />
Results (figure 4.5) show temperature versus time curves for 100m<br />
interval points from the chamber-wall rock contact, points located at the observed<br />
isograds, and a point 400m into the intrusion. The peak metamorphic<br />
temperature, 635°C, occurred at the intrusive contact at t = 1.9E11s (~6000<br />
years). Peak temperature 500m from contact was 510°C at t = 3.2E12s (~1E5<br />
years), and 1000m from the contact, peak temperature was 458°C at t = 6.2E12<br />
(~2E5 years).<br />
The single intrusion model provides a similar gradient trend within the<br />
metamorphosed zone, but the model did not attain the temperatures required to<br />
form the observed peak metamorphic facies (figure 4.6a). For this model, Garnet<br />
and cordierite are stable at temperatures as low as 460°C, which is possible for<br />
low pressure metamorphism (Blatt et al., 2006). This simplified conductive model<br />
cannot fully explain the metamorphic pattern seen for pyroxene, however.<br />
Metamorphic orthopyroxene requires a temperature <strong>of</strong> at least 650°C at 1.5 kbar<br />
pressure or ~5 km depth (Spear et al., 1999; Blatt et al., 2006).<br />
If the pluton contact is not actually vertical, the surface exposures <strong>of</strong> the<br />
metamorphic zones may be oblique from their true thicknesses (figure 4.6b). This<br />
could explain the wider than expected thickness <strong>of</strong> the pyroxene zone and it may<br />
provide a constraint on the geometry <strong>of</strong> the magma reservoir and the Shatter<br />
Zone. If the metamorphic aueole dips outward or inward with respect to the<br />
chamber by 45 degrees, the “true” thickness <strong>of</strong> the pyroxene zone is<br />
39
850<br />
750<br />
650<br />
550<br />
450<br />
400m Into Chamber<br />
Temperature (°C)<br />
350<br />
Chamber Contact: Pyroxene Zone<br />
Cordierite-Garnet Zone: 450m<br />
250<br />
Garnet Zone: 950m<br />
Bio te Zone: 1000m<br />
150<br />
100m Intervals from Contact<br />
0 50000 100000 150000 200000 250000 300000<br />
me (years) a er intrusion<br />
Figure 4.5. A temperature versus time plot from intrusion model results. Colored curves are for points on the isograd<br />
borders. Grey curves are points located on 100m intervals from the reservoir contact.<br />
40
A<br />
650<br />
Orthogonal Distance from Chamber Contact (m)<br />
0 100 200 300 400 500 600 700 800 900 1000<br />
630<br />
610<br />
Peak Temperature (°C)<br />
590<br />
570<br />
550<br />
530<br />
510<br />
B<br />
490<br />
470<br />
450<br />
5710 25710 45710 65710 85710 105710 125710 145710 165710 185710<br />
Time (years) a er intrusion<br />
650<br />
630<br />
610<br />
Orthogonal Distance from Chamber Contact (m)<br />
0 100 200 300 400 500 600 700 800 900 1000<br />
observed Tmax vs. distance trend<br />
45 degree contact dip correc on<br />
Peak Temperature (°C)<br />
590<br />
570<br />
550<br />
530<br />
510<br />
490<br />
470<br />
450<br />
5710 25710 45710 65710 85710 105710 125710 145710 165710 185710<br />
Time (years) a er intrusion<br />
Figure 4.6. Maximum metamorphic temperature with orthogonal distance from<br />
the contact. A) Isograd positions are located from colored points. Cordierite,<br />
garnet, and biotite could form at the observed maximum temperatures, but the<br />
conductive model cannot explain the formation <strong>of</strong> metamorphic pyroxene. B) A<br />
comparison between the apparent thickness <strong>of</strong> metamorphic zones (solid line)<br />
and the thickness <strong>of</strong> zones if the intrusive contact is dipping at 45 degrees<br />
(dashed lines). If the observed contact is oblique, the metamorphic aureole would<br />
be skinnier.<br />
41
approximately 140m thinner. The Shatter Zone thickness is 300m thinner.<br />
Unfortunately, there is not enough data on the depth geometry <strong>of</strong> the Shatter<br />
Zone, and there is no pro<strong>of</strong> for a tilted section on the eastern side <strong>of</strong> the Cadillac<br />
Mountain intrusive complex.<br />
4.4. Evidence for an Actively Mixing Chamber<br />
The maximum temperature achieved by this model does not explain the<br />
existence <strong>of</strong> a pyroxene zone. The assumptions used for this model are therefore<br />
unrealistic for the Cadillac Mountain intrusive complex, proving that magma<br />
reservoir convection and replenishment were active components <strong>of</strong> heat transfer.<br />
Additionally, wall-rock groundwater convection from 2-5km depth likely played a<br />
part in contact metamorphism. The Cadillac Mountain intrusive complex was part<br />
<strong>of</strong> a volcanically active region, which experienced several eruptive sequences<br />
(Chapman, 1962; Berry and Osberg, 1989; Seaman et al., 1995; Seaman et al.,<br />
1999). Widespread presence <strong>of</strong> enclaves (Wiebe et al., 1997b), evidence <strong>of</strong><br />
magma mixing (Chapman, 1962), and the presence <strong>of</strong> interlayered gabbro and<br />
diorite sheets at the chamber base prove that the Cadillac Mountain Granite was<br />
host to magma replenishment and actively mixing before eruption. Bimodal<br />
chamber syste<strong>ms</strong> can <strong>of</strong>ten undergo several sequences <strong>of</strong> reactivation from<br />
mafic dike “entrapment” (e.g. Wiebe, 1994, Wiebe et al., 2004), and chamber<br />
replenishment can lead to overpressurization and potential eruption (e.g. Folch<br />
and Marti, 1998). The thermal input after wall rock brecciation, discussed in<br />
Chapter 7, would have been substantial. The Cadillac Mountain Granite likely<br />
42
followed this open system behavior, therefore contact metamorphism in the<br />
Shatter Zone was additionally affected by 1) convection <strong>of</strong> magma within the<br />
chamber, 2) magma replenishment, which provides an additional thermal input,<br />
and 3) the thermal input from magma intrusion after wall rock brecciation. These<br />
factors contribute greatly to the resulting metamorphic aureole within the Shatter<br />
Zone, and they reflect the crucial link between magma plumbing syste<strong>ms</strong> and<br />
volcanic syste<strong>ms</strong>.<br />
Development <strong>of</strong> the Shatter Zone is directly dependent on the thermal and<br />
mechanical properties <strong>of</strong> the subvolcanic system to which it is linked. Having<br />
discussed how the thermal potential energy <strong>of</strong> the intrusive complex affects the<br />
surrounding wall rock, it is now necessary to discuss the mechanical energy<br />
involved in wall rock fragmentation.<br />
43
Chapter 5<br />
ROCK MECHANICS AND THE FRACTAL BEHAVIOR OF ROCK<br />
As contact metamorphism reflects a part <strong>of</strong> the thermal component <strong>of</strong><br />
volcanic energy, wall rock brecciation is the manifestation <strong>of</strong> the kinematic<br />
component <strong>of</strong> subsurface volcanic energy. In order to begin the physical<br />
description <strong>of</strong> the Shatter Zone, I now describe the component <strong>of</strong> volcanic energy<br />
partitioned into wall rock fragmentation. I use the Griffith fracture theory to<br />
explain the basic physical mechanis<strong>ms</strong> involved in rock fragmentation. It is<br />
possible to link characteristic fragmentation patterns such as clast size<br />
distribution and clast boundary shape to the rock’s original brecciation<br />
mechanism. These characteristic patterns are dependent on the self-similarity <strong>of</strong><br />
rocks and how the fragmentation patterns will tend to repeat the<strong>ms</strong>elves<br />
regardless <strong>of</strong> scale. Methods have been put forward to quantitatively describe<br />
these self-similar patterns to better determine the link between fragmentation<br />
characteristics and brecciation mechanism. Clast size distribution (CSD) and<br />
clast boundary shape (CBS) are two fractal methods used in this <strong>thesis</strong> to<br />
quantitatively determine the origin <strong>of</strong> the Shatter Zone. Clast circularity analysis<br />
(CCA), though not a fractal property, is also used to determine the amount <strong>of</strong><br />
clast wear with distance from the magma reservoir.<br />
44
5.1. Brittle Failure <strong>of</strong> Rock<br />
5.1.1. Basic Principles <strong>of</strong> Griffith Fracture Theory<br />
Failure occurs when a rock is no longer able to support a stress increase<br />
without fracture; for brittle failure this implies the loss <strong>of</strong> cohesion along fractured<br />
planes within the rock. Differential stresses are necessary to provide brittle failure<br />
and shape change in a rock, and the value <strong>of</strong> differential stress achieved at<br />
failure is a measure <strong>of</strong> the rock’s strength (Goodman, 1980; Grady and Kipp,<br />
1987; Hoek and Brown, 1997; Twiss and Moores, 2007). Fracture development<br />
can be described by the work <strong>of</strong> A. A. Griffith (1920), whose theory successfully<br />
explained the inequality between material strength as calculated by the strength<br />
<strong>of</strong> atomic bonds in the material, and the actual observed strength <strong>of</strong> the<br />
respective material. Griffith’s theory states that all solids contain many<br />
microscopic cracks <strong>of</strong> random orientation, which greatly reduce the potential<br />
strength <strong>of</strong> the material. These cracks are meant to represent the imperfections<br />
in crystal lattice planes or grain boundaries, and are typically modeled as<br />
elliptical and penny shaped in three dimensions, with an extremely small radius<br />
<strong>of</strong> curvature at the crack tip (Figure 5.1a).<br />
Failure <strong>of</strong> the material at the fracture tip is determined by a critical tensile<br />
stress<br />
defined as<br />
(5.1)<br />
where is Young’s modulus, is the specific surface energy required to break<br />
the atomic bonds <strong>of</strong> the material (surface tension), and<br />
is the fracture half<br />
45
A<br />
β<br />
δ<br />
σ 1<br />
σ 3<br />
σ t<br />
c<br />
a<br />
σ 1<br />
σ 3<br />
β<br />
Direction <strong>of</strong> crack<br />
propagation<br />
δ<br />
B<br />
σ t<br />
Figure 5.1. An elliptical Griffith crack under compressive stress. Given a crack<br />
orientation normal to β, tensile stress will concentrate at a point along δ. A<br />
greater ratio <strong>of</strong> crack half length (a) to width (c) produces a reater local<br />
concentration <strong>of</strong> tensile stress. B) When the crack fails under compression,<br />
tensile cracks propagate parallel to δ and shear is accommodated along the<br />
fracture walls (modified from Twiss and Moores, 2007).<br />
46
length (Griffith, 1920). The shape <strong>of</strong> the crack plays an important role in stress<br />
concentration: an elliptical crack with a high length to width ratio will provide a<br />
greater concentration <strong>of</strong> stress at the fracture tips, promoting propagation. Given<br />
the same host material, an order <strong>of</strong> magnitude increase in fracture length<br />
decreases the required critical tensile stress by a factor <strong>of</strong> approximately 3.2.<br />
This implies that once large fractures develop, they require less tensile stress to<br />
continue propagation and they have a greater ability for growth than smaller<br />
nearby cracks (Goodman, 1980; Twiss and Moores, 2007). Pore pressure<br />
in<br />
fluid-filled cracks will directly reduce ( ). The fracture will propagate<br />
normal to the stress gradient, parallel to σ 1 . Propagation ends when the fracture<br />
tip reaches an interface that it cannot penetrate, such as the wall <strong>of</strong> another<br />
crack, or when the applied stress decreases to the point at which local stress<br />
concentrations are subcritical.<br />
The orientation <strong>of</strong> the applied stresses with respect to the Griffith crack will<br />
determine the behavior <strong>of</strong> local stress concentrations. The local stress gradient is<br />
dominated by a concentration <strong>of</strong> maximum tensile stress at an angle δ between<br />
the axial length <strong>of</strong> the crack and the maximum principal stress direction σ 1 near<br />
the crack tip. The orientation <strong>of</strong> the most critically stressed Griffith crack under<br />
compression is at an angle between 0-45° from σ 1 , depending on the values <strong>of</strong><br />
σ 1 and minimum principal stress σ 3 , and this is generally the range in which most<br />
shear fractures form (Figure 5.1b). If a Griffith crack’s axial length is parallel to<br />
σ 1 , δ is located at the fracture tip and longitudinal cracking will occur with no<br />
shear component (Mode I). For a crack with axial length not parallel to σ 1 ,<br />
47
friction along the closed crack surfaces caused by the compressive normal<br />
stresses produce a local stress distribution slightly different from those cracks<br />
that experience purely tensile fracture. Tensile cracks begin to form along the<br />
direction <strong>of</strong> δ to allow accommodation <strong>of</strong> shear along the main body <strong>of</strong> the<br />
fracture plane (Mode II and III). The orientation <strong>of</strong> the newly developed tensile<br />
crack tends to migrate parallel to the σ 1 direction. Because <strong>of</strong> this, shear<br />
fracturing in a compressed rock is actually dependent on the development and<br />
growth <strong>of</strong> small tensile fractures (Grady and Kipp, 1987; Twiss and Moores,<br />
2007).<br />
5.1.2. The Self-Similarity <strong>of</strong> Fracture Patterns<br />
Although Griffith fracture theory describes initiation <strong>of</strong> cracks at the<br />
microscopic level, fracture behavior can be described this way at any scale.<br />
Brecciated rocks display the scale independent, or self-similar, characteristics <strong>of</strong><br />
fracture propagation by the patterns produced along fracture surfaces and size<br />
distribution <strong>of</strong> clasts. Physical brecciation is the result <strong>of</strong> fracture propagation<br />
carried over many scales. Breccias form from the nucleation, propagation, and<br />
intersection <strong>of</strong> these fracture paths (Laznicka, 1988). It is the self-similar pattern<br />
<strong>of</strong> these fracture surfaces and frequency <strong>of</strong> intersections that define a breccia.<br />
The form <strong>of</strong> the repeated pattern is dependent on the mechanism <strong>of</strong><br />
fragmentation, and study <strong>of</strong> these patterns can provide information on the<br />
characteristics <strong>of</strong> the resulting breccia. The numerous different mechanis<strong>ms</strong> that<br />
produce breccias provide noticeable differences in their physical characteristics;<br />
48
therefore it is possible to relate a breccia to its mechanism <strong>of</strong> formation by<br />
analyzing these self-similar characteristics.<br />
5.2. Fractal Theory<br />
When an object shows self-similar properties, it is described as fractal.<br />
Fractal theory sprouted from the desire to quantitatively describe geometries<br />
observed in nature. Unlike Euclidean geometry, fractals refer to complex shapes<br />
defined by a fractional, or fractal, dimension (D) (Mandelbrot, 1967, 1983; Urtson,<br />
2005). Founded by Benoit Mandelbrot in 1967, fractal theory has since been<br />
applied to many scientific proble<strong>ms</strong>. The self-similarity <strong>of</strong> fractals implies that<br />
patterns tend to repeat the<strong>ms</strong>elves at all scales, and for a true fractal, the<br />
number <strong>of</strong> scales <strong>of</strong> natural patterns is infinite. For the initial purposes <strong>of</strong> this<br />
<strong>thesis</strong>, it is best to consider the fractal dimension in ter<strong>ms</strong> <strong>of</strong> a repeated pattern<br />
<strong>of</strong> size distribution. Consider the repeated pattern in Figure 5.2 (Sammis et al.,<br />
1987). Sections <strong>of</strong> a cube are repeatedly split into smaller and smaller<br />
components, producing a distribution <strong>of</strong> various sizes. This pattern is quantified<br />
by<br />
(5.2)<br />
Assuming that the pattern <strong>of</strong> size distribution produced by breaking the cube is<br />
fractal, the fractal dimension is a function <strong>of</strong> the number <strong>of</strong> cubes with side<br />
length . For the broken cube, the pattern <strong>of</strong> size distribution is fractal, and =<br />
2.58. This value is unique to this size distribution and any change from this<br />
pattern would produce a different<br />
. Interest lies in the self-similar characteristics<br />
49
h<br />
h/2<br />
h/4<br />
Figure 5.2. A cube displaying self-similar size distribution properties. The cube is<br />
segmented over several scales, with each broken cube equal to half the height<br />
and an eighth the volume <strong>of</strong> the next biggest cube. Using equation 5.2, the fractal<br />
dimension for this object is 2.58 (modified from Sammis et al., 1987).<br />
50
<strong>of</strong> size distributions and surface patterns <strong>of</strong> Shatter Zone clasts, so fractal theory<br />
will now be applied to these breccia characteristics.<br />
5.3. Quantitative Methods <strong>of</strong> Breccia Classification<br />
5.3.1. Clast Size Distribution<br />
Particle size distribution is a commonly applied method for determining<br />
brecciation mechanis<strong>ms</strong> from observed clast characteristics (e.g. Harris, 1966;<br />
Harris, 1968; Hartmann, 1969; Schoutens, 1979; Sammis et al., 1986; Turcotte,<br />
1986; Sammis & Biegel, 1987; Englman et al., 1988; Marone and Scholz, 1989;<br />
Blenkinsop, 1991; Shimamoto and Nagahama, 1992; Nagahama and Yoshii,<br />
1993; McCaffrey & Johnston, 1996; Jebrak, 1997; Tsutsumi, 1999; Perfect, 1997;<br />
Zhang, 1999; Higgins, 2000; Blott & Pye, 2001; Wilson et al., 2001; Elek and<br />
Jaramaz, 2002; Saotome et al., 2002; Clark & James, 2003; Spieler et al., 2003;<br />
Barnett, 2004; Zi-Long et al., 2006; Farris & Paterson, 2007; Bjork et al., 2009).<br />
The term “clast size distribution” (CSD) is preferred because <strong>of</strong> its relevance to<br />
breccias. Brittle materials have the general tendency to fracture in a self-similar<br />
pattern in which clast frequency increases exponentially with a decrease in clast<br />
size, and it has been proven possible to relate the size distribution <strong>of</strong> clasts to the<br />
mechanism <strong>of</strong> brecciation (Turcotte, 1986; Jebrak, 1997; Perfect, 1997). The<br />
relationship between clast size and cumulate frequency is defined by the power<br />
law equation (similar to equation 5.2)<br />
(5.3)<br />
51
where N (≥r) is the count <strong>of</strong> clasts with a radius greater than or equal to r, k is a<br />
unit-dependent constant, and D s is the fractal dimension for clast distribution, and<br />
it is considered to be a measure <strong>of</strong> fracture resistance relative to the mechanism<br />
or process <strong>of</strong> fragmentation. D s is proportional to the magnitude and rate <strong>of</strong><br />
stress loading, the inherent strength properties <strong>of</strong> the rock, and the possibility <strong>of</strong><br />
repeated fracturing events, and therefore can be used to determine the<br />
mechanis<strong>ms</strong> involved in rock fragmentation (Figure 5.3). It is also sensitive to<br />
any secondary mechanis<strong>ms</strong> that may alter the original distribution. The negative<br />
slope signifies the advance <strong>of</strong> clast population with decreased size.<br />
When producing results for CSD, the clasts in breccias are not perfect<br />
spheres, therefore one must correlate the volume <strong>of</strong> the clast with an equivalent<br />
value for radius (equal area diameter <strong>of</strong> Brittain, 2001; Bjork et al., 2009)<br />
calculated by defining a circle with an area identical to that <strong>of</strong> the clast <strong>of</strong> interest<br />
(5.4)<br />
The radius value is directly proportional to the area <strong>of</strong> the clast and is therefore<br />
both suitable for CSD analysis and allows for coherent comparison <strong>of</strong> data to<br />
other studies, as using an equivalent radius/diameter value is the most popular<br />
method to display CSD data from 2 dimensional sources (Barnett, 2004; Farris<br />
and Paterson, 2007; Bjork et al., 2009).<br />
Sample bias from the inability to see the finest clast populations can<br />
produce a non-fractal trend for finer-scale populations; therefore it is necessary<br />
52
53<br />
Figure 5.3. An example clast size distribution plot. Ds is solved by plotting the cumulate number N <strong>of</strong> clasts below a radius<br />
r over several radius intervals. A steeper slope implies a more intense brecciation mechanism as observed from hydraulic,<br />
shear, and explosion breccias.
to place a minimum size limit when measuring clasts (Blenkinsop, 1991; Clark<br />
and James, 2003; Barnett, 2004).<br />
CSD data are commonly presented with respect to 3-dimensional space. If<br />
an object is fractal in 2-dimensions, it is also fractal in 3-dimensions, and<br />
(5.5)<br />
This conversion is validated by the fact that D s refers to the line, surface, or<br />
space that dissects the object. An increase in Euclidean dimension requires the<br />
same increase in D s (e.g. Sammis et al., 1987). This conversion is justified for a<br />
breccia made <strong>of</strong> a homogeneous, isotropic material, but error can be introduced<br />
if this assumption is used on anisotropic materials (e.g. Barnett, 2004; Farris and<br />
Paterson, 2007). To reduce this potential error, outcrops with 3 dimensional<br />
exposures can be used. Clast distribution can also be expressed as a function <strong>of</strong><br />
clast frequency versus mass (e.g. Hartmann, 1969; Blenkinsop, 1991), or percent<br />
sample by weight versus diameter (see Schoutens, 1979), both <strong>of</strong> which are<br />
directly related to a 3-dimensional distribution. These results also pertain to<br />
power law distributions and therefore their slopes are proportional and can be<br />
converted to D s (Blenkinsop, 1991; Perfect, 1997).<br />
5.3.2. The Fractal Dimension-Brecciation Mechanism Link for Clast<br />
Size Distribution (CSD)<br />
Understanding the brecciation mechanism will provide important<br />
information on the mechanical response to subsurface volcanic eruption. As CSD<br />
results are a function <strong>of</strong> the self-similar manner by which fractures proliferate<br />
54
through a medium, the fractal dimension D s is influenced by the intensity <strong>of</strong><br />
fracturing. There are several potential mechanis<strong>ms</strong> that could have formed the<br />
Shatter Zone, and three possible end-members will be discussed: 1) pre-eruptive<br />
magma emplacement caused hydraulic fracture <strong>of</strong> wall rock, 2) caldera<br />
subsidence produced an abrasive collapse breccia along ring faults, or 3) the<br />
rapid volume expansion <strong>of</strong> volatiles during eruption lead to explosive fracture <strong>of</strong><br />
chamber walls. These three mechanis<strong>ms</strong> are fundamentally different and will<br />
therefore produce different breccias with unique D s values.<br />
In rock mechanics studies there are two end-member mechanis<strong>ms</strong> for<br />
minimum and maximum D s : hydraulic fracture and explosion (Jebrak, 1997; Clark<br />
and James, 2003; Barnett, 2004). Abrasive breccias tend to produce size<br />
distributions defined by a relatively intermediate D s (Jebrak, 1997; Sammis et al.,<br />
2007). Hydraulic breccias are well defined by Griffith fracture theory because<br />
they form from fluid assisted (for this paper, magma and groundwater could be<br />
considered) incremental fracture propagation driven by tensile stress loading at<br />
the fracture tip (Goodman, 1980; Clark and James, 2003; Genet et al., 2008).<br />
Fracture propagation is driven by the condition <strong>of</strong> pore fluid pressure (<br />
) in the<br />
cracks (Dutrow and Norton, 1995; Clark et al., 2006; Genet et al., 2008).<br />
Hydraulic fractures typically form due to an increase in<br />
by volume increase<br />
driven by fluid flow and thermal expansion. This is generally an incremental<br />
process, with a rate determined by the amount <strong>of</strong> fluid and interconnected<br />
cracks, the thermal gradient, and the rate <strong>of</strong> fluid flow (Clark and James, 2003).<br />
Cracking usually occurs by an oscillating pattern <strong>of</strong> incremental<br />
buildup to the<br />
55
moment <strong>of</strong> sudden fracture tip failure and sudden reduction <strong>of</strong><br />
(Dutrow and<br />
Norton, 1995). As hydraulic brecciation is a low stress intensity mechanism, the<br />
rate <strong>of</strong> propagation is generally slow and fractures will tend to develop along<br />
inherent planes <strong>of</strong> weakness in the rock. Hydraulic breccias tend to have a<br />
shallow slope for size distribution due to an inability to produce new fractures<br />
(D s =1-2; Jebrak, 1997; Clark and James, 2003; Barnett, 2004; Clark et al., 2006;<br />
Farris and Paterson, 2007).<br />
Abrasive breccias form during shear failure in a rock (Goodman, 1980;<br />
Jebrak, 1997). Shear along ruptured surfaces can lead to abrasive fragmentation<br />
along fracture walls. Like hydraulic breccias, abrasive breccias can also form<br />
incrementally, but simple shear kinematics produce more complex fragmentation<br />
patterns (Sammis et al., 1987; Blenkinsop, 1991). Continued grinding, plucking,<br />
and reduction <strong>of</strong> clast size results in the development <strong>of</strong> fault gouge. Rotation<br />
and flow <strong>of</strong> elongate clasts cause a preferred alignment with respect to flow<br />
(Jebrak, 1997). The characteristics <strong>of</strong> abrasive breccias are more difficult to<br />
constrain due to the complexities that arise in shear kinematics. D s values can<br />
range widely based on strain rate, the amount <strong>of</strong> stress normal to the fracture<br />
plane, and the number and duration <strong>of</strong> abrasion events (Sammis et al., 1986;<br />
Sammis, 1987; Blenkinsop, 1991). For a collapse breccia, a single fragmentation<br />
event linked to caldera subsidence is assumed. This breccia would produce D s<br />
values on the order <strong>of</strong> 2-2.7 (Sammis, 1987; Blenkinsop, 1991). Fabric produced<br />
by sense <strong>of</strong> shear and transport <strong>of</strong> clasts would also be visible, and clasts would<br />
show evidence <strong>of</strong> imbrications and preferred orientation.<br />
56
Explosion breccias are formed by an instantaneous localized volume<br />
expansion and resulting shockwave <strong>of</strong> released elastic energy (Schoutens, 1979;<br />
Ivanov et al., 2005; Goto et al., 2001; Lorenz and Kurszlaukis, 2006; Nikolaevskiy<br />
et al., 2006; Sanchidrian, 2007). Brecciation intensity decreases with distance<br />
from the point source <strong>of</strong> explosion. These breccias tend to have a high gradient<br />
<strong>of</strong> increasing particle frequency with decreasing particle radius (D s ≥2.5;<br />
Schoutens, 1979; Barnett, 2004; Bjork et al., 2009). This is the result <strong>of</strong> a chaotic<br />
proliferation <strong>of</strong> fractures at a finer scale. As opposed to hydraulic brecciation,<br />
explosive fragmentation is driven predominantly by the power <strong>of</strong> the explosion<br />
and the bulk strength <strong>of</strong> the rock (Grady and Kipp, 1987; Jebrak, 1997). Higher<br />
D s values correlate with high power mechanis<strong>ms</strong> because there is skewed<br />
preference for small fracture proliferations during high energy fracture events<br />
(Turcotte, 1986; Jebrak, 1997).<br />
Bedrock anisotropy is an additional variable that can lead to relatively nonuniform<br />
and unexpected fracture patterns when compared to fractures in<br />
homogeneous rock. The fracture patterns in the rock are dominated by inherent<br />
weaknesses, preferring the widening <strong>of</strong> existent fractures as opposed to the<br />
proliferation <strong>of</strong> new fractures (Takashi, 2008). D s would be partially influenced by<br />
structural anisotropy.<br />
5.3.3. Clast Boundary Shape<br />
Boundary shape is another natural expression <strong>of</strong> self-similar patterns. A<br />
fragment’s boundaries appear to be fractal in that the process by which they are<br />
57
produced results in a self-similar geometry. Several authors have successfully<br />
quantified this phenomenon for coastline statistics (Mandelbrot, 1967, 1983;<br />
Klinkenberg, 1992, 1994; Allen et al., 1994; Andrle, 1996; Jiang and Plotnick,<br />
1998; Xiaohua et al., 2004; Tanner et al., 2006) and for boundary analysis <strong>of</strong> rock<br />
fragments and fracture paths (Jebrak, 1997; Berube and Jebrak, 1999; Bonnet et<br />
al., 2001; Dellino and Liotino, 2002; Lorilleux et al., 2002; Jebrak and Lalonde,<br />
2005). For example, consider the repeated pattern in Figure 5.4. Much like<br />
Figure 5.2, boundary shapes are defined by a set <strong>of</strong> repeated patterns and can<br />
be quantified by equation 5.2. The fractal dimension D r increases with greater<br />
pattern complexity (Mandelbrot, 1983). The pattern is defined by the surface’s<br />
tendency to follow a repeated configuration, in the case <strong>of</strong> this paper defined by<br />
fragmentation and modification processes discussed in the next chapters.<br />
Fragment surfaces display fractal-like characteristics but results are limited by<br />
the ability to measure small-scale surface patterns (Lorilleux et al., 2002).<br />
There are four major methods to quantify D r : step method, box counting,<br />
dilation, and Euclidean distance mapping (Danielsson, 1980). Berube and Jebrak<br />
(1999) published a comprehensive analysis <strong>of</strong> several boundary analysis<br />
methods and concluded that Euclidean distance mapping is the most accurate<br />
method to obtain D r for a non-Euclidean geometry. Euclidean distance mapping<br />
is a method suited for computer algorith<strong>ms</strong> applied to a black and white<br />
silhouette <strong>of</strong> the clast (Figure 5.5). The algorithm produces a grayscale image<br />
where each pixel is designated a brightness value proportional to its proximity to<br />
the nearest pixel that makes up the outline <strong>of</strong> the given clast. The result is an<br />
58
L/9<br />
L<br />
Figure 5.4. The Koch snowflake. The boundary shape pattern is self-similar at<br />
any scale. Four length sections are continually repeated, each section spanning<br />
1/3 the length <strong>of</strong> the next biggest feature. The fractal dimension <strong>of</strong> this repeated<br />
pattern is ~1.26.<br />
L/3<br />
59
13<br />
ln(area) (pixels)<br />
12<br />
11<br />
10<br />
9<br />
ln(a) = 0.9322ln(w) + 6.9532<br />
2<br />
D r =1.0678<br />
8<br />
7<br />
0 2 4 6<br />
ln(width) (pixels)<br />
Figure 5.5. Euclidean distance mapping on a clast outline. Given a minimum<br />
grayscale, a ribbon <strong>of</strong> a given area and width is formed from the above clast<br />
outline. This data is plotted and the slope is proportional to the fractal dimension<br />
for CBS using equation (5.6).<br />
60
outline <strong>of</strong> the clast, with a dark backbone directly over the border that brightens<br />
up with distance from the outline. The brightness <strong>of</strong> the pixel is directly<br />
proportional to the distance to the clast border, and an outline <strong>of</strong> known width is<br />
made by setting a threshold to that value <strong>of</strong> brightness. D r can be calculated by<br />
plotting the log <strong>of</strong> ribbon area A versus the grayscale number W and is obtained<br />
by<br />
(5.6)<br />
with S as the slope subtracted from the Euclidean dimension <strong>of</strong> 2 to yield D r . The<br />
Euclidean dimension 2 signifies that the clast exists on a two-dimensional<br />
surface (Berube and Jebrak 1999, Lorilleux et al. 2002).<br />
5.3.4. The Fractal Dimension-Brecciation Mechanism Link for Clast<br />
Boundary Shape (CBS)<br />
The most complex boundary shapes come from chemical breccias (D r<br />
≥1.25), while the simplest are found in hydraulic or magmatic breccias (D r ≤ 1.1)<br />
(Jebrak, 1997; Barnett, 2004). Explosive and abrasive breccias initially produce<br />
angular clasts that may show relative complexity, but D r would still be relatively<br />
low (≤ 1.25). CBS would tend to be low in a physically brecciated material<br />
because fractures tend to align the<strong>ms</strong>elves with the direction <strong>of</strong> the maximum<br />
principal stress. Because the direction <strong>of</strong> fracture would tend not to change, the<br />
surface pattern <strong>of</strong> the fracture is defined by the paths <strong>of</strong> relatively straight cracks<br />
(Berube and Jebrak, 1999). Modification processes that involve clast rounding<br />
and corner break-<strong>of</strong>f would also effectively reduce D r . It is unlikely that chemical<br />
61
eaction processes were involved in the formation <strong>of</strong> the Shatter Zone, so a D r<br />
value greater than 1.25 would not be expected (Jebrak, 1997; Lorrileaux et al.,<br />
2002).<br />
5.3.5. Clast Circularity Analysis<br />
Although it is not a fractal property, circularity is directly influenced by the<br />
degree <strong>of</strong> abrasion, dilation, and transport that occurs in the development <strong>of</strong> a<br />
breccia, and it could prove important in comparing modified and unmodified<br />
clasts (e.g. Dellino and Volpe, 1996, Clark, 1990). The greater the wear on the<br />
clast, the more circular it will become owing to loss <strong>of</strong> high surface-area corners.<br />
Circularity is a measure <strong>of</strong> the compactness <strong>of</strong> a shape, unlike boundary analysis<br />
which is meant to quantify the complexity <strong>of</strong> surface patterns. Because a circle is<br />
the most compact two-dimensional geometry, a shape’s compactness is<br />
compared to the circle as the ratio<br />
(5.7)<br />
To calculate circularity <strong>of</strong> a clast, its area and perimeter must be determined.<br />
Consider the area <strong>of</strong> a circle:<br />
(5.8)<br />
To define the area <strong>of</strong> a circle as a function <strong>of</strong> a given perimeter (the perimeter <strong>of</strong><br />
the noncircular clast), r must be replaced with p:<br />
(5.9)<br />
62
(5.10)<br />
Substituting this into equation (3) for circularity (C):<br />
(5.11)<br />
This successfully produces a ratio between the area <strong>of</strong> a clast and the area <strong>of</strong> an<br />
imaginary circle with perimeter equal to that <strong>of</strong> the clast. The ratio can range from<br />
0 to 1, with very elongate shapes trending to 0 and very compact shapes<br />
trending to 1.<br />
63
Chapter 6<br />
ANALYSIS AND RESULTS<br />
The Shatter Zone represents the brittle response to magma reservoir<br />
pressure fluctuations during evacuation. Reservoir overpressure occurs when the<br />
rate <strong>of</strong> pressure loading cannot be accommodated by visco-elastic deformation<br />
<strong>of</strong> wall rock. The differential stresses produced by overpressurization and<br />
subsequent evacuations are substantial enough to overcome the elastic limit and<br />
fracture wall rock, after which a volatile rich component <strong>of</strong> magma quickly<br />
intrudes the fractures. Luckily, these intrusive features chill relatively quickly,<br />
providing evidence for volcanic activity. The impetus <strong>of</strong> this <strong>thesis</strong> is to better<br />
understand the mechanics <strong>of</strong> rigid rock in a subvolcanic setting. The Shatter<br />
Zone formed from a subvolcanic reaction to volcanic eruption and I explore the<br />
possible brecciation mechanis<strong>ms</strong> that may have been active in the development<br />
<strong>of</strong> the Shatter Zone. Field observations within the Shatter Zone describe the<br />
gradational breccia characteristics. I discuss the methods used to collect CSD,<br />
CBS, and CCA data, then provide the results <strong>of</strong> the analysis and move on to<br />
confirm explosive brecciation as the likeliest developmental mechanism for the<br />
Shatter Zone.<br />
64
6.1. Field Relations in the Shatter Zone<br />
6.1.1. Gradational Characteristics<br />
The Shatter Zone is characterized by a transitional development <strong>of</strong> the<br />
breccia (Figure 6.1) in which the degree <strong>of</strong> rock fragmentation is distributed as a<br />
gradient. This gradient is interpreted to represent various time stages <strong>of</strong> breccia<br />
development. The Shatter Zone can be divided into four breccia types based on<br />
observational differences, three <strong>of</strong> which pertain to this study. The transition<br />
ranges from highly brecciated and intruded rock to weakly brecciated beddingparallel<br />
fractures, finally grading into unfractured bedrock.<br />
6.1.1.1. Type 1. Type 1 Shatter Zone is interpreted to represent the initial<br />
stage <strong>of</strong> breccia development (Figure 6.2). The Type 1 locality is Sols Cliffs,<br />
positioned in northeast Mount Desert Island (44.37363, -68.18903). The<br />
transition from solid, coherent Bar Harbor Formation to Type 1 Shatter Zone is<br />
gradual. Granite veinlets (typically
Type 1<br />
Type 2<br />
500 m<br />
N<br />
Type 1<br />
Type 2<br />
Type 3<br />
Type 3<br />
Figure 6.1. The gradient <strong>of</strong> brecciation intensity through the Shatter Zone. The<br />
gradient is represented by three types, with the greatest intensity <strong>of</strong> brecciation<br />
adjacent to the Cadillac Mountain Granite. Red scale bars are 9cm for Type 1<br />
and 10cm for Types 2 and 3.<br />
66
A<br />
B<br />
Figure 6.2. Type 1 Shatter Zone. A) One outcrop image and B) its outline used<br />
for CSD analysis. Scale bar is 9cm. Partial, uncounted clasts are dark grey.<br />
67
A<br />
B<br />
Figure 6.3. Type 2 Shatter Zone. A) One outcrop image and B) its outline used<br />
for CSD analysis. Scale bar is 10cm. Partial, uncounted clasts are dark grey.<br />
68
A<br />
B<br />
Figure 6.4. Type 3 Shatter Zone. A) One outcrop image and B) its outline used<br />
for CSD analysis. Scale bar is 10cm. Partial, uncounted clasts are dark grey, Bar<br />
Harbor Formation clasts are light grey, and diorite dike clasts are black.<br />
69
A<br />
B<br />
Figure 6.5. Centimeter-scale boudinage textures in Bar Harbor Formation. A)<br />
Overburden cuases rigid calc-silicate layers to be pulled apart by pure shear and<br />
weaker pelitic layers flow around them. B) A closeup image <strong>of</strong> a boudinage neck<br />
filled with quartz.<br />
70
6.1.1.2. Type 2. The observed breccia pockets seen in Type 1 may be a<br />
precursor to those <strong>of</strong> Type 2 (Figure 6.3), which shows a greater frequency <strong>of</strong><br />
higher intensity breccia pockets and is deemed to represent the intermediate<br />
stage in the developmental brecciation time scale. The Type 2 locality is along<br />
Seely Road, located south <strong>of</strong> the Type 1 location (44.36303, -68.18332).<br />
Brecciation in Type 2 outcrops appear to be more chaotic with minimal<br />
preservation <strong>of</strong> the original bedding structures (Figure 6.6). Again, all matrix<br />
material is fine grained and there is no evidence for late stage fracture. Diorite<br />
dikes are more frequent, and some are brecciated.<br />
6.1.1.3. Type 3. Type 3 Shatter Zone is the most evolved stage <strong>of</strong><br />
brecciation, in which isolated clasts are abundant, generally sub-equant, and<br />
completely suspended in granite matrix (Figure 6.4). The Type 3 locality is on<br />
Great Head, in the southeastern section <strong>of</strong> the island (44.32872, -68.17986). The<br />
observed clasts in the Type 3 breccias are dominantly diorite, which contrasts<br />
with Types 1 and 2. Many clasts appear well rounded with concentrations <strong>of</strong><br />
biotite along their ri<strong>ms</strong>. The matrix is generally fine grained with pegmatitic<br />
material present in late stage cracks. Evidence for late stage cracking in diorite is<br />
not uncommon. Many <strong>of</strong> the Bar Harbor clasts appear to have recrystallized, and<br />
the most abundant Bar Harbor Formation clasts appear to be from the more<br />
resilient layers. There are no flow textures in the matrix except for occasional<br />
local features that apparently formed from minor clast rotation and settling<br />
(Figure 6.7).<br />
71
A<br />
B<br />
Figure 6.6. Brecciation textures in Type 2 Shatter Zone. A) A typical brecciation<br />
pattern in Type 2 Bar Harbor Formation clasts. B) Late-stage fracture <strong>of</strong> a diorite<br />
dike near the Type 2 locality leaves freshly fractured, angular clasts in a<br />
pegmatitic matrix.<br />
72
A<br />
B<br />
Figure 6.7. Local flow textures in Type 3 Shatter Zone. A) flow patterns<br />
surrounding a diorite clast. B) Complex flow patterns surrounding relict Bar<br />
Harbor Formation clasts.<br />
73
The final breccia classified in this study, Type 4, is found within the<br />
Cadillac Mountain Granite and consists <strong>of</strong> large, meter scale xenoliths <strong>of</strong> Bar<br />
Harbor Formation, diorite, and felsic volcanics. The matrix is nearly as coarse<br />
grained as the Cadillac Mountain Granite, and there are schlieren textures<br />
surrounding some <strong>of</strong> the xenoliths. No more will be said <strong>of</strong> the Type 4 xenoliths.<br />
There is significant change in clast morphology <strong>of</strong> Bar Harbor Formation<br />
clasts between Type 2 and Type 3. This implies an additional modification<br />
process that altered the original size and shape <strong>of</strong> Type 3 Bar Harbor clasts.<br />
Additionally, outcrop observations suggest that Type 3 diorite clasts exhibit<br />
additional size and shape modification by late stage fracturing (Figure 6.8). I use<br />
clast size distribution (CSD), clast boundary shape (CBS), and clast circularity<br />
analysis (CCA) methods to identify the primary developmental mechanis<strong>ms</strong> and<br />
to determine possible secondary progressions that could lead to clast<br />
modification. The results lead to a discussion involving the use <strong>of</strong> thermalmechanical<br />
modeling to explain the modification <strong>of</strong> clast size and shape, and in<br />
doing so explain the transition from explosive to magmatic breccia.<br />
6.2. Methods<br />
Data from 12,732 clasts have been used to identify the brecciation<br />
mechanism and quantify the physical modifications to clast size and shape. Clast<br />
data were calculated from image mosaics collected from outcrops representative<br />
<strong>of</strong> Types 1, 2, and 3 <strong>of</strong> the Shatter Zone (blue dots on Figure 2.1, Figure 6.1).<br />
Grids were overlain on flat outcrops with individual boxes <strong>of</strong> 30x25cm. High<br />
74
A<br />
B<br />
C<br />
Figure 6.8. Evidence for secondary clast size, shape, and boundary modification.<br />
A) Metapelite clast surface disaggregation and internal melting textures in Bar<br />
Harbor Formation, B) late-stage fracture in a layered clast, and C) fracture <strong>of</strong> a<br />
diorite dike clast imply post-brecciation modification.<br />
75
esolution images <strong>of</strong> each box were stitched to create the image mosaics (Figure<br />
6.9). Clasts were manually outlined from each mosaic in a drafting program to<br />
differentiate between clast and matrix, producing a black (clast) and white<br />
(matrix) image. Manual outlining was required because the grayscale separation<br />
between clasts and matrix was commonly too small to accurately distinguish<br />
them using image analysis s<strong>of</strong>tware (e.g. Sudhakar et al. 2005). The outlines<br />
were analyzed with NIH ImageJ for clast count, area, circularity, and boundary<br />
shape. CSD, CBS, and CCA data were calculated from these output data. The<br />
number <strong>of</strong> clasts used for CBS was limited compared to CSD because each<br />
randomly chosen outline had to be analyzed individually.<br />
For CSD <strong>of</strong> the Shatter Zone breccias, the equivalent radius was used to<br />
plot data on a logarithmic size cumulate frequency plot, with a clast radius<br />
interval <strong>of</strong> 10 0.02 cm. Only clasts greater than 1mm radius were plotted because<br />
<strong>of</strong> difficulty in distinguishing between smaller clasts and the granite matrix.<br />
Cumulate frequency was standardized to the total area covered for each outcrop<br />
location to allow better comparison between locations with greater or smaller<br />
outcrop representation. D s values were calculated from equation (5.3).<br />
CBS data were produced by 42 ribbon width and area measurements for<br />
428 clast outlines. Measurements were taken in NIH ImageJ. The log <strong>of</strong> ribbon<br />
width was plotted with respect to the log <strong>of</strong> ribbon area, and D r was calculated<br />
from the slope using equation (5.6).<br />
76
Figure 6.9. An outcrop grid used for fractal analysis. The 30x25cm grid is lain<br />
over the well exposed outcrop and a picture is taken for each rectangle. Images<br />
are then later stitched together in a drafting program to perform manual clast<br />
boundary tracing.<br />
77
Clast circularity data were produced in NIH ImageJ using equation (5.11).<br />
Clast frequency plots were produced using a 0.05 circularity interval for 0.1-1cm,<br />
1-10cm, and >10cm clast radius intervals.<br />
6.3. Data<br />
6.3.1. Clast Size Distribution (CSD) Data<br />
A total sample size <strong>of</strong> 14 imaged outcrops yielding 12,732 clasts with size<br />
ranges spanning 3 orders <strong>of</strong> magnitude (0.1-40cm) was used for CSD analysis.<br />
Types 1-3 <strong>of</strong> the Shatter Zone are represented and results are shown in Figures<br />
6.10 and 6.11. Data are shown in Table 6.1. Type 1 Shatter Zone shows a<br />
bifractal distribution, or two observed power law distributions divided by a slope<br />
breakpoint, with an average D s value <strong>of</strong> 3.027 above clast radius <strong>of</strong> 1.25cm and<br />
1.5 for clasts below. The R 2 values for these two distributions are 0.9868 above<br />
the breakpoint and 0.9778 below. The curve for Type 1 represents 1,519 clasts<br />
from four outcrop grids with a size range <strong>of</strong> 0.1-23.4cm. Type 1 has 16.1%<br />
average matrix component by area.<br />
Type 2 has an average D s value <strong>of</strong> 3.166 above clast radius <strong>of</strong> 1.52 cm<br />
and D s = 1.875 below. The bifractal R 2 values for the Type 2 distribution are<br />
0.9932 above and 0.9865 below the breakpoint. The total sample size for Type 2<br />
is 5538 outlined clasts from four outcrop with a size range <strong>of</strong> 0.1-13.02cm. Type<br />
2 has 34.4% average matrix component by area.<br />
Clast size populations in Type 3 Shatter Zone are divided by rock type due<br />
to the marked increase in diorite dike clast abundance. These results show the<br />
78
Type 1 Type 2<br />
Type 3<br />
Bar<br />
Harbor<br />
Type 3<br />
Mafic<br />
dike<br />
fine D 1.5 1.875 1.66 2.625<br />
coarse D 3.027 3.166 4.06 2.625<br />
ΔD s 1.527 1.291 2.4 -<br />
breakpoint 1.25 cm 1.52cm 1.6cm -<br />
% matrix 16.10% 34.40% 74.96% 74.96%<br />
# clasts 1519 5538 284 5480<br />
# outcrops 4 4 7 7<br />
Table 6.1. Average CSD values<br />
79
A<br />
1000<br />
Clast Size Distribu on: Type 1<br />
Cumulate Frequency N/m 2<br />
100<br />
10<br />
1<br />
Type 1<br />
D sc<br />
= 3.02<br />
R² = 0.9778<br />
D sf<br />
= 1.51<br />
R² = 0.9868<br />
Count:1519<br />
B<br />
Cumulate Frequency N/m 2<br />
0.1<br />
1000<br />
100<br />
10<br />
1<br />
0.1<br />
0.1 1 10<br />
clast radius r (cm)<br />
Clast Size Distribu on: Type 1<br />
Type 2<br />
D sc<br />
= 3.2<br />
R² = 0.9865<br />
D sf<br />
= 1.9<br />
R² = 0.9932<br />
Count:5538<br />
0.1 1 10<br />
clast radius r (cm)<br />
Figure 6.10. Clast size distribution data for Type 1 and 2 Shatter Zone. A)<br />
Trendlines for Type 1 are split between coarse (D sc ) and fine (D sf ) distributions.<br />
B) Coarse and fine distributions are also presented for Type 2. For comparison to<br />
three dimensional studies from 2 dimensional data, D = slope +1.<br />
80
A<br />
1000<br />
CSD Type 3 compared to Type 2<br />
Type 2 Bar<br />
Harbor clasts<br />
D = 3.2<br />
count: 5538<br />
R² = 0.9865<br />
Type 3 diorite<br />
clasts<br />
D = 2.63<br />
count: 5391<br />
R² = 0.9891<br />
100<br />
Type 3 Bar Non-fractal<br />
Harbor clasts<br />
count: 284<br />
R² = 0.9915<br />
Cumulate frequency/m^2<br />
10<br />
1<br />
cumulate frequency/m^2<br />
1000<br />
100<br />
10<br />
1<br />
B<br />
D sf<br />
= 1.66<br />
R 2 = 0.9867<br />
Diabase clasts (count=5391)<br />
Bar Harbor clasts (count=284)<br />
D sf<br />
= 4.06<br />
R 2 = 0.9492<br />
D = 2.63<br />
R² = 0.9891<br />
0.1<br />
0.1<br />
0.1 1 10<br />
radius (cm)<br />
0.1 1 10<br />
Clast radius r (cm)<br />
Figure 6.11. Clast size distribution data for Type 3 Shatter Zone. A) Type 3 data<br />
are split by rock type: Bar Harbor Formation (red) and diorite (blue) size<br />
distributions are compared to Type 2 distributions. Type 3 Bar Harbor formation<br />
best fits an exponential (i.e., nonfractal) trend. B) An alternative bifractal<br />
interpretation for Type 3 Bar Harbor Formation size distribution trend.<br />
81
diorite dike with D s = 2.62 and R 2 = 0.9865 for the clast size range <strong>of</strong> 0.41-<br />
11.82cm. The Bar Harbor CSD can be best defined in two ways: a bi-fractal<br />
distribution with a breakpoint at 1.6cm and D s equal to 1.66 above and 4.06<br />
below, or a non-fractal, exponential curve. The bifractal R 2 values are 0.9867<br />
above and .9492 below the 1.6cm breakpoint. The R 2 value for the exponential<br />
curve distribution is 0.9915. There are a total <strong>of</strong> 5675 outlined clasts from seven<br />
outcrops, less than 20% <strong>of</strong> which are Bar Harbor Formation clasts. Diorite size<br />
ranges are 0.1-11.8cm and Bar Harbor Formation size ranges are 0.1-4.24cm.<br />
Type 3 has 75% average matrix component by area.<br />
6.3.2. Clast Boundary Shape (CBS) Data<br />
A total <strong>of</strong> 433 clasts from Type 1, 2, and 3 Shatter Zone, with an additional<br />
outcrop (named 2.5) located between types 2 and 3 (44.35714, -68.18371), were<br />
used for CBS (Figure 6.12). The CBS dataset comes from Hawkins and Johnson<br />
(2004). Values <strong>of</strong> D r vary only slightly with most values approaching 1 (1.04-<br />
1.12). Type 1 Shatter Zone has the highest average D r value <strong>of</strong> 1.125 but with a<br />
relatively high standard deviation <strong>of</strong> 0.062 from 123 clasts. Type 2 has an<br />
average D r <strong>of</strong> 1.052 with a standard deviation <strong>of</strong> 0.037 from 79 clasts, and Type<br />
2.5 has an average D r <strong>of</strong> 1.047 with a standard deviation <strong>of</strong> 0.035 from 66 clasts.<br />
Type 3 has an average D r <strong>of</strong> 1.040 with a standard deviation <strong>of</strong> 0.019 from 56<br />
clasts.<br />
82
Dr<br />
1.2<br />
1.18<br />
1.16<br />
1.14<br />
1.12<br />
1.1<br />
1.08<br />
1.06<br />
1.04<br />
1.02<br />
1<br />
Average D r<br />
Clast samples size by type:<br />
Type 1: 123<br />
Type 2: 79<br />
Type 2.5: 66<br />
Type 3: 165<br />
Type 1 Type 2 Type 2.5 Type 3<br />
Figure 6.12. Clast boundary shape data ordered by Shatter Zone type. Error bars<br />
denote one standard deviation from the average value shown by the colored bar<br />
(From Hawkins and Johnson, 2004).<br />
83
6.3.3. Clast Circularity Analysis (CCA) Data<br />
Circularity data were collected for 8,724 outlined clasts over three orders<br />
<strong>of</strong> magnitude for Shatter Zone Types 1-3 (Figure 6.13). Many <strong>of</strong> the same clasts<br />
used for CSD were used for CCA. Type 1 clasts have the lowest average<br />
circularity value <strong>of</strong> 0.48, and the circularity averages for the 0.1-1cm, 1-10cm,<br />
and >10cm intervals are 0.54, 0.36, and 0.19, with population sizes <strong>of</strong> 925, 431,<br />
and 5, respectively. Type 2 clasts have an average circularity <strong>of</strong> 0.58, and the<br />
circularity averages for the 0.1-1cm, 1-10cm, and >10cm intervals are 0.61, 0.47,<br />
and 0.27, with population sizes <strong>of</strong> 2,155, 595, and 9, respectively. Type 3 clasts<br />
have the highest degree <strong>of</strong> circularity with an average <strong>of</strong> 0.76, and the circularity<br />
averages for the 0.1-1cm, 1-10cm, and >10cm intervals are 0.77, 0.67, and 0.63,<br />
with population sizes <strong>of</strong> 3,945, 644, and 14, respectively.<br />
6.3.4. Summary <strong>of</strong> Data<br />
All three types <strong>of</strong> Shatter Zone yield a value <strong>of</strong> D s above 2.5 for<br />
distributions <strong>of</strong> radius greater than 1cm. Below this clast size, D s varies greatly<br />
but is always lower than the D s <strong>of</strong> the coarser size range. The “breakpoint” in the<br />
bifractal slope occurs over a small and consistent size range in Types 1 and 2.<br />
Data from Types 1 and 2 come dominantly from Bar Harbor Formation clasts,<br />
whereas data from Type 3 is split between diorite dike and Bar Harbor Formation<br />
clasts. Magmatic fabric dominates in Type 3, with no clast preferred orientation.<br />
Granitic matrix becomes more abundant with proximity to the Cadillac Mountain<br />
Granite interface. Circularity increases with proximity to the intrusive contact and<br />
84
% <strong>of</strong> clasts<br />
40<br />
35<br />
30<br />
25<br />
20<br />
15<br />
10<br />
Type 1<br />
0.1-1cm radius clasts<br />
1-10cm radius clasts<br />
10+ radius clasts Total mean<br />
1-<br />
10cm<br />
radius,<br />
431<br />
0.1-<br />
1cm<br />
radius,<br />
925<br />
10+cm<br />
radius,<br />
6<br />
5<br />
% <strong>of</strong> clasts<br />
0<br />
40<br />
35<br />
30<br />
25<br />
20<br />
15<br />
10<br />
5<br />
0<br />
35<br />
30<br />
0 0.2 0.4 0.6 0.8 1<br />
Circularity<br />
Type 2<br />
0 0.2 0.4 0.6 0.8 1<br />
Circularity<br />
40<br />
Type 3<br />
1-10cm<br />
radius,<br />
644<br />
10+cm<br />
radius,<br />
14<br />
1-<br />
10cm<br />
radius,<br />
595<br />
0.1-<br />
1cm<br />
radius,<br />
2155<br />
10+cm<br />
radius,<br />
9<br />
Circularity<br />
1<br />
0.9<br />
0.8<br />
0.7<br />
0.6<br />
0.5<br />
0.4<br />
0.3<br />
0.2<br />
0.1<br />
0<br />
Clast Circularity Analysis<br />
0.1-1cm 1-10cm 10+cm<br />
Type 1 Type 2 Type 3<br />
% <strong>of</strong> clasts<br />
25<br />
20<br />
15<br />
0.1-1cm<br />
radius,<br />
3945<br />
10<br />
5<br />
0<br />
0 0.2 0.4 0.6 0.8 1<br />
Circularity<br />
Figure 6.13. Circularity data ordered by Shatter Zone type. Percent <strong>of</strong> clasts with<br />
respect to circularity with slast radius bin sizes <strong>of</strong> 0.1-1, 1-10, and 10+cm<br />
represented by red, green, and blue, respectively. Mean circularity values are<br />
given by the bar graph to the right, and the pie charts display clast bin size<br />
populations. The circularity interval is 0.05.<br />
85
with decreasing clast size in all Types. CBS decreases with proximity to the<br />
intrusive contact (Hawkins and Johnson 2004).<br />
6.4. Discussion<br />
6.4.1. Bifractal Distributions for Type 1 and 2<br />
The change in slope for Types 1 and 2 represent some scale dependent<br />
factor that limits the self-similar nature <strong>of</strong> rock fragmentation to a finite size<br />
range. In this case, there are two clast size distributions with the slope change at<br />
clast radius <strong>of</strong> approximately 1.5cm. Although the data are variable, bifractal<br />
distributions with breakpoints at 1.25cm for Type 1 and 1.52cm for Type 2 best<br />
represent these size distribution data trends.<br />
Two possible factors affecting a rock’s fractal properties include scale<br />
dependent rock heterogeneity (e.g. Clarke et al., 1998) and individual<br />
mechanis<strong>ms</strong> that are limited to a finite size range (Barnett, 2004, Farris and<br />
Paterson, 2007). Interests lie in the mechanism or condition that produces a<br />
relatively large D s for the coarse scale and a small D s for the fine scale. This<br />
would imply greater fragmentation intensity forming the coarse clasts. One<br />
possibility worth consideration involves the secondary modification <strong>of</strong> small clasts<br />
entrained along previously formed fracture paths during intrusion. Soon after<br />
fractures formed, volatile rich magma travelled up the fracture network. With the<br />
introduction <strong>of</strong> a water-rich heat source, small clasts entrained in these fracture<br />
networks would be highly susceptible to thermal disaggregation. This is a<br />
mechanism dependent on clast melt and magmatic flow that produces bifractal<br />
86
and non-fractal distributions (Jebrak, 1997; Clark and James, 2003). The matrix<br />
only makes up 16% <strong>of</strong> volume in Type 1; therefore there would have been<br />
enough heat to disaggregate small clasts, but not large ones, assuming that the<br />
local matrix percentage by volume is greater than 16% in the magma channels<br />
that hosted the smaller clasts (hypothetically, clasts with radius greater than<br />
1.25cm saw little effect <strong>of</strong> disaggregation). This agrees with the high intensity,<br />
large D s value for larger clast sizes (D s >3) and a low intensity, small D s value for<br />
finer clast sizes (D s =1.5) because they are defined by differing mechanis<strong>ms</strong>. The<br />
D s values for the fine clast range <strong>of</strong> Type 1 are within the hydraulic brecciation<br />
range. It is possible that clasts were host to fluid and thermal assisted fracture,<br />
which would produce a D s below 2. The original fine clasts could have<br />
disaggregated during magma intrusion, then new small clasts formed by thermal<br />
fracture could produce a D s value similar to what are seen for the fine Type 1<br />
distributions.<br />
For Type 2, D s increases to 3.17 for the coarse clast size range and 1.875<br />
for the fine range, with a breakpoint at 1.52cm. The matrix <strong>of</strong> Type 2 composes<br />
34% <strong>of</strong> total volume, therefore there is greater potential for disaggregation <strong>of</strong><br />
small clasts. The D s value for the fine clast ranges <strong>of</strong> Type 2 is greater than Type<br />
1, which may imply a greater intensity <strong>of</strong> fluid and thermal assisted fracture at the<br />
fine scale.<br />
Whereas D s values for the fine distributions <strong>of</strong> Types 1 and 2 imply a low<br />
energy manner <strong>of</strong> formation, D s for coarse size distributions are above 3 for<br />
Types 1 and 2, implying a high intensity mechanism. The two most viable<br />
87
possibilities as postulated previously are collapse abrasion and chamber<br />
explosion. Shear is the fundamental mechanism that produces an abrasive<br />
breccia. The clasts <strong>of</strong> Type 1 and 2 fractured in place and they show no shear or<br />
transport fabric. Additionally, the structures observed in the Shatter Zone imply a<br />
450-1000m thick breccia gradient with intensity nearest to the intrusive contact. A<br />
gradient such as this would be formed by a rapid, localized point <strong>of</strong> power<br />
release, such as from the rapid volume expansion <strong>of</strong> volatiles in the magma<br />
reservoir. The calculated D s values are within the explosion range, indicating that<br />
chamber explosion was the likely cause <strong>of</strong> brecciation.<br />
6.4.2. Differing rock types and clast modification evidence in Type 3<br />
If the transitional character <strong>of</strong> the Shatter Zone is a record for the phases<br />
<strong>of</strong> brecciation, Type 3 would be the final stage and closest position to the point<br />
source for peak brecciation intensity. Diorite dike clasts have a D s that relates<br />
well to an explosive breccia (Schoutens, 1979; Turcotte, 1986), but Type 3 may<br />
be unrelated to Types 1 and 2, and could possibly represent a collapse breccia<br />
based solely on the fractal dimension. Collapse breccias typically have lower D s<br />
values (abrasive breccias typically fall between 2-2.7, e.g. Sammis et al. 1987;<br />
Blenkinsop, 1991), and the diorite clasts do have a lower size distribution, but<br />
this is likely caused by a fundamental difference in rock type. The homogeneous,<br />
coarse grained diorite could not be expected to produce a D s equal to the Bar<br />
Harbor metasedimentary rock, which has lower strength due to its composition.<br />
Much like Types 1 and 2, there is also no evidence for clast fabric, imbrication, or<br />
88
sense <strong>of</strong> shear. Type 3 Shatter Zone must be related to Types 1 and 2, which<br />
have been confirmed as explosive.<br />
The transition from fractal to non-fractal CSD slope for Type 3 Bar Harbor<br />
clasts requires a significant change in mechanism, implying that some major<br />
secondary modification process was at work to alter the size and shape <strong>of</strong> clasts.<br />
This modification mechanism is unable to provide a self-similar size distribution,<br />
which ties in to the marked drop in Bar Harbor clast abundance. CBS and CCA<br />
data imply increased clast wear with proximity to the Cadillac Mountain Granite,<br />
which also supports the hypo<strong>thesis</strong> <strong>of</strong> secondary modification having a<br />
noticeable effect on the alteration <strong>of</strong> Type 3 Bar Harbor clasts. In all cases, D r<br />
decreases and circularity increases with closer proximity to the Cadillac Mountain<br />
Granite interface. Much like CSD, one cannot interpret CBS as a complete<br />
product <strong>of</strong> the brecciation event; it is more a manifestation <strong>of</strong> secondary<br />
modification. If the clasts <strong>of</strong> Type 3 were originally as angular as Types 1 and 2,<br />
CCA data show that there is substantial clast rounding after the major explosive<br />
event. Possible modification mechanis<strong>ms</strong> include thermal disaggregation, fluid<br />
assisted fracture, and thermal induced fracture. These potential mechanis<strong>ms</strong> are<br />
fully discussed in the next chapter.<br />
89
Chapter 7<br />
MECHANISMS FOR SECONDARY CLAST MODIFICATION: A DISCUSSION<br />
The thermal influence from the intruded granitic matrix <strong>of</strong> the Shatter Zone<br />
had a significant influence on clast size distribution (CSD) data trends,<br />
specifically for Bar Harbor Formation Type 3 clasts. The marked decrease in<br />
small clast populations and boundary shape values as well as the increase in<br />
clast circularity implies a non-fractal mechanism was active in the modification <strong>of</strong><br />
clast size, shape, and abundance. Potential mechanis<strong>ms</strong> are explored for post<br />
brecciation modification and I determine that disaggregation through partial melt<br />
<strong>of</strong> clasts is the dominant mechanism at play. Transient two-dimensional models<br />
are produced in order to quantitatively characterize the migration <strong>of</strong> solidus<br />
temperatures through a conductively heated clast, and to determine the evolution<br />
<strong>of</strong> CSD as clasts begin to partially melt. I show that disaggregation <strong>of</strong> clasts can<br />
lead to a bi-fractal and eventually non-fractal CSD. Magma flow, a constraint<br />
ignored in the thermal-mechanical model, is required to physically disaggregate<br />
the melted clasts. Thermal fracture is another possible secondary mechanism<br />
and is treated in a transient two-dimensional thermal stress model. Results show<br />
that late-stage thermal fracture occurred in diorite clasts, but less is known about<br />
the thermal stress characteristics <strong>of</strong> the structurally anisotropic Bar Harbor<br />
Formation.<br />
90
7.1. Potential Mechanis<strong>ms</strong> for CSD and CBS modification<br />
A secondary mechanism is required to produce the observed results for<br />
CSD, CBS, and CCA. Potential mechanis<strong>ms</strong> include 1) thermal disaggregation,<br />
or the disintegration <strong>of</strong> clasts, by partial melt and assimilation into the<br />
surrounding magma and 2) thermal fracture <strong>of</strong> clasts during magma intrusion.<br />
These two options are considered because they are are relatively easily treated<br />
numerically, and because field observations suggest that they played important<br />
roles in the modification process. Although abrasion would play a part during the<br />
active stages <strong>of</strong> wall rock readjustment, it cannot explain the nonfractal<br />
distribution <strong>of</strong> sizes for Type 3 Bar Harbor Formation clasts. Clasts that are host<br />
to late stage fracture show no evidence for kinetic impact or abrasion between<br />
other clasts, therefore the only input that could produce fracture at this stage is<br />
heat transfer from the enveloping matrix.<br />
7.1.1. Thermal Attrition<br />
Thermal disaggregation requires supersolidus temperatures to be reached<br />
and presence <strong>of</strong> magma flow to physically disaggregate the clast (e.g. Braun and<br />
Kriegsman, 2001). Thermal fracture is dependent on a heated material’s thermal<br />
expansivity and requires the elastic response to sharp thermal gradients in rock. I<br />
assume these two components to be agents <strong>of</strong> thermal attrition that had a<br />
marked effect on Bar Harbor clasts and less <strong>of</strong> an effect on diorite clasts.<br />
Thermal attrition is defined as any process or mechanism that directly enhances<br />
the potential for removal or assimilation <strong>of</strong> clast material into the intruding<br />
91
magma. To prove the viability <strong>of</strong> thermal attrition, thermal-mechanical equations<br />
are solved using the finite element method (COMSOL Multiphysics). Partial melt<br />
can play a large part in the volumetric removal <strong>of</strong> clasts and has been linked to<br />
alteration <strong>of</strong> clast size distribution trends and reduced D s values (Farris and<br />
Paterson, 2007). I assume that clast volume is disaggregated once the solidus<br />
temperature is achieved, altering clast sizes with respect to time from the start <strong>of</strong><br />
intrusion (Marko et al., 2005; Clarke, 2007). Because <strong>of</strong> this, clast size<br />
distribution evolves with the progression <strong>of</strong> heat conduction. However, this<br />
assumption requires flow <strong>of</strong> the matrix magma in order to disperse the products<br />
<strong>of</strong> partial melting, in addition to diffusional processes that would facilitate mixing.<br />
Field observations do suggest local flow around clasts, but I did not quantitatively<br />
evaluate the problem.<br />
7.2. Methods: Partial Melting <strong>of</strong> Clasts<br />
7.2.1. Model Setup and Important Parameters<br />
In order to address thermal-mechanical coupling, I use two geometries<br />
(figure 7.1): one is an ideal spherical clast and the other is an outcrop image from<br />
Type 3 Shatter Zone. These two geometries are used to compare ideal<br />
conditions with the complex clast geometries observed in the field. The twodimensional<br />
models are closed syste<strong>ms</strong> that examine the instantaneous<br />
immersion <strong>of</strong> Bar Harbor Formation metasedimentary clasts with D s <strong>of</strong> 2.5 in a<br />
hot magma matrix. The model’s outer boundaries are periodic. Nodes are<br />
defined by a triangular mesh. All clast-matrix boundaries have a fine boundary<br />
92
A<br />
B<br />
Figure 7.1. Geometries used for thermal modeling. A) Type 3 Shatter Zone<br />
outcrop geometry and mesh; box is 1x0.8m. B) A spherical clast geometry used<br />
for optimization.<br />
93
mesh to better evaluate large thermal gradients at these boundaries. All models<br />
portray the transient behavior <strong>of</strong> thermal diffusion, and time steps were used to<br />
collect thermal data for clast sizes that cover 3 orders <strong>of</strong> magnitude. Although<br />
there was obviously some magmatic flow to fully disaggregate clasts, field<br />
evidence does not suggest large-scale flow. Therefore, these models are limited<br />
to conductive heat transfer. The ideal isolated spherical clast model was used to<br />
define an ideal trend for phase boundary migration without geometric<br />
interference. The outcrop-scale model was used to plot cooling patterns for the<br />
observed geometry. Models are defined by the parameters in Table 7.1.<br />
Geometry is the dominant factor that determines the pattern <strong>of</strong> conductive<br />
heat transfer (Jaeger, 1961). Conductive heat transfer across a boundary is<br />
fastest when surface area to volume ratios and thermal gradients are large<br />
(Jaeger, 1961; Bowers et al., 1990; Furlong et al., 1991; Stuwe, 2002). I assume<br />
a kinetically static interface between the clast and its granitic matrix; therefore the<br />
rate <strong>of</strong> heat transfer is entirely dependent on the thermal diffusivities <strong>of</strong> the<br />
granitic magma and the metasedimentary clast.<br />
Initial temperatures for clast and magma must be determined to solve the<br />
conductive heating equation. The relatively sparse occurrence <strong>of</strong> pyroxene<br />
implies that the rocks were heated to the lower-temperature end <strong>of</strong><br />
orthopyroxene hornfels facies, so initial clast temperature is set to T clast = 650°C<br />
(e.g. Spear et al., 1999; Milford et al., 2001; Blatt et al., 2006, Kriegsman and<br />
Alvarez-Valero, 2010). Magmatic temperatures are modeled at T magma = 900°C<br />
(Wiebe et al., 1997a). The outcrop-scale model contains 75% matrix by volume,<br />
94
C p solid 850J/kg °K<br />
C p magma 950J/Kg °K<br />
L, Latent heat 4E5J/Kg °K<br />
T intrusion<br />
T clasts<br />
900°C (1173°K)<br />
650°C (923°K)<br />
ΔT 250°C<br />
T granite solidus<br />
T feldspar crystallization<br />
T clast solidus<br />
800°C (1073°K)<br />
825°C (1098°K)<br />
720°C (993°K)<br />
Thermal conductivity 3W/m °K<br />
Density 2650 Kg/m 3<br />
, diffusivity coefficient 1.33E-6 m 2 /s<br />
Model area 0.8m 2<br />
% matrix by area 75%<br />
Table 7.1. Physical constants for thermal solutions.<br />
95
consistent with Type 3 breccias. The solidus for the Bar Harbor Formation is<br />
720°C, calculated using an optimization algorithm in PerpleX (Connolly, 2009)<br />
and the thermodynamic database provided by Holland and Powell (1998).<br />
Chemical data required for the thermodynamic calculations came from mineral<br />
abundance data from Metzger (1959), and results were compared to melt data<br />
from similar metasedimentary and metapelite rocks from the Ballachulish aureole<br />
(Pattison and Harte, 1988) and from metapelite P-T-t paths (Spear et al., 1999).<br />
I assume a single emplacement event in the Shatter Zone as there is no clear<br />
field evidence for multiple injections.<br />
Latent heat <strong>of</strong> granitic magma crystallization must be considered owing to<br />
the large percentage <strong>of</strong> granite matrix in Type 3 Shatter Zone (Nekvasil, 1988;<br />
Bowers et al., 1990; Furlong et al., 1991; Petcovic and Dufek, 2005; Huber et el.,<br />
2009; Lyubetskaya and Ague, 2009; Dufek and Bachmann, 2010, Bea, 2010).<br />
Latent heat correction is obtained by considering the heat <strong>of</strong> fusion in the<br />
calculation <strong>of</strong> the specific heat (C p ) <strong>of</strong> a material. For granite, C p liquid is 100 J kg -1<br />
K -1 greater than C p solid , and latent heat (L) is 4x10 5 J kg -1 (Bea, 2010). The<br />
correction for latent heat would occur within a temperature range, dT, with the<br />
lower limit defined by the solidus. Within dT, the latent-heat corrected C p takes<br />
the form (e.g. Bea, 2010)<br />
(7.1)<br />
For this equation, latent heat is released within the range <strong>of</strong> dT = 100°C above<br />
T granite solidus = 700°C, when most crystallization occurs. Latent heat causes a<br />
heightened rate <strong>of</strong> clast heating when the matrix temperature is within dT and is<br />
96
necessary to account for precise changes in temperature. The model cannot<br />
address the non-linear effect <strong>of</strong> magma crystallization rates, so latent heat is<br />
evenly dispersed during the entire duration dT. I assume that the Bar Harbor<br />
Formation was previously metamorphosed to avoid including endothermic<br />
metamorphic reactions that counterbalance latent heat (Kerrick, 1991). In<br />
addition, the short time frames associated with granite crystallization would<br />
probably limit the progress <strong>of</strong> potential metamorphic reactions.<br />
7.2.2. Methods for Plotting Data<br />
Temperature contouring is a useful method for evaluating the degree and<br />
time frame <strong>of</strong> partial melting in clasts. I took a transient thermal solution and<br />
plotted the continuously migrating solidus <strong>of</strong> the Bar Harbor Formation clasts in<br />
order to determine the rate <strong>of</strong> clast partial melt (the Stefan problem, Turcotte and<br />
Schubert, 1982). Two solidus migration plots are produced. The spherical twodimensional<br />
clast model was used to find the general trend <strong>of</strong> solidus migration<br />
into a clast with time. COMSOL results were used to collect transient thermal and<br />
spatial data along a transect through the clast center. The second plot used data<br />
from outcrop geometry to plot percent partial melt volume with respect to time.<br />
The plot was produced from model images <strong>of</strong> clast area above the solidus<br />
temperature for 30 chosen time steps. Clast area remaining below the solidus<br />
temperature was calculated in NIH ImageJ, and percent partial melt by area<br />
( ) was<br />
calculated for each time step.<br />
97
A temperature versus time plot was made from the ideal clast model<br />
temperature data for points located in the center, edge, and a distance 1.06<br />
times the clast radius into the magma. This plot is used to determine the pattern<br />
<strong>of</strong> heat transfer in the clast for supersolidus temperatures, and to determine the<br />
cooling history <strong>of</strong> surrounding magma similar to that <strong>of</strong> Okaya et al. (in press).<br />
The same data from percent partial melt over time plot was used to<br />
produce hypothetical clast size distribution (CSD) curves. CSD methods for these<br />
plots are similar to those used for results in Chapter 6. Equivalent radius values<br />
are calculated from the area below the solidus temperature for every clast<br />
(collected using NIH ImageJ) and data are plotted with a radius interval <strong>of</strong> 10 0.3 .<br />
7.2.3. Applications for Dimensionless Variables<br />
Okaya et al. (in press) evaluated heat transfer using dimensionless<br />
variables. This is a useful way to compare heat diffusion patterns by removing<br />
the solution’s dependence on clast size, thermal gradient, and thermal diffusivity.<br />
The following dimensionless variables are used to define this heat transfer study<br />
(Okaya et al., in press):<br />
(7.2)<br />
(7.3)<br />
(7.4)<br />
where , , and are dimensionless time, temperature, and clast radius,<br />
respectively. is the diffusivity coefficient <strong>of</strong> the heated material. is a<br />
98
characteristic length and it refers to the clast’s radius in this study. Because is<br />
normalized time with respect to the diffusivity and clast radius ratio, migration <strong>of</strong> a<br />
phase change through any size clast would show similar results. This allows<br />
easy comparison in a breccia with clast sizes spanning more than three orders <strong>of</strong><br />
magnitude.<br />
7.3. Clast Melt Results<br />
Figure 7.2 displays phase boundary migration for the three-dimensional<br />
ideal model. The additional curve is formulated from Turcotte and Schubert<br />
(1982), and defines phase migration in a semi-infinite slab from an infinite heat<br />
source. The time it takes for the ideal clast to completely reach its solidus is =<br />
0.2 (about 15 seconds for a 1 cm radius clast, 150,000 seconds or almost 2 days<br />
for a 1m radius clast). Results (Figure 7.3) from the outcrop model show trends<br />
for 800°C (ΔT = 150°C) and 900°C (ΔT = 250°C) intruding magma. For the ΔT =<br />
250°C model, clasts with radii below 1cm completely reach solidus within 4<br />
seconds, and all clasts with radii below 5cm reach solidus before 300 seconds.<br />
The partially melted area at 300 seconds is equal to 35% <strong>of</strong> the initial bulk clast<br />
area. Approximately 50% <strong>of</strong> clast area achieves solidus by 900 seconds, and all<br />
clast area achieves solidus by 5800 seconds. For the ΔT = 150°C model, solidus<br />
temperatures are achieved later and all clast area achieves solidus by 9000<br />
seconds. Both models achieve equilibrium temperature within approximately 2<br />
days.<br />
99
Dimensionless time<br />
0<br />
0.05<br />
0.1<br />
0.15<br />
R<br />
0 0.2 0.4 0.6 0.8 1<br />
2D clast<br />
Stefan curve (Turco e and<br />
Schubert, 1982)<br />
0.2<br />
Figure 7.2. Solidus migration trend for a spherical clast. The blue curve is the<br />
Stefan analytical solution for a half-infinite block exposed to an infinite heat<br />
source. Red dots mark the position <strong>of</strong> the 720°C isotherm as it migrates through<br />
the clast over time.<br />
100
t = 0 t = 10 t = 100 t = 1500<br />
% Clast partial melt by area<br />
100<br />
90<br />
80<br />
70<br />
60<br />
50<br />
40<br />
30<br />
20<br />
10<br />
0<br />
ΔT=150°C<br />
ΔT=250°C<br />
0 1000 2000 3000 4000 5000 6000 7000 8000 9000<br />
Time (seconds)<br />
Figure 7.3. A plot displaying clast melt over time. The total area <strong>of</strong> clast material<br />
below the 720°C isograd decreases quickly as small clasts melt, then progresses<br />
more slowly when few large clasts remain.<br />
101
Figure 7.4 displays model results from the transient temperature path for<br />
points within the spherical clast model with ΔT = 150°C and ΔT = 250°C runs.<br />
The ΔT = 250°C results show that, for a magmatic breccia with 75% matrix,<br />
homogenization temperature is reached by = 1.6. For this model, clast centers<br />
achieve supersolidus temperatures by = 0.2 for T i = 900°C and = 0.3 for T i =<br />
800°C. Equilibrium temperature is 840°C (θ = 0.76) and 770°C (θ = 0.48)<br />
respectively. Results from the 34% magma by volume model show a constant<br />
intrusion temperature <strong>of</strong> 900°C for T c = 650°C with<br />
= 0.24 and 450°C, which<br />
does not reach the solidus temperature at the clast center. Results from the 16%<br />
magma by volume model show a constant intrusion temperature <strong>of</strong> 900°C for T c<br />
= 650°C and 400°C, both <strong>of</strong> which do not reach the solidus temperature at the<br />
clast center.<br />
7.3.1. Discussion<br />
Based on thermal modeling results and the calculated solidus temperature<br />
<strong>of</strong> 720°C, All Bar Harbor Formation clasts with the average bulk chemistry<br />
(Metzger, 1959) achieved supersolidus temperatures with 75% magma matrix by<br />
volume, allowing partial melt to occur. Small, noncircular clasts melt first, and<br />
because there is such a large population <strong>of</strong> small clasts, there is a rapid increase<br />
in percent partial melt seen in Figure 7.3. The melt percent by area slope<br />
decreases when only larger clasts remain. An order <strong>of</strong> magnitude change in clast<br />
radius will cause two orders <strong>of</strong> magnitude change in the amount <strong>of</strong> time for the<br />
clast to achieve supersolidus temperatures (Okaya et al., in press). Although the<br />
102
A<br />
900<br />
Temperature versus time curves<br />
Spherical clast in 75% matrix<br />
850<br />
R*1.1<br />
T i = 900°C, τ = 0.1995<br />
Temperature ( C)<br />
800<br />
750<br />
R<br />
R*0<br />
Solidus<br />
T i = 800°C, τ = 0.3<br />
700<br />
B<br />
Temperature (°C)<br />
650<br />
900<br />
850<br />
800<br />
750<br />
700<br />
650<br />
600<br />
550<br />
500<br />
0 0.5 1 1.5 2<br />
tK/r2<br />
R*1.1<br />
R<br />
R*0<br />
Temperature versus time curves<br />
Spherical clast in 34% matrix<br />
Solidus<br />
Tc = 650°C, τ = 0.24<br />
Tc = 450°C<br />
C<br />
450<br />
900<br />
850<br />
0 0.2 0.4 0.6 0.8 1<br />
tK/r 2<br />
Temperature versus time curves<br />
Spherical clast in 16% matrix<br />
800<br />
Temperature (°C)<br />
750<br />
700<br />
650<br />
600<br />
550<br />
R<br />
R*1.1<br />
T i = 650°C<br />
T i = 400°C<br />
Solidus<br />
500<br />
450<br />
R*0<br />
400<br />
0 0.1 0.2 0.3 0.4 0.5<br />
tK/r 2<br />
Figure 7.4. Temperature changes over time for points in a clast. R*0, R, and<br />
R*1.1 represent points in the center, edge, and 1/10th the clast radius into the<br />
magma, respectively. A) Magma is initially 75% <strong>of</strong> total volume, T i = 900°C and<br />
800°C, T c = 650°C. B) Magma is initially 34% <strong>of</strong> total volume, T c = 650°C and<br />
450°C, T i = 900°C. C) Magma is initially 16% <strong>of</strong> total volume, T c = 650°C and<br />
400°C, T i = 900°C. Dimensionless time values for when the clast center reaches<br />
720°C are given where applicable.<br />
103
thermal model ignores advection <strong>of</strong> heat due to flow <strong>of</strong> the matrix magma relative<br />
to the clasts, there had to be an advective component at least during magma<br />
intrusion. Flow <strong>of</strong> magma around the partially melting clasts would have<br />
facilitated dissagregation, though “ghosting” <strong>of</strong> some clast margins suggests that<br />
diffusion, or local mixing <strong>of</strong> the two magmas, may have occurred without marked<br />
flow <strong>of</strong> the matrix magma. Flow is the physical component for complete<br />
disaggregation to occur. Without it, clast melting and local mixing would still<br />
occur, but flow is more effective at mixing the melted material into the magma,<br />
essentially removing that clast. Small clasts reach melt temperatures within<br />
seconds after emplacement, when there is a greater potential for magmatic flow.<br />
This could lead to small clast disaggregation well before the cores <strong>of</strong> large clasts<br />
reach solidus. There is no constraint on magma flow because there is no<br />
evidence for its existence except at the local scale. Regardless <strong>of</strong> this, Bar<br />
Harbor Formation clasts with the average bulk chemistry eventually achieve<br />
supersolidus temperatures and given any magmatic flow, they have the potential<br />
to disaggregate.<br />
The degree <strong>of</strong> melt in Bar Harbor Formation clasts is dependent on the<br />
melt temperature, the matrix to clast volume ratio, and the initial temperatures <strong>of</strong><br />
clast and intruding magma. As mentioned in sections (2.3) and (6.1), The Bar<br />
Harbor Formation is heterogeneous with layers consisting <strong>of</strong> pelites, sandstone,<br />
volcanic tuff, detrital quartzite, calc-silicates, and volcanic tuff. It should not be<br />
expected that all Bar Harbor Formation clasts within the Shatter Zone should<br />
have the same solidus temperature, and it is possible that some units did not<br />
104
achieve supersolidus temperatures. For example, volcanic tuff, quartzite, or calcsilicate<br />
layers would not melt with the pelitic layers, leaving a preference to<br />
preserve the clasts produced from the higher melting temperature layers. This<br />
means that not all clasts would follow the same trend <strong>of</strong> melting, and could<br />
explain why not all Bar Harbor Formation clasts completely melted in Type 3<br />
Shatter Zone.<br />
For the 900°C intrusion model, the clasts and matrix reach equilibrium at a<br />
temperature well above Cadillac Mountain Granite feldspar crystallization<br />
temperatures (Wiebe et al., 1997a), but the 800°C intrusion model is well below<br />
the 825°C feldspar crystallization <strong>of</strong> the Cadillac mountain Granite (Wiebe et al.,<br />
1997). Although the temperature remains above the Bar Harbor Formation<br />
solidus for a relatively long time, feldspar crystallization would significantly<br />
increase viscosity (e.g. Baker, 1996; Bea, 2010). If magma partially solidifies<br />
around a clast, there is a reduced chance for disaggregation (e.g. Beard and<br />
Ragland, 2005). For the 900°C intrusion model, the equilibrium temperature is<br />
too high for a viscosity increase, but for the 800°C intrusion model, magma<br />
crystallization may have been able to protect clasts from disaggregation with an<br />
envelope <strong>of</strong> more viscous material.<br />
The initial temperature and volume fraction <strong>of</strong> wall rock and magma<br />
determine the equilibrium temperature. As seen in Figure 7.4, a lower magma<br />
matrix percent by volume would cause less clast melting. Several initial intrusion<br />
and clast temperatures are used to replicate potential magma temperatures and<br />
wall rock temperatures with distance from the reservoir. Type 1 and 2 Shatter<br />
105
Zone experienced a relatively weaker thermal pulse and therefore would have<br />
experienced less melt as compared to Type 3. It is likely that Type 3 Shatter<br />
Zone initially had a lower matrix volume percent, but continued melt and<br />
disaggregation <strong>of</strong> clasts allowed greater accommodation <strong>of</strong> granitic magma. Type<br />
3 Shatter Zone may originally have looked similar to Type 2 because <strong>of</strong> this, and<br />
clast melt may have followed the conditions used for Figure 7.4.B. For a Type 2<br />
geometry, small clasts entrained in the magma channels surrounding larger<br />
clasts would also experience a greater than average exposure to magma. Melt <strong>of</strong><br />
small clasts in these channels would be preferred, while the surrounding larger<br />
clasts could not melt under the conditions.<br />
The characteristics <strong>of</strong> CSD evolution with partial clast melt are visible in<br />
figure 7.5. D s decreases over time with the loss <strong>of</strong> small clasts and generally no<br />
change in large clast populations. Starting with a fractal distribution at time zero,<br />
as small clasts quickly disaggregate, a bifractal trend appears to develop.<br />
Eventually, the slope changes completely to a trend that can be better defined by<br />
an exponential size distribution. This model can explain the progression <strong>of</strong> D s<br />
from Type 2 to Type 3 in Bar Harbor Formation clasts. Type 3 Bar Harbor<br />
Formation size distributions have the most evolved slope and the greatest<br />
thermal exposure. I cannot assume that the Bar Harbor Formation clasts<br />
completely followed this migrating CSD trend because <strong>of</strong> the compositional<br />
differences between layers. CSD for Bar Harbor Formation clasts therefore<br />
reflect the trend <strong>of</strong> partial melt in most <strong>of</strong> the clasts and the remnant clasts that<br />
did not attain melting temperatures.<br />
106
A<br />
1.E+04<br />
1.E+03<br />
N<br />
1.E+02<br />
1.E+01<br />
Modification <strong>of</strong> Clast Size Distribution produced by<br />
modeled transient melt progression<br />
Unexposed<br />
1 second<br />
5 seconds<br />
20 seconds<br />
50 seconds<br />
100 seconds<br />
200 seconds<br />
500 seconds<br />
1000 seconds<br />
1.E+00<br />
B<br />
cumulate frequency<br />
100<br />
10<br />
0.01 0.1<br />
r (cm)<br />
1 10<br />
Evolution <strong>of</strong> clast size distribution caused by<br />
modeled transient melt progression<br />
t = 4<br />
Bifractal:<br />
D = 2, 1.5<br />
t = 100<br />
Non-Fractal<br />
t = 0<br />
D = 2.5<br />
t0<br />
t4<br />
100<br />
1<br />
1 10 100<br />
radius (pixels)<br />
Figure 7.5. The evolution <strong>of</strong> clast size distribution with progressive thermal<br />
exposure. A) A fabricated CSD with D s = 3, T c = 650°C and subjected to T i =<br />
900°C, 34% magma: small clast populations quickly melt, evolving from a fractal<br />
to non-fractal distribution <strong>of</strong> clast sizes. B) CSD results from chosen time steps<br />
from the outcrop model used in Figure 7.3; T i = 900°C, T c = 650°C.<br />
107
7.4. Thermal-Induced Fracture<br />
Field observations, specifically the late stage fractures in diorite clasts,<br />
show that late stage fracturing occurred with the introduction <strong>of</strong> magma into the<br />
Shatter Zone. Clasts when exposed to magma undergo rapid heating and a<br />
transient, non-uniform temperature distribution develops within them. Most<br />
materials tend to volumetrically expand when heated (e.g. Clarke, 1998). No<br />
critical stresses would be induced if the material under uniform heating is free to<br />
expand. Non-uniform volume expansion in a constricted solid, however, leads to<br />
stress buildup and potential fracture propagation. In a clast <strong>of</strong> irregular shape<br />
subjected to surface heating, temperatures in the interior and in the root regions<br />
<strong>of</strong> the corners are lower than those at the surfaces. Tensile stresses thus<br />
develop in these regions <strong>of</strong> non-uniform expansion as the materials there are<br />
stretched by the hotter surface materials, causing potential corner break-<strong>of</strong>f.<br />
Thermal fracture could be significant for CSD because 1) it directly<br />
produces new clasts from the breakdown <strong>of</strong> old ones in a pattern different from<br />
explosion-derived populations, and 2) it increases surface area <strong>of</strong> clasts that<br />
could enhance the speed <strong>of</strong> temperature homogenization. A one-dimensional<br />
equation is used to approximate the required temperature gradient necessary to<br />
cause tensile fracture (Manson, 1953)<br />
(7.5)<br />
where is Young’s Modulus, is Poisson’s ratio, is the coefficient <strong>of</strong> linear<br />
thermal expansion,<br />
is the temperature difference experienced by the body,<br />
and<br />
is the thermally induced tensile stress. An average rock can fracture<br />
108
under 20 MPa <strong>of</strong> tensile stress (critical tensile stress,<br />
), which is achieved when<br />
is greater than approximately 30°K using the material properties listed in<br />
Table 7.2. The temperature difference between magma and clast is 250°K, which<br />
implies that the temperature gradient in the interior part <strong>of</strong> the clast will exceed<br />
30°K required to fracture.<br />
7.4.1. Model Setup<br />
A single clast model is used in a manner identical to the previously<br />
mentioned models, but with a focus on thermal stresses. Finite elements are<br />
used to solve the thermal stress equations. Figure 7.6 shows the clast in a<br />
magma matrix and the finite element mesh used in the simulation. Models are<br />
run for 650°C metasedimentary and diorite clasts in 900°C, low viscosity (~10 6<br />
Pa s, CIPW Norm calculation based on bulk rock chemistry data from Wiebe et<br />
al., 1997a) magma. Strength anisotropy is not considered in the models. The<br />
matrix is an elastic material with assigned properties that allow it to behave<br />
similarly to a magma. Thermal expansion <strong>of</strong> the matrix is set to zero, and<br />
theYoung’s modulus is set to three orders <strong>of</strong> magnitude lower than a typical rock.<br />
This is done in order to accommodate thermal expansion in the clast with limited<br />
resistance, in an attempt to simulate a magma that would be able to flow away<br />
from the site <strong>of</strong> clast expansion. The model is run with confining pressure typical<br />
to 5km depth (~0.13GPa).<br />
109
Metapelite/hornfels Diorite dike<br />
E 70E9 Pa (2) 80E9 Pa (2)<br />
9E-6 K -1 (1) 7E-6 °K -1 (1)<br />
0.25 (1) 0.25 (1)<br />
ΔT 250°K 250°K<br />
-15E6 Pa (2) -20E6 Pa (2)<br />
(1) Clark, 1966; (2) Lama and Vutukuri, 1978<br />
Table 7.2. Physical constants for thermal-mechanical<br />
solutions.<br />
110
Figure 7.6. Clast geometry used for thermal stress analysis. Box is 1.25x1.25m.<br />
111
7.4.2. Results and Discussion<br />
COMSOL follows engineering convention, meaning that tensile stress is<br />
positive and compressive stress is negative. The first principal stress relates to<br />
maximum tensile stress, while the second principal stress relates to minimum<br />
tensile stress for a two-dimensional model. Figure 7.7 shows transient<br />
development <strong>of</strong> the first principal stress distribution in the clast (also see<br />
Animation 2, 3). Local tensile stress buildup begins in the roots <strong>of</strong> sharp corners<br />
and moves inward as the clast heats up. Two patterns <strong>of</strong> fracture are evident<br />
from the experiment. The first phase <strong>of</strong> thermal fracture shows preference for<br />
edge break <strong>of</strong>f. Arrows denote the direction <strong>of</strong> the second principal stress, or the<br />
direction <strong>of</strong> minimum tensile stress that a tensile fracture would prefer to follow.<br />
For this clast there is a preferred cuspate-shaped fracture pattern that would<br />
produce more corners. Eventually the number <strong>of</strong> corners would be reduced by<br />
successive fragmentation and circularity would increase. Next, as the clast<br />
continues to warm, tensile stress in the center <strong>of</strong> the clast reaches a critical<br />
value, allowing larger fractures to nucleate from the center and break the clast in<br />
half. The clast is slightly elongate, and<br />
increases inward and parallel to<br />
elongation. The first principal stress directions run perpendicular to elongation,<br />
preferring to fracture along the short axis. At this time <strong>of</strong> thermal exposure,<br />
originally elongate clasts would be preferentially broken up into more equant<br />
fragments, and each new fracture surface provides a fresh face to repeat the<br />
process. The potential for thermal fracture declines as the clast heats up and the<br />
thermal gradient is reduced.<br />
112
t: 500<br />
t: 5000<br />
A<br />
B<br />
t:500<br />
t:5000<br />
C<br />
Figure 7.7. Time step results for thermal stress in metasedimentary and diorite<br />
clasts. A) Bar Harbor Formation clast exposed to magma at 500 seconds and B)<br />
5000 seconds. C) diorite clast exposed to magma at 500 seconds and D) 5000<br />
seconds. The surface plot displays the first principle stress field, with tensile<br />
stress plotted as red and compressive stress plotted as blue. Arrows designate<br />
the second principle stress direction, or the assumed direction <strong>of</strong> fracture<br />
propagation. Maximum tensile stress is the result <strong>of</strong> nonuniform expansion, first<br />
in the roots <strong>of</strong> corners, then later on in the core <strong>of</strong> the clast as it is continually<br />
heated. Stresses gradually reduce as the clast temperature equilibrates with the<br />
magma.<br />
D<br />
113
This thermal fracture model explains the late stage fracture for diorite<br />
clasts, but it does not take into account the anisotropic nature <strong>of</strong> the Bar Harbor<br />
Formation. Rock heterogeneity creates a far more complex thermal stress<br />
problem because crack formation is not solely dependent on the thermal<br />
gradient. Clarke et al. (1998) discuss the three different possibilities for fracture<br />
development in anisotropic xenoliths. The first is determined by the thermal<br />
gradient and this is used in the above model (thermal gradient cracking). The<br />
second mechanism for crack formation in a layered material becomes operative<br />
when one layer has a differing thermal expansion coefficient than its counterpart<br />
(thermal expansion mismatch cracking). Third, a material may have an<br />
anisotropic fabric that leads to preferred crack propagation in one direction<br />
(thermal anisotropy cracking). Bar Harbor Formation rocks can exhibit all three <strong>of</strong><br />
these fracture types due to their compositional layering, and they may be more<br />
susceptible to thermal fracture than suggested by this model. The thermal<br />
gradient cracking model therefore provides a low end-member possibility for the<br />
proliferation <strong>of</strong> thermal cracks in Bar Harbor clasts.<br />
If thermal fracture was prevalent, each clast would fracture according to a<br />
new size distribution: for thermal fracture, D s = 2.156 (Glazner and Bartley,<br />
2006). The new value <strong>of</strong> D s is the combination <strong>of</strong> the explosive fracture event and<br />
the secondary thermal fracture event, and repeated fracture events always<br />
increase D s by a fractional amount (Jebrak, 1997). Also, field evidence suggests<br />
that not all diorite clasts experienced thermal fracture, therefore late-stage<br />
thermal fracture did not have a significant effect on diorite dike CSD results.<br />
114
7.5. Final Discussion<br />
Results from clast size distribution imply that the Shatter Zone originally<br />
formed from a subvolcanic explosion. The volcanic eruption was likely triggered<br />
by replenishment <strong>of</strong> mafic magma at the chamber base, which reinvigorated the<br />
overlying granite (Wiebe, 1994). The explosion was triggered by rapid volume<br />
expansion <strong>of</strong> volatiles within the chamber. Overpressure <strong>of</strong> the chamber led to<br />
immediate wall rock failure, providing channel ways for incoming magma. Size<br />
distributions for clasts above ~1.5cm radius in Types 1 and 2 record the<br />
explosive origin <strong>of</strong> the chamber walls, whereas distributions for clasts below 1.5<br />
cm radius imply a secondary mechanism related to disaggregation and hydraulicthermal<br />
fracture during magma introduction. Diorite clast size distributions in<br />
Type 3 digress from D s values seen for Types 1 and 2, but they are still also<br />
thought to have an explosive origin. The decrease in D s between Types 1 and 2<br />
and Type 3 is likely related to a change in dominant wall rock type as a function<br />
<strong>of</strong> rock strength differences rather than a difference in brecciation mechanism.<br />
Type 3 Bar Harbor clasts show a non-fractal size distribution trend,<br />
implying a secondary modification process that effectively reduced clast size and<br />
abundance. Data from clast boundary shape and clast circularity analysis also<br />
argue that clast modification has occurred from type 1 to type 3, showing relative<br />
decrease in clast surface complexity and increase in clast compactness with<br />
proximity to the Cadillac Mountain Granite. I suggest that clast modification was<br />
dominantly caused by thermal attrition: the thermal fracture, melt, and<br />
115
disaggregation <strong>of</strong> Bar Harbor clasts driven by the intruding 900°C magma. I<br />
explored the possibility <strong>of</strong> thermal attrition by thermal-mechanical modeling <strong>of</strong><br />
clast geometries instantaneously immersed in an intruding magma. Thermal<br />
fracture and partial melt are likely to occur during magma intrusion, but my<br />
conclusions are limited by the thermal conduction model because disaggregation<br />
requires some component <strong>of</strong> viscous flow <strong>of</strong> the matrix magma to mechanically<br />
disintegrate a clast. Results from the phase boundary migration model show that<br />
all Bar Harbor clasts <strong>of</strong> appropriate composition had potential to melt. Assuming<br />
that the volcanic eruption underwent days <strong>of</strong> activity, this would be enough time<br />
to melt and disaggregate a large component <strong>of</strong> the smallest Bar Harbor clast size<br />
populations. This agrees with the trend that is seen in clast size distribution for<br />
Type 3 Bar Harbor Formation clasts.<br />
Thermal fracture was driven by the immediate intrusion <strong>of</strong> magma after<br />
explosive wall rock fragmentation. Late-stage fractures in diorite clasts are likely<br />
caused by the large thermal gradients caused by the granitic intrusion into the<br />
Shatter Zone. Rapid thermal expansion in clasts provided great enough tensile<br />
stresses to cause fracture propagation <strong>of</strong> corners. Although the thermal fracture<br />
effect on clast size distribution is not as well understood, D s will increase slightly<br />
with repeated fracturing events, assuming that there is no removal <strong>of</strong> any clast<br />
populations through melting. The contribution from thermal fracture is small and<br />
had little effect on diorite clast D s . Diorite clasts did not reach their solidus<br />
temperatures, therefore D s represents the initial fracturing event plus thermal<br />
fracture, presumably creating a fractionally higher D s . Thermal fracture in a<br />
116
structurally anisotropic material is more difficult to constrain because local<br />
stresses are produced by thermal gradient, differing thermal expansion<br />
coefficients <strong>of</strong> layered materials, and the presence <strong>of</strong> materials that have<br />
anisotropic expansion and conduction characteristics. These characteristics are<br />
beyond the scope <strong>of</strong> the current thermal stress models, which are therefore most<br />
applicable to the homogeneous diorite clasts.<br />
117
REFERENCES<br />
Acocella, V. (2007). Understanding caldera structure and development: an<br />
overview <strong>of</strong> analogue models compared to natural calderas. Earth Science<br />
Reviews 85: 125-60.<br />
Accocella, V.; Porreca, M.; Neri, M.; Mattei, M.; Funicello, R. (2006). Fissure<br />
eruptions at Mount Vesuvius (Italy): insights on the shallow propagation <strong>of</strong><br />
dikes at volcanoes. Geology. 34: 673-676.<br />
Aizawa, K.; Acocella, V.; Yoshida, T. (2006). How the development <strong>of</strong> magma<br />
chambers affects collapse calderas: insights from an overview.<br />
Mechanis<strong>ms</strong> <strong>of</strong> Activity and Unrest at Large Calderas 269: 65-81.<br />
Allen, M.; Brown, G.; Miles, N. (1995). Measurement <strong>of</strong> boundary fractal<br />
dimensions: review <strong>of</strong> current techniques. Powder Technology 84: 1-14.<br />
Andrle, R. (1996). The west coast <strong>of</strong> Britain: statistical self-similarity vs.<br />
characteristic scales in the landscape. Earth Surface Processes and<br />
landfor<strong>ms</strong> 21: 955-962.<br />
Annen, C.; Scaillet, B.; Sparks, R.S.J. (2006). Thermal constraints on the<br />
emplacement rate <strong>of</strong> a large intrusive complex: the Manaslu Leucogranite,<br />
Nepal Himalaya. Journal <strong>of</strong> Petrology Advance access.<br />
Annen, C. and Sparks, R.S.J. (2002). Effects <strong>of</strong> repetitive emplacement <strong>of</strong><br />
basaltic intrusions on thermal evolution and melt generation in the crust.<br />
Earth and Planetary Science Letters 203: 937-955.<br />
Apuani, T. and Corazzato, C. (2009). Numerical model <strong>of</strong> the Stromboli volcano<br />
(Italy) including the effect <strong>of</strong> magma pressure in the dyke system. Rock<br />
Mechanics and Rock Engineering. 42: 53-72.<br />
Attoh, K. and Van der Meulen, M. (1984). Metamorphic temperatures in the<br />
Michigamme Formation compared with the thermal effect <strong>of</strong> an intrusion,<br />
Northern Michigan. The Journal <strong>of</strong> Geology 92.4: 417-432.<br />
Bachmann, O. and Bergantz, G.W. (2008). The Magma Reservoirs that feed<br />
supereruptions. Elements 4: 17-21.<br />
Bachman, O.; Miller, C.F.; de Silva, S.L. (2007). The volcanic-plutonic connection<br />
as a stage for understanding crustal magmatism. Journal <strong>of</strong> Volcanology<br />
and Geothermal Research 167: 1-23.<br />
118
Baer, G. and Reches, Z. (1987). Flow patterns <strong>of</strong> magma in dikes, Makhtesh<br />
Ramon, Israel. Geology 15: 569-572.<br />
Baker, D.R. (1996). Granitic melt viscosities: empirical and configurational<br />
entropy models for their calculation. American Mineralogist 81: 126-34.<br />
Barker, S. and Malone, S. (1991). Magmatic system geometry at the Mount St.<br />
Helens modeled from the stress field associated with posteruptive<br />
earthquakes. Journal <strong>of</strong> Geophysical Research 96.B7: 11,883-11,894.<br />
Barnett, W. (2004). Subsidence breccias in kimberlite pipes - an application <strong>of</strong><br />
fractal analysis. Lithos 76: 299-316.<br />
Barnett, W. and Lorig, L. (2007). A model for stress-controlled pipe growth.<br />
Journal <strong>of</strong> Volcanology and Geothermal Research 159: 108-25.<br />
Bartley, J.M.; Coleman, D.; Glazner, A. (2006). Incremental pluton emplacement<br />
by magmatic crack-seal. Transactions <strong>of</strong> the Royal Society <strong>of</strong> Edinburgh:<br />
Earth Sciences 97: 383-396.<br />
Bea, F. (2010). Crystallization dynamics <strong>of</strong> granite magma chambers in the<br />
absence <strong>of</strong> regional stress: multiphysics modeling with natural examples.<br />
Journal <strong>of</strong> Petrology 51.7: 1541-1569.<br />
Beard, J.S. and Ragland, P.C. (2005). Reactive bulk assimilation: a model for<br />
cruat-mantle mixing in silicic magmas. Geology 33.8: 681-684.<br />
Bergantz, G.W. (1991). Physical and chemical characterization <strong>of</strong> plutons.<br />
Kerrick, D.M. and Ribbe, P.H., eds. Reviews in Mineralogy: Contact<br />
Metamorphism 26: 13-42.<br />
Bergantz, G.W. and Barboza, S.A. (2005). Elements <strong>of</strong> a modeling approach to<br />
the physical controls on crustal differentiation. Evolution and<br />
Differentiation <strong>of</strong> the Continental Crust. Brownm Michael and Rushwater,<br />
Tracy eds. Cambridge <strong>University</strong> Press.<br />
Berry, H. N., IV, and Osberg, P.H., 1989, A stratigraphic syn<strong>thesis</strong> <strong>of</strong> eastern<br />
<strong>Maine</strong> and western New Brunswick, in Tucker, R. D., and Marvinney, R.<br />
G. eds., , p. 1-32.<br />
Berube, D., and Jebrak, M. (1999). High precision boundary fractal analysis for<br />
shape characterization. Computers and Geosciences 25: 1059-071.<br />
Billen, M.I. (2008). Modeling the dynamics <strong>of</strong> subducting slabs. Annual Reviews<br />
<strong>of</strong> Earth and Planetary Sciences 36: 325-356.<br />
119
Billen, M.I. and Gurnis, M. (2001). A low viscosity wedge in subduction zones.<br />
Earth and Planetary Sciences 193: 227-236.<br />
Bjork, T.E. and Austrheim, M.H. (2009). Quantifying granular material and<br />
deformation: advantages <strong>of</strong> combining grain size, shape, and mineral<br />
phase recognition analysis. Journal <strong>of</strong> Structural Geology, preprint<br />
submitted to Elsevier.<br />
Blatt, H.; Tracy, R.J.; Owens, B.E. (2006). Petrology. W.H. Freeman Co., New<br />
York, 3 rd edition.<br />
Blenkinsop, T.G. (1991). Cataclasis and processes <strong>of</strong> particle size reduction.<br />
Pure and Applied Geophysics 136.1: 59-86.<br />
Blott, S.J. and Pye, K. (2001). GRADISTAT: a grain size distribution and<br />
statistics package for the analysis <strong>of</strong> unconsolidated sediments. Earth<br />
Surface processes and Landfor<strong>ms</strong> 26: 1237-248.<br />
Bohrson, W.A. (2007). Insight into subvolcanic magma plumbing syste<strong>ms</strong>.<br />
Geology 35.8: 767-768.<br />
Bonnet, E.; Bour, O.; Odling, N.E.; Davy, P.; Main, I.; Cowie, P. and Berkowitz, B.<br />
(2001). Scaling <strong>of</strong> fracture syste<strong>ms</strong> in geological media. Reviews <strong>of</strong><br />
Geophysics 39.3: 347-383.<br />
Bons, P.D.; Arnold, J.; Kalda, J.; Soesoo, A.; Elburg, M.A. (2003a). Accumulation<br />
and transport <strong>of</strong> magma. Geophysical Research Abstracts 5, 04282.<br />
Bons, Paul D. and Soesoo, A. (2003b). Could magma transport and<br />
accumulation be a useful analogue to understand hydrocarbon extraction?<br />
Oil Shale 20.3special: 412-420.<br />
Bowers, J.R.; Kerrick, D.M.; Furlong, K.P. (1990). Conduction model for the<br />
thermal evolution <strong>of</strong> the cupsuptic aureole, <strong>Maine</strong>. American Journal <strong>of</strong><br />
Science 290: 644-665.<br />
Branney, M.J., and Kokelaar, P. (1994). Volcanotectonic faulting, s<strong>of</strong>t-state<br />
deformation, and rheomorphism <strong>of</strong> tuffs during development <strong>of</strong> a<br />
piecemeal caldera, English Lake district. Geological Society <strong>of</strong> America<br />
Bulletin 106: 507-30.<br />
Braun, I. and Kriegsman, L.M. (2001). Partial melting in crustal xenoliths and<br />
anatectic migmatites: a comparison. Physics and Chemistry <strong>of</strong> Earth (A)<br />
26.4-5: 261-266.<br />
120
Brittain, H.G. (2001). Particle-size distribution, part I representations <strong>of</strong> particle<br />
shape, size, and distribution: particle-size determinations are undertaken<br />
to obtain information about the size characteristics <strong>of</strong> an ensemble <strong>of</strong><br />
particles. Pharmaceutical Technology 25.12: 38-45.<br />
Burnham, C.W. and Nekvasil, H. (1986). Equilibrium properties <strong>of</strong> granite<br />
pegmatite magmas. American Mineralogist 71: 239-263.<br />
Carey, S.; Sigurdsson, H.; Gardner, J.E.; Criswell, W. (1990). Variations in<br />
column height and magma discharge during the May 18, 1980 eruption <strong>of</strong><br />
Mount St. Helens. Journal <strong>of</strong> Volcanology and Geothermal Research43:<br />
99-112.<br />
Caruso, F.; Vinciguerra, S.; Latora, V.; Rapisarda, A.; Malone, S. (2006).<br />
Multifractal analysis <strong>of</strong> Mt. St. Helens seismicity as a tool for identifying<br />
eruptive activity. Fractals 3.4.<br />
Cathles, L.M. (1977). An analysis <strong>of</strong> the cooling <strong>of</strong> intrusives by ground-water<br />
convection which includes boiling. Economic Geology 72: 804-826.<br />
Chapman, C.A. (1962). Diabase-granite composite dikes, with pillow-like<br />
structures, Mount Desert Island, <strong>Maine</strong>. Journal <strong>of</strong> Geology 70: 539-564.<br />
Chen, Z.; Jin, Z.-H.; Johnson, S.E. (in press). Transient dike propagation and<br />
arrest near the level <strong>of</strong> neutral buoyancy.<br />
Clague, D.A. (1987). Hawaiian xenoliths populations, magma supply rates, and<br />
development <strong>of</strong> magma chambers. Bulletin <strong>of</strong> Volcanology 49: 577-587.<br />
Clark, A.H (1990). The slump breccias <strong>of</strong> the Toquepala porphyry Cu(Mo)<br />
deposit, Peru: implications for fragment rounding in hydrothermal breccias.<br />
Economic Geology 85: 1677-1685.<br />
Clark, C. and James, P. (2003). Hydrothermal brecciation due to fluid pressure<br />
fluctuations: examples from the Olary Domain, South Australia.<br />
Tectonophysics 366: 187-206.<br />
Clark, C.; Mumm, A. S.; Collins, A. S. (2006). A coupled micro-and<br />
macrostructural approach to the analysis <strong>of</strong> fluid induced brecciation,<br />
Curnamona Province, South Australia. Journal <strong>of</strong> Structural Geology 28:<br />
745-761.<br />
Clark, S.P., Jr. (editor) (1966). Handbook <strong>of</strong> Physical Constsnts. Geological<br />
Society <strong>of</strong> America Memoir, 97.<br />
121
Clarke, D. B. (2007). Assimilation <strong>of</strong> xenocrysts in granitic magmas: principles,<br />
processes, proxies, and proble<strong>ms</strong>. The Canadian Mineralogist 45:5-30.<br />
Clarke, D. B. and Erdmann, S. (2008). Is stoping a volumetrically significant<br />
pluton emplacement process?: Comment. Geological Society <strong>of</strong> America<br />
Bulletin 120: 1072-1074.<br />
Clarke, D.B.; Henry, A.S.; White, M.A. (1998). Exploding xenoliths and the<br />
absence <strong>of</strong> ‘elephants’ graveyards’ in granite batholiths. Journal <strong>of</strong><br />
Structural Geology 20.9/10: 1325-1343.<br />
Clemens, J. and Mawer, C. (1992). Granitic magma transport by fracture<br />
propagation. Tectonophysics 204: 339-360.<br />
Cole, J.W.; Milner, D.M.; Spinks, K.D. (2005). Calderas and caldera structures: a<br />
review. Earth-Science Reviews 69: 1-26.<br />
Connolly, J. A. D. (2009) The geodynamic equation <strong>of</strong> state: what and how.<br />
Geochemistry, Geophysics, Geosyste<strong>ms</strong> 10:Q10014<br />
DOI:10.1029/2009GC002540.<br />
Cook, S.J., Bowman, J.R., and Forster, C.B. (1997) Contact metamorphism<br />
surrounding the Alta stock: Finite element model simulation <strong>of</strong> heat- and<br />
18 O/ 16 O mass transport during prograde metamorphism. American Journal<br />
<strong>of</strong> Science 297: 1–55.<br />
Coombs, M. (1994). Petrology and geochemistry <strong>of</strong> the southern Shatter Zone,<br />
Cadillac Mountain Pluton, Mount Desert Island, <strong>Maine</strong>. Honors <strong>thesis</strong>.<br />
Cruden, A.R. (2005). Emplacement and growth <strong>of</strong> plutons: implications for rates<br />
<strong>of</strong> melting and mass transfer in continental crust. Evolution and<br />
Differentiation <strong>of</strong> the Continental Crust ed. Brown, Michael and Rushmer,<br />
Tracy. Cambridge university Press.<br />
Cruden, A.R. (2008). Emplacement mechanis<strong>ms</strong> and structural influences <strong>of</strong> a<br />
younger granite intrusion into older wall rocks- a principal study with<br />
application to the Gotemar and Uthammar granites. Swedish Nuclear Fuel<br />
and Waste Management Co. Report R-08-138.<br />
Cruden, A.R. and McCaffrey, K. (2001). Growth <strong>of</strong> plutons by floor subsidence:<br />
implications for rates <strong>of</strong> emplacement, intrusion spacing and meltextraction<br />
mechanis<strong>ms</strong>. Physics and Chemistry <strong>of</strong> the Earth 26.4-5: 303-<br />
315.<br />
122
Dahm, T. (2000). Numerical simulations <strong>of</strong> the propagation path and the arrest <strong>of</strong><br />
fluid-filled fractures in the Earth. Geophysical Journal International 141:<br />
623-638.<br />
Danielsson, P. (1980). Euclidean distance mapping. Computer Graphics and<br />
Image Processing 14: 227-48.<br />
Davis, M.; Koenders, M.A.; Petford, N. (2007). Vibro-agitation <strong>of</strong> chambered<br />
magma. Journal <strong>of</strong> Volcanology and Geothermal Research 167: 24-36.<br />
Dellino, P. and Liotino, G. (2002). The fractal and multifractal dimension <strong>of</strong><br />
volcanic ash particles contour: a test study on the utility and volcanological<br />
relevance. Journal <strong>of</strong> Volcanology and Geothermal Research 113: 1-18.<br />
Dellino, P. and Volpe, L. (1996). Image processing analysis in reconstructing<br />
fragmentation and transportation mechanis<strong>ms</strong> <strong>of</strong> pyroclastic deposits. The<br />
case <strong>of</strong> Monte Pilato-Rocche Rosse eruptions, Lipari (Aeolian Islands,<br />
Italy). Journal <strong>of</strong> Volcanology and Geothermal Research 71: 13-29.<br />
Dietyl, C. and Koyi, H. (2008). Formation <strong>of</strong> tabular plutons- results and<br />
implications <strong>of</strong> centrifuge modeling. Journal <strong>of</strong> Geosciences 53: 253-261.<br />
Dufek, J. and Bachmann, O. (2010). Quantum magmatism: magmatic<br />
compositional gaps generated by melt-crystal dynamics. Geology 38: 687-<br />
690.<br />
Dutrow, B. and Norton, D (1995). Evolution <strong>of</strong> fluid pressure and fracture<br />
propagation during contact metamorphism. Journal <strong>of</strong> Metamorphic<br />
Geology 13: 677-686.<br />
Dziak, R.P.; Bohnenstiehl, D.R.; Cowen, J.P.; Baker, E.T.; Rubin, K.H.; Haxel,<br />
J.H.; Fowler, M.J. (2007). Rapid dike emplacement leads to eruptions and<br />
hydrothermal plume release during seafloor spreading events. Geology<br />
35: 579-582.<br />
Elek, P. and Jaramaz, S. (2002). Fragment size distribution in dynamic<br />
fragmentation: geometric probability approach. Faculty <strong>of</strong> Mechanical<br />
Engineering Transactions 36: 59-65.<br />
Englman, R.; Rivier, N.; Jaeger, Z. (1988). Size-distribution in sudden breakage<br />
by the use <strong>of</strong> entropy maximization. Journal <strong>of</strong> Applied Physics 63.9:<br />
4766-4768.<br />
Farris, D.W. and Paterson, S.R. (2007). Contamination <strong>of</strong> silicic magmas and<br />
fractal fragmentation <strong>of</strong> xenoliths in paleocene plutons on Kodiak Island,<br />
Alaska. The Canadian Mineralogist 45: 107-129.<br />
123
Fisher, R.V. (1960). Classification <strong>of</strong> volcanic breccias. Bulletin <strong>of</strong> the Geological<br />
Society <strong>of</strong> America 71: 973-82.<br />
Folch, A. and Marti, J. (1998). The generation <strong>of</strong> overpressure in felsic magma<br />
chambers by replenishment. Earth and Planetary Science Letters 163:<br />
301-314.<br />
Furlong, K.P.; Hanson, R.B.; Bowers, J.R. (1991). Modeling thermal regimes.<br />
Reviews in Mineralogy: Contact Metamorphism 26: 437-498.<br />
Gardner, J.; Hilton, M.; Carroll, M.R. (1999). Experimental constraints on<br />
degassing <strong>of</strong> magma: isothermal bubble growth during continuous<br />
decompression from high pressure. Earth and Planetary Science Letters<br />
30.1-2: 201-218.<br />
Genet, M.; Yan, W.; Tran-Cong, T. (2009). Investigation <strong>of</strong> a hydraulic impact: a<br />
technology in rock breaking. Archive <strong>of</strong> Applied Mechanics 79: 825-841.<br />
Gerbi, C.; Johnson, S.E.; Paterson, S.R. (2004). Implications <strong>of</strong> rapid, dike-fed<br />
pluton growth for host-rock strain rates and emplacement mechanis<strong>ms</strong>.<br />
Journal <strong>of</strong> Structural Geology 26: 583-594.<br />
Gernon, T.M.; Gilbertson, M.A.; Sparks, R.S.; Field, M. (2008). Gas-fluidization in<br />
an experimental tapered bed: insights into processes in diverging volcanic<br />
conduits. Journal <strong>of</strong> Volcanology and Geothermal Research 174; 49-56.<br />
Gilman, R.A., Chapman, C.A., Lowell, T.V., and Borns, Jr., H.W. (1988). The<br />
Geology <strong>of</strong> Mount Desert Island: Bull: 38, <strong>Maine</strong> Geol. Survey, 55pp.<br />
Glazner, A.F. and Bartley, J.M. (2006). Is stoping a volumetrically significant<br />
pluton emplacement process? Geological Society <strong>of</strong> America Bulletin 118:<br />
1185-1195.<br />
Glazner, A.F. and Bartley, J.M. (2008). Reply to comments on “Is stoping a<br />
volumetrically significant pluton emplacement process?”. Geological<br />
Society <strong>of</strong> America Bulletin 120: 1082-1087.<br />
Glazner, A.F.; Bartley, J.M.; Coleman, D.; Gray, W.; Taylor, R. (2004). Are<br />
plutons assembled over millions <strong>of</strong> years by amalgamation from small<br />
magma chambers? GSA Today 14.4-5: 4-11.<br />
Gonnerman, H.M. and Manga, M. (2007). The fluid mechanics inside a volcano.<br />
Annual Review <strong>of</strong> Fluid Mechanics 39: 321-356.<br />
124
Goodman, R.E. (1980). Introduction to Rock Mechanics. John Wiley and Sons,<br />
New York.<br />
Goto, A. and Taniguchi, H. (2001). Effects <strong>of</strong> explosion energy and depth to the<br />
formation <strong>of</strong> blast wave and crater: field explosion experiment for the<br />
understanding <strong>of</strong> volcanic explosion. Geophysical Research Letters 28.22:<br />
4287-4290.<br />
Gottsmann, J. and Battaglia, M. (2008). Deciphering causes <strong>of</strong> unrest at<br />
explosive collapse calderas: recent advances and future challenges <strong>of</strong><br />
joint time-lapse gravimetric and ground deformation studies.<br />
Developments in Volcanology 10: 417-446.<br />
Grady, D.E. and Kipp, M.E. (1987). Dynamic rock fragmentation. Fracture<br />
Mechanics <strong>of</strong> Rock. Kean, Barry ed. London, Academic Press, 429-475.<br />
Griffith, A.A. (1921). The phenomena <strong>of</strong> rupture and flow in solids. Philsophical<br />
transactions <strong>of</strong> the Royal Society <strong>of</strong> London, Series A, 221:163-198.<br />
Grocott, J.; Arevalo, C.; Welkner, D.; Cruden, A. (2009). Fault-assisted vertical<br />
pluton growth: coastal Cordillera, north Chilean Andes. Journal <strong>of</strong> the<br />
Geological Society, London 166: 295-310.<br />
Grosfils, E.B. (2007). Magma reservoir failure on the terrestrial planets:<br />
assessing the importance <strong>of</strong> gravitational loading in simple elastic models.<br />
Journal <strong>of</strong> Volcanology and Geothermal Research 166: 47-75.<br />
Gudmundsson, A.; Marinoni, L.B,; Marti, J. (1999). Injection <strong>of</strong> dykes:<br />
implications for volcanic hazards. Journal <strong>of</strong> Volcanology and Geothermal<br />
Research 88: 1-13.<br />
Hanson, R.B., and Barton, M.D. (1989) Thermal development <strong>of</strong> low-pressure<br />
metamorphic belts: Results from two-dimensional numerical models.<br />
Journal <strong>of</strong> Geophysical Research 94: 10,363–10,377.<br />
Harris, C. C (1966). On the role <strong>of</strong> energy in comminution: a review <strong>of</strong> physical<br />
and mathematical principles. Institution <strong>of</strong> Mining and Metallurgy:<br />
Transactions - Mineral Processing and Extractive Metallurgy 75: 37-56.<br />
Harris, C.C. (1968). Application <strong>of</strong> size distribution equations to multi-event<br />
comminution processes. Transactions <strong>of</strong> the Society <strong>of</strong> Petroleum<br />
Engineers <strong>of</strong> the American Institute <strong>of</strong> Mining, Metallurgical, and<br />
Petroleum Engineers, Incorporated 241: 343-358.<br />
Hart, S. (1964). The petrology and isotropic-mineral age relations <strong>of</strong> a contact<br />
zone in the front range, Colorado. The Journal <strong>of</strong> Geology 72.5: 493-525.<br />
125
Hartmann, W.K. (1969). Terrestrial, lunar, and interplanetary rock fragmentation.<br />
Icarus 10: 201-213.<br />
Hayashi, Y. and Morita, Y. (2003). An image <strong>of</strong> a magma intrusion process<br />
inferred from precise hypocentral migrations <strong>of</strong> the earthquake swarm east<br />
<strong>of</strong> the Izu Peninsula. Geophysics Journal International 153: 159-174.<br />
Hawkins, A.T. and Johnson, S.E. (2004). Apparent brecciation gradient, Mount<br />
Desert Island, <strong>Maine</strong>. American Geophysical Union, Spring meeting,<br />
abstract#V21A-03.<br />
Hedervari, P. (1963). On the energy and magnitude <strong>of</strong> volcanic eruptions.<br />
Bulletin Volcanologique: organe de la Section de Volcanologie de l’Union<br />
ge’ode’sique et pe’ophysique international 25.1: 373-385.<br />
Heffington, W.F. (1982). Volcanic Energy. Energy 7.8: 717-719.<br />
Higgins, M. D. (2000). Measurement <strong>of</strong> crystal size distributions. American<br />
MineralogistI 85: 1105-1116.<br />
Hodge, D.S.; Abbey, D.A.; Harbin, M.A.; Patterson, J.L.; Ring, M.J; Sweeney,<br />
J.F. (1982). Gravity studies <strong>of</strong> subsurface mass distributions <strong>of</strong> granitic<br />
rocks in <strong>Maine</strong> and New Hampshire. American Journal <strong>of</strong> Science 282:<br />
1289-1324.<br />
Hoek, E. and Brown, E.T. (1997). Practical estimates <strong>of</strong> rock mass strength.<br />
International Journal <strong>of</strong> Rock Mechanics and Mining Sciences 34.8: 1165-<br />
1186.<br />
Hogan, J.P. and Sinha, A.K. (1989). Compositional variation <strong>of</strong> plutonism in the<br />
coastal <strong>Maine</strong> magmatic province: mode <strong>of</strong> origin and tectonic setting, in<br />
Tucker, R.D., and Marvinney, R.G., eds., Studies <strong>of</strong> <strong>Maine</strong> geology,<br />
volume 4: Igneous and metamorphic geology. <strong>Maine</strong> Geological Survey,<br />
Department <strong>of</strong> Conservation, p. 1-33.<br />
Holland, T. J. B., & Powell, R. (1998) An internally consistent thermodynamic<br />
data set for phases <strong>of</strong> petrological interest. Journal <strong>of</strong> Metamorphic<br />
Geology 16:309-343.<br />
Huber, C.; Bachmann, O.; Manga, M. (2009). Homogenization processes in<br />
silicic magma chambers by stirring and mushification (latent heat<br />
buffering). Earth and Planetary Science Letters 283: 38-47.<br />
Ivanov, A.G.; Raevskii, V.A. Vorontsova, O.S. (1995). Explosive fragmentation <strong>of</strong><br />
Materials. Combustion, Explosion, and Shock Waves 31.2: 211-215.<br />
126
Jackson, M.D.; Cheadle, M.J.; Atherton, M.P. (2003). Quantitative modeling <strong>of</strong><br />
granitic melt generation and segregation in the continental crust. Journal<br />
<strong>of</strong> Geophysical Research 108.B7: 1-21.<br />
Jaeger, J.C. (1961). The cooling <strong>of</strong> irregularly shaped igneous bodies. American<br />
Journal <strong>of</strong> Science 259: 721-734.<br />
Jaeger, J.C. (1964). Thermal effects <strong>of</strong> intrusions. Reviews <strong>of</strong> Geophysics 2.3:<br />
443-465.<br />
Jebrak, M. (1997). Hydrothermal breccias in vein-type ore deposits: a review <strong>of</strong><br />
mechanis<strong>ms</strong>, morphology and size distribution. Ore geology Reviews 12:<br />
111-34.<br />
Jebrak, M. and Lalonde, M. (2005). The shape <strong>of</strong> fragments in dissolution<br />
processes: fractal analysis <strong>of</strong> virtual breccias.<br />
Jellinek, A. M. and DePaolo, D. (2003). A model for the origin <strong>of</strong> large silicic<br />
magma chambers: precursors <strong>of</strong> caldera-forming eruptions. Bulletin <strong>of</strong><br />
Volcanology 65: 363-381.<br />
Jiang, J. and Plotnick, R. (1998). Fractal analysis <strong>of</strong> the complexity <strong>of</strong> united<br />
States Coastlines. Mathematical Geology 30.5: 535-546.<br />
Johnson, J.W., and Norton, D. (1985) Theoretical prediction <strong>of</strong> hydrothermal<br />
conditions and chemical equilibria during skarn formation in porphyry<br />
copper syste<strong>ms</strong>. Economic Geology and the Bulletin <strong>of</strong> the Society <strong>of</strong><br />
Economic Geologists 80: 1797–1823.<br />
Johnson, S.E.; Albertz, M.; Paterson, S.R. (2001). Growth rates <strong>of</strong> dike-fed<br />
plutons: are they compatible with observations in the middle and upper<br />
crust? Geology 29: 727-730.<br />
Johnson, S.E.; Fletcher, J.M.; Fanning, C.M.; Vernon, R.H.; Paterson, S.R.; Tate,<br />
M.C. (2003). Structure, emplacement, and lateral expansion <strong>of</strong> the San<br />
Jose tonalite pluton, Peninsular Ranges batholith, Baja California, Mexico.<br />
Journal <strong>of</strong> Structural Geology25: 1933-1957.<br />
Johnson, S.E. and Jin, Z.-H. (2009). Magma extraction from the mantle wedge at<br />
convergent margins through dikes: a parametric sensitivity analysis.<br />
Geochemistry Geophysics Geosyste<strong>ms</strong> 10.8.<br />
Johnson, S.E.; Jin, Z.-H.; Naus-Thijssen, F.M.J.; Koons, P.O. (2011). Coupled<br />
deformation and metamorphism in the ro<strong>of</strong> <strong>of</strong> a tabular midcrustal igneous<br />
complex. Geological Society <strong>of</strong> America Bulletin 123: 1016-1032.<br />
127
Johnson, S.E.; Paterson, S.R.; Tate, M.C. (1999). Structure and emplacement<br />
history <strong>of</strong> a multiple-center, cone-sheet-bearing ring complex: the Zarza<br />
Intrusive Complex, Baja California, Mexico. Geological Society <strong>of</strong> America<br />
Bulletin 111.4: 607-619.<br />
Johnson, S.E.; Schmidt, K.L.; Tate, M.C. (2002). Ring complexes in the<br />
Peninsular Ranges batholith, Mexico and USA: magma plumbing syste<strong>ms</strong><br />
in the middle and upper crust. Lithos 61: 187-208.<br />
Johnson, S.E.; Vernon, R.H.; Upton, P. (2004). Foliation development and<br />
progressive strain-rate partitioning in the crystallizing carapace <strong>of</strong> a<br />
tonalite pluton: microstructural evidence and numerical modeling. Journal<br />
<strong>of</strong> Structural Geology 26: 1845-1865.<br />
Kawakami, Y.; Hoshi, H.; Yamaguchi, Y. (2007). Mechanism <strong>of</strong> caldera collapse<br />
and resurgence: observations from the northern part <strong>of</strong> the Kumano Acidic<br />
Rocks, Kii peninsula, southwest Japan. Journal <strong>of</strong> Volcanology and<br />
Geothermal Research 167: 263-281.<br />
Kemp, A.; Hawkesworth, C.; Paterson, B.; Foster, G.; Kinny, P.; Whitehouse, M.;<br />
Maas, R. (2008). Exploring the plutonic-volcanic link: a zircon U-Pb, Lu-Hf<br />
and O isotope study <strong>of</strong> paired volcanic and granitic units in southeastern<br />
Australia. Transactions <strong>of</strong> the Royal Society <strong>of</strong> Edinburgh 97: 337-355.<br />
Kerrick, D.M. (1991). Overview <strong>of</strong> contact metamorphism. Reviews in<br />
Mineralogy: Contact Metamorphism 26: 1-12.<br />
Klinkenberg, B. (1994). A review <strong>of</strong> methods used to determine the fractal<br />
dimensions <strong>of</strong> linear features. Mathematical Geology 26.1: 23-46.<br />
Klinkenberg, B., and Goodchild, M. F. (1992). The fractal properties <strong>of</strong><br />
topography: a comparison <strong>of</strong> methods. Earth Surface processes and<br />
Landfor<strong>ms</strong> 17: 217-34.<br />
Kriegsman, L.M. and Alvarez-Valero, A.M. (2010). Melt-producing versus meltconsuming<br />
reactions in pelitic xenoliths and migmatites. Lithos 116: 310-<br />
320.<br />
Kurszlaukis, S., Lorenz, V. (2006). Root zone and pipe growth processes in the<br />
phreatomagmatic process chain. Kimberlite Emplacement Workshop,<br />
Saskatoon, Saskatchewan.<br />
Labotka, T.C. (1991). Chemical and physical properties <strong>of</strong> fluids. Kerrick, D.M.<br />
and Ribbe, P.H., eds. Reviews in Mineralogy: Contact Metamorphism 26:<br />
43-97.<br />
128
Lama, R.D. and Vutukuri, V.S. (1978). Handbook on mechanical properties <strong>of</strong><br />
rocks: Testing techniques and results, volume 2. Series on Rock and Soil<br />
Mechanics 3.1, Trans Tech Publications, Clausthal, Germany.<br />
Laznicka, P. (1988). Breccias and Coarse Fragmentites: Petrology,<br />
Environments, Associations, Ores. Developments in Economic Geology<br />
25, Elsevier, New York.<br />
Legros, F. and Kelfoun, K. (2000). Sustained blasts during large volcanic<br />
eruptions. Geology 28.10: 895-898.<br />
Lipman, P.W. (1984). The roots <strong>of</strong> ash-flow calderas in western North America;<br />
windows into the tops <strong>of</strong> granitic batholiths. Journal <strong>of</strong> Geophysical<br />
Research 89: 8801– 8841.<br />
Lipman, P.W. (1997). Subsidence <strong>of</strong> ash-flow calderas: relation to caldera size<br />
and magma chamber geometry. Bulletin <strong>of</strong> Volcanology 59: 198-218.<br />
Lipman, P.W. (2007). Incremental assembly and prolonged consolidation <strong>of</strong><br />
Cordilleran magma chambers: evidence from the Southern Rocky<br />
Mountain volcanic field. Geosphere 3.1: 42-70.<br />
Lorenz, V. and Kurszlaukis, S. (2007). Root zone processes in the<br />
phreatomagmatic pipe emplacement model and consequences for the<br />
evolution <strong>of</strong> maar-diatreme volcanoes. Journal <strong>of</strong> Volcanology and<br />
Geothermal Research 159: 4-32.<br />
Lorilleux, G.; Jebrak, M.; Cuney, M.; Baudemont, D. (2002). Polyphase<br />
hydrothermal breccias associated with unconformity-related uranium<br />
mineralization (Canada): from fractal analysis to structural significance.<br />
Journal <strong>of</strong> Structural Geology 24: 323-338.<br />
Lyubetskaya, T. and Ague, J. (2009). Effect <strong>of</strong> metamorphic reactions on thermal<br />
evolution in collisional orogens. Journal <strong>of</strong> Metamorphic Geology 27: 579-<br />
600.<br />
Macias, J.L.; Arce, J.L.; Mora, J.C.; Espindola, J.M.; Saucedo, R. (2003). A 550<br />
year-old Plinian eruption at El Chichon Volcano, Chiapas, Mexico:<br />
explosive volcanism linked to reheating <strong>of</strong> the magma reservoir. Journal <strong>of</strong><br />
Geophysical Research 108.B12: 1-18.<br />
Mader, H.M.; Zhang, Y.; Phillips, J.C.; Sparks, R.S.J.; Sturtevant, B.; Stopler, E.<br />
(1994). Experimental simulations <strong>of</strong> explosive degassing <strong>of</strong> magma.<br />
Nature 372.3: 85-88.<br />
129
Mandelbrot, B.B. (1967). How long is the coast <strong>of</strong> Britain? Statistical selfsimilarity<br />
and fractional dimension. Science 156.3775: 636-38.<br />
Mandelbrot, B.B. (1983). The Fractal Geometry <strong>of</strong> Nature. W.H. Freeman and<br />
Co., New York.<br />
Manea, V. C.; Manea , M.; Kostoglodov, V.; Sewell, G. S. (2005). Thermomechanical<br />
model <strong>of</strong> the mantle wedge in the central Mexican subduction<br />
zone and a blob tracing approach for magma transport, Physics <strong>of</strong> the<br />
Earth and Planetary Interiors 149: 165–186,<br />
doi:10.1016/j.pepi.2004.08.024.<br />
Manson, S.S. (1953). Behavior <strong>of</strong> materials under conditions <strong>of</strong> thermal stress.<br />
NACA technical note 2933.<br />
Marko, W.; Barnes, W.; Vietti, L.; McCulloch, L.; Anderson, H.; Barnes, C.;<br />
Yoshinobu, A. (2005). Xenolith incorporation, distribution, and<br />
dissemination in a mid-crustal granodiorite, Vega pluton, central Norway.<br />
American Geophysical Union, Fall Meeting 2005 abstract #V13E-0596.<br />
Marianelli, P.; Sbrana, A.; Proto, M. (2006). Magma chamber <strong>of</strong> the Campi<br />
Flegrei supervolcano at the time <strong>of</strong> eruption <strong>of</strong> the Campanian Ignimbrite.<br />
Geology 34: 937-940.<br />
Marone, C. and Scholz, C.H. (1989). Particle-size distribution and<br />
microstructures within simulated fault gouge. Journal <strong>of</strong> Structural Geology<br />
11.7: 799-814.<br />
McCaffrey, K. and Johnston, J.D. (1996). Fractal analysis <strong>of</strong> a mineralized vein<br />
deposit; Curraghinatt gold deposit, County Tyrone. Mineralium Deposita<br />
31: 52-58.<br />
McLeod, P. and Tait, S. (1999). The growth <strong>of</strong> dykes from magma chambers.<br />
Journal <strong>of</strong> Volcanology and Geothermal Research 92: 231-245.<br />
Metcalf, R.V. (2004). Volcanic-plutonic links, plutons as magma chambers and<br />
crust-mantle interaction: a lithospheric scale view <strong>of</strong> magma syste<strong>ms</strong>.<br />
Transactions <strong>of</strong> the Royal Society <strong>of</strong> Edinburgh: Earth Sciences 95: 357-<br />
374.<br />
Metzger, W.J. (1959). Petrography <strong>of</strong> the Bar Harbor series, Mount Desert<br />
Island, <strong>Maine</strong>. Masters <strong>thesis</strong>.<br />
Metzger, W.J. (1979). Stratigraphy and geology <strong>of</strong> the Bar Harbor Formation,<br />
Frenchman Bay, <strong>Maine</strong>. Shorter Contributions to the Geology <strong>of</strong> <strong>Maine</strong>,<br />
<strong>Maine</strong> Geological Bulletin 1: 1-17.<br />
130
Metzger, W.J. and Bickford, M.E. (1972). Rb-Sr chronology and stratigraphic<br />
relations <strong>of</strong> Silurian rocks, Mt. Desert Island, <strong>Maine</strong>. Geological Society <strong>of</strong><br />
America Bulletin 83: 497-504.<br />
Michel, J.; Baumgartner, L.; Pulitz, B.; Schaltegger, U.; Ovtcharova, M. (2008).<br />
Incremental growth <strong>of</strong> the Patagonian Torres del Paine laccolith over<br />
90k.y. Geology 36.6: 459-462.<br />
Miller, J.S. (2008). Assembling a pluton…one increment at a time. Geology 36.6:<br />
511-512.<br />
Milord, I.; Sawyer, E.W.; Brown, M. (2001). Formation <strong>of</strong> diatexite migmatites and<br />
granite magma during anatexis <strong>of</strong> semi-pelitic metasedimentary rocks; an<br />
example from St. Malo, France. Journal <strong>of</strong> Petrology 42.3: 487-505.<br />
Nagahama, H. and Yoshii, K. (1993). Fractal dimension and fracture <strong>of</strong> brittle<br />
rocks. International Journal <strong>of</strong> Rock Mechanics and Mining Science &<br />
Geomechanics Abstracts 30.2: 173-175.<br />
Nekvasil, H. (1988). Calculation <strong>of</strong> equilibrium crystallization paths <strong>of</strong><br />
compositionally simple hydrous felsic melts. American Mineralogist 73:<br />
956-965.<br />
Nichols, G.T. and Wiebe, R.A. (1998). Desilication veins in the Cadillac Mountain<br />
Granite (<strong>Maine</strong>, USA): a record <strong>of</strong> reversals in the SiO 2 solubility <strong>of</strong> H 2 O-<br />
rich vapour released during subsolidus cooling. Journal <strong>of</strong> Metamorphic<br />
Geology 16: 795-808.<br />
Nikolaevskiy, V.N.; Kapustyanskiy, S.M.; Thiercelin, M. and Zhilenkov, A.G.<br />
(2006). Explosion dynamics in saturated rocks and solids. Transport in<br />
Porous Media 65: 485-504.<br />
Norton, D. and Knight, J. (1977). Transport phenomena in hydrothermal syste<strong>ms</strong>:<br />
cooling plutons. American Journal <strong>of</strong> Science 277: 937-981.<br />
Norton, D., and Taylor, H.P. (1979). Quantitative simulations <strong>of</strong> the hydrothermal<br />
syste<strong>ms</strong> <strong>of</strong> crystallizing magmas on the basis <strong>of</strong> transport theory and<br />
oxygen isotope data: An analysis <strong>of</strong> the Skaergaard intrusion. Journal <strong>of</strong><br />
Petrology 20: 421–486.<br />
Okaya, D.A.; Paterson, S.R., Pignotta, G.S. (in press) Physical behavior <strong>of</strong><br />
stoped blocks in magma chambers. Geosphere.<br />
131
Oliver, N.H.S.; Rubenach, M.J.; Fu, B.; Baker, T.; Blenkinsop, T.G.; Cleverly,<br />
J.S.; Marshall, L.J. and Ridd, P.J. (2006). Granite-related overpressure<br />
and volatile release in the mid crust: fluidized breccias from the Cloncurry<br />
District, Australia. Ge<strong>of</strong>luids 6: 346-358.<br />
Parmentier, E.M., and Schedl, A. (1981). Thermal aureoles <strong>of</strong> igneous intrusions:<br />
Some possible implications <strong>of</strong> hydrothermal convective cooling. The<br />
Journal <strong>of</strong> Geology: 89 1–22.<br />
Paterson, S.R. and Farris, D.W. (2008). Downward host rock transport nd the<br />
formation <strong>of</strong> rim monoclines during the emplacement <strong>of</strong> Cordilleran<br />
batholiths. Transactions <strong>of</strong> the Royal Society <strong>of</strong> Edinburgh; Earth Sciences<br />
97: 397-413.<br />
Paterson, S.R. and Fowler, T. (1993). Re-examining pluton emplacement<br />
processes. Journal <strong>of</strong> Structural Geology 15.2: 191-206.<br />
Pattison, D. and Harte, B. (1988). Evolution <strong>of</strong> structurally contrasting anatectic<br />
migmatites in the 3-kbar Ballachulish aureole, Scotland. Journal <strong>of</strong><br />
Metamorphic Geology 6: 475-494.<br />
Perfect, E. (1997). Fractal models for the fragmentation <strong>of</strong> rocks and soils: a<br />
review. Engineering Geology 48: 185-198.<br />
Petcovic, H. and Dufek, J. (2005). Modeling magma flow and cooling in dikes:<br />
implications for emplacement <strong>of</strong> Columbia River flood basalts. Journal <strong>of</strong><br />
Geophysical Research 110: B10201, doi:10.1029/2004JB003432<br />
Petford, N.; Cruden, A.R.; McCaffrey, K.J.W.; Vigneresse, J.-L. (2000). Granite<br />
magma formation, transport, and emplacement in the Earth’s crust. Nature<br />
408: 669-673.<br />
Pignotta, G.S., Paterson, S.R.; Coyne, C.C.; Anderson, J.L. (2010). Processes<br />
involved during incremental growth <strong>of</strong> the Jackass Lakes pluton, central<br />
Sierra Nevada batholith. Geosphere 6.2: 130-159.<br />
Pinel, V. and Jaupart, C. (2004). Magma storage and horizontal dyke injection<br />
beneath a volcanic edifice. Earth and Planetary Science Letters 221: 245-<br />
262.<br />
Rubin, A.M. (1995a). Getting granite dikes out <strong>of</strong> the source region. Journal <strong>of</strong><br />
Geophysical Research 100.B4: 5911-5929.<br />
Rubin, A.M. (1995b). Propagation <strong>of</strong> magma-filled cracks. Annual Review <strong>of</strong><br />
Earth and Planetary Sciences 23:287-336.<br />
132
Rutherford, M.J. and Devine, J. (1991). Pre-eruption conditions and volatiles in<br />
the 1991 Pinatubo magma. EOS, Transactions-American Geophysical<br />
Union 72: 62.<br />
Saito, S.; Arima, M.; Nakajima, T. (2007). Hybridization <strong>of</strong> a shallow ‘I-Type’<br />
granitoid pluton and its host migmatites by magma-chamber wall collapse:<br />
the Tokuwa Pluton, Central Japan. Journal <strong>of</strong> Petrology 48.1: 79-111.<br />
Sammis, C.G. and Biegel, R.L. (1987). Fractals, fault-gouge, and friction. Pure<br />
and Applied geophysics 131: 255-271.<br />
Sammis, C.G.; King, G.; Biegel, R. (1987). The kinematics <strong>of</strong> gouge deformation.<br />
Pure and Applied Geophysics 125.5: 777-812.<br />
Sammis, C. G.; Osborne, R. H.; Anderson, J.L.; Banerdt, M.; White, P. (1986).<br />
Self-similar cataclasis in the formation <strong>of</strong> fault gouge. Pure and Applied<br />
Geophysics 124.1/2: 53-78.<br />
Sanchidrian, J.A.; Segarra, P. and Lopez, L.M. (2007). Energy components in<br />
rock blasting. International Journal <strong>of</strong> Rock Mechanics and Mining<br />
Sciences 44: 130-147.<br />
Saotome, A.; Yoshinaka, R.; Osada, M.; Sugiyama, H. (2002). Constituent<br />
material properties and clast-size distribution <strong>of</strong> volcanic breccias.<br />
Engineering Geology 64: 1-17.<br />
Scandone, R. (1996). Factors controlling the temporal evolution <strong>of</strong> explosive<br />
eruptions. Journal <strong>of</strong> Volcanology and Geothermal Research 72: 71-83.<br />
Scandone, R.; Cashman, K.V.; Malone, S.D. (2007). Magma supply, magma<br />
ascent and the style <strong>of</strong> volcanic eruptions. Earth and Planetary Science<br />
Letters 253: 513-529.<br />
Scandone, R. and Giacomelli, L. (2001). The slow boiling <strong>of</strong> magma chambers<br />
and the dynamics <strong>of</strong> explosive eruptions. Journal <strong>of</strong> Volcanology and<br />
Geothermal Research 110.1-2: 121-136.<br />
Scandura, Danila; Currenti, Gilda; Del Negro, Ciro (2007). 3D finite element<br />
models <strong>of</strong> ground deformation and stress field in viscoelastic medium.<br />
Proceedings from the COMSOL Users Conference, Grenoble.<br />
Scandura, D.; Currenti, G.; Del Negro, C. (2008). Finite element models <strong>of</strong><br />
elasto-plastic deformation in volcanic areas. Proceedings <strong>of</strong> the COMSOL<br />
Conference, Hannover.<br />
133
Schoutens, J.E. (1979). Empirical Analysis <strong>of</strong> Nuclear and High-Explosive<br />
Cratering and Ejecta. Nuclear Geoplosics Sourcebook 55.2, section 4:<br />
Defense Nuclear Agency, Bethesda, Maryland.<br />
Seaman, S.J.; Scherer, E.E.; Wobus, R.A.; Zimmer, J.H.; Sales, J.G. (1999).<br />
Late Silurian volcanism in coastal <strong>Maine</strong>: the Cranberry Island series.<br />
Geological Society <strong>of</strong> maine Bulletin 111: 686-708.<br />
Seaman, S.J.; Wobus, R.A.; Wiebe, R.A.; Lubick, N.; Bowring, S.A. (1995).<br />
Volcanic expression <strong>of</strong> bimodal magmatism: the Cranberry Island-Cadillac<br />
Mountain complex, coastal <strong>Maine</strong>. The Journal <strong>of</strong> Geology 103.3: 301-<br />
311.<br />
Shemeta, J.E. and Weaver, C.S. (1986). Seismicity accompanying the May 18,<br />
1980 eruption <strong>of</strong> Mount St. Helens, Washington. In: S.A.C. Keller, ed. Mt.<br />
St. Helens: Five Years Later. Eastern Washington <strong>University</strong> Press,<br />
Cheney, WA: 44-58.<br />
Shimamoto, T. and Nagahama, H. (1992). An argument against the crush origin<br />
<strong>of</strong> pseudotachylytes based on the analysis <strong>of</strong> clast-size distribution.<br />
Journal <strong>of</strong> Structural Geology 14.8/9: 999-1006.<br />
Shimozuru, D. (1968). Discussion on the energy partition <strong>of</strong> volcanic eruption.<br />
Bulletin volcanologique: organe de la section de volcanologie de l’union<br />
ge’ode’sique et ge’ophysique international 32.2: 383-394.<br />
Spear, F.S.; Kohn, M.J.; Cheney, John T. (1999). P-T paths from anatectic<br />
pelites. Contributions to Mineral Petrology 134:17-32.<br />
Spieler, O.; Alidibirov, M.; Dingwell, D. (2003). Grain-size characteristics <strong>of</strong><br />
experimental pyroclasts <strong>of</strong> 1980 Mount Saint Helens cryptodome dacite:<br />
effects <strong>of</strong> pressure drop and temperature. Bulletin <strong>of</strong> Volcanology 65: 90-<br />
104.<br />
Stuwe, K. (2002). Geodynamics <strong>of</strong> the Lithosphere. An Introduction. Springer-<br />
Verlag, New York.<br />
Sudhakar, J.; Adhikari, G. R. and Gupta, R. N. (2006). Comparison <strong>of</strong><br />
fragmentation measurements by photographic and image analysis<br />
techniques. Rock mechanics and Rock Engineering 39.2: 159-68.<br />
Sweeney, J.F. (1976). Subsurface distribution <strong>of</strong> granitic rocks, south-central<br />
<strong>Maine</strong>. Geological Society <strong>of</strong> America Bulletin 87: 241-249.<br />
134
Takashi, S.; Hideki, S.; Takayuki, S.; Masatomo, I.; Kikuo, M. (2008). Study on<br />
control <strong>of</strong> rock fragmentation at limestone quarry. Journal <strong>of</strong> Coal Science<br />
and Engineering. 14.3: 365-368.<br />
Tanner, B.; Perfect, E.; Kelley, J. (2006). Fractal analysis <strong>of</strong> <strong>Maine</strong>’s glaciated<br />
shoreline tests established coastal classification scheme. Journal <strong>of</strong><br />
Coastal Research 22.5: 1300-1304.<br />
Tsutsumi, A. (1999). Size distribution <strong>of</strong> clasts in experimentally produced<br />
pseudotachylytes. Journal <strong>of</strong> Structural Geology 21: 305-312.<br />
Turcotte, D.L. (1986). Fractals and Fragmentation. Journal <strong>of</strong> Geophysical<br />
Research 91.B2: 1921-1926.<br />
Turcotte, D.L. and Schubert, G. (1982). Geodynamics: Applications <strong>of</strong> Continuum<br />
Physics to Geological Proble<strong>ms</strong>. John Wiley and Sons, inc, New York.<br />
Twiss, R.J. and Moores, E.M. (2007). Structural Geology. W.H. Freeman Co.,<br />
New York, 2 nd edition.<br />
Urtson, K. (2005). Melt segregation and accumulation: an analogue and<br />
numerical modeling approach. M.Sc. Thesis.<br />
Wadge, G. (1981). The variation <strong>of</strong> magma discharge during basaltic eruptions.<br />
Journal <strong>of</strong> Volcanology and Geothermal Research 11: 139-168.<br />
Walker, B.A.; Miller, C.F.; Claiborne, L. Lowery; Wooden, J.L.; Miller, J.S. (2007).<br />
Geology and geochronology <strong>of</strong> the Spirit Mountain batholiths, southern<br />
Nevada: implications for timescales and physical processes <strong>of</strong> batholiths<br />
construction. Journal <strong>of</strong> Volcanology and Geothermal Research 167: 239-<br />
262.<br />
Walther, J.V. (1990) Fluid dynamics during progressive regional metamorphism,<br />
in Bredehoeft, J.D., and Norton, D.L., eds., The Role <strong>of</strong> Fluids in Crustal<br />
Processes. Washington, D.C., National Academy Press, p. 64–71.<br />
Weinberg, R.F. and Podladchikov, Y. (1994). Diapiric ascent <strong>of</strong> magmas through<br />
power law crust and mantle. Journal <strong>of</strong> Geophisical Research 99.B5:<br />
9543-9559.<br />
Wiebe, R. (1993). The Pleasant Bay layered gabbro-diorite, coastal <strong>Maine</strong>:<br />
ponding and crystallization <strong>of</strong> basaltic injections into a silicic magma<br />
chamber. JOurnal <strong>of</strong> Petrology 34: 461-489.<br />
135
Wiebe, R.; Holden, J.; Coombs, M.; Wobus, R.; Schuh, K.; Plummer, B. (1997a).<br />
The Cadillac Mountain intrusive complex, <strong>Maine</strong>: The role <strong>of</strong> shallow-level<br />
magma chamber processes in the generation <strong>of</strong> A-type granites. In: Sinha,<br />
A.K.; Whalen, J.B.; and Hogan, J.P.; eds. The nature <strong>of</strong> Magmatism in the<br />
Appalachian Orogen: Boulder, Colorado, Geological Society <strong>of</strong> America<br />
Memoir 191.<br />
Wiebe, R.; Smith, D.; Sturm, M; King, E.M.; Seckler, M.S. (1997b) Enclaves in<br />
the Cadillac Mountain Granite (coastal <strong>Maine</strong>): samples <strong>of</strong> hybrid magma<br />
from the base <strong>of</strong> the chamber. Journal <strong>of</strong> Petrology 38.3: 393-423.<br />
Wiebe, R.; Manon, M.; Hawkins, D.; McDonough (2004). Late-stage mafic<br />
injection and thermal rejuvenation <strong>of</strong> the Vinalhaven Granite, coastal<br />
<strong>Maine</strong>. Journal <strong>of</strong> Petrology 45.11: 2133-2153.<br />
Wilson, L.T.; Reedal, D.R.; Kuhns, L.D.; Grady, D.E.; Kipp, M.E. (2001). Using a<br />
numerical fragmentation model to understand the fracture and<br />
fragmentation <strong>of</strong> naturally fragmenting munitions <strong>of</strong> differing materials and<br />
geometries. 19 th International symposium <strong>of</strong> ballistics, Interlaken, Sweden.<br />
Wohletz, K.H. (1986). Explosive magma-water interactions: thermodynamics,<br />
explosion mechanis<strong>ms</strong>, and field studies. Bulletin <strong>of</strong> Volcanology 48: 245-<br />
264.<br />
Xiaohua, Z.; Yunlong, C.; Xiuchun, Y. (2004). On the fractal dimensions <strong>of</strong><br />
China’s coastlines. Mathematical Geology 36.4: 447-461.<br />
Yoshinobu, A.S. and Barnes, C.G. (2008). Is stoping a volumetrically significant<br />
pluton emplacement process?: Discussion. Geological Society <strong>of</strong> America<br />
Bulletin 120: 1080-1081.<br />
Zhang, L.; Jin, X.; He, H. (1999). Prediction <strong>of</strong> fragment number and size<br />
distribution in dynamic fracture. Journal <strong>of</strong> Physics D: Applied Physics 32:<br />
612-615.<br />
Zi-long, Z.; Xi-bing, L.; Yu-jun, Z.; Liang, H. (2006). Fractal characteristics <strong>of</strong> rock<br />
fragmentation at strain rate <strong>of</strong> 10 0 – 10 2 s -1 . Journal <strong>of</strong> Central South<br />
<strong>University</strong> <strong>of</strong> Technology 13.3: 290-294.<br />
136
BIOGRAPHY OF THE AUTHOR<br />
Samuel Ge<strong>of</strong>frey Roy was born in Waterville, <strong>Maine</strong> on September 9, 1985. He<br />
was raised in Oakland, <strong>Maine</strong> and graduated from Messalonskee High School in 2004.<br />
He attended the <strong>University</strong> <strong>of</strong> <strong>Maine</strong> and graduated in 2008 with a Bachelor’s degree in<br />
Earth Sciences. After an internship at the Stillwater Mining Company in Nye, Montana,<br />
and a semester <strong>of</strong> graduate courses at Southern Illinois <strong>University</strong>, Carbondale, Samuel<br />
returned to the <strong>University</strong> <strong>of</strong> <strong>Maine</strong> in 2009 and entered the Earth Sciences graduate<br />
program. Samuel is a candidate for the Master <strong>of</strong> Science degree in Earth Sciences<br />
from the <strong>University</strong> <strong>of</strong> <strong>Maine</strong> in May, 2011.<br />
137