Mechanics of Lithospheric Deformation - USC Geodynamics

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GEOL534: Mechanics of Lithospheric Deformation
Course organiser: Profs. J. P. Platt and T. W. Becker
Assessment: Final written exam 40%; Lab exercises 40%;
Class participation 20%
Dates: Fall semester, 2009.
Summary. This is an introductory course on the mechanical aspects of lithospheric deformation
and mantle dynamics. It is intended as a core course for graduate students in geology and geophysics
in the context of the PhD program in Earth Sciences. Students will learn basic procedures for the
mechanical description of deformational processes at both lithospheric and mantle scales, and how
to interpret geological and geophysical data in terms of these processes. The course aims to
stimulate understanding of the application of physical and mechanical principles to the dynamics of
the Earth’s lithosphere and mantle system. It begins with a review of the history and principles of
plate tectonics, and the mechanical framework in which tectonic processes can be understood. It
continues with discussion of the elastic behaviour of the lithosphere, its thermal structure, the forces
that drive plate tectonics, and mantle convection. Tectonic processes related to different types of
plate interaction are then analysed in terms of seismicity, geodetically defined deformation fields,
and a range of different approaches to mechanical analysis, including thin-viscous-sheet theory,
block tectonics, critical wedge theory, and fluid mechanics.
For geodynamics students, GEOL534 serves as an introductory class to Numerical Geodynamics
(GEOL540) and Deep Earth Seminar (last taught as GEOL599).
Course Requirements and Grades. Assessment will be based on a final written examination (take
home, open book) (40%), laboratory assignments (40%), and class participation (20%).
Week 1, Aug 24 – 28. JPP & TWB
Plate tectonics. Review of mechanical and geometrical concepts. Determination of relative plate
motions from seismicity, magnetic anomalies and palaeomagnetism. Geometrical analysis of plate
motions. Driving forces of plate tectonics.
Lab exercise: Kinematic analysis of plate-boundary evolution. Triple junction analysis.
Determination of Euler poles and relative velocity vectors.
Week 2, Aug 31 – Sept 4. TWB
Basic mechanical concepts: stress, strain, strain-rate. Plane strain, plane stress. Simple and pure
shear. State of stress in crust and lithosphere.
Lab exercise: Calculation of forces and stress in the lithosphere.
Week 3, Sept 7 – 11. TWB, JPP
Rheology. Elastic, brittle, plastic, and viscous deformation. Rheological elements (Maxwell,
Kelvin-Voigt, SLS). Non-dimensional numbers to quantify material behavior. Microscopic

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deformation mechanisms: Elasticity, diffusion creep, dislocation creep. Byerlee's “law”.
Deformation maps. Strength profiles in crust and lithosphere.
Lab exercise: Rheology of the upper mantle.
Week 4, Sept 14 – 18. No meeting: SCEC.
Week 5, Sept 21 - 25. JPP
Displacement gradients, rotation, and strain. Velocity gradients, vorticity, and strain-rate. Direct
measurement of the velocity field using GPS. Determination of fault slip vectors from seismic focal
mechanisms. Seismic moment. Determination of strain-rates from the seismic moment tensor and
from fault slip-vector data.
Lab exercise: Determination of rates of strain and rotation from geodetic data.
Week 6, Sept 28 – Oct 2. JPP
Buckling and flexure of an elastic plate. Concept of effective elastic thickness of lithosphere. Flexural
moat and peripheral bulge around seamounts. Flexural origin of deep-sea trenches. Flexural
(foreland) basins in front of thrust belts.
Lab exercise: Determination of effective elastic thickness from surface topography and gravity data.
Week 7, Oct 5 – 9. TWB
Thermal structure of the lithosphere. Heat flow, steady state geotherms. Time-variable conductive
solutions. Half-space cooling and thermal subsidence of oceanic lithosphere: relationship between
bathymetry and heat flow. Definition of lithosphere in terms of mechanical and thermal boundary
layers.
Lab exercise: Calculation of plate driving forces
Week 8, Oct 12 – 16. TWB
Fluid dynamics, channel flow and Stokes problem. Thermal convection. Boundary layer theory.
Linear stability analysis. Numerical solutions of the thermal convection equation.
Reading: Rayleigh Tayleigh instability.
Week 9, Oct 19 - 23. TWB
Thermal state of the Earth. Adiabatic gradient. Global heat budgets. Oceanic plate tectonics.
Structure of oceanic and continental crust and lithosphere. Ridges: active and passive spreading,
melting extent and geometry, axial highs and axial lows. Transform fault boundaries: segmentation,
leaky transformss (flower structures, pull-apart basins), micro-plates. Subduction zones: seismicity,
slab structure. Plumes and hotspots.

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Lab exercise: Gravitational potential energy of a mid-ocean ridge.
Week 10, Oct 26 – 30. JPP
Velocity distribution around continental transforms: thin viscous sheet versus elastic dislocation
models. Continental transform faults. Block models, and the role of vertical axis rotations.
Lab exercise: Analysis of the velocity field across the San Andreas fault zone
Week 11, Nov 2 – 6. TWB
Transient deformation along transform faults. Large scale time-dependent deformation, post-glacial
adjustment, uplift, geoid. Constraints on the viscosity of upper crust, lower crust and lithosphere.
Discussion session: Creme Brulee vs. Jelly Sandwich views of the lithosphere
Week 12, Nov 9 – 13. JPP
Continental extension. McKenzie model for extensional basins, predicted thermal structure and
subsidence history. Implications and tests of more complicated models of crustal and lithospheric
extension.
Lab exercise: Backstripping exercise to determine thermal subsidence history.
Week 13, Nov 16 - 20. JPP
Mechanical descriptions of continental collision: indentation/extrusion models, thin-sheet models.
Behaviour of sub-continental mantle in collision zones. Plateau uplift and late-orogenic extension.
Lab exercise: The role of gravitational potential energy in lithospheric deformation.
No sessions Week 14, Nov 23 – 27.
Week 15, Nov 30 – Dec 4. JPP
Mechanics of accretionary wedges and thin-skinned fold-and-thrust belts. Interpretation of structural
geometry in terms of mechanical processes.
Lab exercise: Analysis of cross-sections and seismic profiles across thrust belts and accretionary
wedges.
Final Examination:
To be arranged