August 28, 2006
Syllabus: GG
5210& 6211: Seismology I
Instructor: Robert B. Smith 3 semester hours credit
Prerq: Differential equations,
partial differential equations, linear algebra, vector analysis, and
programming experience or equivalent
Objectives: This course is designed to teach the
principles of Earth deformation and
wave propagation in elastic and inelastic continua. The course will provide a basic
understanding of continuum mechanics applied to rock deformation and of
boundary value problems, followed the development of the elastic wave theory
and properties of wave propagation. Tensor and vector operators, partial
differential equations, and linear algebra will be routinely used in
mathematical developments.
The
topics will be used to examine Earth processes such as earthquakes and
faulting, plastic flow, Earth structure, etc.
Computer
applications and practical problems in geophysics and tectonophysics will
be emphasized. Students should
have a command of UNIX/Linux for use of Matlab or Maple on the SUN workstations
or on a PC or Mac.
Outline:
I. Introduction
Concept
of a continuum,
Vectors
and tensors and their transformations,
II. Stress
Stress
tensor representations,
Principal
stresses and principal stress axes,
Stress
representation and eigenvalue problems,
Stress
measurements and state of stress in the Earth,
III. Shear
Failure in Earth Material's
Coulomb
and Coulomb-Navier failure criteria,
Griffith's
theory of fracture.
IV. Finite
and Infinitesimal Strain
Green's
and Cauchy's finite deformation tensors,
Measurements
of finite strain--geodetic and macroscopic rock deformation,
V. Constitutive
Laws (stress-strain Relationships)
Constitutive
equations and 4th rank tensors,
Compliance/stiffness
matrices,
Elastic
modulii,
Helmholz's theorem of
elasticity,
VI. Strain
Measurements
Examples
of micro- and macro-scale earth deformation.
Global
Positioning Systems (GPS)
Strain
field of the Earth
Fault
and volcano strain fields
Stress
field inversion.
VII. Viscosity and
Creep
Strain
rate tensors,
Navier-Stokes
equation.
Plasticity
and yield criteria,
Viscoelastic
deformation and other non-linear deformation mechanisms
Rheological
models,
VIII. Equilibrium Conditions
Equations
of motion,
Compatibility
equations and biharmonic equations,
Examples
of stress solutions by biharmonic equations.
IX.
Geodynamics
Kinematics
and dynamics of plates
Models
of Earth deformation
Introduction
to boundary element methods of modeling
X.
Elastic
Wave Theory
Dynamic
wave equations and Body wave propagation.
Method
of potentials for solution of wave equations,
Solutions
of wave equations in various coordinates
Boundary
condition solutions of wave equations
XI. Wave
Transmission
Geometrical
spreading
Anelastic
attenuation and Q-1.
XII. Refraction and
Reflection Of Elastic Waves
Solution
of wave equations by potentials,
Energy
partition at a boundary,
Zoeppritz's
equations.
XIII. Geometric Ray Theory
Fermat's
principal and generalized Snell's law,
Eikonal
equations
Ray
tracing--parametric equations for traveltimes and amplitudes.
General
Earth velocity models, PREM, from refraction measurements
Crust
mantle structure
Tectonic
implications of seismic models
Books:
Smith, R. B., 2004,
Introduction to tectonophysics and
elastic waves, notes available on class web site: http://www.mines.utah.edu/~rbsmith/TEACHING/GG525/gg525.html
A disc of my notes will be made available
Stein, S., and M.
Wysession, 2002, Introduction To Seismology, Earthquakes, and Earth Structure,
available in October, 2002.
Turcotte, D.L. and G.
Schubert, 2002, Geodynamics, J. Wiley and Sons, 2nd edition.
Additional references
available in the Marriott Library reserve section or in instructors office.
Fung, Y.C., 1977, A
First Course In Continuum Mechanics, Prentice Hall, Inc. -- the standard
continuum mechanics text.
Malvern, L., 1969,
Introduction to mechanics of a continuous medium, Prentice-Hall,713 pp.
Ranalli, G., 1995,
Rheology of the Earth, Chapman and Hall, 2nd Edition.
Sheriff, R.E. and
L.P. Geldart, 1982, Exploration Seismology, Volume 1, History, theory, and data acquisition, Cambridge
University Press -- a good and simple review of wave transmission and
traveltime equations
Sneider, R.
A., 2001, A. Guided Tour of Mathematical Physics, Cambridge Univ. Press, pp:
421, ISBN 0-521-78751-3
Timoshenko. S. P., and
J. M. Gere, 1997, Mechanics of materials, PWS Publishing Co., 912 pp.
Twiss R.J. and E.M.
Moores, 1992, Structural Geology, W.H. Freeman and Co. -- this book has new
approaches to numerical calculations in stress and strain.
Wallace, T. C. and T.
Lay, 1995, Modern global seismology, Academic Press.
Backus, G, Continuum Mechanics
Kennett, B., Continuum Mechanics
Sharipov, R., 2004, A Quick
Introduction to Tensor Analysis,
Computing: Use of Matlab (or Maple, which is not
supported by us) and related programs on the college SUN workstations and on
Macs and PCs as available.
Accounts on the college SUN workstations will be available (required)
for the class. For those who do
not have a UNIX background, a UNIX Tutorial program (Windows environment) is
available to get you started. This
program is located on the SUN workstations served by the college SUN server.
Reading: Reading in
professional papers with written abstracts and classroom discussions will be assigned.
Term
Project and Final Exam: A term project will be developed by students in groups of
two that demonstrates the methodologies and principles of the course. The projects will be done in pairs of
graduate and undergraduate students where possible. The project may take the
place of the final exam depending on class progress.
Expectations: 2 hours of study and homework for each
hour of lecture.
Grading:
One mid term exams 30%
Homework,
reading, computer problems 30%
Term
project 20%
Final 20%
Total 100%
Teaching
Assistants:
Wu-Lung Chang
Jamie Farrell
Christine Puskas