|
Mathematics
in Geosciences, September 2001 - June 2002
Winter
2002
IMA Lectures:
Ray
Theory for the Elastic Wave Equation
Robert Burridge
Earth Resources
Laboratory
Massachusetts Institute of Technology (MIT)
burridge@erl.mit.edu
Slides:
pdf
3
1-hour lectures, March 4-6, 2002
All
lectures start at 11:15am in Lind 409
Syllabus
Introduction.
Ray theory for the scalar wave equation and scalar Helmholtz
equation
- The ray theory ansatz, amplitude and phase, slowness and
travel time
- The eikonal equation
- The transport equation(s)
- The ray-tube-area method to obtain the amplitudes
- Caustics
Dynamic ray theory
- The second derivatives of the phase function
- The first variation of the ray equations
- The transverse components of the Hessian of the phase
- The dynamic ray equation and the simultaneous solution of
the ray and dynamic ray equations
- The solution of the transport equation using the results
of dynamic ray theory
The elastic wave equation
- Isotropy
- Isotropy: P and S waves
- The transport of the S polarization
- Anisotropic ray theory
Ray theory for a symmetric hyperbolic system
- Group velocity: various properties
The aim for the course is to be self contained at the expense
of being formal. For instance, methods of calculating coefficients
in an asymptotic series will be treated without proving that
the series is indeed asymptotic.
Prerequisites: The material
will be strictly classical. The audience is expected to be familiar
with the solution of first order PDE's by the method of characteristics,
cartesian tensors, vector and dyadic notation, and the theory
of the eigenvalues and eigenvectors of symmetric matrices.
LIST
OF CONFIRMED PARTICIPANTS
| Name |
Department |
Affiliation |
| Santiago Betelu |
Mathematics |
University of
North Texas |
| Robert Burridge |
Earth Resources
Laboratory |
Massachusetts
Institute of Technology |
| Jamylle Carter |
|
Institute for
Mathematics & its Applications |
| Christine Cheng |
Institute for
Mathematics & its Applications |
University of
Minnesota |
| Dacian Daescu |
University of
Minnesota |
Institute for
Mathematics and its Applications |
| Gregory S. Duane |
University of
Minnesota |
Institute for
Mathematics and its Applications |
| Michael Efroimsky |
University of
Minnesota |
Institute for
Mathematics and its Applications |
| Selim Esedoglu |
|
Institute for
Mathematics & its Applications |
| Daniel Kern |
|
|
| Anna Mazzucato |
Mathematics |
Yale University |
| Aurelia Minut |
University of
Minnesota |
Institute for
Mathematics and its Applications |
| M. Yvonne Ou |
University of
Minnesota |
Institute for
Mathematics and its Applications |
| Jianliang Qian |
|
Institute for
Mathematics & its Applications |
| Toshio Yoshikawa |
University of
Minnesota |
Institute for
Mathematics and its Applications |
Slides:
pdf
Mathematics
in Geosciences, September 2001 - June 2002
|
