Math/AMath 595A:
Numerical Methods for Inverse Problems and Tomography
Ken Bube
Winter 1999, MW 3:30-4:45
We will cover some numerical methods used in geophysical inverse problems
for some time-dependent partial differential equations. The differential
equations are linear wave quations (acoustic, elastic, etc.) with coefficients
which depend on spatial location but not on time. Parts of solutions
of these equations are measured, and the goal is to determine the coefficients
from these measurements. We will give some background on the inverse
problems for the differential equations, and discuss a number of issues
related to their numerical solution (discretization issues, solving ill-posed
problems numerically, regularization, efficient computation of Jacobian
matrices, etc.). We will also discuss closely related traveltime
tomography problems and numerical issues involved in their solution (ray-tracing,
traveltime computation using eikonal solvers, SVD, resolution matrices,
use of a priori information, etc.).