|
Applied Math Seminar
How to solve a simple inverse problem in seismology
|
|
The simplest version of the main inverse problem of concern to reflection seismologists concerns a layered model of the earth: the sedimentary crust is approximated as an elastic solid whose mechanical properties depend only on depth. After a more approximations, all widely accepted as reasonable, at least in some circumstances, one arrives at a simple model inverse problem. I will show how to turn this problem into an optimization problem, in such a way that all stationary points of the (nonquadratic) smooth objective occur at values close to the global minimum. Thus all stationary points are equally acceptable solutions, which justifies the use of a rapidly convergent quasi-Newton method. Examples with field seismic data show that this technique is actually usable, and also suggest its limitations. |