We study the inversion of data from reflection seismology in the usual, partially linearized approach, where it is assumed that the medium is a small, oscillatory perturbation of an unknown, smooth background medium.
The estimation of this background model from the data is a non-linear inverse problem. Based on the wave equation approach to imaging we derive an ``error function'' for the background that takes its minimum at the correct background under weak assumptions. The assumptions in particular allow for the presence of caustics in the wave fronts that propagate in the background medium. The estimation can now be done by minimizing this functional over some class of background media. Because our error function is smooth this leads to economical computations. We will show some initial numerical results (joint work with Peng Shen and Bill Symes from Rice University).
Copyright. All Rights Reserved.