Thu, 23 July, 2009, 17:15-18:15, Foyer
The seismic survey is a widely used tool to obtain an image of the subsurface. Usually, an explosive source is placed just below the surface and the scattered wavefield is recorded at the surface. The physical parameters that describe the subsurface, in particular the soundspeed, can now be obtained by solving a PDE-constrained, strongly non-linear optimization problem. The problem can be linearized under the assumption that waves scatter only once in the subsurface. The linearized inverse problem can be solved by simple back-projection. Its solution represents the discontinuities of the medium parameters, e.g., the layer boundaries. This still leaves the slowly varying part of the medium parameters unresolved. Fortunately, there are algorithms to deal with these kind of problems. They first resolve the linear part of the unknowns, given the non-linear part. The remaining inverse problem then only depends on the non-linear parameters. With the latter, we can recompute the linear part of the parameters, and so on. Unfortunately, the linear problem has to be solved very accurately at each iteration. If not, the non-linear optimization may result in a wrong solution. As a remedy, we propose a different formulation of the functional for the non-linear optimization. We include numerical examples to illustrate the approach.
Presentation slides (pdf, 296 KB)
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