DIFFERENTIAL GEOMETRY/PDE SEMINAR

Wednesday, May 14, 2003 Padelford C-36 3:45 pm

The inverse problem from reflection seismology: velocity analysis using wave-equation imaging

Christiaan Stolk (Ecole Polytechnique, France)

In a seismic experiment one generates acoustic waves in a medium using source at the boundary and one measures the wave field at the surface due to each source over some period of time. The purpose is to reconstruct the local propagation velocity of the waves inside the medium from the reflections present in the data. As is common in this problem we assume a partial linearization (single scattering approximation), such that the data becomes linear in the high-frequency components of the medium coefficient, but nonlinear in the low-frequency background medium. The forward map is then a linear map acting on the high-frequency component of the medium, that depends on the background medium. Generally the data for this problem is redundant. We construct an extension of this map that can be used to characterize its range. Based on this we derive a new estimation method for the background medium. The approach is valid under relatively weak assumptions on the background medium, that in particular allow for the presence of caustics in the wave fronts propagating in the background medium.

For more information about this seminar, visit the DG/PDE Seminar Web page (from the Math Department home page, www.math.washington.edu, follow the link Seminars, Colloquia, and Conferences).

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