Wednesday, June 18

1:00 PM-1:45 PM
Rio Grande Ballroom Chair: Mrinal Sen, University of Texas, Austin

IP8
The Role of Convex and Nonconvex Duality in the Inversion of the Reflection in Seismic Data for Velocities

Reflection seismic data are one important source of information -- if not the most important one -- on the structure of the underlying earth. The depths being investigated range from a few ten meters for civil engineering applications, to a few kilometers for oil and gas prospection.

An accurate knowledge of the sound velocities in the investigated domain is critical for the migration (back-projection) of the data to provide a crisp image of the earth. Velocity determination is the most difficult step for the interpretation of seismic data. It is usually performed by tomography or by migration velocity analysis (MVA), both of which require human expertise for the picking of horizons or the interpretation of coherency panels. For a couple of years, these methods have been challenged by the least squares (LS) full waveform inversion which eliminates the need for human intervention but suffers from native nonoptimizability by local gradient methods.

After explaining the mathematical relation between the gradient of the (LS) objective function and the migration imaging process, the speaker will show how the use of convex duality provides reformulations of the (LS) approach which are more amenable to minimization by local methods, and indicate how the apparently unrelated (MVA) and (LS) approaches can be seen as dual, but not strictly equivalent problems.

Guy Chavent
INRIA, France

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TJF, 2/6/97
MMD, 2/20/97