On the stationary points of the seismic reflection tomography and differential semblance functionals in laterally homogeneous media
Stolk, Christiaan C.
This paper concerns the determination of the reference medium (velocity model) in reflection seismology by optimization. Several objective functionals have been proposed, that attain their minimum or maximum at the correct medium. We study the local minima of two of these, the differential semblance and reflection tomography functionals, both depending on the traveltimes of reflected waves. It is assumed that the medium contains a single, horizontal reflector, and that it depends smoothly on the vertical coordinate above the reflector. We show that stationary points of both functionals are global minima when the medium above the reflector is non-constant. For reflection tomography we study the Hessian at a constant medium to show that all local minima are in fact global minima. To obtain these results we study the linearization of the map from medium properties to the traveltime of reflected waves around a non-constant medium.
Citable link to this pagehttps://hdl.handle.net/1911/101980
MetadataShow full item record
- CAAM Technical Reports