LINEARIZED INVERSION OF MULTIOFFSET SEISMIC-REFLECTION DATA IN THE OMEGA-K DOMAIN - DEPTH-DEPENDENT REFERENCE MEDIUM

The computation of synthetic seismograms can be linearized with respect to a reference medium that is close to the actual medium. Using a least-squares formulation, the inverse problem can then be set up as a problem of quadratic optimization. The inverse problem is greatly simplified if the reference medium is symmetric. For a homogeneous reference medium, a rigorous and economic solution can be obtained by Fourier transforming all spatial variables. However, the assumption of a homogeneous reference medium is generally not realistic. In some situations, the reference medium can be depth-dependent. It can then be shown that by Fourier transforming time and all spatial variables except depth, the inverse problem also has an elegant and economic solution.