An Approach to the Inverse Seismic Problem
, by Robert H. Stolt and Bert Jacobs
A formal method for inverting multi-dimensional seismic data is
developed, borrowing freely from the concepts of quantum scattering
theory. It is shown that the measured quantity in the seismic
experiment is essentially the on-shell T matrix of that theory. An
expansion of the T matrix in powers of inverse source amplitude
yields successive approximations to the seismic parameters. The
first approximation is essentially a migration. Each successive
approximation requires calculation of a forward problem and a
migration. The forward calculation involves volume integrals and
appears in general to be computationally prohibitive. However,
under circumstances where higher order terms are due mainly to
surface multiples, the computational magnitude drops substantially.
STANFORD