FOURIER FINITE-DIFFERENCE MIGRATION

Many existing migration schemes cannot simultaneously handle the two m ost important problems of migration: imaging of steep dips and imaging in media with arbitrary velocity variations in all directions. For ex ample, phase-shift (omega, k) migration is accurate for nearly all dip s but it is limited to very simple velocity functions. On the other ha nd, finite-difference schemes based on one-way wave equations consider arbitrary velocity functions but they attenuate steeply dipping event s. We propose a new hybrid migration method, named ''Fourier finite-di fference migration,'' wherein the downward-continuation operator is sp lit into two downward-continuation operators: one operator is a phase- shift operator for a chosen constant background velocity, and the othe r operator is an optimized finite-difference operator for the varying component of the velocity function. If there is no variation of veloci ty, then only a phase-shift operator will be applied automatically. On the other hand, if there is a strong variation of velocity, then the phase-shift component is suppressed and the optimized finite-differenc e operator will be fully applied. The cascaded application of phase-sh ift and finite-difference operators shows a better maximum dip-angle b ehavior than the split-step Fourier migration operator. Depending on t he macro velocity model, the Fourier finite-difference migration even shows an improved performance compared to conventional finite-differen ce migration with one downward-continuation step. Finite-difference mi gration with two downward-continuation steps is required to reach the same migration performance, but this is achieved with about 20 percent higher computation costs. The new cascaded operator of the Fourier fi nite-difference migration can be applied to arbitrary velocity functio ns and allows an accurate migration of steeply dipping reflectors in a complex macro velocity model. The dip limitation of the cascaded oper ator depends on the variation of the velocity field and, hence, is vel ocity-adaptive.