Efficient wavefield separation by reformulation of two-way wave-equation depth-extrapolation scheme

Abstract

In two-way wave-equation depth migration by either time extrapolation or depth extrapolation, an efficient wavefield separation scheme (to separate two-way wavefields into their one-way counterparts: down- and upgoing waves) is typically required for high-quality imaging. For a depth-extrapolation scheme, this wavefield separation is conventionally accomplished by using two wavefields, the pressure p and its derivative [Formula: see text]. However, that wavefield separation scheme presents a significant challenge in the accuracy and the computational cost for two-way wave-equation-based depth migration. To address this challenge, we have developed a new wavefield separation algorithm for a two-way wave-equation depth-extrapolation scheme, in which a new pressure wavefield q is introduced to replace the pressure derivative wavefield [Formula: see text] in boundary conditions and propagator of the conventional formulation. Because the pressure wavefield p represents the sum of down- and upgoing waves, whereas the pressure wavefield q denotes the difference between down- and upgoing waves, wavefield separation in the new algorithm becomes very simple and efficient — a summation and subtraction operation only at each depth step. The performance of our algorithm for wavefield separation is verified and demonstrated by numerical experiments conducted on several synthetic models. These experiments include examples of wavefield separation of the source and the receiver, migration tests on the 2D SEG/EAGE salt model (regarding one-way versus two-way depth extrapolation and comparison of evanescent-wave-suppression methods), and turning wave migration tests on three complex velocity models: the step model, the salt dome model, and the BP salt model.