DSR One‐Way Wave Equation Prestack τ Migration

Abstract

By transforming the classical double-square-root (DSR) one-way wave equation from depth domain to two-way vertical traveltime (τ ) domain, we derive a one-way DSR wave propagator which can be applied to implement the imaging concept of "survey sinking". Its algorithm to recursively continue the source and receiver wavefields, which includes a wavenumber domain phase shift in a constant background medium followed by a phase correction in the space domain that accommodates lateral velocity variations, can tackle the effects of lateral velocity variations under complex overburdens. Applying the zero-offset, zero-time imaging condition, we develop a DSR equation prestack migration method in which the wavefield continuation and imaging are operated in the τ space. To address the problems that full volume 3-D DSR equation migration could meet with in practical application, we present a feasible common-azimuth prestack τ migration approach based on the theory of cross-line common-offset migration. Numerical tests show that our prestack τ migration provides a significant improvement over the traditional prestack time migration in laterally varying media.