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.