Explicit marching method for reverse‐time migration

Abstract

In this abstract we propose a new method to solve the two‐way wave equation which we call the “Explicit Marching” (EM) algorithm. By introducing a square‐root operator, the two‐way wave equation can be formulated as a first‐order PDE in time which is similar to the one‐way wave equation. To solve the new wave equation, we use a stable explicit extrapolation method in the time direction and handle the lateral velocity variations in both the space and wavenumber domains. Unlike the conventional explicit finite‐difference schemes, this new method does not suffer from numerical stability or numerical dispersion problems. Therefore, it can be used to design a cost‐effective and high quality reverse‐time migration.