Explicit Marching Method For Reverse-time Migration

In this abstract we propose a new method to solve the twoway 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.