We propose to solve the two-way time domain acoustic wave equation in a generalized Riemannian coordinate system via finite-differences. The coordinate system is defined in such a way that one of its independent variables conforms to the primary wavefront, for example, using a ray coordinate system with the traveltime being one of the coordinates. At each finite-difference time-step, the solution domain is limited to a narrow corridor around the primary wavefront, leading to an increase in the computational performance. A new finite-difference scheme is introduced to stabilize the solution and facilitate its implementation. This new scheme is a blend of the simple explicit and the stable implicit schemes. As a proof of concept, the proposed method is compared to the classical explicit finite-difference scheme performed in Cartesian coordinates on two synthetic velocity models with varying complexities. At a reduced cost, the proposed method produces similar results to the classical one; however, some amplitude differences arise due to various implementation issues. The most direct application for the proposed method is the source side of reverse time migration.

You do not have access to this content, please speak to your institutional administrator if you feel you should have access.