On the Stability of Finite-Difference Schemes of Higher-Order Approximate One-Way Wave Equations

Abstract

The finite difference migration, proposed and developed by J.F. Claerbout, is now widely used in seismic data processing. The method has a limitation that the events are not dipping too much. Guanquan ZHANG derived a new version of higher-order approximation of one-way wave equation in the form of systems of lower-order equations. For these systems he constructed some suitable difference schemes and developed a new algorithm of finite-difference migration for steep dips. In this paper, we discuss the stability of these difference schemes by the method of energy estimation.