Introduction

In 1988 John Etgen described in detail a staggered-grid finite-difference scheme for arbitrary anisotropic media. He showed forward modeling examples in the plane of symmetry for transverse isotropic (TI) media. He also showed a reverse-time migration image using SH waves. In this paper I will use his staggered-grid method and implement a general anisotropic imaging condition. The possibilities are abundant for implementing imaging conditions for reverse time migrations. These approaches differ in how the forward-modeled shot is handled in the migration step. The use of one-way wave equations or ray-tracing methods leads to fast algorithms, but such short cuts also give incorrect amplitude information. The development of the imaging condition for arbitrary anisotropic media used in this paper follows Peter Mora's description (1989) of the conjugate elastic wave-equation operator. He showed the relationship between the imaging condition and conjugate-gradient computation. When the right imaging condition is chosen, prestack migration becomes one step in the conjugate-gradient iteration.