Although Kirchhoff migration can incorporate anisotropy into migration, it fails to handle the multi-pathing problem. Wave-equation-based methods are able to handle the multi-pathing problem and image the complicated subsurface structure. However, it is still challenging to image steeply dipping reflectors in the subsurface, such as a salt flank. Wavefield extrapolation in tilted coordinates Etgen (2002); Shan and Biondi (2004) is useful for these steeply dipping reflectors. The energy related to these steeply dipping reflectors propagates almost horizontally and is greatly affected by the anisotropy of the sediment. In tilted coordinates, VTI media become tilted TI media in the extrapolation direction. It is useful therefore to develop a wavefield-extrapolation scheme for tilted TI media.
During the last decade, methods have been developed to incorporate anisotropy into wavefield extrapolation in TI media. As with isotropic extrapolation operators, anisotropic extrapolation operators include the implicit method Ristow and Ruhl (1997), phase-shift-plus-interpolation (PSPI) Rousseau (1997), non-stationary phase-shift Ferguson and Margrave (1998), explicit operator Zhang et al. (2001); Zhang et al. (2001); Uzcategui (1995), and reference anisotropic phase-shift with an explicit correction filter Baumstein and Anderson (2003).
In this paper, we incorporate anisotropy into wavefield extrapolation by adding an explicit anisotropic correction operator to the normal isotropic extrapolation operator. This new extrapolation scheme is capable of propagating waves in an anisotropic, heterogeneous medium with strong lateral variation. The explicit correction operator is designed by weighted, least-squares fitting to the true anisotropic phase-shift operator in the wavenumber domain Thorbecke (1997). In our method, we handle the lateral velocity variation by using a mixed-domain isotropic operator and the lateral anisotropic parameter variation by using explicit correction operator. At each depth level, we don't need to run the explicit correction operator for isotropic points. Therefore, it is efficient for a medium with both isotropic and anisotropic points. Furthermore, it is useful for VTI media with tilted coordinates where for each depth level most points are isotropic.