Full Wavefield Modeling in Anisotropic Media

Abstract

With the increase in accuracy required for seismic exploration one must include more physics in modeling seismic waves. In this paper we extend Full Wavefield Modeling (FWMod) to handle anisotropic media. FWMod is an integral-based approach that model's reflection events. It considers primary as well as multiple scattered reflections. We make use of the pseudo-elastic assumption for the acoustic wave-equation for anisotropic media to simplify the equations and reduce the cost associated with modeling. This introduces anisotropic kinematics into the acoustic wave equation, however this comes with two main limitations. The first limitation is that a pseudo S-wave is generated when the source is on, or near, an anisotropic layer. The pseudo S-wave manifests as a diamond shaped shear wave. The second limitation is an exponential growth in the solution for negative values of η. Attenuating these artifacts in finite-difference modeling is difficult and, in many cases, suboptimal. However, with a phase shift method such as FWMod attenuating these limitations is relatively straightforward. The pseudo S-wave can be clearly recognized in the absolute value of the phase shift extrapolator. In this domain it can be identified and attenuated. As for negative values of η, with this type of representation of the extrapolators, one can ensure that we always have evanescent decay rather than exponential growth in the solution. We include the anisotropic kinematics in the FWMod formulation and demonstrate the effectiveness of this method using a synthetic model.