Separate P‐ and SV‐wave equations for VTI media

Abstract

In isotropic media we use the scalar acoustic wave equation to perform reverse time migration (RTM) of the recorded pressure wavefleld data. In anisotropic media P‐ and SV‐waves are coupled and the elastic wave equation should be used for RTM. However, an acoustic anisotropic wave equation is often used instead. This results in significant shear wave energy in both modeling and RTM. To avoid this undesired SV‐wave energy, we propose a different approach to separate P‐ and SV‐wave components for vertical transversely isotropic (VTI) media. We derive independent pseudo‐differential wave equations for each mode. The derived equations for P‐ and SV‐waves are stable and reduce to the isotropic case. The equations presented here can be effectively used to model and migrate seismic data in VTI media where |ε − δ| is small. The SV‐wave equation we develop is now well‐posed and triplications in the SV wavefront are removed resulting in stable wave propagation. We show modeling and RTM results using the derived pure P‐wave mode in complex VTI media and use the rapid expansion method (REM) to propagate the waveflelds in time.