Wave Modes Study for Acoustic VTI Equations

Abstract

The application of reverse-time migration (RTM) on a large scale has become affordable and has led to significant advances in seismic depth imaging in complex areas, especially for sub-salt imaging. For imaging in anisotropic media with tilted transverse isotropy (TTI), RTM is usually based on an acoustic TTI approximation of the elastic wave equation by setting the shear-wave velocity to zero. However, these equations generate artificial pseudo shear-waves that spoil any seismic imaging process. For the general anelliptic TTI case, when the Thomsen parameters ϵ ≠ δ, one of the eigenvalues associated to the 2D TTI acoustic equations is not null and it is mainly responsible for the generation of the spurious pseudo-shear mode. This work shows that as long as we do not deal with high wavenumbers, i.e., if care is taken in the modeling to excite the medium with the usual marine seismic wavelengths, the spurious pseudo-shear wave is not generated or very weak compared to the P-wave mode. We illustrate this fact, for the case of a homogeneous medium modelling and for the more realistic case of a 2D Salt body modelling. Both cases are made to demonstrate our concept in TTI media.