Elastic wave-mode separation for TTI media

S wave-mode amplitudes

Although the procedure used in this chapter to separate S-waves into SV- and SH- modes is simple, the amplitudes of S-modes are not accurate because the S-wave separators are not normalized for any given wavenumbers. The amplitudes of S-modes obtained in this way are zero in the symmetry axis direction and they gradually increase to one in the symmetry plane.

The main problem that prevents one from constructing the 3D global shear wave separators is that the SV and SH polarization vectors are singular in the symmetry axis direction, i.e., they are not defined by the plane-wave solution of the TI elastic wave equation. Various studies (Tsvankin, 2005; Kieslev and Tsvankin, 1989) show that S-waves excited by point forces can have non-linear polarizations in several special directions. For example, in the direction of the source, the S-wave can deviate from the linear polarization. This phenomenon exists even in isotropic media. Anisotropic velocity and amplitude variations can also cause the S-waves to be polarized non-linearly. For instance, S-wave triplication, S-wave singularities, and S-wave velocity maximum can all result in S-wave polarization anomalies. In these special directions, SV- and SH-mode polarizations are incorrectly defined by my convention. One possibility for obtaining more accurate S-wave amplitudes is to approximate the anomalous polarization with the major axes of the quasi-ellipses of the S-wave polarization, which can be obtained by incorporating the first-order term in the ray tracing method. This extension remains outside the scope of this chapter.

Although the simplified approach used in this chapter ignores the complicated polarization behavior in some wave propagation directions, it does successfully separate fast and slow shear modes kinematically. This allows one to use the separated scalar shear-modes for the subsequent imaging condition and obtain images with clear physical meaning.

Elastic wave-mode separation for TTI media