Elastic wave-mode separation for TTI media

Published as Geophysics, 76, no. 4, T65-T78, (2011)

Elastic wave-mode separation for TTI media

Jia Yan and Paul Sava
Center for Wave Phenomena
Colorado School of Mines
jyan@mines.edu, psava@mines.edu

Abstract:

Seismic waves propagate through the earth as a superposition of different wave-modes. Seismic imaging in areas characterized by complex geology requires techniques based on accurate reconstruction of the seismic wavefields. A crucial component of the methods in this category, collectively known as wave-equation migration, is the imaging condition which extracts information about the discontinuities of physical properties from the reconstructed wavefields at every location in space. Conventional acoustic migration techniques image a scalar wavefield representing the P wave-mode, in contrast with elastic migration techniques which image a vector wavefield representing both the P and S wave-modes. For elastic imaging, it is desirable that the reconstructed vector fields are decomposed in pure wave-modes, such that the imaging condition produces interpretable images, characterizing for example PP or PS reflectivity. In anisotropic media, wave-mode separation can be achieved by projection of the reconstructed vector fields on the polarization vectors characterizing various wave modes. For heterogeneous media, the polarization directions change with position, therefore wave-mode separation needs to be implemented using space-domain filters. For transversely isotropic media with a tilted symmetry axis (TTI), the polarization vectors depend on the elastic material parameters, including the tilt angles. Using these parameters, I separate the wave-modes by constructing nine filters corresponding to the nine Cartesian components of the three polarization directions at every grid point. Since the S polarization vectors in TI media are not defined in the singular directions, e.g. along the symmetry axes, I construct these vectors by exploiting the orthogonality between the SV and SH polarization vectors, as well as their orthogonality with the P polarization vector. This procedure allows one to separate S wave-modes which are only kinematically correct. Realistic synthetic examples show that this wave-mode separation is effective for both 2D and 3D models with high heterogeneity and strong anisotropy.

Elastic wave-mode separation for TTI media