τ-p analysis in transversely isotropic media

Incorporating the effects of anisotropy in seismic processing is an active area of research. Here we describe a method for the analysis of P -wave seismic reflection data in the plane-wave domain for transversely isotropic media with a vertical axis of symmetry. The generalization of τ–p methods to include transverse isotropy is straightforward in that we simply replace the isotropic vertical slowness term with one appropriate for anisotropy. Exact expressions for the vertical slowness do exist; P and SV require four parameters and SH require two. The P -wave traveltime trajectories are not sensitive to all four parameters and can be expressed as a function of two parameters only. We have developed a series representation for P -wave vertical slowness in terms of increasing powers of horizontal slowness; it is also convenient for interactive moveout analysis. The two-term expression derived from this series is adequate for the analysis of data from weakly anisotropic media and brings out the physics of wave propagation clearly. Thus our development is analogous to the non-hyperbolic normal moveout expression used in the offset-time domain. The τ–p analysis enables us to derive interval anisotropy parameters directly without a two-point ray tracing, which can be used in further processing. We have developed a computer algorithm to iteratively and interactively fit the τ–p trajectories to derive anisotropy parameters. The technique is demonstrated with applications to synthetic and field reflection seismic data from the Gulf of Mexico.