Ray tracing and amplitude calculation in anisotropic layered media

Abstract

In an anisotropic medium, the direction of the energy propagation is different from the plane-wave propagation. This difference will cause velocity variation in different angles. Therefore, velocity modelling in anisotropic media is different from that in an isotropic medium. In this paper, a conventional algorithm has been extended based on ray tracing through an anisotropic model. The velocity model for ray tracing is parametrized in terms of blocky trapezoid cells where the velocity values change inside the cells linearly. Thomsen's approximations in weakly anisotropic media were used to estimate anisotropic velocity vectors. Rays were traced along the group vector in vertical transversely isotropic (VTI) media so that the phase angle and phase velocities satisfy the anisotropic Snell's law across the interface. To compute seismic amplitudes in the anisotropic media, a new parameter was defined as a partitioning factor which controls the seismic energy propagation in each interface. The effect of geometrical spreading was calculated by using Ursin's procedure. Synthetic models are computed to demonstrate the new ray tracing algorithm and to verify correctness of the traveltimes and amplitude calculations. It is shown that the difference between isotropic and anisotropic traveltimes increases with offset, especially when the ratio offset/depth exceeds 1.5. To calculate amplitudes in VTI media, a new parameter q was introduced and applied as the energy partitioning factor, which helps us obtaining a more accurate amplitude calculation. Ray tracing was also performed for the velocity model extracted from a large offset 2-D seismic line located on the southwest of Iran. Anisotropic parameters were estimated from seismic data under the elliptical anisotropic assumption. Reflected traveltimes were computed by ray tracing from top of the reservoir horizon (fifth reflector) in the anisotropic model. The calculated traveltimes once we explicitly included anisotropic velocities showed a much improved correlation with the seismic real data.