Long-offset Parametric Moveout Approximation for VTI Elastic Layered Media

This study presents an enhancement to the existing parametric traveltime approximations in VTI elastic layered media by accounting for long-offset wave propagation in a more correct manner. The method is applicable for all types of pure-mode and converted waves, and it is highly accurate for all waves, except SV with strong anisotropy, dominated by cusps. We suggest a parametric approach where both the offset and the traveltime are functions of the horizontal slowness whose finite upper bound (critical slowness) corresponds to infinite offset and traveltime. We distinguish between the layer with the fastest horizontal velocity (“fast” layer) and the other (“slow”) layers. In vertically varying 1D layered media, the horizontal slowness is constant for all layers in both incident and reflected waves, for all wave types. Thus, for a power series approximation, the coefficients representing the contributions of the individual VTI layers to the total offset and traveltime can be summed. For nearly critical slowness, the contributions of the “fast” and “slow” layers are decoupled; this separation gives a better physical insight into the nature of longoffset wave propagation. The accuracy of the method is demonstrated by comparing the approximated offsets and traveltimes with numerical ray tracing.