Long-offset Moveout Approximation for VTI Elastic Layered Media

This study is an enhancement to existing moveout approximations in VTI layered media for large offsets. We suggest two new approximations that include five parameters. The first three parameters are conventional: zero-offset time, NMO velocity and quartic coefficient. The two additional parameters are related to large offsets. One of them describes nearly horizontal propagation in the fast layer of the overburden, while the other characterizes the remaining finite wave propagation distance and the finite traveltime across the slower velocity layers. Our approximations can be used with either a finite or an infinite offset match. In the case of an infinite match, the approximations converge to an exact theoretical asymptote. Another possibility is to establish the parameters of the approximation from a least squares fit within a given offset range, rather than for a specified offset point (either finite or infinite). Both new approximations match the exact ray tracing traveltime very well for P, P-SV and SH waves.