Long Offset Asymptotic Moveout for Compressional Waves in Layered Orthorhombic Media

In this study, we derive the fourth-order moveout approximation for compressional waves in a locally 1D layered orthorhombic model with asymptotic correction for long and infinite offsets, in the phase velocity azimuth domain. The orthorhombic layers have a common vertical axis but different azimuthal orientations of horizontal axes. The moveout is computed parametrically. The lengthwise (along the phase velocity azimuth) and transverse components of the lateral propagation and the traveltime are defined as functions of the horizontal slowness magnitude and azimuth. We compute the power series coefficients for infinitesimal slowness and for nearly critical slowness. With these coefficients, we design continuous parametric functions valid for the whole offset range, whose Tailor series expansions match the given coefficients. In addition to the zero offset time, we keep two “head” coefficients for small offsets and two “tail” coefficients for nearly critical slowness, per azimuth. One of the tail coefficients characterizes the propagation in the layer with the fastest horizontal velocity for the given azimuth. The other tail coefficient depends on the propagation and traveltime in the slow layers when the slowness reaches its critical value. We verify the accuracy of the approximation for all feasible reflection angles vs. exact analytical ray tracing.