Fourth-order NMO Velocity for Compressional Waves in Layered Orthorhombic Media

We derive azimuthally dependent fourth-order effective velocity and moveout parameters for compressional waves propagating in a layered model that consists of orthorhombic layers. The subsurface layered medium is considered as a locally 1D model, where each layer can be characterized by orthorhombic parameters. The orthorhombic layers have a common vertical axis but different azimuthal orientations of horizontal axes. For a 1D vertically varying anisotropic model, the azimuth of the phase velocity is the same for all layers, while the azimuths of the ray velocity are generally different. We extend the existing studies on the moveout in an azimuthally anisotropic model, accounting for the azimuthal deviation between the phase and ray velocities. We compute the lag between the azimuth of the surface offset (source-receiver vector) and the phase velocity azimuth. An effective model that replaces the multilayer model with a single azimuthally anisotropic layer is derived, whose moveout and offset azimuth are identical to those of the layer package up to the fourth-order terms. We verify the accuracy of the approximation for small to moderate reflection angles vs. exact analytical ray tracing. The proposed approximation is in particular important when analyzing residual moveouts measured along full-azimuth common image reflection angle gathers.