Moveout Approximation for Compression Waves in Layered Orthorhombic Medium

Orthorhombic models comprise subsurface anisotropy caused by vertical azimuthally-aligned fractures and layering, or by two orthogonal sets of vertical fractures, with or without layering. In this paper we derive new relations for hyperbolic and non-hyperbolic moveout approximations for pure compression waves, considering a 1D model that consists of a set of orthorhombic layers. The layers have a common vertical axis but different orientations of horizontal orthorhombic axes. For 1D models, 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 moveout in an orthorhombic model, accounting for the azimuthal deviation between the phase and ray velocities. We then formulate the azimuthally-dependent NMO velocity for a package of layers. Finally, we compare the derived full quartic moveout term with its acoustic approximation, and verify the accuracy of the approximation vs. exact analytical ray tracing.