Shear-Wave Reflection Moveout For Azimuthally Anisotropic Media

Abstract

The presence of azimuthal anisotropy causes shear wave propagation to split into fast and slow shear waves. The most common azimuthally anisotropic models used to describe fractured reservoirs are transverse isotropy with a horizontal axis of symmetry (HTI), and orthorhombic. In this paper, we study shear-wave reflection moveout in azimuthally anisotropic media with special attention paid to orthorhombic media with horizontal interfaces. In such cases the shear-wave reflection moveout is azimuthally variant and nonhyperbolic. We analyze the azimuthal dependence of normal moveout (NMO) velocity and we validate the accuracy of the conventional hyperbolic moveout equation. The azimuthal variation of NMO velocity is elliptical for both wave modes. In the presence of anisotropy-induced, nonhyperbolic moveout (NHMO), the hyperbolic moveout equation loses its accuracy with increasing offset (e.g., offset-to-depth ratio> 1). To study the azimuthal behavior of the NHMO for shear-wave reflections, we introduce an analytic representation for the quartic coefficient of the Taylor's series expansion of the two-way traveltime. In an orthorhombic medium the quartic coefficient for shearwave reflections has a relatively simple form, especially in comparison to P-wave. The reflection moveout for each shear-wave mode in a homogeneous orthorhombic medium is purely hyperbolic in the direction normal to the polarization. The nonhyperbolic portion of the moveout, on the other hand, reaches its maximum along the polarization direction, and it reduces rapidly away from the direction of pOlarization. As a result, the anisotropy-induced, nonhyperbolic reflection moveout is significant in the vicinity of the polarization directions (e.g., ±30° and for large offset-to-depth ratios). The implementation of the NHM0 equation and the utilization of the moveout coefficients allow for not only enhanced seismic imaging but also provide the link between seismic signatures and medium parameters.