Normal Moveout Series Coefficients for Pure-mode and Converted Waves in Horizontally-layered Triclinic Media

Abstract

Summary Considering all types of pure-mode and converted waves, we derive the azimuthally-dependent normal moveout (NMO) series coefficients of near normal-incidence reflection waves in general anisotropic (triclinic) horizontally layered media, for a leading error term of order six. The NMO series can be either a function of the invariant horizontal-slowness (slowness domain) or the surface-offset (offset domain). The NMO series coefficients of different orders, also referred to as effective parameters, are associated with the corresponding azimuthally-dependent NMO velocity functions. We distinguish between local (single-layer) and global (overburden multilayer) effective parameters, where the local and global effective parameters are related by forward and inverse Dix-type transforms. We first consider the case in which the reciprocity assertion for incidence and reflected waves holds, i.e. pure-mode waves for general anisotropic horizontally-layered media, and converted waves for anisotropic horizontally-layered models sharing a common horizontal symmetry plane. Considering reciprocity, the odd-power coefficients of the NMO series cancel, and the remaining coefficients are zero-offset time, three second-order and five fourth-order effective parameters. Next we consider converted waves in general anisotropic media, where reciprocity no longer holds. Twelve additional parameters are required: two firstorder, four third-order and six fifth-order effective parameters.