3-D moveout inversion in azimuthally anisotropic media with lateral velocity variation: Theory and a case study

Abstract

Reflection moveout recorded over an azimuthally anisotropic medium (e.g., caused by vertical or dipping fractures) varies with the azimuth of the source‐receiver line. Normal‐moveout (NMO) velocity, responsible for the reflection traveltimes on conventional‐length spreads, forms an elliptical curve in the horizontal plane. While this result remains valid in the presence of arbitrary anisotropy and heterogeneity, the inversion of the NMO ellipse for the medium parameters has been discussed so far only for horizontally homogeneous models above a horizontal or dipping reflector. Here, we develop an analytic moveout correction for weak lateral velocity variation in horizontally layered azimuthally anisotropic media. The correction term is proportional to the curvature of the zero‐offset traveltime surface at the common midpoint and, therefore, can be estimated from surface seismic data. After the influence of lateral velocity variation on the effective NMO ellipses has been stripped, the generalized Dix equation can be used to compute the interval ellipses and evaluate the magnitude of azimuthal anisotropy (measured by P-wave NMO velocity) within the layer of interest. This methodology was applied to a 3-D “wide‐azimuth” data set acquired over a fractured reservoir in the Powder River Basin, Wyoming. The processing sequence included 3-D semblance analysis (based on the elliptical NMO equation) for a grid of common‐midpoint “supergathers,” spatial smoothing of the effective NMO ellipses and zero‐offset traveltimes, correction for lateral velocity variation, and generalized Dix differentiation. Our estimates of depth‐varying fracture trends in the survey area, based on the interval P-wave NMO ellipses, are in good agreement with the results of outcrop and borehole measurements and the rotational analysis of four‐ component S-wave data.