Reflection moveout inversion in azimuthally anisotropic media: Accuracy, limitations and acquisition

Parameter estimation from the elliptical variations in the normal-moveout (NMO) velocity in azimuthally anisotropic media is sensitive to the angular separation between the survey lines in 2D, or equivalently, the source-to-receiver azimuth in 3D, and to the set of azimuths used in the inversion procedure. The accuracy in estimating the orientation of an NMO ellipse, in particular the parameter α, is also sensitive to the magnitude of anisotropy. On the other hand, the accuracy in estimating the semi-axes of the NMO-velocity ellipse is about the same for any magnitude of anisotropy. To invert for the NMO ellipse parameters at least three NMO-velocity measurements along distinct azimuth directions are needed. In order to maximize the accuracy and stability in parameter estimation, it is best to have the azimuths for the three source-to-receiver directions 60°apart. Having more than three distinct source-to-receiver azimuths (e.g. full azimuthal coverage) provides a useful data redundancy that enhances the quality of the estimates. In order to maximize quality in the inversion process, it is recommended to design the seismic data acquisition such that it contains small sectors (≤10°) with adequate fold and offset distribution. Using three NMO-velocity measurements, 60°apart, an azimuthally anisotropic layer overlain by an azimuthally isotropic overburden (as might occur for fractured reservoirs) should have a relative thickness (in time) with respect to the total thickness at least equal to the ratio of the error in the NMO (stacking) velocity to the interval anisotropy of the fractured layer. Coverage along more than three azimuths, however, improves this limitation, which is imposed by Dix differentiation, by at most 50%, depending on the number of observations (NMO velocities) that enter the inversion procedure.