Reflection moveout inversion for horizontal transverse isotropy: Accuracy, limitation, and acquisition

Horizontal transverse isotrophy (HTI) is the simplest azimuthally anisotropic model used to describe vertical fracturing in an isotropic matrix. Assuming that the sub-surface is laterally homogeneous, and using the elliptical variation of P-wave NMO velocity with azimuth measured in at least three different source-to-receiver orientations, we can estimate three key parameters of HTI media: the vertical velocity, anisotropy, and the azimuth of the symmetry axis. Such parameter estimation is sensitive to the angular separation between the survey lines in 2-D acquisition or, equivalently, to source-to-receiver azimuths in 3-D acquisition and the set of azimuths used in the inversion procedure. The accuracy in estimating the azimuth, in particular, is also sensitive to the strength of anisotropy, while the accuracy in resolving vertical velocity and anisotropy is about the same for any strength of anisotropy. To maximize the accuracy and stability in parameter estimation, it is best to have the azimuths for the source-to-receiver directions 60°apart when only three directions are used. This requirement is feasible in land seismic data acquisition where wide azimuthal coverage can be designed. In marine streamer acquisition, however, the azimuthal data coverage is limited. Multiple survey directions are necessary to achieve such wide azimuthal coverage in streamer surveys. To perform the inversion using three azimuth directions, 60° apart, an HTI layer overlain by an azimuthally isotropic overburden should have a time thickness, relative to the total time, of at least the ratio of the error in the NMO (stacking) velocity to the interval anisotropy strength of the HTI layer. Having more than three source-to-receiver azimuths (e.g., full azimuthal coverage), however, provides a useful data redundancy that enhances the quality of the estimates, thus allowing acceptable parameter estimation at smaller relative thicknesses.