Moveout inversion of P-wave data for horizontal transverse isotropy

The transversely isotropic model with a horizontal symmetry axis (HTI media) has been extensively used in seismological studies of fractured reservoirs. In this paper, a parameter-estimation technique originally developed by Grechka and Tsvankin for the more general orthorhombic media is applied to horizontal transverse isotropy. Our methodology is based on the inversion of azimuthally-dependent P-wave normal-moveout (NMO) velocities from horizontal and dipping reflectors. If the NMO velocity of a given reflection event is plotted in each azimuthal direction, it forms an ellipse determined by three combinations of medium parameters. The NMO ellipse from a horizontal reflector in HTI media can be inverted for the azimuth beta of the symmetry axis, the vertical velocity V-P0, and the Thomsen-type anisotropic parameter delta((V)). We describe a technique for obtaining the remaining (for P-waves) anisotropic parameter eta((V)) (or epsilon((V))) from the NMO ellipse corresponding to a dipping reflector of arbitrary azimuth. The interval parameters of vertically inhomogeneous HTI media are recovered using the generalized Dix equation that operates with NMO ellipses for horizontal and dipping events. High accuracy of our method is confirmed by inverting a synthetic multiazimuth P-wave data set generated by ray tracing for a layered HTI medium with depth-varying orientation of the symmetry axis. Although estimation of eta((V)) can be carried out by the algorithm developed for orthorhombic media, for more stable results the HTI model has to be used from the outset of the inversion procedure. It should be emphasized that P-wave conventional-spread moveout data provide enough information to distinguish between HTI and lower-symmetry models. We show that if the medium has the orthorhombic symmetry and is sufficiently different from HTI, the best-fit HTI model cannot match the NMO ellipses for both a horizontal and a dipping event. The anisotropic coefficients responsible for P-wave moveout can be combined to estimate the crack density and predict whether the cracks are fluid-filled or dry. A unique feature of the HTI model that distinguishes it from both vertical transverse isotropy and orthorhombic media is that moveout inversion provides not just zero-dip NMO velocities and anisotropic coefficients, but also the true vertical velocity. As a result, reflection P-wave data acquired over HTI formations can be used to build velocity models in depth and perform anisotropic depth processing.