Theory

Alkhalifah and Tsvankin (1995) demonstrated that, for transversely isotropic (TI) media with a vertical symmetry axis (VTI media), just two parameters are sufficient for performing all time-related processing, such as NMO correction (including nonhyperbolic moveout correction, if necessary), DMO correction, and prestack and poststack time migration. One of these two parameters, $\eta$, is a dimensionless parameter, whose departure from zero implies anisotropy, and the other, $V_{{\rm nmo}}$, is the short-spread normal moveout (NMO) velocity for horizontal reflectors. These two parameters can be obtained solely from surface seismic P-wave data, using estimates of stacking velocity for reflections from interfaces having two distinct dips (Alkhalifah and Tsvankin, 1995). VTI media induce nonhyperbolic moveout of reflections that depends on $V_{{\rm nmo}}$ and $\eta$ at large offsets. Alkhalifah (1997) showed that these two parameters can be obtained by analyzing the moveout at far offsets. The direct output from such an inversion (or velocity analysis) is the effective values of $V_{{\rm nmo}}$ and $\eta$, which include the combined (average) influence of the overburden. These effective values are converted to interval values using layer-stripping equations. Interval $\eta$ estimates resulting from the inversion are a direct low-resolution indicator of lithology, in which low $\eta$ values indicate sand-dominated intervals, and positive $\eta$ values indicate shale-dominated intervals.