Conclusions

We derived an eikonal equation that describes the kinematics of wave propagation in the time-domain. This eikonal equation provides exact traveltimes for a general inhomogeneous VTI, or isotropic, media. One of its main features is its independence from the vertical P-wave velocity in VTI media, assuming that the ratio of the vertical-to-NMO velocity in VTI media is laterally homogeneous, or in other words, that the anisotropy parameter $\delta$ does not change laterally. Even if $\delta$varies laterally, the impact of the variation on traveltimes is generally small. As a result, for practical purposes, traveltime calculation in this new $(x-\tau)$-domain is dependent on two parameters in VTI media, and one in elliptically anisotropic media. Using the eikonal equation, we derive an acoustic wave equation that describes wave propagation in the $(x-\tau)$domain. The existence of this wave equation implies that the amplitudes are also accurately calculated in the $(x-\tau)$-domain. In summary, this paper establishes the basis for a full inhomogeneous time-processing scheme in VTI media that is dependent on only v and $\eta$, and independent of the vertical P-wave velocity.