Time-domain processing in arbitrarily inhomogeneous media

Constructing the seismic image in vertical time, as opposed to depth, eliminates the inherent ambiguity of resolving the vertical P -wave velocity from surface seismic data, in transversely isotropic media with a vertical axis of symmetry (VTI media). We show that, in the (x- τ)- domain, the raytracing and eikonal equations are completely independent of the vertical P-wave velocity, on the condition that the ratio of the vertical to normal-moveout (NMO) P-wave velocity (α) is laterally invariant. Practical size departures of α from lateral homogeneity affect traveltimes only slightly. As a result, for all practical purposes, the VTI equations in the (x-τ)-domain are dependent on only two parameters in laterally inhomogeneous media: the NMO velocity for a horizontal reflector, and an anisotropy parameter, ŋ. In summary, we have established the basis for a full inhomogeneous time-processing scheme for VTI media that is independent of the vertical P-wave velocity.