The space-time domain: theory and modelling for anisotropic media

In transversely isotropic media with a vertical axis of symmetry (VTI media ), we represent the image in vertical time, as opposed to depth, thus elimi nating the inherent ambiguity of resolving the vertical P-wave velocity fro m surface seismic data. In this new (x-tau)-domain, the ray tracing and eik onal equations are completely independent of the vertical P-wave velocity, with the condition that the ratio of the vertical to normal-moveout (NMO) P -wave velocity (rn) is laterally invariant. Moderate size departures of a f rom lateral homogeneity affect traveltimes only slightly. As a result, for all practical purposes, the VTI equations in the (x-tau)-domain become depe ndent on only two parameters in laterally inhomogeneous media: the NMO velo city for a horizontal reflector, and an anisotropy parameter, eta. An acous tic wave equation in the (x-tau)-domain is also independent of the vertical P-wave velocity. It includes an asymmetric Laplacian operator to accommoda te the unbalanced axis units in this new domain. In summary, we have establ ished the basis for a full inhomogeneous time-processing scheme in VTI medi a that is dependent on only v and eta, and independent of the vertical P-wa ve velocity.