Time-domain anisotropic processing in arbitrarily inhomogeneous media

Tariq Alkhalifah, Sergey Fomel, and Biondo Biondi

tariq@sep.stanford.edu, sergey@sep.stanford.edu, biondo@sep.stanford.edu

ABSTRACT

In transversely isotropic media with a vertical axis of symmetry (VTI media), we can represent the image in vertical time, as opposed to depth, thus eliminating the inherent ambiguity of resolving the vertical P-wave velocity from surface seismic data. In this new $(x-\tau)$-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 ($\alpha$) is laterally invariant. Practical size departures of $\alpha$ from lateral homogeneity affect traveltimes only slightly. As a result, for all practical purposes, the VTI equations in the $(x-\tau)$-domain become dependent on only two parameters in laterally inhomogeneous media: the NMO velocity for a horizontal reflector, and an anisotropy parameter, $\eta$. An acoustic wave equation in the $(x-\tau)$-domain is also independent of the vertical velocity. It includes an unsymmetric Laplacian operator to accommodate the unbalanced axis units in this new domain. In summary, we have established 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.