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

Tariq Alkhalifah*, Sergey Fomel, Biondo Biondi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

64 Scopus citations


In transversely isotropic media with a vertical axis of symmetry (VTI media), we 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 (χ-τ)-domain, the ray tracing and eikonal 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 (α) is laterally invariant. Moderate size departures of x from lateral homogeneity affect traveltimes only slightly. As a result, for all practical purposes, the VTI equations in the (x-τ)-domain become dependent on only two parameters in laterally inhomogeneous media: the NMO velocity for a horizontal reflector, and an anisotropy parameter, η. An acoustic wave equation in the (x-τ)-domain is also independent of the vertical P-wave velocity. It includes an asymmetric 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 ν and η, and independent of the vertical P-wave velocity.

Original languageEnglish (US)
Pages (from-to)105-113
Number of pages9
JournalGeophysical Journal International
Issue number1
StatePublished - 2001
Externally publishedYes


  • Anisotropy
  • Modellinhg
  • Traveltime

ASJC Scopus subject areas

  • Geophysics
  • Geochemistry and Petrology


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