Fast sweeping methods for factored TTI eikonal equation

U. Waheed*, T. Alkhalifah

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations


The finite-difference based eikonal solution for a point-source initial condition has an upwind singularity at the source position. As a result, even the high-order finite-difference schemes exhibit at most polluted first-order convergence, as the errors around the source location spread to the whole computational domain. We apply factorization approach to obtain clean first-order solutions for the tilted transversely isotropic (TTI) eikonal equation. The idea relies on factoring the unknown traveltime function into two terms. One of these two factors is utilized to capture the source singularity; thus, the other function is smooth in the neighborhood of the source. We solve a sequence of factored tilted elliptically anisotropic eikonal equations, each time by updating the effective velocities needed to capture the higher order nonlinearity of the TTI eikonal equation. We design an iterative monotone fast sweeping scheme to compute the TTI eikonal solution. Numerical tests show significant improvement in accuracy due to the factorization approach compared to directly solving the eikonal equation.

Original languageEnglish (US)
Title of host publication77th EAGE Conference and Exhibition 2015
Subtitle of host publicationEarth Science for Energy and Environment
PublisherEuropean Association of Geoscientists and Engineers, EAGE
Number of pages5
ISBN (Electronic)9781510806627
StatePublished - Jan 1 2015
Event77th EAGE Conference and Exhibition 2015: Earth Science for Energy and Environment - Madrid, Spain
Duration: Jun 1 2015Jun 4 2015


Conference77th EAGE Conference and Exhibition 2015: Earth Science for Energy and Environment

ASJC Scopus subject areas

  • Geochemistry and Petrology
  • Geophysics


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