Implementing the fast marching eikonal solver: Spherical versus Cartesian coordinates

Tariq Alkhalifah*, Sergey Fomel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

75 Scopus citations


Spherical coordinates are a natural orthogonal system for describing wavefronts emanating from a point source. A regular grid distribution in the Cartesian-coordinate system tends to undersample the wavefront description near the source (at the highest wavefront curvature) and oversample it away from the source. Spherical coordinates, in general, provide a more balanced grid distribution for characterizing point-source wavefronts. Our numerical implementation confirms that the recently introduced fast marching algorithm is both a highly efficient and an unconditionally stable eikonal solver. However, its first-order approximation of traveltime derivatives can induce relatively large traveltime errors for waves propagating in a diagonal direction with respect to the coordinate system. Examples, including the IFP Marmousi and the SEG/EAGE 3D salt-dome models, show that a spherical-coordinate implementation of the method results in far fewer errors in traveltime calculation than the conventional Cartesian-coordinate implementation, and with practically no loss in computational advantages.

Original languageEnglish (US)
Pages (from-to)165-178
Number of pages14
JournalGeophysical Prospecting
Issue number2
StatePublished - Mar 2001
Externally publishedYes

ASJC Scopus subject areas

  • Geophysics
  • Geochemistry and Petrology


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