TY - JOUR
T1 - Implementing the fast marching eikonal solver: Spherical versus Cartesian coordinates
AU - Alkhalifah, Tariq
AU - Fomel, Sergey
N1 - Generated from Scopus record by KAUST IRTS on 2023-09-21
PY - 2001/3/1
Y1 - 2001/3/1
N2 - 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.
AB - 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.
UR - http://doi.wiley.com/10.1046/j.1365-2478.2001.00245.x
UR - http://www.scopus.com/inward/record.url?scp=0035278841&partnerID=8YFLogxK
U2 - 10.1046/j.1365-2478.2001.00245.x
DO - 10.1046/j.1365-2478.2001.00245.x
M3 - Article
SN - 0016-8025
VL - 49
SP - 165
EP - 178
JO - Geophysical Prospecting
JF - Geophysical Prospecting
IS - 2
ER -