Open AccessFinite Difference Traveltime Calculation For Anisotropic Media
Author(s) -
Eaton David W. S.
Publication year - 1993
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1993.tb03915.x
Subject(s) - eikonal equation , transverse isotropy , wavefront , isotropy , anisotropy , seismic anisotropy , seismic wave , mathematical analysis , gravitational singularity , finite difference , geometry , physics , mathematics , optics , geophysics
SUMMARY Seismic traveltimes for anisotropic elastic media are determined by numerical solution of the eikonal equation using a 2‐D finite difference approach. Most previous examples of this technique have been restricted to the geometrical‐optics form of the eikonal equation associated with isotropic media. Here, a general anisotropic form is used, with particular solutions for media with transversely isotropic (TI) symmetry. the algorithm tracks arrivals corresponding to a particular wave type (i.e. qP, qS) using an expanding‐wavefront scheme on a hexagonal mesh. In a homogeneous example, the method is demonstrated to be accurate for qP waves, but prone to large errors for qS waves in the vicinity of wavefront cuspidal edges and along shear wave singularities. Two other examples that incorporate both anisotropy and inhomogeneity demonstrate the potential usefulness of this algorithm for calculating qP traveltimes in more complex models.