Coupled S waves in inhomogeneous weakly anisotropic media using first-order ray tracing

Veronique Farra & Ivan Psencik


We present a modification of our recently proposed approximate procedure for computing coupled S waves in inhomogeneous weakly anisotropic media. The new procedure can be used to compute S waves propagating in smooth inhomogeneous isotropic or anisotropic media. In isotropic media, it reduces to standard ray theory procedure for S waves. In anisotropic media, it can be used to study coupled as well as decoupled S waves. As the previous procedure, the new one is also based on the approximately computed common S-wave ray. First-order ray tracing and dynamic ray tracing, originally developed for computations of P-wave fields, is used to compute common S-wave rays and the dynamic ray tracing along them. The principal difference between the previous and new procedure consists in implicit incorporation of the second-order common S-wave traveltime correction and more accurate estimate of traveltime difference in the modified coupling equations. This leads to a substantial increase of accuracy of the coupling equations, which are solved along the common ray to evaluate S-wave amplitudes. The new coupling equations provide, first of all, more accurate traveltimes, but they also allow modelling of decoupled S waves, which could hardly be done with the original coupling equations. There is no need for a choice of a reference medium. The reference medium is determined uniquely from the actual medium.

The new procedure has all the advantages of the previous procedure. Among the basic advantages is that it can describe the coupling of S waves. The procedure eliminates problems with ray tracing in the vicinity of singularities; the common S-wave ray tracing is as stable as P-wave ray tracing. Due to the use of perturbation formulae, the ray tracing, dynamic ray tracing and coupling equations are much simpler and more transparent than in the exact case. As a byproduct of both coupling procedures, we get formulae for approximate evaluation of traveltimes of separate S waves. These formulae can find applications in migration and traveltime tomography.

The accuracy of the previous and modified coupling procedures is studied on several models of varying strength of anisotropy. First, we investigate the accuracy of perturbation formulae in homogeneous models, in which coupling does not exist. Then we study both coupling and accuracy of perturbation formulae in inhomogeneous models.We compare the results obtained by the coupling procedures with the results of the quasi-isotropic approach and standard ray theory.


Body waves, seismic anisotropy, wave propagation.

Geophys. J. int., 180 (2010), 405-417.
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