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

Veronique Farra & Ivan Psencik


We present a generalization of the 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 S-wave ray tracing. 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 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 it. The principal difference between the previous and new procedure consists in 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.

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. There is no need to construct a reference medium as, for example, in the quasi-isotropic approach. 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 new 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 perturbation effects in inhomogeneous models. We compare the results obtained with the coupling procedures with the results of the quasi-isotropic approach and standard ray theory.


Body waves, seismic anisotropy, wave propagation.

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In: Seismic Waves in Complex 3-D Structures, Report 19, pp. 63-91, Dep. Geophys., Charles Univ., Prague, 2009.
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