A useful byproduct of studying shear-wave coupling in inhomogeneous weakly anisotropic media are formulae for approximate evaluation of traveltimes of separate S waves. The traveltimes can be obtained from perturbations computed along so-called first-order S-wave common rays. The perturbations consist of two parts. The first represents correction of the traveltime computed along the first-order common ray. The other controls separation of S waves. Both parts can be simply evaluated by quadratures along the common ray. The formulae have applications in migration and traveltime tomography.
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