The Traveltime Modelling in Factorized Anisotropic Inhomogeneous Media by the Perturbation Methods

Abstract

Traveltime computations in factorized anisotropic inhomogeneous (FAI) media are performed by ray tracing and perturbation methods. In the FAI media the spatial variation of a2l density normalized elastic parameters is assumed to be tlle same. a...1¡ ) : fl(.x )A .,,. wlrere flx ) is a continuous smooth function of Cartesian "oórdiíìuiôs , àìd Ñ,-i,,are consiaäts, independent ofx.. The types of anisotropy (4,,,,) and inhoìnogen'diies [f(x-)] are not reitricted, buttheir effècts are separaied. Tffe results of computations obtained by both methods are used to check the accuracy and limitations ofthe perturbation approach. The advantage of this method is that rays computed by the 2-D isotropic ray tracing can be used to estimate travel times in a more general 3-D anisotropic media. The least-squares criterium is used to minimize the differences between perturbed and background media. Examples of orthorhombic and transversely isotropic media are presented, with VSP and surface acquisition geometries, including layered media.