Explicit analytical expressions for qP-wave Green functions in weakly anisotropic multilayered media of arbitrary symmetry.

Analytical expressions for Green functions in arbitrary inhomogeneous elast ic media have been published in the literature. However most of the quantit ies (traveltime, wave front curvature... etc.) defining these expressions a re not explicitly given but must be numerically estimated, for instance usi ng ray tracing codes. Here we propose explicit analytical equations for qP- wave far-field high-frequency solution of the Green function in layered mod els constituted by weakly anisotropic media of arbitrary symmetry (triclini c). These equations are tested on a synthetic model with layers of contrast ed anisotropy type (from isotropic to triclinic) and strength (anisotropy p arameters from 0 to about 20%). All the results (in terms of traveltime, di splacement amplitude, polarisation vector and normal vector) are in a good agreement with the results obtained with ray tracing codes even for relativ ely large incidence angles (up to 45 degrees). Beside of the good fit of ou r results, these equations allow for a considerable reduction in computatio n time. Compared to ray tracing codes, in our tests, a time reduction by a factor of a few hundreds was obtained. Thus, these equations are, for insta nce, particularly adapted to time and true amplitude migration software (wh ich is the primary motivation of these developments), or more generally, to inversion software for which particularly intensive computation of direct problems are needed.