INVERSION FOR ELASTIC PARAMETERS IN WEAKLY ANISOTROPIC MEDIA

Abstract

Linearized inversion equations of quasi P waves (qP) and quasi S waves (qS) in arbitrary weakly anisotropic media are presented. The equations can be used for local determination of weak anisotropy (WA) parameters in inhomogeneous media. The equations for qS waves hold not only in regular directions but also in singularities. In the case of qS-wave coupling, the first arrival of qS waves can be used alone for inversion. We obtain three equations for each wave expressed in terms of WA parameters. One of the equations relates the WA parameters to slowness and the other two relate the WA parameters to polarization vectors. By eliminating one or two components of the slowness vector from the three equations, we get a new equation system which enables us to perform inversion when two (or one) components of the slowness vector are known. Since a coordinate system is selected to be identical to the polarization vectors, the inversion formulae for qS waves become linear ones. A synthetic multi-azimuthal multiple-source walkaway vertical seismic profile experiment for an orthorhombic inhomogeneous medium with tilted symmetry axes is carried out to illustrate the applicability and efficiency of the method.