The kinematic inverse problem for weakly laterally inhomogeneous anisotropic media

Abstract

The analysis of the kinematic inverse problem in anisotropic elastic media displays the indeterminacy of such problems in the presence of anisotropy. Some quantitative information about the elastic moduli must be available a priori. In view of the perturbational treatment applied here it is also assumed that elastic moduli are known in the zero approximation. The objective is to find corrections to elastic moduli corresponding to the observed deviations of travel time data from the zero approximation. If the deviations of travel times as well as the required supplementary information are available, then the kinematic inverse problem can be solved numerically. Allowance is made for weak lateral inhomogeneities. The method presented here applies to the layers lying above the first low velocity layer below the Earth's surface.