Wave-equation shear wave splitting tomography

Abstract

The main focus of this paper is the development of a theoretical framework for the tomographic inversion of (broad-band) shear wave splitting measurements in terms of anisotropic structure in the upper mantle. We show that the partial differential equations (PDEs) that govern wave equation shearwave splitting tomography are, upon linearization with the Born approximation, similar in structure to the equations that describe wave equation transmission and reflection tomography. For full broad-band analysis these PDEs can be evaluated numerically, butwe show here the leading order asymptotic (i.e. ‘ray born’) behaviour of the associated finite-frequency sensitivity kernels. For simplicity we assume that the anisotropic model is invariant in one horizontal direction. This 2.5-D geometry is well suited for studying upper-mantle anisotropy associated with subduction of lithospheric plates if the trench-slab system is approximately 2-D.With the so-called splitting intensity as the metric for data fit, and under the assumption of weak anisotropy, we derive expressions for the sensitivity kernels.We focus on two anisotropic parameters that describe tilted transverse isotropy: the dip θ 0 of the symmetry axis with respect to the horizontal plane and the anellipticity parameter ЄA, which represents the strength of the anisotropy.We illustrate the finite-frequency effects both for homogeneous and heterogeneous (anisotropic) background models. The sensitivity kernels in heterogeneous media are calculated for initial models obtained from numerical modelling of flow and finite strain beneath the Ryukyu arc. Kernels calculated in heterogeneous media differ substantially from those in a homogeneous background. This demonstrates the importance of iterative model (and kernel) assessment for reaching the full (resolution) potential of finite frequency tomography.