An efficient and flexible approach to the calculation of three-dimensional full-wave Fréchet kernels for seismic tomography-II. Numerical results

Abstract

Seismic tomography has been developed largely on the basis of the Born approximation, in which any waveform-derived seismic observable, such as a perturbation in traveltime, is linearly related to the local perturbation of a model parameter, such as the speed of a seismic wave. This relation defines a Fréchet kernel which can be expressed as the convolution of two strain Green's tensors from the source and receiver to the perturbation location. We develop a new approach for computing the Fréchet kernels using pre-calculated databases of strain Green's tensors. After deriving the general expressions of Fréchet kernels in terms of the strain Green's tensors, we obtain specific expressions for the sensitivities of traveltime and amplitude to both isotropic and anisotropic perturbations of the elastic moduli. We also derive the Fréchet kernels of the SKS-splitting intensity for anisotropic model parameters. Numerical examples of Fréchet kernels are presented for a variety of seismic phases to demonstrate the efficiency and flexibility of this new approach and its potential for both regional and global finite-frequency tomography applications.