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

Abstract

SUMMARY We propose a new approach to computing the sensitivity kernels used in seismic tomography based on a Green's function database. For any perturbation in the Earth's structural model, the waveform Frechet derivative can be expressed in terms of strain Green's tensors, which are themselves functions of the reference Earth model only. The Frechet derivative of any seismic observable can then be obtained from waveform Frechet derivative. Given a reference model, a strain Green's tensor database can be established, thus eliminating the need for repetitive wavefield evaluations in all subsequent synthetic and kernel calculations, and reducing the CPU time. For a spherically symmetric reference Earth model, the strain Green's tensor database can be constructed on a (r, Δ) grid by normal-mode summation. The stored strain Green's tensors can then be used to quickly evaluate the wavefield between any source and receiver. The generality of the strain Green's tensors makes it possible to compute the Frechet kernels for any phase on a seismogram (P, S, Pdiff, surface waves, etc.), for any type of data (traveltime, amplitude, splitting intensity, waveform, etc.), and for any parameter (isotropic, anisotropic, attenuation, etc.). The kernel calculation at each point in the medium is reduced to the convolution of two sets of strain Green's tensors extracted from the database, which makes the approach extremely efficient.