Grid dispersion minimization in Green's tensor used in Scattering Integral (SI) inversion method

Abstract

Theories of three‐dimensional seismic tomography using full physics of waveform have been around for decades but were not widely used until the last decade when computing power started to grow rapidly. Two different formulations for structural inversions have been investigated in recent years. One of them is the Adjoint‐Wavefield method and the other one is Scattering Integral (SI) method. In this paper, we have discussed step by step procedures for computing data sensitivity kernels required for structural inversion using Scattering Integral (SI) method. In the SI method, data functionals are linearly related to model perturbations using source‐receiver specific sensitivity kernels. Data sensitivity kernels are functional derivatives of data with respect to model parameters around a background structure. The Green's function for each source‐receiver pair and source wavefield required for data sensitivity (Fréchet) kernels was generated using staggered‐grid finite‐difference method. One of the issues in this finite‐difference method for calculating Green's function is grid‐dispersion. A FIR (Finite Impulse Response) filtering technique is used to minimize grid dispersion, and thus to reduce noise in the sensitivity kernels. This method of calculating source‐receiver Green's function provided better results in sensitivity kernels. A two‐dimensional acoustic case is implemented in this paper for simplicity, but this approach can easily be extended to three‐dimensional and elastic case.