Seismic full waveform inversion for fracture parameters in anisotropic media

Abstract

Vertical fractures are often reported in sedimentary rocks. The detection of these inherent fractures is important before carrying out the carbon dioxide sequestration in these rocks. The detection of the fractures is also crucial for an accurate estimation of the moment tensor from microseismic waveform data. In this study, we use the distorted Born iterative method to perform seismic full waveform inversion for the parameters of vertical fractures in sedimentary formations. The distorted Born iterative method is based on transforming a nonlinear inverse scattering problem into a series of linear inverse problems by using the distorted Born approximation. We work in the frequency domain and use a volume integral equation method to solve the direct scattering problem. A heterogeneous, generally anisotropic medium, is iteratively updated using the matrix-free formulation of Fréchet derivatives and their adjoint. In the distorted Born iterative method, the heterogeneous medium Green's function is also updated after each iteration, which is not done in the classical Born iterative method. In our implementation, we assume that the fractures are thin, vertical and parallel to each other. The background, in which fractures are embedded, is transversely isotropic with a vertical axis of symmetry. The vertically transversely isotropic background can be inhomogeneous. In an isotropic background, it is common to invert for a single tangential fracture weakness along with a normal fracture weakness. However, in a vertically transversely isotropic background, the horizontal-tangential and the vertical-tangential fracture weaknesses vary, and therefore we invert for three fracture weaknesses. In numerical experiments, we employ a cross-hole seismic configuration and invert synthetic waveform data for fracture weaknesses. The radiation pattern analysis is performed to investigate the cross-talk among different fracture weaknesses. It is found that the horizontal-tangential fracture weakness is better resolved than the other fracture weaknesses, which is confirmed through the numerical results.