Linearized inversion of vertically fractured media

Abstract

In this paper we obtain a linearized reflection coefficient for quasi-compressional waves in fracture-related equivalent media, with respect to fracture density and infill material. We study the conditioning number of the inverse problem by analysis of eigenvalues and eigenvectors of this reflection coefficient. This is then used to investigate different acquisition geometries, either with varying azimuth or with varying offset. In the reservoir context, with fluid fill, only fracture density can be inverted using the P-wave AVO analysis.