Enhanced characterization of fracture compliance heterogeneity using multiple reflections and data-driven Green's function retrieval

Abstract

The spatial heterogeneity along a fracture is a key determinant for fracture-associated mechanical and hydraulic properties of the subsurface. Laboratory experiments have been performed to test the applicability of the nonwelded interface representation to predict the frequency- and angle-dependent elastic response of a single fracture. The observation that nonwelded interface model can represent quite well the frequency- and angle-dependent reflection response of a fracture has led us to develop a new methodology for estimating the spatially heterogeneous fracture compliance from the reflection response along a fracture surface. A data-driven approach based on Marchenko equation coupled with inverse scattering to solve the nonwelded interface boundary condition has been formulated. The approach estimates the elastic wavefield along a fracture accurately, including the multiple reflections. As an extension, it offers the possibility to estimate fracture compliance using the multiple reflections. We illustrate the concept by numerically modeling 2-D SH waves sensing the heterogeneous tangential compliance of a fracture. The stationary phase method is applied to single and double spatial integrals to analyze the effect of source and receiver aperture on the Green's function retrieval. Our results show that the use of multiple reflections allows a better estimation of the heterogeneous fracture compliance than using primary reflections alone, especially for the far offsets on the fracture plane.