Characterization of heterogeneous fracture compliance using multiple reflections coupled with data-driven Green's function retrieval

The spatial heterogeneity along a fracture is a key determinant for fracture-associated hydraulic properties. We propose a new method to estimate the heterogeneous compliance distribution of a fracture from the reflection response at the fracture surface. For this purpose, we formulate a data-driven approach for Green's function retrieval based on Marchenko equation coupled with the inverse scattering to solve the linear-slip boundary condition. The approach estimates the wavefield along the fracture accurately, including the multiple reflections. Furthermore, it offers the opportunity to estimate compliance using multiple reflections, which was not possible so far. We show this concept by numerically modeling 2D SH waves sensing the heterogeneous tangential compliance of a fracture. Our results show that the use of multiple reflections leads to a better estimation of the heterogeneous fracture compliance than using primary reflection alone, especially for the far offsets on the fracture plane