Validation of the boundary conditions to model the seismic response of fractures

Fractures in fluid-saturated poroelastic media can be modeled as extremely thin, highly permeable, and compliant layers or by means of suitable boundary conditions that approximate the behavior of such thin layers. Since fracture apertures can be very small, the numerical simulations would require the use of extremely fine computational meshes and the use of boundary conditions would be required. In this work, we study the validity of using boundary conditions to describe the seismic response of fractures. For this purpose, we compare the corresponding scattering coefficients to those obtained from a thin-layer representation. The boundary conditions are defined in terms of fracture apertures that, in the most general case, impose discontinuity of displacements, fluid pressures, and stresses across a fracture. Furthermore, discontinuities of either fluid pressures, stresses, or both can be removed, or displacement jumps proportional to the stresses and/or pressures can be expressed via shear and normal dry compliances in order to simplify. In the examples, we vary the permeability, thickness, and porosity of the fracture and the type of fluid saturating the background medium and fractures. We observe good agreement of the scattering coefficients in the seismic range obtained with the two different approaches.