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

Abstract

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