Thin Dielectric Sheet-Based Surface Integral Equation for the Scattering Simulation of Fractures in a Layered Medium

Abstract

Electromagnetic simulation of fractures has a growing importance in geophysical exploration, where the formation is usually inhomogeneous and modeled as a layered medium (LM). In this paper, we have developed the first integral-equation based solver to simulate the scattering of fractures straddling an LM. We refer to this solver as LM-thin dielectric sheet (TDS)-surface integral equation (SIE), since it is built on the TDS-based SIE and the LM Green's function (LMGF). Compared with the traditional finite element method (FEM) and volume integral equation (VIE), LM-TDS-SIE achieves excellent efficiency by taking advantage of the multiscale feature of fracture, rather than being restricted by its volumetric mesh. Good accuracy but the lower computational cost of LM-TDS-SIE is well demonstrated by investigating several typical examples, where reference results are obtained by the commercial software COMSOL. In addition to fractures, LM-TDS-SIE can also be used to simulate the scattering from other types of TDS.