3D modeling of fractional diffusion to describe electromagnetic induction in fractured geological media

Abstract

Summary The fractional diffusion of the electromagnetic (EM) induction in fractured media is modeled using the 3D finite difference (FD) method in frequency domain. The EM fractional diffusion is one subset of anomalous transport processes, which is usually induced by the heterogeneities with various scales in the media. The governing equation of this process is based on the classical Maxwell equation and modified according to the continuous time random walk (CTRW) theory. The roughness parameter β in the new equation is directly related to the degree of heterogeneity of formations. To access the performance of this theory, the 3D FD modeling experiments are developed. The calculated EM response of a 1D layered model is compared with the analytical solution to validate the accuracy of the code. Then the classical Ex response to a halfspace model containing a 3D fractured subsurface zone is calculated to compare with responses of fractional diffusion model, and uniform halfspace reference model. The comparable classical models are expected to obtain to explore the relationship between the roughness β with the heterogeneities of the media.