Mixed Total Field/Scattered Field-Based Discontinuous Galerkin Frequency-Domain Method for Subsurface Sensing

Abstract

To model the responses of electromagnetic surveys for geophysical subsurface sensing, a mixed total field/scattered field-based discontinuous Galerkin frequency-domain (TF/SF DGFD) method is proposed in this paper. The proposed TF/SF DGFD method is implemented at a subdomain level based on the domain decomposition technique. Different subdomains can employ either the TF DGFD framework or the SF DGFD framework, which are then coupled through the Riemann transmission condition. To balance the computation efficiency and accuracy for practical applications, the proposed method prefers to using the SF DGFD framework for subdomains with sources and using the TF DGFD framework for the remaining subdomains. At the interfaces between total field and scattered field subdomains, the Riemann transmission condition is slightly modified by incorporating the background fields due to the physically imposed sources in the background media. In this way, the proposed method only requires surface integrals of the background fields as extra overhead instead of elementwise integration of the scattering objects for the purely scattered field-based method, which can improve the computational efficiency. Also, it is more accurate than the purely TF DGFD method given the same mesh. Numerical examples are studied to examine the performance of the proposed method, which is proven to have better accuracy than the TF DGFD method. The TF/SF DGFD method will facilitate modeling of electromagnetic surveys under complicated geophysical environments for subsurface sensing.