Interface-Flattening Transform for EM Field Modeling in Tilted, Cylindrically-Stratified Geophysical Media

TL;DR

This paper introduces an interface-flattening transformation based on Transformation Optics to accurately model electromagnetic fields in tilted, cylindrically-layered geophysical media, overcoming limitations of previous methods.

Contribution

The proposed method applies Transformation Optics to improve EM field modeling in tilted layered media, handling complex boundary conditions and medium properties more robustly than prior techniques.

Findings

Method is robust against absorption, anisotropy, and eccentering.

Applicable across a wide range of frequencies.

Analytical and preliminary numerical validation.

Abstract

We propose and investigate an "interface-flattening" transformation, hinging upon Transformation Optics (T.O.) techniques, to facilitate the rigorous analysis of electromagnetic (EM) fields radiated by sources embedded in tilted, cylindrically-layered geophysical media. Our method addresses the major challenge in such problems of appropriately approximating the domain boundaries in the computational model while, in a full-wave manner, predicting the effects of tilting in the layers. When incorporated into standard pseudo-analytical algorithms, moreover, the proposed method is quite robust, as it is not limited by absorption, anisotropy, and/or eccentering profile of the cylindrical geophysical formations, nor is it limited by the radiation frequency. These attributes of the proposed method are in contrast to past analysis methods for tilted-layer media that often place limitations on the source and medium characteristics. Through analytical derivations as well as a preliminary numerical investigation, we analyze and discuss the method's strengths and limitations.