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

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.