Full-Wave Algorithm to Model Effects of Bedding Slopes on the Response of Subsurface Electromagnetic Geophysical Sensors near Unconformities

TL;DR

This paper introduces a full-wave pseudo-analytical electromagnetic algorithm that models the effects of bedding slopes on subsurface sensors, using Transformation Optics to handle tilted interfaces efficiently and accurately.

Contribution

The novel algorithm employs Transformation Optics to model arbitrarily tilted geological interfaces with minimal computational overhead, improving upon previous methods that assumed parallel bed junctions.

Findings

The algorithm accurately models wave interactions with tilted interfaces.

Numerical results show error trends related to material properties and sensor configurations.

Sensor responses vary significantly with formation anisotropy, loss, and tilt.

Abstract

We propose a full-wave pseudo-analytical numerical electromagnetic (EM) algorithm to model subsurface induction sensors, traversing planar-layered geological formations of arbitrary EM material anisotropy and loss, which are used, for example, in the exploration of hydrocarbon reserves. Unlike past pseudo-analytical planar-layered modeling algorithms that impose parallelism between the formation's bed junctions however, our method involves judicious employment of Transformation Optics techniques to address challenges related to modeling relative slope (i.e., tilting) between said junctions (including arbitrary azimuth orientation of each junction). The algorithm exhibits this flexibility, both with respect to loss and anisotropy in the formation layers as well as junction tilting, via employing special planar slabs that coat each "flattened" (i.e., originally tilted) planar interface, locally redirecting the incident wave within the coating slabs to cause wave fronts to interact with the flattened interfaces as if they were still tilted with a specific, user-defined orientation. Moreover, since the coating layers are homogeneous rather than exhibiting continuous material variation, a minimal number of these layers must be inserted and hence reduces added simulation time and computational expense. As said coating layers are not reflectionless however, they do induce artificial field scattering that corrupts legitimate field signatures due to the (effective) interface tilting. Numerical results, for two half-spaces separated by a tilted interface, quantify error trends versus material and sensor characteristics. We finally exhibit responses of sensors traversing three-layered media, where we vary the anisotropy, loss, and relative tilting of the formations and explore the sensitivity of the sensor's complex-valued measurements.