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

摘要

We propose a full-wave pseudo-analytical numerical electromagnetic (EM)algorithm to model subsurface induction sensors, traversing planar-layeredgeological formations of arbitrary EM material anisotropy and loss, which areused, for example, in the exploration of hydrocarbon reserves. Unlike pastpseudo-analytical planar-layered modeling algorithms that impose parallelismbetween the formation's bed junctions however, our method involves judiciousemployment of Transformation Optics techniques to address challenges related tomodeling relative slope (i.e., tilting) between said junctions (includingarbitrary azimuth orientation of each junction). The algorithm exhibits thisflexibility, both with respect to loss and anisotropy in the formation layersas well as junction tilting, via employing special planar slabs that coat each"flattened" (i.e., originally tilted) planar interface, locally redirecting theincident wave within the coating slabs to cause wave fronts to interact withthe flattened interfaces as if they were still tilted with a specific,user-defined orientation. Moreover, since the coating layers are homogeneousrather than exhibiting continuous material variation, a minimal number of theselayers must be inserted and hence reduces added simulation time andcomputational expense. As said coating layers are not reflectionless however,they do induce artificial field scattering that corrupts legitimate fieldsignatures due to the (effective) interface tilting. Numerical results, for twohalf-spaces separated by a tilted interface, quantify error trends versusmaterial and sensor characteristics. We finally exhibit responses of sensorstraversing three-layered media, where we vary the anisotropy, loss, andrelative tilting of the formations and explore the sensitivity of the sensor'scomplex-valued measurements.