Spectral-domain-based scattering analysis of fields radiated by distributed sources in planar-stratified environments with arbitrarily anisotropic layers

Abstract

We discuss the numerically stable, spectral-domain computation and extraction of the scattered electromagnetic field excited by distributed sources embedded in planar-layered environments, where each layer may exhibit arbitrary and independent electrical and magnetic anisotropic response and loss profiles. This stands in contrast to many standard spectral-domain algorithms that are restricted to computing the fields radiated by Hertzian dipole sources in planar-layered environments where the media possess azimuthal-symmetric material tensors (i.e., isotropic, and certain classes of uniaxial, media). Although computing the scattered field, particularly when due to distributed sources, appears (from the analytical perspective, at least) relatively straightforward, different procedures within the computation chain, if not treated carefully, are inherently susceptible to numerical instabilities and (or) accuracy limitations due to the potential manifestation of numerically overflown and (or) numerically unbalanced terms entering the chain. Therefore, primary emphasis herein is given to effecting these tasks in a numerically stable and robust manner for all ranges of physical parameters. After discussing the causes behind, and means to mitigate, these sources of numerical instability, we validate the algorithm's performance against closed-form solutions. Finally, we validate and illustrate the applicability of the proposed algorithm in case studies concerning active remote sensing of marine hydrocarbon reserves embedded deep within lossy, planar-layered media.

Spectral-Domain Computation of Fields Radiated by Sources in Non-Birefringent Anisotropic Media

“…depth z coinciding). The error variation trend versus angle has been observed before [12] even when the source resided in non-NBAM media, and hence the increased error versus observation angle is not likely due to instabilities in the presented NBAM-robust algorithm. We conjecture rather that the increasing error (versus observation angle) arises due to commensurately increasing numerical cancellation 9 that can only be partially offset by a (computer resource limited) finite extent of hp integration refinement performed using finite precision arithmetic.…”

“…In both scenarios, the source resides at depth z = 0m within a threelayer NBAM, occupying the region while the bottom layer (z ≤ −1m) is a perfect electric conductor (PEC); note that this layered-medium configuration was specifically chosen to facilitate comparison with closedform solutions through invocation of T.O. and EM Image theory [12]. Indeed the EM field solution within z ≥ −1m, for our five-layered configuration involving a VED source, can be shown identical to the closed-form field result of two VED's (located at depths z = −1.75m and z = −19.25m) of identical orientation to the original VED and radiating in homogeneous, unbounded vacuum.…”

Full-wave algorithm to model effects of bedding slopes on the response of subsurface electromagnetic geophysical sensors near unconformities

“…In the interest of obtaining a good trade-off between the forward modeler's solution speed while still satisfactorily modeling the EM behavior of the environment's dominant geophysical features, a layered-medium approximation of the geophysical formation often proves very useful. Indeed cylindrical layering, planar layering, and a combination of the two (for example, to model the cylindrical exploratory borehole and invasion zone embedded within a stack of planar formation beds) are arguably three of the most widely used layering approximations in subsurface geophysics [2,4,5,[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], for both onshore and offshore geophysical exploration modeling [23][24][25][26][27][28][29][30][31][32][33]. The prevalence of layered-medium approximations stems in large part, at least from a computational modeling standpoint, due to the typical availability of closed-form eigenfunction expansions to compute the EM field [34][Ch.…”

“…[2][3]. These full-wave techniques are quite attractive since they can robustly deliver rapid solutions with high, user-controlled accuracy under widely varying conditions with respect to anisotropy and loss in the formation's layers, orientation and position of the electric or (equivalent) magnetic current-based sensors (viz., electric loop antennas), and source frequency [19,33]. The robustness to physical parameters is highly desirable in geophysics applications since geological structures are known to exhibit a wide range of inhomogeneity profiles with respect to conductivity, anisotropy, and geometrical layering [2,6,10].…”

“…2]. Our choice rests upon robust error control capabilities and speed performance of the 2-D integral transform with respect to source radiation frequency, source distribution, and material properties [5,33]. The use of eigenfunction expansions for modeling EM behavior of non-parallel layers is enabled here by the use of Transformation Optics (T.O.)…”