Sainath Kamalesh, Teixeira Fernando L
ElectroScience Laboratory, The Ohio State University, 1330 Kinnear Road, Columbus, Ohio 43212, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Dec;90(6):063302. doi: 10.1103/PhysRevE.90.063302. Epub 2014 Dec 1.
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.
我们讨论了嵌入平面分层环境中的分布式源所激发的散射电磁场的数值稳定谱域计算与提取,其中每层介质可能呈现任意且独立的电各向异性、磁各向异性响应及损耗分布。这与许多标准谱域算法形成对比,那些算法仅限于计算平面分层环境中赫兹偶极子源辐射的场,且该环境中的介质具有方位对称的材料张量(即各向同性以及某些类别的单轴介质)。尽管计算散射场,特别是由分布式源产生的散射场(至少从分析角度来看)似乎相对简单,但计算链中的不同步骤若处理不当,由于计算链中可能出现数值溢出和(或)数值不平衡项,会固有地易受数值不稳定性和(或)精度限制的影响。因此,本文主要强调以数值稳定且稳健的方式针对所有物理参数范围执行这些任务。在讨论了这些数值不稳定性的成因及缓解方法后,我们对照闭式解验证了算法的性能。最后,我们在涉及对深埋于有损平面分层介质中的海洋碳氢化合物储量进行有源遥感的案例研究中,验证并说明了所提算法的适用性。