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Pade Approximant ELF VED Fields in the Earth-Ionosphere Cavity
Radio Science ( IF 1.6 ) Pub Date : 2021-06-29 , DOI: 10.1029/2020rs007226 PengFei Liang 1, 2, 3 , QingYun Di 1, 2, 3 , Changmin Fu 1, 2, 3 , Ruo Wang 1, 2, 3 , Jianbao Fan 1, 2, 3 , Ya Gao 1, 2, 3
Radio Science ( IF 1.6 ) Pub Date : 2021-06-29 , DOI: 10.1029/2020rs007226 PengFei Liang 1, 2, 3 , QingYun Di 1, 2, 3 , Changmin Fu 1, 2, 3 , Ruo Wang 1, 2, 3 , Jianbao Fan 1, 2, 3 , Ya Gao 1, 2, 3
Affiliation
Electromagnetic (EM) fields in the extremely low-frequency (ELF) domain that can be excited by the vertical electric dipole (VED) and propagated in the Earth-ionosphere spherical cavity have received tremendous attention owing to their exploitation in many fields such as communication, earthquake prediction, and geophysical investigations. Some researchers use the planar model and curvature correction terms to simulate EM fields in a spherical cavity, while others directly solve the differential functions and estimate the excited EM fields represented by spherical Bessel and associated Legendre functions. Regarding the divergence problem of a series when simulating EM fields, several numerical methods are available such as Watson transformation method, W. K. B. J method, and speeding algorithm. In this study, Pade approximant is utilized to estimate EM fields propagating in the Earth-ionosphere spherical cavity, where new asymptotic expansions of spherical Bessel functions are introduced for estimating their products for high orders. These EM fields are then interpreted as a sum of the dominant incident fields and the increase of multiple scattering fields. The convergence of series expressions of EM fields estimated by Pade approximant is theoretically guaranteed, with its computational complexity lower than that of the speeding algorithm. The EM fields are further verified by numerical tests. The effects of the height and conductivity of the ionosphere, the conductivity of air, the VED height, and the frequencies of the resonance phenomenon are also highlighted. The proposed method is helpful to capture the true nature of the field distribution within a spherical cavity.
中文翻译:
地球-电离层空腔中的 Pade 近似 ELF VED 场
可被垂直电偶极子(VED)激发并在地-电离层球腔中传播的极低频(ELF)域中的电磁(EM)场由于其在通信等许多领域的开发而受到了极大的关注。 、地震预测和地球物理调查。一些研究人员使用平面模型和曲率校正项来模拟球腔中的电磁场,而其他人则直接求解微分函数并估计由球面贝塞尔和相关勒让德函数表示的激发电磁场。对于模拟电磁场时级数的发散问题,有几种数值方法可用,如沃森变换法、WKB J 法和超速算法。在这项研究中,Pade 近似用于估计在地球-电离层球形腔中传播的电磁场,其中引入了球形贝塞尔函数的新渐近展开来估计它们的高阶乘积。然后将这些 EM 场解释为主要入射场和多个散射场增加的总和。Pade近似估计的电磁场级数表达式的收敛性在理论上是有保证的,其计算复杂度低于超速算法。电磁场通过数值测试进一步验证。还强调了电离层的高度和电导率、空气的电导率、VED 高度和共振现象频率的影响。
更新日期:2021-07-13
中文翻译:
地球-电离层空腔中的 Pade 近似 ELF VED 场
可被垂直电偶极子(VED)激发并在地-电离层球腔中传播的极低频(ELF)域中的电磁(EM)场由于其在通信等许多领域的开发而受到了极大的关注。 、地震预测和地球物理调查。一些研究人员使用平面模型和曲率校正项来模拟球腔中的电磁场,而其他人则直接求解微分函数并估计由球面贝塞尔和相关勒让德函数表示的激发电磁场。对于模拟电磁场时级数的发散问题,有几种数值方法可用,如沃森变换法、WKB J 法和超速算法。在这项研究中,Pade 近似用于估计在地球-电离层球形腔中传播的电磁场,其中引入了球形贝塞尔函数的新渐近展开来估计它们的高阶乘积。然后将这些 EM 场解释为主要入射场和多个散射场增加的总和。Pade近似估计的电磁场级数表达式的收敛性在理论上是有保证的,其计算复杂度低于超速算法。电磁场通过数值测试进一步验证。还强调了电离层的高度和电导率、空气的电导率、VED 高度和共振现象频率的影响。