Research on direct integration algorithm of electromagnetic field in homogeneous layered media for a wide range of frequencies and transceiver distances
DAI Shikun1,2, ZENG Ling1,2, ZHOU Yinming1,2,3, LI Kun1,2, CHEN Qingrui1,2, LING Jiaxuan1,2
1. School of Geosciences and Info-physciences, Central South University, Changsha, Hunan 410083, China; 2. Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring of Ministry of Education, Central South University, Changsha, Hunan 410083, China; 3. GME & Geochemical Surveys, BGP, CNPC, Zhuozhou, Hebei 072751, China
Abstract:In geophysical exploration,the analytic expression of electromagnetic field in homogeneous layered media is Hankel integral,whose kernel function is Bessel function of order 0 and 1.With the increase of its synthesis,Bessel function presents the characteristics of fast oscillation and slow attenuation,which makes Hankel integral difficult to calculate with high efficiency and accuracy,especially in the case of high frequency and large receiving distance.In order to solve this problem,this paper proposes a direct integration method which is efficient and of high precision.The basic idea is that Bessel function can be divided into two intervals and expanded by different polynomials.Hankel integral of each interval can be divided into the sum of multiple unit integrals.The integrated function of each unit is represented by a cubic spline interpolation function,from which the analytic solution of the integral can be obtained.The numerical solution of Hankel integral can be obtained by superposition.On this basis,using the analytical solution to the electromagnetic field of the electric dipole in the uniform whole space,the correct selection of the integral range and the appropriate partition of the integral element are studied.The comparison between the numerical solution and the a-nalytical solution shows that the algorithm is correct and reliable.The comparison between the algorithm proposed in this paper and the digital filter-ing algorithm shows that the algorithm is widely applicable to the calculation of electromagnetic fields with different frequencies and different receiving distances.Therefore it is used very universally.
戴世坤, 曾铃, 周印明, 李昆, 陈轻蕊, 凌嘉宣. 频率和收发距广普适用的均匀层状介质电磁场直接积分算法[J]. 石油地球物理勘探, 2020, 55(6): 1364-1372,1394.
DAI Shikun, ZENG Ling, ZHOU Yinming, LI Kun, CHEN Qingrui, LING Jiaxuan. Research on direct integration algorithm of electromagnetic field in homogeneous layered media for a wide range of frequencies and transceiver distances. Oil Geophysical Prospecting, 2020, 55(6): 1364-1372,1394.
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