层状介质任意位置点源场快速计算  

Fast Computation of Fields from Point Sources at Arbitrary Positions in Layered Media

作　　者：吴延强 凌嘉宣 韦舒柳 梁丽君 WU Yanqiang;LING Jiaxuan;WEI Shuliu;LIANG Lijun(Guangxi Water&Power Design Institute,Nanning,Guangxi 530023,China;College of Computer Science and Engineering,Guilin University of Aerospace Technology,Guilin,Guangxi 541004,China;Guangxi Region Geological Survey Institute,Nanning,Guangxi 530023,China)

机构地区：[1]广西壮族自治区水利电力勘测设计研究院有限责任公司,广西南宁530023 [2]桂林航天工业学院计算机科学与工程学院,广西桂林541004 [3]广西壮族自治区地质调查院,广西南宁530023

出　　处：《桂林航天工业学院学报》2025年第1期112-121,共10页Journal of Guilin University of Aerospace Technology

基　　金：广西自然科学基金项目“任意各向异性介质中直流电阻率法三维反演方法研究”(2025GXNSFBA069422);桂林航天工业学院博士教授科研启动项目“基于积分解的直流电阻率法三维正反演方法研究”(KX202300101);广西高校中青年教师科研能力提升项目“半航空频率域电磁法三维高效数值模拟研究”(2024KY0800);桂林航天工业学院特色优势交叉学科发展战略研究专项课题“广西-东盟锰矿胁迫指示植物遥感时谱流变特征的产生机理及识别机制研究”(TS2024452)。

摘　　要：文章推导了层状介质中点源在任意位置的电位和电场的通用表达式。为了提高计算效率,开发了一种优化的滤波算法,该算法首先计算并存储每个波数下与z轴无关的平面层系数,随后通过这些层系数与z轴相关的指数项相乘并累加,快速得到任意节点的电位和电场值。通过一系列算例分析,验证了所提算法的正确性和高效率,特别是在处理具有大量地层和节点的复杂模型时,优化算法的优势尤为突出。此外,文章还详细展示了层状介质中电位和电场在空间中分布特征。This paper derives the mathematical expressions for the potential and electric field generated by a point source at any location within layered media.To improve computational efficiency,an optimized filtering algorithm is introduced.This novel approach initially computes and archives the plane layer coefficients,which are independent of the z-axis for each wavenumber.Subsequently,it swiftly determines the potential and electric field values at any given node by multiplying these coefficients with the z-axis-dependent exponential terms and aggregating the results.Through a series of numerical example analyses,the correctness and high efficiency of the proposed algorithm have been verified.Particularly when handling complex models with a large number of strata and nodes,the advantages of the optimization algorithm are particularly prominent.Furthermore,it elucidates the spatial distribution patterns of potential and electric fields within layered media.

关 键 词：层状介质 滤波法 任意位置 快速计算 

分 类 号：P631.3[天文地球—地质矿产勘探]