基于泊松方程的空间波数混合域二度体磁异常数值模拟  

Two-Dimensional Numerical Modeling of Magnetic Anomalies Based on Poisson Equation in Space-Wavenumber Mixed Domain

作　　者：赵东东 王旭龙[2,3] 周印明 戴世坤 Zhao Dongdong;Wang Xulong;Zhou Yinming;Dai Shikun(Nanjing Center,China Geological Survey,Nanjing 210016,China;School of Geosciences and Info-physics,Central South University,Changsha410083,China;Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring(Central South University),Ministry of Education,Changsha410083,China;School of Information and Electrical Engineering,Hunan University of Science and Technology,Xiangtan411201,Hunan,China)

机构地区：[1]中国地质调查局南京地质调查中心,南京210016 [2]中南大学地球科学与信息物理学院,长沙410083 [3]有色金属成矿预测与地质环境监测教育部重点实验室(中南大学),长沙410083 [4]湖南科技大学信息与电气工程学院,湖南湘潭411201

出　　处：《吉林大学学报（地球科学版）》2022年第2期592-601,共10页Journal of Jilin University：Earth Science Edition

基　　金：国家自然科学基金项目(41574127)。

摘　　要：正演数值模拟是反演成像的基础.为了实现磁法勘探精细化反演成像与定量解释,本文利用把一个大问题分解为多个小问题的思路,提出一种基于泊松方程的高效、高精度空间波数混合域二度体磁异常数值模拟方法.该方法利用傅里叶变换把二度体磁位偏微分方程转换为一维常微分方程,并采用基于二次插值的一维有限单元法求解该方程,进而通过反傅里叶变换得到空间域磁异常.在模型算例中,分别设计截面为矩形的常磁化率和变磁化率二度体模型,针对本文算法的计算精度和计算效率进行了验证.模型算例结果表明:该算法计算精度高,相对误差绝对值均小于1%;计算速度快,网格节点剖分2501×2501的模型模拟时间为4.18s;适用于任意复杂地形模型.Forward numerical simulation is the basis of inversion imaging.In order to realize fine inversion imaging and quantitative interpretation of magnetic exploration,in this paper,the authors make a full use of the idea of decomposing a large problem into several small parts,and propose an efficient and high-precision numerical simulation method for two-dimensional magnetic anomalies in a space-wavenumber mixed domain based on Poisson equation.In this method,the partial differential equation is transformed into an ordinary differential equation with different wave numbers by one-dimensional Fourier transform,and then the ordinary differential equation is solved by the one-dimensional finite element method with quadratic interpolation,and finally,the magnetic anomaly value in spatial domain is obtained by inverse Fourier transform.In the model example,the two-dimensional models of constant susceptibility and variable susceptibility with rectangular cross sections are designed respectively,and the calculation accuracy and efficiency of the algorithm are verified.The modeling results of synthesis models show that the algorithm has high accuracy and efficiency,the absolute values of relative error are less than 1%,and the simulation time of 2501×2501 model nodes is 4.18 s.What’s more,it is suitable for any complex terrain model.

关 键 词：磁异常 空间波数混合域 二度体 正演 

分 类 号：P631.2[天文地球—地质矿产勘探]