空间波数混合域磁异常场积分解三维数值模拟  

Three-dimensional modeling of magnetic anomaly integral solution in a mixed space-wavenumber domain

作　　者：李昆 戴世坤[1,2,3] 陈轻蕊[1,2,3] 张钱江 赵东东[1,2,3] 王顺国 凌嘉宣[1,2,3] LI Kun;DAI ShiKun;CHEN QingRui;ZHANG QianJiang;ZHAO DongDong;WANG ShunGuo;LING JiaXuan(Hunan Key Laboratory of Nonferrous Resources and Geological Hazards Exploration,Changsha 410083, China;Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring of Ministry of Education, Central South University, Changsha 410083, China;School of Geosciences and Info-Physics of Central South University, Changsha 410083, China;Scripps Institution of Oceanography, UC San Diego, San Diego 92092, USA;School of College of Earth Sciences of Guilin University of Technology, Guilin Guangxi 541004, China)

机构地区：[1]有色资源与地质灾害探查湖南省重点实验室,长沙410083 [2]中南大学有色金属成矿预测与地质环境监测教育部重点实验室,长沙410083 [3]中南大学地球科学与信息物理学院,长沙410083 [4]加州大学圣地亚哥分校Scripps海洋研究所,美国92092 [5]桂林理工大学地球科学学院,广西桂林541004

出　　处：《地球物理学报》2019年第11期4437-4450,共14页Chinese Journal of Geophysics

基　　金：国家重点研发计划(2017YFC0601305,2018YFC0603602);国家自然科学基金项目(41574127);中南大学研究生自主探索创新项目(2017zzts176);湖南省自然科学基金(2018JJ3642);广西自然科学基金(2018GXNSFAA050070);桂林理工大学科研启动基金资助项目(GUTQDJJ2018034)联合资助.

摘　　要：本文提出一种空间波数混合域磁异常场三维数值模拟方法.该方法利用磁位三维空间域积分为卷积的特点,沿水平方向进行二维傅里叶变换,把空间域磁位满足的三维积分问题转化为不同波数之间相互独立的垂向一维积分问题.保留垂向为空间域,优势之一在于便于浅层单元剖分可适当加密,随着深度增加,单元剖分适当稀疏,可以准确模拟任意复杂地形和磁性体的磁异常,兼顾了计算精度与计算效率;优势之二在于一维积分垂向可离散为多个单元积分之和,每个单元采用二次形函数表征磁化强度,可得出单元积分的解析表达式,计算精度高、效率高.该方法充分利用一维形函数积分的高效和高精度、快速傅里叶变换的高效性及算法高度并行性,实现了磁异常场高效、高精度的数值模拟.设计棱柱体模型,将模型解析解与空间波数混合域法的数值解对比,结果表明该方法计算精度高、效率高.设计了组合棱柱体复杂模型,对比分析了标准FFT扩边法与Gauss-FFT法的计算精度与计算效率,总结了标准FFT的扩边系数选取策略.针对任意复杂地形条件下的磁异常模拟问题,本文提出一种适用于起伏地形条件下的磁异常场快速计算方法,并对其有效性进行了验证.The paper presents a three-dimensional (3D) modeling method, engaged with a mixed space-wavenumber domain, for the magnetic anomaly field. Based on the fact that the 3D space domain integral for magnetic potential is convolution, the 3D integral problem of magnetic potential in space domain can be transformed into one dimensional (1D) integral problems in vertical direction independently to each other using the two-dimensional (2D) Fourier transform along the horizontal directions. By the proposed method, the depth direction is kept in space domain, which can provide two advantages in the modeling. Firstly, the shallow grid can be as fine as necessary for topography, however, with the increase of depth, the grid becomes coarse in order to reduce calculation cost. Thus, the calculation accuracy and efficiency in modeling can be guaranteed simultaneously. Secondly, the one-dimensional integral can be discretized into the sum of multiple element integrals along the depth direction. Each unit uses the second-order shape function to calculate the magnetization with the analytical expression of element integral. This method makes full use of1D shape function for high accuracy, high parallelization among different wavenumbers, and fast Fourier transform to achieve high efficiency and high accuracy modeling of magnetic anomaly field. A prismatic model is designed to verify the correctness and high accuracy of the method by the comparison between the analytical solution and the numerical solution obtained by the proposed method. A complex model is designed to compare the accuracy and efficiency of the standard FFT expansion method and of the Gauss-FFT method. The strategy of edge selection for standard FFT method was also summarized based on the complex model. The paper presents a fast magnetic anomaly field calculation method and verify its validity in order to solve the problem of magnetic anomaly simulation under any complex terrain conditions.

关 键 词：磁异常场三维数值模拟 空间波数混合域 傅里叶变换 形函数法 

分 类 号：P631[天文地球—地质矿产勘探]