空间—波数域二维强磁场及其梯度张量数值模拟研究  

Numerical simulation of two-dimensional strong magnetic field and its gradient tensor in space-wavenumber domain

作　　者：戴世坤[1,2] 冉应强 张莹[1,2] 陈轻蕊 凌嘉宣 贾金荣 DAI Shikun;RAN Yingqiang;ZHANG Ying;CHEN Qingrui;LING Jiaxuan;JIA Jinrong(Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring,Ministry of Education,Central South University,Changsha,Hunan 410083,China;School of Geosciences and Info-physics,Central South University,Changsha,Hunan 410083,China)

机构地区：[1]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,湖南长沙410083 [2]中南大学地球科学与信息物理学院,湖南长沙410083

出　　处：《石油地球物理勘探》2023年第1期228-237,共10页Oil Geophysical Prospecting

基　　金：中南大学研究生自主探索创新项目“二维强磁场及其张量梯度正反演算法研究”(2022ZZTS0557)资助。

摘　　要：基于磁位泊松方程提出了一种空间—波数混合域二维数值模拟方法。该方法将二维强磁性体磁位满足的偏微分方程通过一维傅里叶变换转化为不同波数之间相互独立的常微分方程,即将二维数值模拟问题转换为一维数值模拟问题,并利用一维有限元法进行求解,可大大降低存储需求和计算量。对求得的强磁场利用紧算子进行迭代以获得高精度近似解。算法中保留垂向为空间域,可根据需求对网格进行灵活剖分,有利于复杂条件下的模拟。另外,不同波数之间常微分方程相互独立,具有较好的并行性。算法充分利用了傅里叶变换的快速性和迭代算法的稳定性,实现了强磁场及其梯度张量的二维数值模拟。设计三个模型(水平地形下的圆柱体模型、棱柱体模型及起伏地形模型)进行计算,对文中方法数值解与解析解、COMSOL软件所得的数值解进行对比,结果表明该算法计算速度快、精度高,适用于起伏地形条件下的数值计算。On the basis of the Poisson equation of magnetic potential,a two-dimensional numerical simulation method of the mixed space-wavenumber domain is proposed.The method uses the one-dimensional Fourier transform and transforms the partial differential equation suitable for the magnetic potential of a two-dimensional strong magnetic body into an ordinary differential equation with independent different wavenumbers.In other words,it changes the two-dimensional numerical simulation question into a one-dimensional one for solutions and employs the one-dimensional finite element method to solve the one-dimensional numerical simulation question,so as to greatly reduce storage demands and computational loads.Furthermore,a high-precision approximate solution of the solved strong magnetic field is obtained by using a compact operator for iteration.In the algorithm,the vertical direction is reserved as the spatial domain,and the mesh can be flexibly divided according to the demand,which is conducive to simulating complex conditions.In addition,the ordinary differential equation among different wavenumbers is independent and has excellent parallelism.The algorithm makes full use of the rapidness of the Fourier transform and the stability of the iterative algorithm and realizes the two-dimensional numerical simulation of the strong magnetic field and its gradient tensor.Three models(cylinder and prism models under horizontal terrain and model under undulating terrain)are calculated,and the numerical solution is compared with the analytical solution and the numerical solution by COMSOL software.The results show that the algorithm is fast and highly accurate and thus is suitable for undulating terrain.

关 键 词：强磁场 梯度张量 空间—波数混合域 二度体正演 

分 类 号：P631[天文地球—地质矿产勘探]