基于球坐标系下有限差分的地磁测深三维正演

doi:10.13278/j.cnki.jjuese.20170061

摘要/Abstract

摘要： 为了计算全球尺度电磁感应的响应，本文介绍地磁测深频率域三维正演。正演算法采用球坐标系下的交错网格有限差分方法，从Maxwell方程的积分形式出发，采用PARDISO对离散后的方程组求解，避免了迭代求解的散度校正。为了验证本文结果的正确性和精度，与前人的有限元和有限差分方法进行了对比，一维层状模型的三维交错网格有限差分数值结果和解析解相对误差小于5%，双半球模型的计算结果与前人的计算结果完全吻合。三维"棋盘模型"计算表明磁场分量对异常体的大小和位置具有很好的分辨能力。

关键词: 地磁测深, 球坐标, 三维正演, 有限差分, 地磁响应函数

Abstract: In order to compute the global-scale electromagnetic induction responses, this paper introduces a 3-D forward method of the frequency domain geomagnetic depth sounding (GDS). The method is based on the Staggered-grid finite difference method (FDM) in spherical coordinate. The difference equations are derived from the integral form of Maxwell equations. The PARDISO Solver is used to solve the discrete equations to avoid the divergence correction of iterations. To validate our code, we compared the results to the solutions of the finite element method and FDM. The relative error between the finite difference numerical result of the three-dimensional staggered grid and the analytical solution is less than 5%. The accuracy of the two hemispheres model is also high enough. The calculation results of the three-dimensional checkerboard model show that the magnetic field components have a good resolution to the size and position of an abnormal body.

Key words: geomagnetic depth sounding, spherical coordinate, 3-D forward modeling, finite difference, geomagnetic response function

中图分类号:

P631.2

李建平, 翁爱华, 李世文, 李大俊, 李斯睿, 杨悦, 唐裕, 张艳辉. 基于球坐标系下有限差分的地磁测深三维正演[J]. 吉林大学学报(地球科学版), 2018, 48(2): 411-419.

Li Jianping, Weng Aihua, Li Shiwen, Li Dajun, Li Sirui, Yang Yue, Tang Yu, Zhang Yanhui. 3-D Forward Method for Geomagnetic Depth Sounding Based on Finite Difference Method in Spherical Coordinate[J]. Journal of Jilin University(Earth Science Edition), 2018, 48(2): 411-419.

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