基于非结构网格的三种CSEM有限元三维正演系统分析

doi:10.13810/j.cnki.issn.1000-7210.2021.05.025

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摘要高精度、高效率的CSEM三维正演算法一直是电磁场正演研究的核心和热点问题之一。当前，求解CSEM的三维正演公式包含电场公式和两种结构的A-Φ耦合势公式，文中采用有限元技术对这三类求解公式的应用效果进行分析。首先，从CSEM满足的边值问题出发，推导了有限元系统下的电场方程及双旋度结构和拉普拉斯结构的A-Φ耦合势方程；然后，为了消除场源奇异问题，采用非结构化四面体网格对求解区域进行离散，并结合场源局部细化技术，实现了统一形式的场源积分精确求解；最后，采用Krylov子空间迭代算法和PARDISO直接求解器实现了这三种方程的CSEM三维快速求解。利用均匀半空间地电模型，分别用这三种方程计算磁偶源和电偶源的电磁响应，验证了文中算法的正确性。最后，对低阻异常体地电模型对比了这三种方程的收敛性、内存消耗和求解精度。测试结果表明，在计算规模较小的情况下，基于矢量有限元的电场方程具有较高的求解精度和效率；在计算规模较大的情形下，基于拉普拉斯结构的A-Φ耦合势方程比另外两种方程更适合开展后期的CSEM三维反演研究。

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关键词 ：可控源电磁法, 有限元, 非结构化网格, 正演模拟

Abstract：High-precision and efficient 3D CSEM forward modeling algorithms have always been one of the key and hot issues in the study of electromagnetic forward modeling. Currently, one electric field equation and two A-Φ coupling potential equations with different structures are often used to solve 3D CSEM forward modeling problems. In this paper, the application effects of these three equations were analyzed by a finite element method. Firstly, in view of the CSEM boundary value problem, an electric field equation and two A-Φ coupling potential equations with a curl-curl structure and a Laplacian structure, respectively, were derived. Secondly, for elimination of field source singularity, the computational regions were discretized with unstructured tetrahedral grids. A local refinement technique for the field source was also applied for an accurate solution to the unified field source integration. Lastly, the three equations were fast solved through a Krylov subspace iterative algorithm and the PARDISO solver. The correctness of the algorithms developed in this paper was verified by calculation of the electromagnetic responses of the magnetic dipole source and the electric dipole source via the three equations, respectively, with a homogeneous half-space geoelectric model. The convergence, memory consumption and solution accuracy of the three CSEM forward equations were analyzed with a geoelectric model of low-resistance anomalous bodies. The results show that within a small computational region, the electric field equation based on vector finite elements has higher solution accuracy and higher solution efficiency. Otherwise, the A-Φ coupling potential equation with a Laplacian structure is more suitable than the other two equations for 3D CSEM forward modeling studies.

Key words： CSEM finite-element unstructured grid forward modeling

收稿日期: 2021-03-05

PACS:

P631

基金资助:本项研究受国家自然科学基金项目“基于A-Φ势三维CSEM高阶自适应有限元正演”（42004061）、“基于物性约束的广域电磁法自适应三维反演与岩性识别方法研究”（41830107）、江西省科技厅计划项目“城市多参数可控电磁勘探理论研究”（S2019ZR MSB0661）、东华理工大学放射性地质与勘探技术国防重点学科实验室开放基金项目“下庄铀矿田的三维多场源可控源电磁法正演研究”（2020RGET07）、自然资源部地球物理电磁法探测技术重点实验室开放课题基金项目“基于ASBP算法的三维可控源电磁法有限内存快速反演研究”（KLGEPT201903）和中国地质调查局地质调查项目“长江下游重点盆地地球物理基础调查”（DD20201164）联合资助。

通讯作者: 陈煌,湖南省长沙市麓山南路932号中南大学校本部地学楼322,410083。Email:csuchenhuang@csu.edu.cn E-mail: csuchenhuang@csu.edu.cn

作者简介: 周峰讲师,硕士生导师,1989年生;2012年毕业于东华理工大学,获勘查技术与工程专业学士学位;2015年获该校地球物理学专业硕士学位;2019年获中南大学地球探测与信息技术专业博士学位。SEG会员,现就职于东华理工大学地球物理与测控技术学院,主要从事电磁法数值模拟与反演成像等领域的教学与科研工作。

引用本文:

周峰, 张志勇, 陈煌, 汤井田, 邓居智, 李勇. 基于非结构网格的三种CSEM有限元三维正演系统分析[J]. 石油地球物理勘探, 2021, 56(5): 1190-1202. ZHOU Feng, ZHANG Zhiyong, CHEN Huang, TANG Jingtian, DENG Juzhi, LI Yong. Analysis of 3D finite-element forward modeling of CSEM data using three different formulas and unstructured grids. Oil Geophysical Prospecting, 2021, 56(5): 1190-1202.

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