| 面向目标自适应三维大地电磁正演模拟 |
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| 引用本文： | 殷长春,张博,刘云鹤,蔡晶.面向目标自适应三维大地电磁正演模拟[J].地球物理学报,2017,60(1):327-336. |
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| 作者姓名： | 殷长春 张博 刘云鹤 蔡晶 |
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| 作者单位： | 吉林大学地球探测科学与技术学院, 长春 130026 |
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| 基金项目： | 国家自然科学基金重点和面上项目（41530320，41274121）和国家青年基金项目（41404093）、国家重大科研装备研究项目（ZDYZ2012-1-03和20130523MTEM05）联合资助. |
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| 摘 要： | 本文将面向目标的自适应算法应用于三维大地电磁数值模拟.使用基于非结构网格的矢量有限单元法对起伏地表大地电磁正演模拟问题进行求解.使用利用垂向电流密度在物性界面上的连续性对后验误差进行估算的算法指导网格优化.由于全局自适应算法针对观测点优化网格的能力较差,本文通过求解正演问题的对偶问题计算后验误差的加权系数,并对相关加权系数进行改进,从而实现了面向目标的自适应算法.与传统基于结构化网格的电磁正演算法相比,采用非结构网格能够更好地拟合起伏地表和地下不规则异常体.由于使用了面向目标的自适应算法,本文能够使用更少的网格达到较高的计算精度.通过对比本文模拟结果与半空间响应和全局自适应算法计算结果,并通过对比使用改进前和改进后加权系数得到的网格剖分结果验证了本文算法的有效性.
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| 关 键 词： | 大地电磁 三维正演 矢量非结构有限元法 面向目标自适应 |
| 收稿时间： | 2016-01-05 |
A goal-oriented adaptive algorithm for 3D magnetotelluric forward modeling |
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| YIN Chang-Chun,ZHANG Bo,LIU Yun-He,CAI Jing.A goal-oriented adaptive algorithm for 3D magnetotelluric forward modeling[J].Chinese Journal of Geophysics,2017,60(1):327-336. |
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| Authors: | YIN Chang-Chun ZHANG Bo LIU Yun-He CAI Jing |
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| Institution: | College of Geo-exploration Sciences and Technology, Jilin University, Changchun 130026, China |
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| Abstract: | Magnetotelluric (MT) exploration has been widely used in geological survey, mineral and oil and gas exploration, and the research on deep structures of the earth. With the models in the MT method becoming more and more complicated, conventional modeling methods based on structured grids cannot satisfy the accuracy requirement. To better simulate the complex earth, we adopt unstructured grids in the MT modeling. Since an effective mesh can greatly improve the modeling accuracy and save the cost, we present a goal-oriented unstructured adaptive finite-element method for MT modeling.
Starting from the frequency-domain Maxwell's equations, a vector Helmholtz equation is obtained for a stable solution with existing air. We use the Galerkin method to discretize the Helmholtz equation. The continuity condition for normal current density is used to evaluate the posterior error,while the weighted coefficient is obtained by solving a dual forward modeling problem. Besides, we multiply the weighted coefficients proposed by previous researches by the conductivity that proves to be more effective for grid refinement. Finally, we define a convergence rule to determine receivers used to calculate the weighted coefficients in the next refinement.
The response of a homogeneous half-space model is simulated by both the goal-oriented and global adaptive finite element methods to verify the accuracy and to demonstrate advantages of our goal-oriented adaptive method over the global one. We further calculate MT response for a classical model to check the effectiveness of our method on topography models. Then, we calculate the response for a topographic model with an abnormal body embedded to demonstrate that our method can not only refine meshes near the source on the topographic earth surface but also refine meshes on physical interfaces between the abnormal body and surrounding medium.
From the adaptive meshes and modeling results we can draw the following conclusions:1) Our goal-oriented adaptive finite-element algorithm for MT modeling can obtain higher accuracy with less grids in comparison to the global method. 2) Our algorithm is effective for MT topographic modeling. 3) The algorithm presented in this paper can not only effectively refine the meshes close to the topographic surface with receivers, but also refine the meshes near the abnormal body in the earth. 4) The improved weighted coefficient is more effective than the traditional one in terms of grids refinement. |
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| Keywords: | Magnetotelluric (MT) 3D forward modeling Unstructured vector finite-element method Goal-oriented adaptive |
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