基于矢量有限元的大地电磁快速三维正演研究

doi:10.11720/wtyht.2020.0343

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Abstract

The finite element method has the characteristics of strong adaptability in simulating the electromagnetic response of rugged topography and complex geological bodies. In recent years, it has been widely used in the three-dimensional (3D) forward modeling of magnetotelluric (MT) sounding. However, the finite element method also has some shortcomings in terms of computational efficiency. The large amount of calculation and long running time of the method are the main factors that lead to the lag of the practical process of the 3D MT inversion technology based on the finite element method compared with the 3D MT inversion technology based on the finite difference method. In order to improve the 3D forward speed of MT, the authors adopt the forward modeling scheme which uses the direct solver PARDISO and does not need divergence correction to solve the large-scale linear equations corresponding to the vector finite element method, and obtain the MT response of the geoelectric model under such different terrain conditions as flat and rugged topography. Under the conditions of medium-scale calculation, through the comparison between the direct solution method without divergence correction and the iterative solution method with divergence correction, the authors have detected that the direct solution method without divergence correction has advantages in calculation accuracy and calculation time, especially in the calculation. In terms of time, the ratio of the calculation speed of the direct solution and the iterative solution is raised by more than ten times.

Key words： magnetotelluric vector finite element method 3D forward PARDISO

Received: 02 July 2020 Published: 29 December 2020

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	Guan-Wen GU
	Ye WU
	Yan-Bin SHI

Cite this article:

Guan-Wen GU,Ye WU,Yan-Bin SHI. Research on fast three-dimensional forward algorithm of magnetotelluric sounding based on vector finite element[J]. Geophysical and Geochemical Exploration, 2020, 44(6): 1387-1398.

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https://www.wutanyuhuatan.com/EN/10.11720/wtyht.2020.0343 OR https://www.wutanyuhuatan.com/EN/Y2020/V44/I6/1387

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Section diagram of numerical modeling domain for 3D MT with topography^[11]

Domain subdivision of the vector finite element method
a—domain subdivision; b—location of electric field components

Comparison of vector finite element solution and analytical solution of uniform half space model

Comparison of 3D forward apparent resistivity (a) and phase (b) of homogeneous half space model with analytical solution

Parameters of H-type layered model

Comparison of vector finite element solution and analytical solution of H-type layered model

Comparison of apparent resistivity (a) and phase (b) of 3D forward modeling of H-type layered model with analytical solutions

Parameters of K-type layered model

Comparison between vector finite element solution and analytical solution of K-type layered model

Comparison of 3D forward apparent resistivity (a) and phase (b) of K-type layered model with analytical solution

Schematic diagram of COMMEMI3D-2

Comparison between the calculation results of vector finite element forward algorithm and IE method
a—Z_xy mode forward apparent resistivity;b—Z_yx mode forward apparent resistivity;c—Z_xy mode forward impedance phase;d—Z_yxmode forward impedance phase

3D topography and grid
a—sketch of 3D topography; b—topography meshing and distribution of MT measurement sites

Sketch of 2D ridge

Comparision between modeling results of 3DVFEM(PARDISO) and 2DFEM for 2D ridge
a—forward apparent resistivity; b—forward impedance phase

Comparison of calculation results of VFE-PARDISO without divergence correction and VFE-BICG with divergence correction
a—forward apparent resistivity; b—forward impedance phase

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