ZHOU JianMei,
LIU WenTao,
LI Xiu et al
.2018.Research on the 3D mimetic finite volume method for loop-source TEM response in biaxial anisotropic formation.Chinese Journal Of Geophysics,61(1): 368-378,doi: 10.6038/cjg2018K0598
双轴各向异性介质中回线源瞬变电磁三维拟态有限体积正演算法
周建美, 刘文韬, 李貅, 戚志鹏, 刘航
长安大学地质工程与测绘学院, 西安 710054
Research on the 3D mimetic finite volume method for loop-source TEM response in biaxial anisotropic formation
ZHOU JianMei, LIU WenTao, LI Xiu, QI ZhiPeng, LIU Hang
College of Geology Engineering and Geomatics, Chang'an University, Xi'an 710054, China
Abstract：In this paper, a 3D forward modeling of loop-source transient electromagnetic (TEM) response in biaxial anisotropic formation is proposed by using the mimetic finite volume method (MFVM). Firstly, the definition of inner product is introduced, and the governing equation of TEM method is transformed into a weak form under a natural boundary condition. The computational domain is divided into a series of control volume units. The staggered grid is used to simulate the finite volume space discretization of the governing equations, including the curl operator discretization and the spatial inner product discretization. Discretization of the curl operator is based on Stokes' Theorem. Discretization of inner product in the biaxial anisotropic formation is based on midpoint average. The backward Euler time stepping method, which is unconditionally stable, is chosen to discretize the governing equation in the time domain. Electromagnetic field distribution at the initial time is obtained by solving the magnetic field of the stable current loop source in the uniform space. When solving the governing equations in the time domain, the MFVM adopts double time step size for each m constant time steps (here m is an input parameter) and uses the direct method solver PARDISO to ensure the accuracy and efficiency where the coefficient matrix just needs to decompose only once for each m time steps. Finally, the computational accuracy and computational efficiency of the proposed algorithm are verified by comparing the results of the forward modeling with a layered model and the anisotropic half-space model. The forward response of the 3D biaxial anisotropy model shows that the horizontal conductivity has a significant impact on the electromagnetic response, while the vertical direction of the conductivity change has little effect. The main reason is that the induced current generated by the loop source is mainly horizontal, so the response is primarily affected by the conductivity in the horizontal direction, while the conductivity in the vertical direction has little effect.
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