2.5D direct‐current resistivity forward modelling and inversion by finite‐element–infinite‐element coupled method |
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| Authors: | Yuan Yuan Jianke Qiang Jingtian Tang Zhengyong Ren Xiao Xiao |
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| Affiliation: | Key Laboratory of Metallogenic Prediction of Nonferrous Metals, Ministry of Education, School of Geosciences and Info‐Physics, Central South University, Changsha, China |
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| Abstract: | To reduce the numerical errors arising from the improper enforcement of the artificial boundary conditions on the distant surface that encloses the underground part of the subsurface, we present a finite‐element–infinite‐element coupled method to significantly reduce the computation time and memory cost in the 2.5D direct‐current resistivity inversion. We first present the boundary value problem of the secondary potential. Then, a new type of infinite element is analysed and applied to replace the conventionally used mixed boundary condition on the distant boundary. In the internal domain, a standard finite‐element method is used to derive the final system of linear equations. With a novel shape function for infinite elements at the subsurface boundary, the final system matrix is sparse, symmetric, and independent of source electrodes. Through lower upper decomposition, the multi‐pole potentials can be swiftly obtained by simple back‐substitutions. We embed the newly developed forward solution to the inversion procedure. To compute the sensitivity matrix, we adopt the efficient adjoint equation approach to further reduce the computation cost. Finally, several synthetic examples are tested to show the efficiency of inversion. |
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| Keywords: | Resistivity Potential field Modelling Numerical study Inversion Finite‐element method (FEM) Infinite‐element method (IFEM) Shape function |
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