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Fictitious Point Technique Based on Finite-Difference Method for 2.5D Direct-Current Resistivity Forward Problem

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  • Xiaozhong Tong

    (School of Geosciences and Info-Physics, Central South University, Changsha 410083, China
    Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring, Ministry of Education, Central South University, Changsha 410083, China
    Key Laboratory of Non-Ferrous and Geological Hazard Detection, Central South University, Changsha 410083, China)

  • Ya Sun

    (School of Geosciences and Info-Physics, Central South University, Changsha 410083, China
    Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring, Ministry of Education, Central South University, Changsha 410083, China)

Abstract

With the widespread application of the direct-current resistivity method, searching for accurate and fast-forward algorithms has become the focus of research for geophysicists and engineers. Three-dimensional forward modeling can be the best way to identify geo-electrical anomalies but are hampered by computational limitations because of the large amount of data. A practical compromise, or even alternative, is represented by 2.5D modeling characterized using a 3D source in a 2D medium. Thus, we develop a 2.5D direct-current resistivity forward modeling algorithm. The algorithm incorporates the finite-difference approximation and fictitious point technique that can improve the efficiency and accuracy of numerical simulation. Firstly, from the boundary value problem of the electric potential generated by the point source, the discrete expressions of the governing equation are derived from the finite-difference approach. The numerical solutions of the discrete electric potential are calculated after the approximate treatment of the boundary conditions with a finite-difference method based on a fictitious point scheme. Secondly, through the simulation of a homogeneous half-space model and a one-dimensional model, and compared with the analytical results, the correctness and stability of the finite-difference forward algorithm are verified. Lastly, through the numerical simulation for a two-dimensional model, 2.5D direct-current sounding responses are summarized, which can provide a qualitative interpretation of field data.

Suggested Citation

  • Xiaozhong Tong & Ya Sun, 2024. "Fictitious Point Technique Based on Finite-Difference Method for 2.5D Direct-Current Resistivity Forward Problem," Mathematics, MDPI, vol. 12(2), pages 1-22, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:269-:d:1318920
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    References listed on IDEAS

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    1. Yang, Xuehua & Wu, Lijiao & Zhang, Haixiang, 2023. "A space-time spectral order sinc-collocation method for the fourth-order nonlocal heat model arising in viscoelasticity," Applied Mathematics and Computation, Elsevier, vol. 457(C).
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    Cited by:

    1. Wei Xie & Wendi Zhu & Xiaozhong Tong & Huiying Ma, 2024. "PDE-Based Two-Dimensional Radiomagnetotelluric forward Modelling Using Vertex-Centered Finite-Volume Scheme," Mathematics, MDPI, vol. 12(13), pages 1-19, July.

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