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Meshfree Method in Geophysical Electromagnetic Prospecting: The 2D Magnetotelluric Example

College of Instrumentation and Electrical Engineering, Jilin University, No. 938 Ximinzhu, Street, Changchun, 130026, P. R. China

Key Laboratory of Geo-Exploration Instrumentation, Ministry of Education, Jilin University, No. 938 Ximinzhu Street, Changchun, 130026, P. R. China

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Tingzhe Huang

http://orcid.org/0000-0002-6405-6383

College of Instrumentation and Electrical Engineering, Jilin University, No. 938 Ximinzhu, Street, Changchun, 130026, P. R. China

Key Laboratory of Geo-Exploration Instrumentation, Ministry of Education, Jilin University, No. 938 Ximinzhu Street, Changchun, 130026, P. R. China

E-mail Address: tingzhe_huang@163.com

Corresponding author.

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Wanyu Huang

College of Instrumentation and Electrical Engineering, Jilin University, No. 938 Ximinzhu, Street, Changchun, 130026, P. R. China

Key Laboratory of Geo-Exploration Instrumentation, Ministry of Education, Jilin University, No. 938 Ximinzhu Street, Changchun, 130026, P. R. China

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, and

Liangliang Rong

State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, No. 865, Changning Road, Shanghai, 200050 P. R. China

E-mail Address: rong_elec@mail.sim.ac.cn

Co-corresponding author.

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https://doi.org/10.1142/S0219876217500840Cited by:3 (Source: Crossref)

Abstract

As an important supplement and development of traditional methods, the meshfree method has received a great deal of attention in the field of engineering calculation, and has been successfully used to solve many problems which traditional methods have difficulty in solving. However, the application of meshfree method is relatively less in the area of geophysics. In this paper, we apply the meshfree method to the numerical simulation of geophysical electromagnetic prospecting, taking the 2D magnetotelluric as an example and deduce the corresponding meshfree radial point interpolation method (RPIM) equivalent linear equations in detail. The high-efficiency and accurate solutions of large-scale sparse linear equations are solved by the quasi-minimal residual method based on Krylov subspace. The optimal values of the shape parameters are given by numerical experiments. The correctness of the meshfree method is verified by a layered model. The root mean square error of the calculation results is no more than 0.35%, its accuracy is superior to the finite element method. We also compare the meshfree solution with FEM solution by calculating an inclined vein body model, and the calculation results are in good agreement. A continuously changing fault model and undulating terrain model which traditional methods have difficulty in simulating are respectively calculated, the sectional profiles of the apparent resistivity accurately reflect the trend of the anomalies. The meshfree method does not require the complicated mesh generation, and the physical parameters are loaded at a series of points, thus it is especially suitable for the calculation of the complex geological models. With the rapid development of computational science, the meshfree techniques will certainly become a new robust numerical simulation method in geophysical electromagnetic prospecting.

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References

Atluri, S. N. and Zhu, T. [1998] “ A new meshfree local Petrov-Galerkin (MLPG) approach in computational mechanics,” Comput. Mech. 22(2), 117–127. Web of Science, Google Scholar
Belytschko, T., Krongauz, Y., Organ, D., Fleming, M. and Krysl, P. [1996] “ Meshless methods:An overview and recent developments,” Comput. Methods Appl. Mech. Eng. 139(1–4), 3–47. Web of Science, Google Scholar
Bouhamidi, A. and Jbilou, K. [2008] “ Meshless thin plate spline methods for the modified Helmholtz equation,” Comput. Methods Appl. Mech. Eng. 197(45–48), 3733–3741. Web of Science, Google Scholar
Bouhamidi, A., Hached, M. and Jbilou, K. [2013] “ A meshless method for the numerical computation of the solution of steady Burgers-type equations,” Appl. Numer. Math. 74(74), 95–110 Web of Science, Google Scholar
Coggon, J. H. [1971] “ Electromagnetic and electrical modelling by the finite element method,” Geophysics 36(1), 132–155. Web of Science, Google Scholar
Feng, D. S., Guo, R. W. and Wang, H. H. [2015] “ An element-free Galerkin method for ground penetrating radar numerical simulation,” J. Central South Univ. 22(1), 261–269 Web of Science, Google Scholar
Franke, A., Börner, R. U. and Spitzer K. [2007] “ Adaptive unstructured grid finite element Simulation of two-dimensional magnetotelluric fields for arbitrary surface and seafloor topography,” Geophys. J. Int. 171(1), 71–86. Web of Science, Google Scholar
Jia, X. F., Hu, T. Y. and Wang, R. Q. [2006] “ Wave equation modeling and imaging by using element free method,” Prog. Geophys. 21(1), 11–17. Google Scholar
Key, K. and Chester, W. [2006] “ Adaptive finite-element modeling using unstructured grids: The 2D magnetotelluric example,” Geophys. 71(6), 291–299. Web of Science, Google Scholar
Liu, G. R., Zhang, G. Y., Gu, Y. T. and Wang, Y. Y. [2005] “ A meshfree radial point interpolation method (RPIM) for three-dimensional solids,” Comput. Mech. 36(6), 421–430. Web of Science, Google Scholar
Liu, G. R. [2009] Meshfree Methods: Moving Beyond the Finite Element Method, 2nd edition (CRC Press, Boca Raton, USA). Google Scholar
Liu, G. R., Xu, X., Zhang, G. Y. and Nguyen-Thoi, T. [2009] “ A superconvergent point interpolation method (SC-PIM) with piecewise linear strain field using triangular mesh,” Int. J. Numer. Methods Eng. 77(10), 1439–1467. Web of Science, Google Scholar
Liu, G. R. [2016] “ An overview on meshfree methods: For computational solid mechanics,” Int. J. Comput. Methods 13(5), 1–42. Link, Web of Science, Google Scholar
Liu, G. R. and Gu, Y. T. [2001] “ A point interpolation method for two-dimensional solids,” Int. J. Numer. Methods Eng. 50(4), 937–951. Web of Science, Google Scholar
Liu, G. R. and Gu, Y. T. [2005]. An Introduction to Meshfree Methods and Their Programming (Springer, Germany). Google Scholar
Mauriello, P. and Patella, D. [1999] “ Principles of probability tomography for natural-source electromagnetic induction fields,” Geophys. 64(5), 1403–1417. Web of Science, Google Scholar
Tanaka, Y. and Kunisada, E. [2011] “ Study on meshless method using RPIM for transient electromagnetic field,” IEEE Trans. Magn. 47(5), 1178–1181. Web of Science, Google Scholar
Tanaka, Y., Tone, R. and Fujimoto, Y. [2013] “ Study of an explicit meshless method using RPIM for electromagnetic fields,” IEEE Trans. Magn. 49(5), 1577–1580. Web of Science, Google Scholar
Tanaka, Y., Watanabe, S. and Oko, T. [2015] “ Study of eddy current analysis by a meshless method using RPIM,” IEEE Trans. Magn. 51(3), 1–4. Web of Science, Google Scholar
Wang, J. G. and Liu, G. R. [2002] “ A point interpolation meshless method based on radial basis functions,” Int. J. Numer. Methods Eng. 54(11), 1623–1648. Web of Science, Google Scholar
Wang, J. G. and Liu, G. R. [2002] “ On the optimal shape parameters of radial basis functions used for 2-D meshless methods,” Comput. Methods Appl. Mech. Eng. 191(23–24), 2611–2630. Web of Science, Google Scholar
Wannamaker, P. E., Stodt, J. A. and Rijo, L. [1986] “ Two - dimensional topographic responses in magnetotellurics modeled using finite elements,” Geophys. 51(11), 2131–2144. Web of Science, Google Scholar
Wendland, H. [1999] “ Meshless Galerkin methods using radial basis functions,” Math. Comput. 68(228) 1521–1531. Web of Science, Google Scholar
Wittke, J. and Tezkan, B. [2014] “ Meshfree magnetotelluric modeling,” Geophys. J. Int. 198(2), 1255–1268. Web of Science, Google Scholar
Xu Shi-zhe. [1994] Finite element method in geophysics (Science Press, Beijing, China), pp. 229–239. Google Scholar
Yu, Y. and Chen, Z. [2012] “ The CPML absorbing boundary conditions for the unconditionally stable meshless modeling,” IEEE Antennas Wirel. Propag. Lett. 11(11), 468–472 Google Scholar
Yu, Y. and Chen, Z. [2009] “ A 3-D radial point interpolation method for meshless time-domain modeling,” IEEE Trans. Microw. Theory Techn. 57(8), 2015–2020 Web of Science, Google Scholar
Zhadanov, M. S., Varentsov, I. M., Weaver, J. T., Golubev, N. G. and Krylov, V. A. [1997] “ Methods for modelling electromagnetic fields results from COMMEMI: the international project on the comparision of modeling methods for electromagnetic induction,” J. Appl. Geophys. 37(3–4), 133–271. Web of Science, Google Scholar