3-D Numerical modeling of an electromagnetic field in geoelectrics using the Trefftz method

Izvestiya, Physics of the Solid Earth

Volumn 45, Issue 9, 2009, Pages 812-821

  Yegorov, I V ^a  

^a SHIRSHOV INSTITUTE OF OCEANOLOGY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70349103778     PISSN: 10693513     EISSN: None     Source Type: Journal    
DOI: 10.1134/S1069351309090092     Document Type: Article

References (65)

1. D. A. Aruliah, U. M. Ascher, E. Haber, and D. W. Oldenburg, "A Method for the Forward Modeling of 3-D Electromagnetic Quasi-Static Problems," Mathematical Models in Applied Sciences (M3AS) 11, 1 (2001).
2. D. B. Avdeev, "Method of Integral Equations for Solving Forward Problems of Geoelectrics," in Elektroagnitnye Issledovaniya Zemnykh Nedr (Nauchnyi Mir, Moscow, 2005), pp. 11-32.
3. E. A. Badea, M. E. Everett, G. A. Newman, and O. Brio, "Finite-Element Analysis of Controlled-Source Electromagnetic Induction Using Coulomb-Gauged Potentials," Geophysics 66, 786 (2001).
4. A. S. Barashkov, "Solution of Three-Dimensional Problem for the Fundamental MTS Mode," Fizika Zemli, No. 5, 58 (1988)
5. E. M. Best, P. Duncan, E. J. Jacobs, and W. L. Scheen, "Numerical Modeling of the Electromagnetic Response of Three-Dimensional Conductors in Layered Earth," Geophysics 50, 665 (1985).
6. U. C. Das and S. K. Verma, "Numerical Consideration on Computing the EM Response of Tree-Dimensional Inhomogeneities in a Layered Earth," Geophys. J. Roy. Astron. Soc. 66 (3), 733 (1981).
7. T. W. Dawson and J. T. Weaver, "Three-Dimensional Induction in a Nonuniform Thin Sheet at the Surface of a Uniformly Conducting Earth," Geoph. J. Roy. Astron. Soc. 59 (3), 445 (1979).
8. A. S. Debabov, "On Computerized Modeling Electromagnetic Fields in Heterogeneous Media," Dokl. Akad. Nauk SSSR 250 (2), 326 (1980).
9. V. I. Dmitriev and V. Yu. Pleshko, "On Calculation of Electromagnetic Field in a Layered Media with a Local Heterogeneity," in Vychislitel'nye Metody i Programmirovanie, (MGU, Moscow, 1982), Vyp. 36, pp. 27-35.
10. V. I. Druskin and L. A. Knizhnerman, "The Spectral Differential-Difference Method of Numerical Solving 3-D Nonstationary Problems of Electric Prospecting," Izvestiaya Acad. Nauk SSSR, Ser. Fizika Zemli, No. 8, 63 (1988).
11. L. Felsen and N. Markuvitz, Radiation and Scattering of Waves (Wiley, New York, 2003).
12. E. Yu. Fomenko and T. Mogi, "A New Computation Method for a Staggered Grid of 3-D EM Field Conservative Modeling," Earth Planets Space 54, 499 (2002).
13. P. K. Gupta, L. A. Bennett, and A. P. Raiche, "Hybrid Calculations of the Three-Dimensional Electromagnetic Response of Buried Conductors," Geophysics 52, 301 (1987).
14. E. Haber, U. M. Ascher, D. A. Aruliah, and D. W. Oldenburg, "Fast Simulation of 3-D Electromagnetic Problems Using Potentials," Journal of Computational Physics 163, 150 (2000).
15. W. C. Hahn, "A New Method for Calculations of Cavity Resonators," Journal of Applied Physics 12 (1), 62 (1941).
16. I. Herrera, "Trefftz Method: A General Theory," Numerical Methods of Partial Differential Equations 16 (6), 561 (2000).
17. R. D. Hibbs and F. W. Jones, "Electromagnetic Induction in Three-Dimensional Structures for Various Source Fields," J. Geomagn. and Geoelec. 30 (1), 1 (1978).
18. G. W. Hohmann, "Three-Dimensional EM Modeling," Geophysics 40 (2), 309 (1975).
19. M. Hvozdara, P. Kaikkonen, and I. M. Varentsov, "Algorithm for Solving 3-D Problem of EM Induction by Means of a Vector Integral Equation," Stud. Geoph. et Geod. 31, 369 (1987).
20. S. Kaczmarz, "Angenaherte Auflosung von Systemen Linearer Gleichunger," Bulletin International de l'Academie Polonaise des Sciences, Lett. A 35, 355 (1937).
21. A.V. Kuvshinov, D.V. Avdeev, O. V. Pankratov, and S. A. Golyshev, "Modeling EM Fields in 3-D Spherical Earth Using Integral Equation Approach," in Proceeding of the Second International Symposium on Three-Dimensional Electromagnetics (Salt Lake City, USA, 1999), pp. 37-40.
22. K. H. Lee, D. F. Pridmore, and Y. F. Morrison, "A Hybrid Three-Dimensional Electromanetic Modeling Scheme," Geophysics 46 (5), 769 (1981).
23. E. H. Liu and Y. Lamontagne, "EM Modeling Using Surface Integral Equations," in 3-D Electromagnetics, Eds. B. Series and M. Oristaglio (SDR, Ridgefield, 1995), pp. 121-130.
24. D. Livelybrooks, "Program 3-D Fem: A Multidimensional Electromagnetic Finite Element Model," Geoph. J. Int. 114, 443 (1993).
25. R. I. Mackie, T. R. Madden, and P.E. Wannamaker, "Three-Dimensional Magnetotelluric Modeling Using Difference Equations. Theory and Comparisons to Integral Equation Solutions," Geophysics 58 (2), 215 (1993).
26. G. I. Marchuk, Methods of Computational Mathematics (Nauka, Moscow, 1989) [in Russian].
27. Y. Mitsuhata and T. Uchida, "3-D Magnetotelluric Modeling Using the T-□ Finite-Element Method," Geophysics (1), 108 (2004).
28. F. Natterer, The Mathematics of Computerized Tomography (Wiley, Chichester, 1986).
29. V. V. Nikol'skii and T. A. Lavrova, "The Method of Minimum Autonomus Bloks and its Application to Waveguide Diffraction Problems," Radio Eng. Electron. Phys. (23) (2), 1 (1978).
30. V. V. Nikol'skii and T. I. Nikol'skaya, Decomposition Approach in Problems of Electrodynamics (Nauka, Moscow, 1983) [in Russian].
31. V. V. Nikol'skii and T. I. Nikol'skaya, Electrodynamics and Propagation of Waves (Nauka, Moscow, 1989) [in Russian].
32. B. Petrick, "Application of the Sink-Galerkin Method to Time Solution of the 3-D Source-3-D Body Electromagnetic Scattering Problem," in Proc. of Workshop on Modeling of Electrical and Electromagnetic Methods (Berkley, 1978), pp. 158-176.
33. C. Popa, "Preconditioned Kaczmarz-Extended Algorithm with Relaxation Parameters," Korean Journal of Comp. and Appl. Mathematics 6 (3), 523 (1999).
34. D. F. Pridmore and K. H. Lee, "A hybrid 3-D Electromagnetic Modeling Scheme," Geophysics 45 (4), 553 (1980).
35. A. P. Raiche, "An Integral Equation Approach to Three-Dimensional Modeling," Geoph. J. Roy. Astron. Soc. 36 (2), 363 (1974).
36. I. K. Reddy, D. Rankin, and R. J. Phillips, "Three-Dimensional Modeling in Magnetotelluric and Magnetic Variational Sounding," Geophys. J. Roy. Astron. Soc. 39, 312 (1977).
37. Y. Saad and H. A Van Der Vorst, "Iterative Solution of Linear Systems in the 20th Century," Journal of Computational and Applied Mathematics 123 (1-2), 1 (2000).
38. B. V. Sestroretskii, "Balanced RLC- and R□-Schemes of Elementary Space Volume," in Voprosy Radioelektron iki, ser. Obshchie Voprosy Radioelektroniki, Vyp. 5, (1983), pp.7-33.
39. X. Shi, H. Utada, J. Wang, and W. Wu, "Three-Dimensional Magnetotelluric Forward Modeling Using Vector Finite Element Method Combined with Divergence Corrections (VFE++)," in 17th IAGA WG 1.2 Workshop on Electromagnetic Induction in the Earth, (Hyderabad, October 18-23, 2004), pp. 1-6.
40. Yu. Shlepnev, "Trefftz Finite Elements for Electromagnetics," IEEE Transaction of Microwave Theory and Techniques 50 (5), 1328 (2002).
41. B. Sh. Singer and E. B. Fainberg, "Generalization of the Iterative-Dissipative Method for Modeling Electromagnetic Fields in Non-Uniform Media with Displacement Currents," Journal of Applied Geophysics 34, 41 (1995).
42. J. T. Smith, "Conservative Modeling of 3-D Electromagnetic Fields, Part 1. Properties and Error Analysis," Geophysics 61, 1308 (1996).
43. V. A. Sobolev, "Solve Incompatible System," Soros Educational Journal 6 (4), 116 (2000).
44. V.V. Spichak, Magnetotelluric Fields in 3-D Geoelectric Models, (Nauchnyi Mir, Moscow, 1999) [in Russian].
45. T. Strohmer and R. A. Vershinin, "A Randomized Kaczmarz Algorithm with Exponential Convergence," Journal of Fourier Analysis and Applications (Birkhouser, Boston, 2008), pp.1531-5851 (Online). DCI 10, 1007/s00041-008-9030-4.
46. L. A. Tabarovskii, Application of the Integral Equation Method to the Problems of Geoelectrics (Nauka, Novosibirsk, 1975) [in Russian].
47. K. Tanabe, "Projection Method for Solving a Singular System of Linear Equations and its Applications," Numer. Math. 17, 203 (1971).
48. A. N. Tikhonov, "On Determination of Electric Characteristics of Deep Crustal Layers," Dokl. Akad. Nauk SSSR, Novaya Ser. 73, 295 (1950).
49. S. C. Ting and G. W. Hohmann, "Integral Equation Modeling of Three-Dimensional Magnetotelluric Response," Geophysics 46 (2), 182 (1981).
50. C. Torres-Verdin, "Implication of the Born Approximation for the Magnetotelluric Problem in Three-Dimensional Environments," in Ph. D. Thes (Austin, 1985), p. 185.
51. E. Trefftz, "Ein Gegenstuck Zum Ritzchen Verfahren," in Intern. Kongress Technische Mechanik (Verhandl d. 2. Zurich, 1926), pp. 131-137.
52. R. B. Vaganov and B. Z. Katsenelenbaum, Foundations of the Diffraction Theory (Nauka, Moscow, 1982) [in Russian.
53. I. M. Varentsov, "Modern Trends in the Solution of Forward and Inverse 3-D Electromagnetic Induction Problems," Geoph. Surv. 6, 55 (1983).
54. P. E. Wannamaker, "Advances in Three-Dimensional Magnetoteluric Modeling Using Integral Equations," Geophysics 56 (11), 1716 (1991).
55. J. T. Weaver and C. R. Brewitt-Taylor. "Improved Boundary Conditions for the Numerical Solution of E-Polarization Problems in Geomagnetic Induction," Geophys. J. Roy. Astron. Soc. 54 (2), 309 (1978).
56. P. Weidelt, "Electromagnetic Induction in Three-Dimensional Structures," J. Geoph. 42 (1), p. 85 (1975).
57. Z. Xiong, "Electromagnetic Modeling of 3-D Structures by the Method of System Iteration Using Integral Equations," Geophysics 57 (12), 1556 (1992).
58. I. V. Yegorov, "Modeling the Electromagnetic Field in a Neighborhood of an Arbitrary Inhomogeneous Body," in Proceeding of the Second International Symposium on Tree-Dimensional Electromagnetics (Salt Lake City, USA, 1999), pp. 37-40.
59. I. V. Yegorov, "Solution of 3-D Problems of Geoelectrics Based on the Trefftz Method," in Vtoraya Vserossiiskaya Shkola-Seminar po Elektromagnitnym Zondirovaniyam Zemli (MAKS Press, 2005), pp. 62-63.
60. M. N. Yudin and V. A. Shneider, "On Calculation Magnetotelluric Field in a Three-Dimensional Media by the Net Method," in Geomagnitnye Issledovaniya (Radio i Svyaz', Moscow, 1982), No. 29, pp. 84-90.
61. E. V. Zakharov and I. V. Il'in, "Method of Calculation of Electromagnetic Fields in a Plane-Parallel Layered Medium with Local Heterogeneities," in Vychislitel'nye Metody i Programmirovanie (MGU, Moscow, 1971), Vyp. 16, pp. 83-108.
62. M. S. Zhdanov and V. V. Spichak, Mathematical Modeling of Electromagnetic Fields in Three-Dimensional Heterogeneous Media (Nauka, Moscow, 1992) [in Russian].
63. M. S. Zhdanov, I. M. Varentsov, and N. G. Golubev, Preprint No. 350301, (Institute of Terrestrial Magnetism, Ionosphere, and Radio-Wave Propagation, Russian Academy of Sciences, Troitsk, Moscow oblast, Russia)
64. M. S. Zhdanov et al., "Methods for Modeling Electromagnetic Fields. Results from COMMEMI-the International Project on the Comparison of Modeling Methods for Electromagnetic Induction Electromagnetic Modeling," Journal of Applied Geophysics 37, 133 (1997).
65. F. I. Zyserman and J. E. Santos, "Parallel Finite Element Algorithm with Domain Decomposition for Three-Dimensional Magnetotelluric Modeling," Journal of Applied Geophysics," 44, 337 (2000).