PIER B
 
Progress In Electromagnetics Research B
ISSN: 1937-6472
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 44 > pp. 261-282

ELECTROMAGNETIC FIELD OF ARBITRARILY ORIENTED COIL ANTENNAS IN COMPLEX UNDERGROUND ENVIRONMENT

By N. Yuan, C. R. Liu, and X. Nie

Full Article PDF (426 KB)

Abstract:
In this paper, a finite-difference based method is presented to simulate the electromagnetic field generated by arbitrarily-oriented coil antennas in three-dimensional (3-D) complex underground media. The media have multiple layers in both the vertical and horizontal direction and can be fully anisotropic. The developed finite-difference method uses a staggered grid to approximate a vector equation in terms of the scattered electric field. The resultant linear sparse matrix is solved iteratively using a generalized minimal residual (GMRES) algorithm and an incomplete LU precondition technique is applied to improve the convergence behavior of the linear equation, thus accelerate the solution. The developed algorithm is validated by numerical examples and then applied to the simulation and study of the popular triaxial induction tools in electrical well logging engineering for anisotropy detection.

Citation:
N. Yuan, C. R. Liu, and X. Nie, "Electromagnetic Field of Arbitrarily Oriented Coil Antennas in Complex Underground Environment," Progress In Electromagnetics Research B, Vol. 44, 261-282, 2012.
doi:10.2528/PIERB12072314

References:
1. Moran, J. H. and S. Gianzero, "Effects of formation anisotropy on resistivity-logging measurements," Geophysics, Vol. 44, 1266-1286, 1984.
doi:10.1190/1.1441006

2. Anderson, B. and S. K. Chang, "Synthetic induction logs by the finite element method," The Log Analyst, Vol. 23, 17-26, 1982.

3. Anderson, B., "Simulation of induction logging by the finite-element method," Geophysics, Vol. 49, 1943-1958, 1984.
doi:10.1190/1.1441606

4. Everett, M. E., E. A. Badea, L. C. Shen, G. A. Merchant, and C. J. Weiss, "3-D finite element analysis of induction logging in a dipping formation," IEEE Trans. Geoscience and Remote Sensing, Vol. 39, 2244-2252, 2001.
doi:10.1109/36.957287

5. Han, W. S., "3D finite element simulation method of induction and MWD tools,", Ph.D. Dissertation, University of Houston, 2004.

6. Zhdanov, M. S., S. K. Lee, and K. Yoshioka, "Integral equation method for 3D modeling of electromagnetic fields in complex structures within homogeneous background conductivity," Geophysics, Vol. 67, 333-345, 2006.
doi:10.1190/1.2358403

7. Fang, S., G. Z. Gao, and C. Torres-Verdin, "Efficient 3D electromagnetic modeling in the presence of anisotropic conductive media, using integral equations," Exploration Geophysics, Vol. 37, 239-244, 2006.
doi:10.1071/EG06239

8. Nie, X. C., N. Yuan, and R. Liu, "Simulation of LWD tool response using a fast integral equation method," IEEE Trans. on Geoscience and Remote Sensing, Vol. 48, No. 1, 72-81, Jan. 2010.
doi:10.1109/TGRS.2009.2027112

9. Weiss, C. J. and G. A. Newman, "Electromagnetic induction in a fully 3-D anisotropic earth," Geophysics, Vol. 67, No. 4, 1104-1114, Jul.-Aug. 2002.
doi:10.1190/1.1500371

10. Wang, T. and S. Fang, "3-D electromagnetic anisotropic modeling using finite difference," Geophysics, Vol. 66, No. 5, 1386-1398, Sept.-Oct. 2001.
doi:10.1190/1.1486779

11. Davydycheva, S., V. Druskin, and T. Habashy, "An efficient finite-difference scheme for electromagnetic logging in 3D anisotropic inhomogeneous media," Geophysics, Vol. 68, No. 5, 1525-1536, Sept.-Oct. 2003.
doi:10.1190/1.1620626

12. Newman, G. A. and D. L. Alumbaugh, "Three-dimensional induction logging problems, Part 2: A finite-difference solution," Geophysics, Vol. 67, No. 2, 484-491, Mar.-Apr. 2002.
doi:10.1190/1.1468608

13. Streich, R., "3D finite-difference frequency-domain modeling of controlled-source electromagnetic data: Direct solution and optimization for high accuracy," Geophysics, Vol. 74, F95-F105, 2009.
doi:10.1190/1.3196241

14. Davydycheva, S., D. Homan, and G. Minerbo, "Triaxial induction tool with electrode sleeve: FD modeling in 3D geometries," Journal of Applied Geophysics, Vol. 67, 98-108, 2009.
doi:10.1016/j.jappgeo.2008.10.001

15. Hou, J. S., R. K. Mallan, and C. Torres-Verdin, "Finite-difference simulation of borehole EM measurements in 3D anisotropic media using coupled scalar-vector potentials," Geophysics, Vol. 71, No. 5, G225-G233, Sept.-Oct. 2006.
doi:10.1190/1.2245467

16. Novo, M. S., L. C. da Silva, and F. L. Teixeira, "Finite volume modeling of borehole electromagnetic logging in 3-D anisotropic formations using coupled scalar-vector potentials," IEEE Antennas and Wireless Propagation Letters, 549-552, 2007.
doi:10.1109/LAWP.2007.906301

17. Novo, M. S., L. C. da Silva, and F. L. Teixeira, "Comparison of coupled-potentials and field-based finite-volume techniques for modeling of borehole EM tools," IEEE Geoscience and Remote Sensing Letters, Vol. 5, No. 2, Apr. 2008.
doi:10.1109/LGRS.2008.915740

18. Saad, Y. and M. H. Schultz, "GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems," SIAM Journal of Sci. STAT. Comput., Vol. 7, No. 3, 856-869, 1986.
doi:10.1137/0907058

19. Saad, Y., "ILUT: A dual threshold incomplete LU factorization," Numer. Linear Algebra Appl., Vol. 1, No. 4, 387-402, 1994.
doi:10.1002/nla.1680010405

20. Yuan, N., X. C. Nie, Y. B. Gan, T. S. Yeo, and L. W. Li, "Accurate analysis of conformal antenna arrays with finite and curved frequency selective surfaces," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 13, 1745-1760, 2007.

21. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propagat., Vol. 14, No. 3, 302-307, Jan. 1984.

22. Yuan, N., X. C. Nie, and R. Liu, "Electromagnetic field response of triaxial induction logging tools in 1-D multi-layered anisotropic formations," 2010 IEEE AP-S International Symposium on Science Meeting, Toronto, ON, Canada, Jul. 11-17, 2010.


© Copyright 2010 EMW Publishing. All Rights Reserved