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2008-01-03
Vector Finite Element Analysis of Multicomponent Induction Response in Anisotropic Formations
By
Progress In Electromagnetics Research, Vol. 81, 21-39, 2008
Abstract
Multicomponent induction logging responses are simulated by using hierarchical mixed order vector finite element method (FEM). In order to modeling three orthogonal magnetic dipoles, we adopt the method that the total field is separated into incident field and secondary field, and only the secondary field is computed by FEM. In addition, two techniques are applied to improve the modeling accuracy and computational efficiency: 1) Hierarchical mixed order vector basis functions are applied to FEM. Different order basis functions are used in different elements in accordance with the changing speed of the field. The mixed order scheme reduces greatly the number of unknowns without reducing accuracy, and can attain much higher computational efficiency. 2) The systemof the FEM equations is solved by Distributed-SuperLU, and the results of multiple measure points can be got simultaneously. The FEM result is validated against volume integral equation method and the approach of planar layered media Green's functions, and the comparisons show very good agreement. Finally, the multicomponent induction response in anisotropic formations involving eccentric tools and dipping beds is included to demonstrate the flexibility of the method.
Citation
Xiang Sun, and Zai-Ping Nie, "Vector Finite Element Analysis of Multicomponent Induction Response in Anisotropic Formations," Progress In Electromagnetics Research, Vol. 81, 21-39, 2008.
doi:10.2528/PIER07121502
References

1. Kriegshauser, B., O. Fanini, S. Forgang, G. Itskovich, M. Rabinovich, L. Tabarovsky, L. Yu, M. Epov, et al. "A new multicomponent induction loggingtool to resolve anisotropic formations," SPWLA 40th Ann. Log. Symp., 2000.

2. Davydycheva, S., V. Druskinz, and T. Habashyz, "An efficient finite-difference scheme for electromagnetic logging in 3D anisotropic inhomogeneous media," Geophysics, Vol. 68, No. 5, 1525-1535, 2003.
doi:10.1190/1.1620626

3. Wang, T. and S. Fang, "3-D electromagnetic anisotropy modeling using finite differences," Geophysics, Vol. 66, No. 6, 1386-1398, 2001.
doi:10.1190/1.1486779

4. Jin, J. M., The Finite Element Method in Electromagnetics, John Wiley & Sons, Inc., New York, 2002.

5. Zhang, Z. Q. and Q. H. Liu, "Applications of the BCGS-FFT method to 3-D induction well logging problem," IEEE Trans. Geoscience and Remote Sensing, Vol. 41, No. 5, 998-1004, 2003.
doi:10.1109/TGRS.2003.811547

6. Ilic, M. M. and B. M. Notaros, "Higher order hierarchical curved hexahedral vector finite elements for electromagnetic modeling," IEEE Trans. Geosci. Remote Sens., Vol. 51, No. 3, 1026-1033, 2003.

7. Shen, J. S., "Modeling of the 3-D electromagnetic responses to the anisotropic medium by the edge finite element method," Well Logging Technology of China, Vol. 28, No. 2, 11-15, 2004.

8. 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, No. 10, 2244-2252, 2003.
doi:10.1109/36.957287

9. Liu, J. W. H., "The role of elimination trees in sparse factorization," SIAM J. Matrix Anal. Appl., Vol. 11, 134-172, 1990.
doi:10.1137/0611010

10. Demmel, J. W., S. C. Eisenstat, J. R. Gilbert, and X. Y. Li, "A supernodal approach to sparse partial pivoting," SIAM J. Matrix Anal. Appl., Vol. 20, 720-755, 1999.
doi:10.1137/S0895479895291765

11. Demmel, J. W., J. R. Gilbert, and X. Y. Li, SuperLU Users' Guide, 1999., 1999.

12. Zhdanov, M. S.W. D. Kennedy, A. B. Cheryauka, and E. Peksen, "Principles of tensor induction well logging in a deviated well in an anisotropic medium," SPWLA 42nd Annual Logging Symposium, 17-20, 2001.

13. Sun, X. Y., Z. P. Nie, A. Y. Li, and L. Xi, "Numerical modeling of multicomponent induction response in planar layered anisotropic formation," Chinese Geophysics.

14. Avdeev, D. B., A. V. Kuvshinov, O. V. Pankratov, and G. A. Newman, "Three-dimensional induction logging problems, Part 1: An integral equation solution and model comparisons," Geophysics, Vol. 67, No. 2, 413-426, 2002.
doi:10.1190/1.1468601

15. Zhdanov, M. S., D. Kennedy, and E. Peksen, "Foundation of the tensor induction well logging," Perophysics, Vol. 42, No. 6, 588-610, 2001.

16. Riddolls, R. J., "Near-field response in lossy media with exponential conductivity inhomogeneity," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 11, 1551-1558, 2006.
doi:10.1163/156939306779274354

17. Golestani-Rad, L. and J. Rashed-Mohassel, "Rigorous analysis of EM-wave penetration into a typical roomusing FDTD method: The transfer function concept," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 7, 913-926, 2006.
doi:10.1163/156939306776149851

18. Chen, X., D. Liang, and K. Huang, "Microwave imaging 3- D buried objects using parallel genetic algorithmcom bined with FDTD technique," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 13, 1761-1774, 2006.
doi:10.1163/156939306779292264

19. Uduwawala, D., "Modeling and investigation of planar parabolic dipoles for GPR applications: A comparison with bow-tie using FDTD," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 2, 227-236, 2006.
doi:10.1163/156939306775777224

20. Ding, W., Y. Zhang, P. Y. Zhu, and C. H. Liang, "Study on electromagnetic problems involving combinations of arbitrarily oriented thin-wire antennas and inhomogeneous dielectric objects with a hybrid MOM-FDTD method," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 11, 1519-1533, 2006.
doi:10.1163/156939306779274255

21. Zainud-Deen, S. H., W. M. Hassen, E. M. Ali, K. H. Awadalla, and H. A. Sharshar, "Breast cancer detection using a hybrid finite difference frequency domain and particle swarm optimization techniques," Progress In Electromagnetics Research B, Vol. 3, 35-46, 2008.
doi:10.2528/PIERB07112703

22. Liu, Q. H., "Electromagnetic field generated by an off-axis source in a cylindrically layered medium with an arbitrary number of horizontal discontinuities," Geophysics, Vol. 58, No. 50, 616-625, 1993.
doi:10.1190/1.1443445

23. Pingenot, J., "Full wave analysis of signal attenuation in a lossy rough surface cave using a high order time domain vector finite element method," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 12, 1695-1705, 2006.
doi:10.1163/156939306779292408

24. Hernandez-Lopez, M. A. and M. Quintillan-Gonzalez, "A finite element method code to analyse waveguide dispersion," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 3, 397-408, 2007.
doi:10.1163/156939307779367396

25. Hatamzadeh-Varmazyar, S., "An integral equation modeling of electromagnetic scattering from the surfaces of arbitrary resistance distribution," Progress In Electromagnetics Research B, Vol. 3, 157-172, 2008.
doi:10.2528/PIERB07121404

26. Jiang, G. X., H. B. Zhu, and W. Cao, "Implicit solution to modified form of time domain integral equation," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 5, 697-707, 2007.
doi:10.1163/156939307780667328

27. Wu, C. G. and G. X. Jiang, "Stabilization procedure for the timedomain integral equation," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 11, 1507-1512, 2007.

28. Franceschini, G., "A comparative assessment among iterative linear solvers dealing with electromagnetic integral equations in 3D inhomogeneous anisotropic media," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 7, 899-914, 2007.
doi:10.1163/156939307780749048