volume | PIER Journals

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.

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. Google Scholar

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 Google Scholar

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 Google Scholar

4. Jin, J. M., The Finite Element Method in Electromagnetics, John Wiley & Sons, 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 Google Scholar

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. Google Scholar

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. Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

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 Google Scholar

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

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

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 Google Scholar

Dr. Xiangyang Sun

Professor Zai-Ping Nie