Simulation of multifrequency borehole resistivity measurements through metal casing using a goal-oriented hp finite-element method

IEEE Transactions on Geoscience and Remote Sensing

Volumn 44, Issue 8, 2006, Pages 2125-2134

  Pardo, David ^b   Torres Verdín, Carlos ^a,b   Demkowicz, Leszek F ^b  

^a IEEE   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Goal oriented adaptivity; Hp finite elements; Through casing resistivity tools (TCRTs)

Indexed keywords

BOREHOLE RESISTIVITY; GOAL-ORIENTED ADAPTIVITY; HP-FINITE ELEMENTS; THROUGH-CASING RESISTIVITY TOOLS (TCRT);

COMPUTER SIMULATION; FINITE ELEMENT METHOD; FREQUENCIES; NUMERICAL METHODS; OIL WELL CASINGS; STEEL;

BOREHOLES;

EID: 33746904755     PISSN: 01962892     EISSN: None     Source Type: Journal    
DOI: 10.1109/TGRS.2006.872094     Document Type: Article

References (17)

1. A. A. Kaufman, "The electrical field in a borehole with casing," Geophysics, vol. 55, no. 1, pp. 29-38, 1990.
2. W. Vail, S. Momii, R. Woodhouse, M. Alberty, R. Peveraro, and J. Klein, "Formation resistivity measurements through metal casing," Proc. SPWLA 34th Annu. Logging Symp. Jun. 13-16, 1993, Paper F.
3. C. J. Schenkel and H. F. Morrison, "Electrical resistivity measurement through metal casing," Geophysics, vol. 59, no. 7, pp. 1072-1082, 1994.
4. X. Wu and T. M. Habashy, "Influence of steel casings on electromagnetic signals," Geophysics, vol. 59, no. 3, pp. 378-390, 1994.
5. I. Babuska and A. Miller, 'The post-processing approach in the finite element method. I. Calculation of displacements, stresses and other higher derivatives of the displacements," Int. J. Numer, Methods Eng., vol. 20, no. 6, pp. 1085-1109, Jun. 1984.
6. D. Pardo, L. Demkowicz, and C. Torres-Verdin, "A goal-oriented hpadaptive finite element method with electromagnetic applications. Part I: Electrostatics," Int. J. Numer, Methods Eng., vol. 65, no. 8, pp. 1269-1309, Feb. 2006.
7. W. Cecot, W. Rachowicz, and L. Demkowicz, "An hp-adaptive finite element method for electromagnetics. Ill: A three-dimensional infinite element for Maxwell's equations," Int. J. Numer. Methods Eng., vol. 57, no. 7, pp. 899-921, Jun. 2003.
8. I. Babuska and B. Q. Guo, "Regularity of the solution of elliptic problems with piecewise analytic data. I. Boundary value problems for linear elliptic equation of second order," SIAM J. Math. Anal., vol. 19, no. 1, pp. 172-203, 1988.
9. I. Babuska and B. Quo, "Approximation properties of the h-p version of the finite element method," Comput. Methods Appl. Mech. Eng., vol. 133, no. 3/4, pp. 319-346, Jul. 1996.
10. C. Schwab, "p- and hp-finite element methods," in Theory and Applications in Solid and Fluid Mechanics, ser. Numerical Mathematics and Scientific Computation. New York: Clarendon, 1998.
11. G. J. Zhang, G. L. Wang, and H. M. Wang, "Application of novel basis functions in a hybrid method simulation of the response of induction logging in axisymmetrical stratified media," Radio Sci., vol. 34, no. 1, pp. 19-26, 1999.
12. G. J. Zhang, H. M. Wang, and G. L. Wang, "AC logging response in stratified media," Acta Geophysica Sin., vol. 38, no. 6, pp. 840-849, 1995.
13. W. C. Chew, S. Barone, B. Anderson, and C. Hennessy, "Diffraction of axisymmetric waves in a borehole by bed boundary discontinuities," Geophysics, vol. 49, no. 10, pp. 1586-1595, Oct. 1984.
14. J. R. Lovell, "Finite element methods in resistivity logging," Ph.D. dissertation, Delft Univ. Technol., Delft, The Netherlands, 1993.
15. 1, H(curl), and H(div) conforming projection-based interpolation in three dimensions: Quasi optimal p-interpolation estimates," Comput. Methods Appl. Mech. Eng., vol. 194, no. 2-5, pp. 267-296, Feb. 2005.
16. L. Demkowicz, W. Rachowicz, and P. Devloo, "A fully automatic Hp-adaptivity," J. Sci. Comput., vol. 17, no. 1-4, pp. 117-142, 2002.
17. W. Rachowicz, D. Pardo, and L. Demkowicz, "Fully automatic hp-adaptivity in three dimensions," ICES Rep., Univ. Texas, Austin, Tech. Rep. 04-22, 2004.