A parallel goal-oriented adaptive finite element method for 2.5-D electromagnetic modelling

Geophysical Journal International

Volumn 186, Issue 1, 2011, Pages 137-154

  Key, Kerry ^a   Ovall, Jeffrey ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF KENTUCKY   (United States)

Author keywords

Electromagnetic theory; Magnetotelluric; Marine electromagnetics; Numerical approximations and analysis; Numerical solutions

Indexed keywords

ELECTROMAGNETIC THEORIES; ELECTROMAGNETICS; MAGNETOTELLURIC; NUMERICAL APPROXIMATIONS; NUMERICAL SOLUTION;

CLUSTER COMPUTING; CLUSTERING ALGORITHMS; COMPUTER GRAPHICS; ELECTRIC FIELDS; ELECTROMAGNETISM; ERROR ANALYSIS; HYDROCARBONS; MAGNETOTELLURICS; NUMERICAL METHODS; PARAMETER ESTIMATION;

FINITE ELEMENT METHOD;

ALGORITHM; ELECTROMAGNETIC METHOD; ERROR ANALYSIS; FINITE ELEMENT METHOD; HYDROCARBON RESERVOIR; MAGNETOTELLURIC METHOD; MATHEMATICAL ANALYSIS; SEAFLOOR; TOPOGRAPHY;

EID: 79959253426     PISSN: 0956540X     EISSN: 1365246X     Source Type: Journal    
DOI: 10.1111/j.1365-246X.2011.05025.x     Document Type: Article

References (58)

1. Abubakar, A., Habashy, T.M., Druskin, V.L., Knizhnerman, L. & Alumbaugh, D., 2008. 2.5D forward and inverse modeling for interpreting low-frequency electromagnetic measurements, Geophysics, 73(4), F165-F177.
2. Adams, R.A. & Fournier, J.J.F., 2003. Sobolev Spaces, 2nd edn, Vol. 140, Elsevier/Academic Press, Amsterdam .
3. Ainsworth, M. & Oden, J.T., 2000. A posteriori error estimation in finite element analysis, in Pure and Applied Mathematics, Wiley-Interscience (John Wiley & Sons), New York .
4. Anderson, W.L., 1979. Numerical-integration of related Hankel transforms of orders 0 and 1 by adaptive digital filtering, Geophysics, 44(7), 1287-1305.
5. Babuška, I. & Miller, A., 1984a. The post-processing approach in the finite-element method. 1. Calculation of displacements, stresses and other higher derivatives of the displacements, Int. J. Numer. Methods Eng., 20(6), 1085-1109.
6. Babuška, I. & Miller, A., 1984b. The post-processing approach in the finite-element method. 2. the calculation of stress intensity factors, Int. J. Numer. Methods Eng., 20(6), 1111-1129.
7. Babuška, I. & Miller, A., 1984c. The post-processing approach in the finite-element method. 3. A posteriori error-estimates and adaptive mesh selection, Int. J. Numer. Methods Eng., 20(12), 2311-2324.
8. Bank, R.E., 1996. Hierarchical bases and the finite element method, in Acta Numerica, 1996, Vol. 5, pp. 1-43, Cambridge Univ. Press, Cambridge .
9. Bank, R.E. & Xu, J.C., 2003. Asymptotically exact a posteriori error estimators, Part II: General unstructured grids, SIAM J. Numer. Anal., 41, 2313-2332.
10. Becker, R. & Rannacher, R., 2001. An optimal control approach to a posteriori error estimation in finite element methods, Acta Numer., 10, 1-102.
11. Chen, J., Hoversten, G.M., Key, K. & Nordquist, G., 2010. Stochastic inversion of 2D magnetotelluric data using sharp boundary parameterization, SEG Technical Program Expanded Abstracts, 29(1), 609-613.
12. Constable, S. & Weiss, C.J., 2006. Mapping thin resistors and hydrocarbons with marine EM methods: insights from 1D modeling, Geophysics, 71(2), G43-G51.
13. Constable, S., Key, K. & Lewis, L., 2009. Mapping offshore sedimentary structure using electromagnetic methods and terrain effects in marine magnetotelluric data, Geophys. J. Int., 176(2), 431-442.
14. Demmel, J.W., Eisenstat, S.C., Gilbert, J.R., Li, X.S. & Liu, J.W.H., 1999. A supernodal approach to sparse partial pivoting, SIAM J. Matrix Anal. Appl., 20(3), 720-755.
15. Devroye, L., Lemaire, C. & Moreau, J.M., 2004. Expected time analysis for Delaunay point location, Comput. Geometry-Theory Appl., 29(2), 61-89.
16. Eidesmo, T., Ellingsrud, S., MacGregor, L., Constable, S., Sinha, M., Johansen, S., Kong, F. & Westerdahl, H., 2002. Sea bed logging (SBL), a new method for remote and direct identification of hydrocarbon filled layers in deepwater areas, First Break, 20, 144-152.
17. Eisenberg, M. & Malvern, L., 1973. On finite element integration in natural co-ordinates, Int. J. Numer. Methods Eng., 7(4), 574-575.
18. Estep, D., Holst, M. & Larson, M., 2005. Generalized Green's functions and the effective domain of influence, SIAM J. Sci. Comput., 26(4), 1314-1339.
19. Evans, L.C., 2010. Partial differential equations, in Graduate Studies in Mathematics, 2nd edn, Vol. 19, American Mathematical Society, Providence, RI.
20. Everett, M. & Edwards, R., 1992. Transient marine electromagnetics: the 2.5-D forward problem, Geophys. J. Int., 113, 545-561.
21. Franke, A., Börner, R.U. & Spitzer, K., 2007. Adaptive unstructured grid finite element simulation of two-dimensional magnetotelluric fields for arbitrary surface and seafloor topography, Geophys. J. Int., 171(1), 71-86.
22. Golub, G.H. & Van Loan, C.F., 1996. Matrix Computations, 3rd edn, Johns Hopkins University Press, Baltimore, MD .
23. Guptasarma, D. & Singh, B., 1997. New digital linear filters for Hankel J(0) and J(1) transforms, Geophys. Prospect., 45(5), 745-762.
24. Hackbusch, W., 2010. Elliptic differential equations, in Theory and Numerical Treatment, Springer Series in Computational Mathematics, Vol. 18, Springer-Verlag, Berlin.
25. Ihlenburg, F., 1998. Finite element analysis of acoustic scattering, in Applied Mathematical Sciences, Vol. 132, Springer-Verlag, New York, NY .
26. Kennel, M.B., 2004. KDTREE 2: Fortran 95 and C++ software to efficiently search for near neighbors in a multi-dimensional Euclidean space, arXiv:physics/0408067.
27. Key, K., 2009. 1D inversion of multicomponent, multifrequency marine CSEM data: methodology and synthetic studies for resolving thin resistive layers, Geophysics, 74(2), F9-F20.
28. Key, K. & Constable, S., 2011. Coast effect distortion of marine magnetotelluric data: insights from a pilot study offshore northeastern Japan, Phys. Earth planet. Inter., 184(3-4), 194-207, doi:.
29. Key, K. & Weiss, C., 2006. Adaptive finite element modeling using unstructured grids: the 2D magnetotelluric example, Geophysics, 71(6), G291-G299.
30. Kong, F.N., Johnstad, S.E., Røsten, T. & Westerdahl, H., 2008. A 2.5D finite-element-modeling difference method for marine CSEM modeling in stratified anisotropic media, Geophysics, 73(1), F9-F19.
31. Lee, K.H. & Morrison, H.F., 1985. A numerical-solution for the electromagnetic scattering by a two-dimensional inhomogeneity, Geophysics, 50(3), 466-472.
32. Li, Y. & Constable, S., 2007. 2D marine controlled-source electromagnetic modeling, part 2: the effect of bathymetry, Geophysics, 72(2), WA63-WA71.
33. Li, Y. & Key, K., 2007. 2D marine controlled-source electromagnetic modeling, part 1: an adaptive finite element algorithm, Geophysics, 72(2), WA51-WA62.
34. Li, Y. & Pek, J., 2008. Adaptive finite element modelling of two-dimensional magnetotelluric fields in general anisotropic media, Geophys. J. Int., 175(3), 942-954.
35. Mackie, R.L., Madden, T.R. & Wannamaker, P.E., 1993. Three-dimensional magnetotelluric modeling using difference equations: theory and comparisons to integral equation solutions, Geophysics, 58(02), 215-226.
36. Mitsuhata, Y., 2000. 2-D electromagnetic modeling by finite-element method with a dipole source and topography, Geophysics, 65(2), 465-475.
37. Monk, P., 2003. Finite element methods for Maxwell's equations, in Numerical Mathematics and Scientific Computation, Oxford University Press, New York, NY .
38. Myer, D., Constable, S. & Key, K., 2011. Broad-band waveforms and robust processing for marine CSEM surveys, Geophys. J. Int., 184, 689-698.
39. Newman, G.A. & Alumbaugh, D.L., 1995. Frequency-domain modelling of airborne electromagnetic responses using staggered finite differences, Geophys. Prospect., 43(8), 1021-1042.
40. Nitsche, J.A. & Schatz, A.H., 1974. Interior estimates for Ritz-Galerkin methods, Math. Comp., 28, 937-958.
41. Orange, A., Key, K. & Constable, S., 2009. The feasibility of reservoir monitoring using time-lapse marine CSEM, Geophysics, 74(2), F21-F29.
42. Ovall, J.S., 2004. Duality-based adaptive refinement for elliptic PDEs, Ph.D. thesis, University of California, San Diego, La Jolla, CA .
43. Ovall, J.S., 2006. Asymptotically exact functional error estimators based on superconvergent gradient recovery, Numer. Math., 102(3), 543-558.
44. Ovall, J.S., 2007. Function, gradient, and Hessian recovery using quadratic edge-bump functions, SIAM J. Numer. Anal., 45(3), 1064-1080 (electronic).
45. Schwalenberg, K. & Edwards, R.N., 2004. The effect of seafloor topography on magnetotelluric fields: an analytic formulation confirmed with numerical results, Geophys. J. Int., 159, 607-621.
46. Shewchuk, J.R., 1996. Triangle: engineering a 2D quality mesh generator and Delaunay triangulator, in Applied Computational Geometry: Towards Geometric Engineering, Lecture Notes in Computer Science, Vol. 1148, pp. 203-222, eds Lin, M.C. & Manocha, D., Springer-Verlag, Berlin .
47. Shewchuk, J., 2002a. What is a good linear finite element? Interpolation, conditioning, anisotropy, and quality measures, in Proc. 11th Int. Meshing Roundtable. Available at .
48. Shewchuk, J.R., 2002b. Delaunay refinement algorithms for triangular mesh generation, Comput. Geometry-Theory Appl., 22, 21-74.
49. Stoyer, C.H. & Greenfield, R.J., 1976. Numerical-solutions of response of a 2-dimensional earth to an oscillating magnetic dipole source, Geophysics, 41(3), 519-530.
50. Unsworth, M. & Oldenburg, D., 1995. Subspace inversion of electromagnetic data: application to mid-ocean-ridge exploration, Geophys. J. Int., 123(1), 161-168.
51. Unsworth, M.J., Travis, B.J. & Chave, A.D., 1993. Electromagnetic induction by a finite electric dipole source over a 2-D Earth, Geophysics, 58(02), 198-214.
52. Wahlbin, L.B., 1991. Local behavior in finite element methods, in Handbook of Numerical Analysis, Vol. II, pp. 353-522, North-Holland, Amsterdam .
53. Wannamaker, P.E., Stodt, J.A. & Rijo, L., 1986. Two-dimensional topographic responses in magnetotellurics modeled using finite elements, Geophysics, 51(11), 2131-2144.
54. Wannamaker, P.E., Stodt, J.A. & Rijo, L., 1987. A stable finite-element solution for two-dimensional magnetotelluric modeling, Geophys. J. R. astr. Soc., 88, 277-296.
55. Ward, S.H. & Hohmann, G.W., 1988. Electromagnetic theory for geophysical applications, in Electromagnetic Methods in Applied Geophysics, 1st edn, pp. 131-312, ed. Nabighian, M.N., Soc. Expl. Geophys, Tulsa, OK .
56. Weaver, J., LeQuang, B. & Fischer, G., 1985. A comparison of analytic and numerical results for a two-dimensional control model in electromagnetic induction.1. B-polarization calculations, Geophys. J. R. astr. Soc., 82, 263-277.
57. Weaver, J., LeQuang, B. & Fischer, G., 1986. A comparison of analytical and numerical results for a 2-D control model in electromagnetic induction, 2. E-polarization calculations, Geophys. J. R. astr. Soc., 87, 917-948.
58. Zhu, Y. & Cangellaris, A.C., 2006. Multigrid Finite Element Methods for Electromagnetic Field Modeling, John Wiley and Sons Ltd, Hoboken, NJ .