Geoelectromagnetic induction in a heterogeneous sphere: A new three-dimensional forward solver using a conservative staggered-grid finite difference method

Geophysical Journal International

Volumn 140, Issue 3, 2000, Pages 636-650

  Uyeshima, M ^a   Schultz, A ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Electrical conductivity; Electromagnetic induction; Electromagnetic modelling; Mantle; Numerical techniques

Indexed keywords

ELECTRICAL CONDUCTIVITY; MANTLE; MODELING;

EID: 0034029522     PISSN: 0956540X     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.1365-246X.2000.00051.x     Document Type: Article

References (47)

1. Abramowitz, M. & Stegun, I.A., 1965. Handbook of Mathematical Functions, Dover, New York.
2. Axelsson, O., 1980. Conjugate gradient type methods for unsymmetric and inconsistent systems of linear equations, Linear Algebra and its Appl., 29, 1-16.
3. Axelsson, O., 1994. Iterative Solution Methods, Cambridge University Press, Cambridge.
4. Bai, Q. & Kohlstedt, D.L., 1993. Effects of chemical environment of the solubility and incorporation mechanism for hydrogen in olivine, Phys. Chem. Min., 19, 460-471.
5. Banks, R.J., 1969. Geomagnetic variations and the electrical conductivity of the upper mantle, Geophys. J. R. astr. Soc., 266, 123-192.
6. Bahr, K., Olsen, N. & Shankland, T.J., 1993. On the combination of the magnetotelluric and the geomagnetic depthsounding method for resolving an electrical conductivity increase at 400 km depth, Geophys. Res. Lett., 20, 2937.
7. Egbert, G. & Booker, J.R., 1992. Very long period magnetotellurics at Tucson observatory: implications for mantle conductivity, J. geophys. Res., 97(B11), 15 099-15 112.
8. Egbert, G., Booker, J.R. & Schultz, A., 1992. Very long period magnetotellurics at Tucson observatory: estimation of impedances, J. geophys. Res., 97(B11), 15 113-15 128.
9. Everett, M.E. & Schultz, A., 1995. Geomagnetic induction in eccentrically nested spheres, Phys. Earth planet. Inter., 92, 189-198.
10. Everett, M.E. & Schultz, A., 1996. Geomagnetic induction in a heterogeneous sphere: azimuthally symmetric test computations and the response of an undulating 660-km discontinuity, J. geophys. Res., 101, 2765-2783.
11. Fainberg, E.B., Pankratov, O.V. & Singer, B.S., 1993. Thin sheet modelling of surface and deep inhomogeneities, Geophys. J. Int., 113, 144-154.
12. Fujii, I., Utada, H. & Yumoto, K., 1995. Averaged distribution of electrical conductivity of the Philippine Sea Plate, IUGG, XXI General Assembly, Week B, Abstracts, 21, 63-64.
13. Fujii, I. & Schultz, A., 1998. The sensitivity of mantle electrical modelling to the spatial distribution of the global magnetic observatory system - a new requirement for an old network, EOS, Trans. Am. geophys. Un., Suppl., 79, F64.
14. Hirsch, L.M. & Shankland, T.J., 1993. Quantitative olivine-defect chemical model: insights on electrical conduction, diffusion and the role of Fe content, Geophys. J. Int., 114, 21-35.
15. Hirsch, L.M., Shankland, T.J. & Duba, A.G., 1993. Electrical conduction and polaron mobility in Fe-bearing olivine, Geophys. J. Int., 114, 36-44.
16. Karato, S., 1990. The role of hydrogen in the electrical conductivity of the upper mantle, Nature, 347, 272-273.
17. Koyama, T. & Utada, H., 1998. Induction modelling in the 3D global Earth - modified Neumann Series, Proc. Conductivity Anomaly Symp. 279-286 (in Japanese).
18. Kuvshinov, A.V. & Pankratov, O.V., 1994. Electromagnetic induction in a spherical Earth with inhomogeneous conducting mantle: thin sheet forward problem, Proc. 12th Workshop on the Earth, Brest, France, 83.
19. Kuvshinov, A.V., Avdeev, D.B. & Pankratov, O.V., 1998. Electromagnetic modelling in a spherical Earth with surface and deep conducting inhomogeneities: multi-shell solution, 14th Workshop on Electromagnetic Induction in the Earth, Sinaia, Romania, Abstracts, 129-130.
20. Lizarralde, D., Chave, A., Hirth, G. & Schultz, A., 1995. Long period magnetotelluric study using Hawaii-to-California submarine cable data: implications for mantle conductivity, J. geophys. Res., 100(B9), 17 873-17 854.
21. Lahiri, B.N. & Price, A.T., 1939. Electromagnetic induction in non-uniform conductors, and the determination of the conductivity of the Earth from terrestrial magnetic variations, Phil. Trans. R. Soc. Lond., A237, 509-540.
22. Mackie, R.L. & Madden, T.R., 1993. Conjugate direction relaxation solutions for 3-D magnetotelluric modeling, Geophysics, 58, 1052-1057.
23. 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, 215-226.
24. Mackie, R.L., Smith, J.T & Madden, T.R., 1994. Three-dimensional electromagnetic modeling using finite difference equations: the magnetotelluric example, Radio Sci., 29, 923-935.
25. Martinec, Z., 1998. Geomagnetic induction in multiple eccentrically nested spheres, Geophys. J. Int., 132, 96-110.
26. Martinec, Z., 1999. Spectral-finite element approach to three-dimensional electromagnetic induction in a spherical Earth, Geophys. J. Int., 136, 229-250.
27. Olsen, N., 1998. The electrical conductivity of the mantle beneath Europe derived from C-responses from 3 to 720 hr, Geophys. J. Int., 133, 298-308.
28. Olsen, N., 1999. Long-period (30 days-1 year) electromagnetic sounding and the electrical conductivity of the lower mantle beneath Europe, Geophys. J. Int., 138, 179-187.
29. Rokityansky, I.I., 1982. Geoelectromagnetic Investigation of the Earth's Crust and Mantle, Springer-Verlag, Berlin.
30. Schultz, A., 1990. On the vertical gradient and lateral heterogeneity in midmantle electrical conductivity, Phys. Earth planet. Inter., 64, 68-86.
31. Schultz, A. & Larsen, J.C., 1987. On the electrical conductivity of the mid-mantle, I-calculation of equivalent scalar magnetotelluric response functions, Geophys. J. R. astr. Soc., 88, 733-762.
32. Schultz, A. & Larsen, J.C., 1990. On the electrical conductivity of the mid-mantle, 2-delineation of heterogeneity by application of extremal inverse solutions, Geophys. J. Int., 101, 565-580.
33. Schultz, A., Kurtz, R.D., Chave, A.D. & Jones, A.G., 1993. Conductivity discontinuities in the upper mantle beneath a stable craton, Geophys. Res. Lett., 20, 2941-2944.
34. Schultz, A. & Pritchard, G., 1998. A three-dimensional inversion for large-scale structure in a spherical domain, in Three-Dimensional Electromagnetics, Geophysical Developments Series, pp. 451-476, eds Spies, B. & Oristigliano, M., SEG, Tulsa.
35. Schultz, A., Semenov, V.Yu., 1993. Modelirovanie Strykturi elektroprovodnosti mantii zemli (Modelling the electrical conductivity structure of the Earth's mantle), Phyzika Zemli (Phys. Earth Russian Acad. Sci.), 10, 39-44 (in Russian).
36. Schultz, A. & Zhang, T.S., 1994. Regularised spherical harmonic analysis and the three dimensional electromagnetic response of the Earth, Geophys. J. Int., 116, 141-156.
37. Shankland, T.J. & Duba, A.G., 1997. Correlation of olivine electrical conductivity change with water, EOS, Trans. Am. geophys. Un., 78, 46.
38. Shankland, T.J., Peyronneau, J. & Poirier, J.P., 1993. Electrical conductivity of the Earth's lower mantle, Nature, 366, 453-455.
39. Singer, B.Sh., 1995. Method for solution of Maxwell's equations in non-uniform media, Geophys. J. Int., 120, 590-598.
40. Singer, B.Sh. & Fainberg, E.B., 1985. Electromagnetic Induction in Non-Uniform Thin Sheets and Shells, IZMIRAN, Moscow (in Russian).
41. Smith, J.T., 1996a. Conservative modeling of 3-D electromagnetic fields, Part 1: properties and error analysis, Geophysics, 61, 1308-1318.
42. Smith, J.T., 1996b. Conservative modeling of 3-D electromagnetic fields, Part 2: biconjugate gradient solution and an accelerator, Geophysics, 61, 1319-1324.
43. Tarits, P., Wahr, J. & Lognonné, P., 1999. Influence of conductivity heterogeneities at and near the core-mantle boundary on the geomagnetic secular variation, Geophys. J. Int., submitted.
44. Toh, H., Schultz, A. & Uyeshima, M., 1999. Biconjugate gradient solution of a spherical 3D EM forward solver using staggered-grid integral formulation and its acceleration over multi-frequencies, Int. Symp. in 3-D Electromagnetic Modeling (3DEM-2), Oct. 27-29, University of Utah, Salt Lake City (extended abstract).
45. Xu, Y., Poe, B.T., Shankland, T.J. & Rubie, D.C., 1998a. Electrical conductivity of olivine, wadsleyite, and ringwoodite under upper-mantle conditions, Science, 280, 1415-1419.
46. Xu, Y., McCammon, C. & Poe, B.T., 1998b. The effect of alumina on the electrical conductivity of silicate perovskite, Science, 282, 922-924.
47. Zhang, T.S. & Schultz, A., 1992. A three-dimensional perturbation solution for the EM induction problem in a spherical Earth the forward problem, Geophys. J. Int., 111, 319-334.