Stochastic modeling of the Earth's magnetic field: Inversion for covariances over the observatory era

Geochemistry, Geophysics, Geosystems

Volumn 14, Issue 4, 2013, Pages 766-786

  Gillet, N ^a   Jault, D ^a   Finlay, C C ^b,c   Olsen, N ^c  

^a UNIVERSITÉ GRENOBLE ALPES   (France)

^b ETH ZURICH   (Switzerland)

^c TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

covariances; geomagnetic secular variation; stochastic processes

Indexed keywords

BUILDINGS; COVARIANCE MATRIX; DATA PROCESSING; MAGNETIC FIELDS; OBSERVATORIES; RANDOM PROCESSES; TIME DOMAIN ANALYSIS;

CORE-MANTLE BOUNDARY; COVARIANCE FUNCTION; COVARIANCES; EARTH'S MAGNETIC FIELD; GEOMAGNETIC SECULAR VARIATION; SECOND ORDER STATISTICS; SPHERICAL HARMONIC COEFFICIENT; STOCHASTIC APPROACH;

GEOMAGNETISM;

CORE-MANTLE BOUNDARY; DATA ASSIMILATION; GEOMAGNETISM; MAGNETIC FIELD; MODELING; SECULAR VARIATION; STOCHASTICITY;

EID: 84878349539     PISSN: None     EISSN: 15252027     Source Type: Journal    
DOI: 10.1002/ggge.20041     Document Type: Article

References (75)

1. Backus, G. E., (1983), Application of mantle filter theory to the magnetic jerk of 1969, Geophys. J. R. astr. Soc., 74, 713-746.
2. Backus, G. E., (1988), Bayesian inference in geomagnetism, Geophysical Journal, 92, 125-142.
3. Bartels, J., (1963), Discussion of time-variations of geomagnetic activity, indices Kp and Ap, 1932-1961, Annales de Geophysique, 19, 1.
4. Beggan, C., and, K. Whaler, (2009), Forecasting change of the magnetic field using core surface flows and ensemble Kalman filtering, Geophys. Res. Lett., 36 (18).
5. Bloxham, J., and, A. Jackson, (1992), Time-dependent mapping of the magnetic field at the core-mantle boundary, J. Geophys. Res., 97, 19,537-19,563.
6. Bouligand, C., G. Hulot, A. Khokhlov, and, G. A. Glatzmaier, (2005), Statistical paleomagnetic field modeling and dynamo numerical simulation, Geophys. J. Int., 161, 603-626. (Pubitemid 40829869)
7. Brendel, K., J. Kuipers, G. Barkema, and, P. Hoyng, (2007), An analysis of the fluctuations of the geomagnetic dipole, Phys. Earth Planet. Inter., 162, 249-255. (Pubitemid 46958925)
8. Cain, J. C., and, R. E. Sweeney, (1973), The POGO data, J. Atmos. Terr. Phys., 35, 1231-1247.
9. Christensen, U. R., I. Wardinski, and, V. Lesur, (2012), Timescales of geomagnetic secular acceleration in satellite field models and geodynamo models, Geophys. J. Int., 190, 243-254, doi:10.1111/j.1365-246X.2012.05508.x.
10. Constable, C., and, C. Johnson, (2005), A paleomagnetic power spectrum, Phys. Earth Planet. Int., 153 (1-3), 61-73. (Pubitemid 41722864)
11. Currie, R. G., (1968), Geomagnetic spectrum of internal origin and lower mantle conductivity, J. Geophys. Res., 73, 2779-2786.
12. de Boor, C., (2001), A Practical Guide to Splines, Springer.
13. De Santis, A., D. Barraclough, and, R. Tozzi, (2003), Spatial and temporal spectra of the geomagnetic field and their scaling properties, Phys. Earth Planet. Int., 135 (2), 125-134. (Pubitemid 36370902)
14. Eymin, C., and, G. Hulot, (2005), On core surface flows inferred from satellite magnetic data, Phys. Earth Planet. Inter., 152, 200-220. (Pubitemid 41435276)
15. Finlay, C. C., A. Jackson, N. Gillet, and, N. Olsen, (2012), Core surface magnetic field evolution 2000-2010, Geophys. J. Int., 189, 761-781, doi:10.1111/j.1365-246X.2012.05395.x.
16. Fournier, A., J. Aubert, and, E. Thébault, (2011), Inference on core surface flow from observations and 3-D dynamo modelling, Geophys. J. Int., 186, 118-136.
17. Gallet, Y., A. Genevey, and, V. Courtillot, (2003), On the possible occurrence of "archaeomagnetic jerks" in the geomagnetic field over the past three millennia, Earth Planet. Sci. Lett., 214 (1-2), 237-242, doi:10.1016/S0012-821X(03)00362-5. (Pubitemid 37118597)
18. Gavoret, J., D. Gibert, M. Menvielle, and, J.-L. L. Mouël, (1986), Long-term variations of the external and internal components of the Earth's magnetic field, J. Geophys. Res., 91, 4787-4796.
19. Gillet, N., M. A. Pais, and, D. Jault, (2009), Ensemble inversion of time-dependent core flow models, Geochem. Geophys. Geosyst., 10 (6), Q06,004, doi: 10.1029/2008GC002,290.
20. Gillet, N., V. Lesur, and, N. Olsen, (2010), Geomagnetic core field secular variation models, Space Sci. Rev., doi:10.1007/s11,214-009-9586-6.
21. Gubbins, D., (1983), Geomagnetic field analysis-I. Stochastic inversion, Geophys. J. R. Astr. Soc., 73, 641-652.
22. Gubbins, D., and, J. Bloxham, (1985), Geomagnetic field analysis-III. Magnetic fields on the core-mantle boundary, Geophys. J. R. Astr. Soc., 80, 695-713.
23. Haines, G. V., (1993), Modelling geomagnetic secular variation by main-field differences, Geophys. J. Int., 114 (3), 490-500, doi:10.1111/j.1365- 246X.1993.tb06982.x. (Pubitemid 24418947)
24. Holme, R., (2007), Large scale flow in the core, in Treatise in Geophysics, Core Dynamics, vol. 8, edited by, P. Olson, and, G. Schubert, chap. 4, pp. 107-129, Elsevier.
25. Holme, R., and, J. Bloxham, (1996), The treatment of attitude errors in satellite geomagnetic data, Phys. Earth Planet. Inter., 98, 221-223.
26. Holme, R., N. Olsen, and, F. Bairstow, (2011), Mapping geomagnetic secular variation at the core-mantle boundary, Geophys. J. Int., 186, 521-528.
27. Hongre, L., G. Hulot, and, A. Khokhlov, (1998), An analysis of the geomagnetic field over the past 2000 years, Phys. Earth Planet. Int., 106, 311-335. (Pubitemid 28441275)
28. Hulot, G., and, J.-L. Le Mouël, (1994), A statistical approach to the Earth's main magnetic field, Phys. Earth Planet. Int., 82, 167-183.
29. Jackson, A., and, C. C. Finlay, (2007), Geomagnetic secular variation and applications to the core, in Treatise in Geophysics, Geomagnetism, vol. 5, chap. 5, pp. 147-193, eds., M. Kono, and, G. Schubert,.
30. Jackson, A., and, P. Livermore, (2009), On Ohmic heating in the Earth's core I: Nutation constraints, Geophys. J. Int., pp. doi: 10.1111/j.1365-246X. 2008.04,008.x.
31. Jackson, A., A. R. T. Jonkers, and, M. R. Walker, (2000), Four centuries of geomagnetic secular variation from historical records, Phil. Trans. R. Soc. Lond. A, 358, 957-990.
32. Jazwinski, A.H., (1970), Stochastic Processes and Filtering Theory, Academic Press, New York.
33. Jonkers, A. R. T., A. Jackson, and, A. Murray, (2003), Four centuries of geomagnetic data from historical records, Rev. Geophys., 41, 1006 doi:10.1029/2002RG000,115.
34. Korte, M., C. Constable, F. Donadini, and, R. Holme, (2011), Reconstructing the holocene geomagnetic field, Earth Planetary Science Letters, 312, 497-505.
35. Kuang, W., A. Tangborn, Z. Wei, and, T. Sabaka, (2009), Constraining a numerical geodynamo model with 100-years of geomagnetic observations, Geophys. J. Int., 179, 1458-1468.
36. Kuipers, J., P. Hoyng, J. Wicht, and, G. Barkema, (2009), Analysis of the variability of the axial dipole moment of a numerical geodynamo model, Phys. Earth Planet. Int., 173 (3-4), 228-232, doi: 10.1016/j.pepi.2008.12.001.
37. Kuvshinov, A., and, N. Olsen, (2006), A global model of mantle conductivity derived from 5 years of CHAMP, Ørsted, and SAC-C magnetic data, Geophys. Res. Lett., 33, L18301, doi: 10.1029/2006GL027083. (Pubitemid 351147881)
38. Langel, R. A., and, R. H. Estes, (1985 a), The near-Earth magnetic field at 1980 determined from MAGSAT data, J. Geophys. Res., 90, 2495-2510.
39. Langel, R. A., and, R. H. Estes, (1985 b), Large-scale, near-field magnetic fields from external sources and the corresponding induced internal field, J. Geophys. Res., 90, 2487-2494. (Pubitemid 15514432)
40. Langel, R. A., J. R. Ridgeway, M. Sugiura, and, K. Maezawa, (1988), The geomagnetic field at 1982 from DE-2 and other magnetic field data, J. Geomag. Geoelectr, 40, 1103-1127.
41. Langel, R. A., T. J. Sabaka, R. T. Baldwin, and, J. A. Conrad, (1996), The near-Earth magnetic field from magnetospheric and quiet-day ionospheric sources and how it is modeled, Phys. Earth Planet. Int., 98, 235-267. (Pubitemid 126380724)
42. Lesur, V., I. Wardinski, M. Hamoudi, and, M. Rother, (2010 a), The second generation of the GFZ reference internal magnetic model: GRIMM-2, Earth Planets Space, 62, 765-773.
43. Lesur, V., I. Wardinski, S. Asari, B. Minchev, and, M. Mandea, (2010 b), Modelling the Earth's core magnetic field under flow constraints., Earth Planets Space, 62, 503-516.
44. Lühr, H., and, S. Maus, (2010), Solar cycle dependence of quiet-time magnetospheric currents and a model of their near-Earth magnetic field, Earth Planets Space, 62, 843-848.
45. McLeod, M. G., (1996), Spatial and temporal power spectra of the geomagnetic field, J. Geophys. Res., 101, 2745-2763.
46. Moritz, H., (1980), Advanced Physical Geodesy, Herbert Wichmann Verlag, Karlsruhe.
47. Neubert, T., et al. (2001), Ørsted satellite captures high-precision geomagnetic field data, Eos, Transactions American Geophysical Union, 82, 81.
48. Olsen, N., and, M. Mandea, (2007), Investigation of a secular variation impulse using satellite data: The 2003 geomagnetic jerk, Earth Planetary Science Letters, 255, 94-105.
49. Olsen, N., H. Lühr, T. J. Sabaka, and, M. Mandea, (2006), CHAOS-A model of Earth's magnetic field derived from CHAMP, Oersted, and SAC-C magnetic satellite data, Geophys. J. Int., 166, 67-75. (Pubitemid 43984352)
50. Olsen, N., M. Mandea, T. Sabaka, and, L. Tøffner-Clausen, (2010 a), The CHAOS-3 geomagnetic field model and candidates for the 11th generation IGRF, Earth Planets Space, 62, 719-727.
51. Olsen, N., H. Lühr, T. Sabaka, I. Michaelis, J. Rauberg, and, L. Tøffner-Clausen, (2010 b), CHAOS-4-A high-resolution geomagnetic field model derived from low-altitude CHAMP data, American Geophysical Union Fall Meeting, abstract no. GP21A-0992.
52. Olson, P. L., U. R. Christensen, and, P. E. Driscoll, (2012), From superchrons to secular variation: A broadband dynamo frequency spectrum for the geomagnetic dipole, Earth Planetary Science Letters, 319-320, 75-82, doi: 10.1016/j.epsl.2011.12.008.
53. Pais, M. A., and, D. Jault, (2008), Quasi-geostrophic flows responsible for the secular variation of the Earth's magnetic field, Geophys. J. Int., 173, 421-443.
54. Panovska, S., (2012), Modelling holocene geomagnetic field evolution, Ph.D. Thesis, ETH (Zürich).
55. Percival, D., and, A. Walden, (1993), Spectral Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques, Cambridge University Press.
56. Pinheiro, K., and, A. Jackson, (2008), Can a 1-D mantle electrical conductivity model generate magnetic jerk differential time delays?, Geophys. J. Int., 173, 781-792.
57. Rasmussen, C. E., and, C. K. I. Williams, (2006), Gaussian Processes for Machine Learning, The MIT Press, Cambridge.
58. Reigber, C., H. Lühr, and, P. Schwintzer, (2002), CHAMP mission status, Adv. Space Res., 30, 129-134. (Pubitemid 34854000)
59. Sabaka, T., R. Langel, R. Baldwin, and, J. Conrad, (1997), The geomagnetic field 1900-1995, including the large-scale field from magnetospheric sources, and the NASA candidate models for the 1995 revision of the IGRF, J. Geomag. Geoelectr., 49, 157-206.
60. Sabaka, T. J., N. Olsen, and, M. E. Purucker, (2004), Extending comprehensive models of the Earth's magnetic field with Oersted and CHAMP data, Geophys. J. Int., 159, 521-547. (Pubitemid 39520402)
61. Sabaka, T. J., D. D. Rowland, S. B. Luthcke, and, J.-P. Boy, (2010), Improving global mass flux solutions from Gravity Recovery and Climate Experiment (GRACE) through forward modeling and continuous time correlation, J. Geophys. Res., 115 (B11403), doi:10.1029/2010JB007533.
62. Schmucker, U., (1991), Solar cycle variations and corrected annual means for external effects at Fürstenfeldbruck 1951-1968, in "150 Years Earthmagnetic Observatories München-Maisach-Fürstenfeldbruck", Vol. 5, 217-248 pp., eds M. Beblo and H. Soffel, München, Münchner Geophysikalische Mitteilungen.
63. Siebert, M., and, J. Meyer, (1996), Geomagnetic activity indices, The Upper Atmosphere: Data Analysis and Interpretation (Eds., W. Dieminger, G.K. Hartmann, R. Leitinger,), pp. 887-911.
64. Silverman, B., (1984), Spline smoothing: The equivalent variable kernel method, Annals of Statistics, 12, 898-916.
65. Sivia, D. S., and, J. Skilling, (2006), Data Analysis. A Bayesian tutorial, Oxford University Press, Oxford.
66. Stein, M., (1999), Interpolation of Spatial Data: Some Theory for Kriging, Springer-Verlag, New-York.
67. Ultré-Guérard, P., D. Jault, M. Alexandrescu, and, J. Achache, (1998), Improving geomagnetic field models for the period 1980-1999 using Ørsted data, Earth Planets Space, 50, 635-640. (Pubitemid 29154245)
68. Velímský, J., (2010), Electrical conductivity in the lower mantle: Constraints from champ satellite data by time-domain EM induction modelling, Phys. Earth Planet. Int., 180 (3-4), 111-117, doi: 10.1016/j.pepi.2010.02.007.
69. Velímský, J., and, C. C. Finlay, (2011), Effect of a metallic core on transient geomagnetic induction, Geochem. Geophys. Geosyst., 12 (5), Q05,011, doi: 10.1029/2011GC003557.
70. Von Kármán, T., (1948), Progress in the statistical theory of turbulence, Proc. Natl. Acad. Sci. USA, 34 (11), 530-539.
71. Wardinski, I., and, R. Holme, (2011), Signal from noise in geomagnetic field modelling: Denoising data for secular variation studies, Geophys. J. Int., 185, 653-662.
72. Wardinski, I., and, V. Lesur, (2012), An extended version of the C 3FM geomagnetic field model-Application of a continuous frozen-flux constraint, Geophys. J. Int., 189, 1409-1429, doi:10.1111/j.1365-246X.2012. 05384.x.
73. Yaglom, A., (1987), Correlation Theory of Stationary and Related Random Functions, Springer-Verlag, New York.
74. Yukatake, T., and, J. C. Cain, (1979), Solar cycle variations of the first-degree spherical harmonic components of the geomagnetic field, J. Geomag. Geoelec, 31, 509-544.
75. Yukatake, T., and, J. C. Cain, (1987), Solar cycle variations in the annual mean values of the geomagnetic components of observatory data, J. Geomag. Geoelec, 39, 10-49.