Special Issue: Swarm—The Earth’s Magnetic Field and Environment Explorers
- Open Access
Enhancing comprehensive inversions using the Swarm constellation
Earth, Planets and Space volume 58, pages 371–395 (2006)
This paper reports on the findings of a simulation study designed to test various satellite configurations suggested for the upcoming Swarm magnetic mapping mission. The test is to see whether the mission objectives of recovering small-scale core secular variation (SV) and lithospheric magnetic signals, as well as information about mantle conductivity structure, can be met. The recovery method used in this paper is known as comprehensive inversion (CI) and involves the parameterization of all major fields followed by a co-estimation of these parameters in a least-squares sense in order to achieve proper signal separation. The advantage of coestimation over serial estimation of parameters is demonstrated by example. Synthetic data were calculated for a pool of six Swarm satellites from a model based heavily on the CM4 comprehensive model, but which has more small-scale lithospheric structure, a more complicated magnetospheric field, and an induced field reflecting a 3-D conductivity model. These data also included realistic magnetic noise from spacecraft and payload. Though the parameterization for the CI is based upon that of CM4, modifications have been made to accommodate these new magnetospheric and induced fields, in particular with orthogonality constraints defined so as to avoid covariance between slowly varying induced fields and SV. The use of these constraints is made feasible through an efficient numerical implementation. Constellations of 4, 3, 2, and 1 satellites were considered; that with 3 was able to meet the mission objectives, consistently resolving the SV to about spherical harmonic (SH) degree n = 15 and the lithosphere to a limited n < 90 due to external field leakage, while those with 2 and 1 were not; 4 was an improvement over 3, but was much less than the improvement from 2 to 3. The resolution of the magnetospheric and induced SH time-series from the 3 satellite configuration was sufficient enough to allow the detection of 3-D mantle conductivity structure in a companion study.
Arkani-Hamed, J. and D. W. Strangway, Intermediate-scale magnetic anomalies of the Earth, Geophysics, 50, 2817–2830, 1985a.
Arkani-Hamed, J. and D. W. Strangway, Lateral variations of apparent susceptibility of lithosphere deduced from Magsat data, J. Geophys. Res., 90, 2655–2664, 1985b.
Arkani-Hamed, J. and D. W. Strangway, Band-limited global scalar magnetic anomaly map of the Earth derived from Magsat data, J. Geophys. Res., 91, 8193–8203, 1986.
Arkani-Hamed, J., R. A. Langel, and M. E. Purucker, Magnetic anomaly maps of Earth derived from POGO and Magsat data, J. Geophys. Res., 99, 24,075–24,090, 1994.
Bertsekas, D. P., Nonlinear Programming, Athena Scientific, Belmont, MA, 1995.
Cohen, Y. and J. Achache, New global vector magnetic anomaly maps derived from Magsat data, J. Geophys. Res., 95, 10,783–10,800, 1990.
Cohen-Tannoudji, C., B. Diu, and F. Laloë, Quantum mechanics, Volume I, J. Wiley & Sons, New York, 1977.
Counil, J., Y. Cohen, and J. Achache, The global continent-ocean magnetization contrast, Earth Planet. Sci. Lett., 103, 354–364, 1991.
Demmel, J. W., Applied numerical linear algebra, SIAM, Philadelphia, 1997.
Friis-Christensen, E., H. Lühr, and G. Hulot, Swarm: A constellation to study the Earth’s magnetic field, Earth Planets Space, 58, this issue, 351–358, 2006.
Golub, G. H. and C. F. Van Loan, Matrix Computations, Johns Hopkins Univ. Press, Baltimore, 1989.
Green, A. A., A comparison of adjustment procedures for leveling aeromagnetic survey data, Geophysics, 48, 745–753, 1983.
Hamoudi, M., Y. Cohen, and J. Achache, Can the thermal thickness of the continental lithosphere be estimated from Magsat data?, Tectonophys., 284, 19–29, 1998.
Kuvshinov, A., T. Sabaka, N. Olsen, 3-D electromagnetic induction studies using the Swarm constellation: Mapping conductivity anomalies in the Earth’s mantle, Earth, Planets and Space, 58, this issue, 417–427, 2006.
Langel, R. A., The Main Field, in wGeomagnetism, vol. 1, edited by J. A. Jacobs, pp. 249–512, Academic Press, London, 1987.
Luyendyk, A. P. J., Processing of airborne magnetic data, J. Austr. Geol. Geophys., 17(2), 31–38, 1997.
Maus, S., M. Rother, R. Holme, H. Lühr, N. Olsen, and V. Haak, First scalar magnetic anomaly map from CHAMP satellite data indicates weak lithospheric field, Geophys. Res. Lett., 29(14), doi: 10.1029/2001GL013,685, 2002.
Maus, S., H. Lühr, and M. Purucker, Simulation of the high-degree lithospheric field recovery for the Swarm constellation of satellites, Earth Planets Space, 58, this issue, 397–407, 2006.
Minty, B. R. S., Simple micro-levelling for aeromagnetic data, Expl. Geophys., 22, 591–592, 1991.
Olsen, N., The electrical conductivity of the mantle beneath Europe derived from C-Responses from 3 h to 720 h, Geophys. J., 133, 298–308, 1998.
Olsen, N., F. Lowes, and T. J. Sabaka, Ionospheric and induced field leakage in geomagnetic field models, and derivation of candidate models for DGRF 1995 and DGRF 2000, Earth Planets Space, 57, 1191–1196, 2005.
Olsen, N., R. Haagmans, T. J. Sabaka, A. Kuvshinov, S. Maus, M. E. Purucker, M. Rother, V. Lesur, and M. Mandea, The Swarm End-to-End mission simulator study: A demonstration of separating the various contributions to Earth’s magnetic field using synthetic data, Earth Planets Space, 58, this issue, 359–370, 2006.
Parkinson, W. D. and V. R. S. Hutton, The Electrical Conductivity of the Earth, in Geomagnetism, vol. 3, edited by J. A. Jacobs, pp. 261–321, Academic Press, London, 1987.
Ravat, D. N., R. A. Langel, M. E. Purucker, J. Arkani-Hamed, and D. E. Alsdorf, Global vector and scalar Magsat magnetic anomaly maps, J. Geophys. Res., 100, 20,111–20,135, 1995.
Richmond, A. D., Ionospheric Electrodynamics Using Magnetic Apex Coordinates, J. Geomagn. Geoelectr., 47, 191–212, 1995.
Sabaka, T. J., N. Olsen, and R. A. Langel, A comprehensive model of the quiet-time, near-Earth magnetic field: phase 3, Geophys. J. Int., 151, 32–68, 2002.
Sabaka, T. J., N. Olsen, and M. E. Purucker, Extending comprehensive models of the Earth’s magnetic field with Èrsted and CHAMP data, Geophys. J. Int., 159, 521–547, doi: 10.1111/j.1365-246X.2004.02,421.x, 2004.
Sorenson, H., Parameter Estimation, Marcel Dekker, Inc., New York, 1980.
Toutenburg, H., Prior Information in Linear Models, J. Wiley & Sons, New York, 1982.
About this article
Cite this article
Sabaka, T.J., Olsen, N. Enhancing comprehensive inversions using the Swarm constellation. Earth Planet Sp 58, 371–395 (2006). https://doi.org/10.1186/BF03351935
- Earth’s magnetic field
- comprehensive modelling
- electromagnetic induction