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Enhancing comprehensive inversions using the Swarm constellation


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.


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Correspondence to Terence J. Sabaka.

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Sabaka, T.J., Olsen, N. Enhancing comprehensive inversions using the Swarm constellation. Earth Planet Sp 58, 371–395 (2006).

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Key words

  • Earth’s magnetic field
  • comprehensive modelling
  • electromagnetic induction
  • ionosphere
  • lithosphere
  • magnetosphere