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Study of an Improved Comprehensive Magnetic Field Inversion Analysis for Swarm MTR, E2Eplus Study

Study of an Improved Comprehensive Magnetic Field Inversion Analysis for Swarm MTR, E2Eplus Study. Work performed by Nils Olsen, Terence J. Sabaka, Luis R. Gaya-Pique, Lars Tøffner-Clausen, and Alexei Kuvshinov, Presented by: Nils Olsen. Draft Agenda.

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Study of an Improved Comprehensive Magnetic Field Inversion Analysis for Swarm MTR, E2Eplus Study

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  1. Study of an Improved Comprehensive Magnetic Field Inversion Analysis for SwarmMTR, E2Eplus Study Work performed by Nils Olsen, Terence J. Sabaka, Luis R. Gaya-Pique, Lars Tøffner-Clausen, and Alexei Kuvshinov, Presented by: Nils Olsen

  2. Draft Agenda Swarm E2Eplus Mid Term Review, June 26 2006, at ESTEC, Noordwijk 11:00 Welcome 11:05 Presentation of activities done so far (NIO) Summary of activities already presented at PM1 Forward calculation, Constellations #3 and #4 Results of Gradient Approach First results of multi-satellite in-flight alignment List of failure and imperfection cases Plans for the near future 13:00 lunch 14:00 General discussion Telecon with Terence J. Sabaka and L. R. Gaya-Pique, GSFC 17:00 Adjourn 26. June 2006 | MTR E2Eplus | page 2

  3. E2Eplus Study Logic • Status of June 2006: • New, fast orbit generation scheme • Gradient approach • Multi-satellite alignment (tests partly concluded) 26. June 2006 | MTR E2Eplus | page 3

  4. Forward calculationConstellation #3 and #4 26. June 2006 | MTR E2Eplus | page 4

  5. Fast Orbit Prediction • circular near-polar orbits • realistic drift in local time • realistic altitude decay (solar activity effects …) • realistic maintenance of constellation Validation of method with CHAMP orbits 26. June 2006 | MTR E2Eplus | page 5

  6. Constellation #3 and #4 • Constellation #3 • Essentially similar to constellation #2, but using new orbit propagation method • Data only used for test purposes. This constellation will not be considered further • Constellation #4 • Launch on July 1, 1998 (1.5 years later than in Phase A, to account for launch delay) • Inclination Swarm A+B: 87.4ºSwarm C: 88.0º • Initial altitude: 450 km (A+B) and 530 km (C) • Longitudinal difference between Swarm A and B: 1.4º 26. June 2006 | MTR E2Eplus | page 6

  7. Solar and geomagnetic activity 26. June 2006 | MTR E2Eplus | page 7

  8. Orbit decay for Swarm A, for various launch times 26. June 2006 | MTR E2Eplus | page 8

  9. Local Time and altitude evolution, constellation #4 26. June 2006 | MTR E2Eplus | page 9

  10. Impact of higher sampling rate on lithospheric field recovery 26. June 2006 | MTR E2Eplus | page 10

  11. Re-analysis of Constellation #2 data 26. June 2006 | MTR E2Eplus | page 11

  12. The Gradient Method in the Comprehensive Inversion Approach 26. June 2006 | MTR E2Eplus | page 12

  13. “Selective Infinite Variance Weighting” Development of an approach that produces/identifies data subsets that are particularly sensitive to certain parameter subsetsand applying appropriate weighting such that these data strongly influence the determination of such parameters • Example: high-order crustal field is resolved by gradient information (data difference) low-order field is resolved by all data d1, d2, d3 are data of Swarm 1,2,3 ds, dd, are sum and difference of Swarm 1,2 x is all model parameters but crustal field (sensed by all satellites) yl is low-order crustal field (sensed by ds, dd, d3) yh is high-order crustal field (sensed by dd) 26. June 2006 | MTR E2Eplus | page 13

  14. Results: Gradient approach Difference data contribute only to lithospheric field coefficients of order m > 20 All data (sums and differences) contribute to all other coefficients 26. June 2006 | MTR E2Eplus | page 14

  15. Results: Gradient approach 26. June 2006 | MTR E2Eplus | page 15

  16. Multi-Satellite In-flight Alignment 26. June 2006 | MTR E2Eplus | page 16

  17. The principle of in-flight alignment Model parameters:SHA expansion coefficients gnm, hnm Euler angles a,b,g • New: • CI approach BNEC includes all relevant contributions to Earth’s magnetic field: internal and external potential fields plus toroidal fields • Simultaneous estimation of the Euler angles for all Swarm satellites 26. June 2006 | MTR E2Eplus | page 17

  18. Tests • Data from all 3 satellites (constellation #4) • Solved for 3 x 3 Euler angles plus magnetic field model • Only solved for the contributions that are included in the synthetic data • Test 1: core field only (up to n=13, temporal variation described by splines) • Test 2: lithospheric field (up to n=150) added • Test 3: magnetospheric (primary and induced field) added • Test 4: ionospheric (primary and induced field) added • Test 5: toroidal field added Tests 1 – 3 successfully completed (near perfect recovery of core and lithospheric field and Euler angles) Test 4 partly completed(good recovery of core and lithospheric field, but retrieved Euler angles are different from the true ones) 26. June 2006 | MTR E2Eplus | page 18

  19. Result of Test 3 Input data contain core, lithospheric and magnetospheric (primary and induced) field Difference between true and retrieved Euler angles < 1 arcsec 26. June 2006 | MTR E2Eplus | page 19

  20. Result of Test 4 Input data contain static internal field (n = 1-150, no SV!) and ionospheric plus magnetospheric (primary and induced) field Difference between true and retrieved Euler angles: 26. June 2006 | MTR E2Eplus | page 20

  21. Result of Test 4 • Spectra of model differences 26. June 2006 | MTR E2Eplus | page 21

  22. Plans for the near Future • Further tests of the multi-satellite alignment • Inclusion of ionospheric field: what went wrong, if anything? • Inclusion of toroidal fields (first tests completed) • The Great Unified Code: Combination of gradient and multi-satellite approach • Tests • Application to various imperfection and failure scenarii 26. June 2006 | MTR E2Eplus | page 22

  23. Failure and Imperfection Cases • Failure of VFM and/or STR on a single satellite • Only scalar (no vector) data available for Swarm A • Only scalar (no vector) data available for Swarm C • Impact of a S/C magnetic field on a single satellite (Swarm A) • Constant S/C dipole moment (hard magnetization), corresponding to 2 nT at the location of the ASM • Induced S/C dipole moment (soft magnetization), corresponding to 3 nT at the location of the ASM over the poles (i.e. the area of maximum Earth’s magnetic field strength) • Noise in the CRF attitude of a single satellite (Swarm A) • Time dependent attitude noise (all components) 2 sin(wt) arcsecs + 10 sin(2pT/24) arcsecswhere t is UT, w is orbital frequency, and T is Local Time in hours. • Failure of one or more satellite (extension of Phase A analysis) • Magnetic data from all 3 satellites (Swarm A, B and C) • Magnetic data from (Swarm A and C) only • Magnetic data from (Swarm A and B) only • Magnetic data from (Swarm A) only 26. June 2006 | MTR E2Eplus | page 23

  24. 26. June 2006 | MTR E2Eplus | page 24

  25. Work Breakdown Structure 26. June 2006 | MTR E2Eplus | page 25

  26. Updated list of proposed Meetings and Deliverables 26. June 2006 | MTR E2Eplus | page 26

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