On the Observability of the Time-Variable Lithospheric Signal in Satellite Magnetic Data

  • Josef SeberaEmail author
  • Roger Haagmans
  • Eldar Bakyiev
  • Aleš Bezděk


The lithospheric magnetic field, which is one of the main objectives of ESA’s mission Swarm, is slowly varying in time due to an induced component. This variation is small (usually it is omitted in the lithospheric modelling) but recent advances in processing strategies and still-growing amount of satellite data open questions whether such an effect should be considered in the development of the lithospheric models—when using data from missions like CHAMP and Swarm. This effect can now be estimated over a period of 17 years (since the launch of CHAMP), and it is shown how the satellite measurements (over the observable part of the spectrum) can be referenced to one common epoch. For this purpose, we first inverted the magnetic field vector from CHAOS-6 over degrees 21–120, after subtraction of a remanent model, to a vertically integrated susceptibility map. Using this susceptibility distribution and taking into account the evolving core fields from the CHAOS-6 model, the time-varying lithospheric signal is computed. The results depend on the time span and the altitude considered, e.g., an altitude of 400 km and a span of 17 years can produce more than 0.5 nT variations resulting in a peak-to-peak value of nearly 1 nT. The vertically integrated quantities appear to be a useful choice for parameterising lithospheric time variations, also for providing data corrections at the satellite altitude. The effect of the choice of the core field, which enters the inversion, on the lithospheric time variation is also studied—this effect is found less important even for core fields 20 years apart.


Geomagnetic field Lithosphere Swarm Time variation 



Josef Sebera acknowledges the European Space Agency for providing an inspiring environment in which a large part of this study was carried out during the research fellowship. Eldar Baykiev was supported by the Research Council of Norway as part of the project “Swarm Explorer: Combined use of satellite and airborne magnetic field data to explore lithospheric magnetization”, No. 222678. Special thanks go to Leonardo Uieda for his gravity calculation code that was used to create magnetic tesseroids and to Martin Pitoňák for the discussion on the VCE method. Aleš Bezděk was supported by the project LG15003. The editor-in-chief and the anonymous reviewers are acknowledged for the help with the manuscript. We also thank the authors of CHAOS-6 for making the model public at


  1. Arkani-Hamed J, Dyment J (1996) Magnetic potential and magnetization contrasts of Earth’s lithosphere. J Geophys Res Solid Earth 101(B5):11401–11425. Google Scholar
  2. Arkani-Hamed J, Strangway DW (1986) Effective magnetic susceptibility of the oceanic upper mantle derived from MAGSAT data. Geophys Res Lett 13(10):999–1002. Google Scholar
  3. Baykiev E, Ebbing J, Brönner M, Fabian K (2016) Forward modeling magnetic fields of induced and remanent magnetization in the lithosphere using tesseroids. Comput Geosci 96:124–135. Google Scholar
  4. Finlay CC, Olsen N, Kotsiaros S, Gillet N, Tøffner-Clausen L (2016) Recent geomagnetic secular variation from Swarm and ground observatories as estimated in the CHAOS-6 geomagnetic field model. Earth Planets Space 68(1):112. Google Scholar
  5. Friis-Christensen E, Lühr H, Hulot G (2006) Swarm: a constellation to study the Earth’s magnetic field. Earth Planets Space 58(4):351–358. Google Scholar
  6. Gradstein FM, Ogg JG, van Kranendonk M (2008) On the geologic time scale 2008. Newslett Stratigr 43(1):5–13. Google Scholar
  7. Hemant K, Maus S (2005) Geological modeling of the new CHAMP magnetic anomaly maps using a geographical information system technique. J Geophys Res Solid Earth. Google Scholar
  8. Hildebrand FB (1987) Introduction to numerical analysis. Courier Dover Publications, MineolaGoogle Scholar
  9. Hulot G, Olsen N, Thébault E, Hemant K (2009) Crustal concealing of small-scale core-field secular variation. Geophys J Int 177(2):361–366. Google Scholar
  10. Hulot G, Sabaka T, Olsen N, Fournier A (2015) 5.02—the present and future geomagnetic field. In: Schubert G (ed) Treatise on geophysics, 2nd edn. Elsevier, Oxford, pp 33–78. Google Scholar
  11. Jackson A (1994) Statistical treatment of crustal magnetization. Geophys J Int 119(3):991–998Google Scholar
  12. Jackson A, Winch D, Lesur V (1999) Geomagnetic effects of the Earth’s ellipticity. Geophys J Int 138(1):285–289. Google Scholar
  13. Koch KR, Kusche J (2002) Regularization of geopotential determination from satellite data by variance components. J Geodesy 76(5):259–268. Google Scholar
  14. Kusche J (2003a) A Monte–Carlo technique for weight estimation in satellite geodesy. J Geodesy 76(11):641–652. Google Scholar
  15. Kusche J (2003b) Noise variance estimation and optimal weight determination for GOCE gravity recovery. Adv Geosci 1:81–85Google Scholar
  16. LaBrecque JL, Raymond CA (1985) Seafloor spreading anomalies in the magsat field of the north atlantic. J Geophys Res Solid Earth 90(B3):2565–2575. Google Scholar
  17. Langel RA, Estes RH (1985) The near-Earth magnetic field at 1980 determined from Magsat data. J Geophys Res Solid Earth 90(B3):2495–2509. Google Scholar
  18. Laske G, Masters G, Ma Z, Pasyanos M (2013) Update on CRUST1.0—A 1-degree Global Model of Earth’s CrustGoogle Scholar
  19. Müller RD, Sdrolias M, Gaina C, Roest WR (2008) Age, spreading rates, and spreading asymmetry of the world’s ocean crust. Geochem Geophys Geosyst. Google Scholar
  20. Olsen N, Stolle C (2012) Satellite geomagnetism. Ann Rev Earth Planet Sci 40(1):441–465. Google Scholar
  21. Olsen N, Holme R, Hulot G, Sabaka T, Neubert T, Tøffner-Clausen L, Primdahl F, Jørgensen J, Léger JM, Barraclough D, Bloxham J, Cain J, Constable C, Golovkov V, Jackson A, Kotzé P, Langlais B, Macmillan S, Mandea M, Merayo J, Newitt L, Purucker M, Risbo T, Stampe M, Thomson A, Voorhies C (2000) Ørsted initial field model. Geophys Res Lett 27(22):3607–3610. Google Scholar
  22. Olsen N, Lühr H, Sabaka TJ, Mandea M, Rother M, Tøffner-Clausen L, Choi S (2006) CHAOS-a model of the Earth’s magnetic field derived from CHAMP, Ørsted, and SAC-C magnetic satellite data. Geophys J Int 166(1):67–75. Google Scholar
  23. Olsen N, Hulot G, Sabaka TJ (2010) Measuring the Earth’s magnetic field from space: concepts of past, present and future missions. Space Sci Rev 155(1):65–93. Google Scholar
  24. Purucker M, Whaler K (2015) 5.06—crustal magnetism. In: Schubert G (ed) Treatise on geophysics, 2nd edn. Elsevier, Oxford, pp 185–218. Google Scholar
  25. Purucker ME, Langel RA, Rajaram M, Raymond C (1998) Global magnetization models with a priori information. J Geophys Res Solid Earth 103(B2):2563–2584. Google Scholar
  26. Reigber C, Lühr H, Schwintzer P (2002) CHAMP mission status. Adv Space Res 30(2):129–134. Google Scholar
  27. Shen Y, Xu P, Li B (2012) Bias-corrected regularized solution to inverse ill-posed models. J Geod 86(8):597–608. Google Scholar
  28. Stolle C et al (2013) Product specification for L2 products and auxiliary products. Doc no SW-DS-DTU-GS-0001Google Scholar
  29. Thébault E, Hemant K, Hulot G, Olsen N (2009) On the geographical distribution of induced time-varying crustal magnetic fields. Geophys Res Lett. Google Scholar
  30. Thébault E, Purucker M, Whaler KA, Langlais B, Sabaka TJ (2010) The magnetic field of the Earth’s Lithosphere. Space Sci Rev 155(1):95–127. Google Scholar
  31. Thébault E, Lesur V, Kauristie K, Shore R (2017) Magnetic field data correction in space for modelling the lithospheric magnetic field. Space Sci Rev 206(1):191–223. Google Scholar
  32. Whaler K, Langel R (1996) Minimal crustal magnetizations from satellite data. Phys Earth Planet Inter 98(3):303–319. Google Scholar
  33. Xu P, Shen Y, Fukuda Y, Liu Y (2006) Variance component estimation in linear inverse Ill-posed models. J Geod 80(2):69–81. Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Kiel UniversityKielGermany
  2. 2.ESA-ESRINFrascatiItaly
  3. 3.Astronomical InstituteCzech Academy of SciencesOndřejovCzech Republic
  4. 4.ESA-ESTECNoordwijkThe Netherlands
  5. 5.Dublin Institute for Advanced StudiesDublinIreland

Personalised recommendations