Earth, Planets and Space

, Volume 53, Issue 1, pp 31–44 | Cite as

Shift of the mean magnetic field values: Effect of scatter due to secular variation and errors

Open Access


Paleomagnetic data are mostly given in the form of field directions (inclinations and declinations) which depend nonlinearly on the model parameters (Gauss coefficients). Because of this nonlinearity, the means of the data are affected not only by the means of the parameters but also by their fluctuations. Defining the mean directions by the Fisher method decreases this effect but does not completely eliminate it. For various mean fields, we evaluate the effect of secular variation on the means of Fisher-averaged directions by the analytical (Taylor expansion to the second order) as well as by the numerical (Monte Carlo) method. It was shown that a significant amount of offset occurs in the field values because of the fluctuation caused by secular variation. In the case of an inclination anomaly, the effect of secular variation as a function of latitude is antisymmetric about the equator, similar to that of the axial octupole term (g 3 0 ). We also show that the measurement errors do not induce biases in the mean field data, provided that they are random and isotropic.


Secular Variation Direction Cosine Paleomagnetic Data Axial Dipole Nonlinear Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Barton, C. E., International Geomagnetic Reference Field: The seventh generation, J. Geomag. Geoelectr,49, 123–148, 1997.CrossRefGoogle Scholar
  2. Benkova, N. P., N. V. Adam, and T. N. Cherevko, Application of spherical harmonic analysis to magnetic declination data, Geomagn. Aeron., 10, 673 (Engl. Trans. 527–532), 1970 (in Russian).Google Scholar
  3. Constable, C. G. and C. L. Johnson, Anisotropic paleosecular variation models: implications for geomagnetic field observables, Phys. Earth Planet. Inter., 115, 35–51, 1999.CrossRefGoogle Scholar
  4. Constable, C. G. and R. L. Parker, Statistics of the geomagnetic secular variation for the past 5 m.y., J. Geophys. Res., 93, 11569–11581, 1988.CrossRefGoogle Scholar
  5. Cox, A. V, Latitude dependence of the angular dispersion of the geomagnetic field, Geophys. J. R. astr. Soc, 20, 253–269, 1970.CrossRefGoogle Scholar
  6. Creer, K. M., D. T. Georgi, and W. Lowrie, On the representation of the Quaternary and late tertiary geomagnetic fields in terms of dipoles and quadrupoles, Geophys. J. R. astr. Soc., 33, 323–345, 1973.CrossRefGoogle Scholar
  7. Fisher, R. A., Dispersion on a sphere, Proc. R. Soc. Lond., A217, 295–305, 1953.CrossRefGoogle Scholar
  8. Glatzmaier, G. A. and P. H. Roberts, A three-dimensional self-consistent computer simulation of a geomagnetic field reversal, Nature, 377, 203–209, 1995.CrossRefGoogle Scholar
  9. Gubbins, D., Geomagnetic field analysis—I. stochastic inversion, Geophys. J. R. astr. Soc., 73, 641–652, 1983.CrossRefGoogle Scholar
  10. Gubbins, D. and J. Bloxham, Geomagnetic field analysis—III. Magnetic fields on the core-mantle boundary, Geophys. J. R. astr. Soc., 80, 695–713, 1985.CrossRefGoogle Scholar
  11. Gubbins, D. and P. Kelly, Persistent patterns in the geomagnetic field over the past 2.5 Myr, Nature, 365, 829–832, 1993.CrossRefGoogle Scholar
  12. Hoffman, K. A., Dipolar reversal states of the geomagnetic field and core-mantle dynamics, Nature, 359, 789–794, 1992.CrossRefGoogle Scholar
  13. Hulot, G., A. Khokholov, and J.-L. Le Mouël, Uniqueness of mainly dipolar magnetic fields recovered from directional data, Geophys. J. Int., 129, 347–354, 1997.CrossRefGoogle Scholar
  14. Jackson, D. D., The use of a priori data to resolve non-uniqueness in linear inversion, Geophys. J. R. astr. Soc., 57, 137–157, 1979.CrossRefGoogle Scholar
  15. Johnson, C. L. and C. G. Constable, The time-averaged geomagnetic field as recorded by lava flows over the past 5 Myr, Geophys. J. Int., 122, 488–519, 1995.Google Scholar
  16. Johnson, C. L. and C. G. Constable, The time-averaged geomagnetic field: global and regional biases for 0-5 Ma, Geophys. J. Int., 131, 643–666, 1997.CrossRefGoogle Scholar
  17. Kelly, P. and D. Gubbins, The geomagnetic field over the past 5 Myr, Geophys. J. Int., 128, 315–330, 1997.CrossRefGoogle Scholar
  18. Kono, M., Uniqueness problems in their spherical harmonic analysis of the geomagnetic field direction data, J. Geomag. Geoelectr., 28, 11–29, 1976.CrossRefGoogle Scholar
  19. Kono, M. Paleosecular variation in field directions due to randomly varying Gauss coefficients, J. Geomag. Geoelectr., 49, 615–631, 1997a.CrossRefGoogle Scholar
  20. Kono, M. Distributions of paleomagnetic directions and poles, Phys. Earth Planet. Inter., 103, 313–327, 1997b.CrossRefGoogle Scholar
  21. Kono, M. and O. Hiroi, Paleosecular variation of field intensities and dipole moments, Earth Planet. Sci. Lett., 139, 251–262, 1996.CrossRefGoogle Scholar
  22. Kono, M. and H. Tanaka, Mapping the Gauss coefficients to the pole and the models of paleosecular variation, J. Geomag. Geoelectr., 47, 115–130, 1995.CrossRefGoogle Scholar
  23. Kono, M., H. Tanaka, and H. Tsunakawa, Spherical harmonic analysis of paleomagnetic data: the case of linear mapping, J. Geophys. Res., 105, 5817–5833, 2000a.CrossRefGoogle Scholar
  24. Kono, M., A. Sakuraba, and M. Ishida, Dynamo simulation and paleosecular variation models, Phil. Trans. R. Soc. Lond., A358, 1123–1139, 2000b.CrossRefGoogle Scholar
  25. Langel, R. A., The main field, in Geomagnetism, vol. 1, edited by J. A. Jacobs, pp. 249–512, Academic Press, London, 1987.Google Scholar
  26. Langel, R. A. and R. H. Estes, A geomagnetic field spectrum, Geophys. Res. Lett., 9, 250–253, 1982.CrossRefGoogle Scholar
  27. McElhinny, M. W., P. L. McFadden, and R. T. Merrill, The time-averaged paleomagnetic field 0-5 Ma, J. Geophys. Res., 101, 25007–25027, 1996.CrossRefGoogle Scholar
  28. McFadden, P. L., R. T. Merrill, and M. W. McElhinny, Dipole/quadrupole family modeling of paleosecular variation, J. Geophys. Res., 93, 11583–11588, 1988.CrossRefGoogle Scholar
  29. Proctor, M. R. E. and D. Gubbins, Analysis of geomagnetic directional data, Geophys. J. Int., 100, 69–77, 1990.CrossRefGoogle Scholar
  30. Shure, L., R. L. Parker, and G. E. Backus, Harmonic splines for geomagnetic modelling, Phys. Earth Planet. Inter., 28, 215–229, 1982.CrossRefGoogle Scholar
  31. Tanaka, H., Circular asymmetry of the paleomagnetic directions observed at low latitude volcanic sites, Earth Planets Space, 51, 1279–1286, 1999.CrossRefGoogle Scholar
  32. Wilson, R. L., Permanent aspects of the Earth’s non-dipole magnetic field over upper tertiary times, Geophys. J. R. astr. Soc., 19, 417–437, 1970.CrossRefGoogle Scholar
  33. Wilson, R. L., Dipole offset—The time average palaeomagnetic field over the past 25 million years, Geophys. J. R. astr. Soc., 22, 491–504, 1971.CrossRefGoogle Scholar

Copyright information

© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences. 2001

Authors and Affiliations

  1. 1.Department of Earth and Planetary ScienceUniversity of TokyoBunkyo-ku, TokyoJapan
  2. 2.Institute for Study of the Earth’s InteriorOkayama UniversityMisasa, TottoriJapan

Personalised recommendations