Analysis of the hypothesis of a giant gaussian process as a means for describing secular variations of the geomagnetic field vector

Cover Page

Cite item


The consistency of the empirical data on paleointensity and paleoinclinations contained in the BOROKPINT paleointensity world database with the Geocentric Axial Dipole (GAD) hypothesis and Giant Gaussian Process (GGP) model describing the geomagnetic field variations in the Brunhes epoch is tested. The calculations are based on the geomagnetic field potential representation by the sum of spherical functions of spatial coordinates with random coefficients, enabling computer simulation of the data with the given statistical characteristics of the coefficients. The estimates show that the Kolmogorov–Smirnov and Anderson–Darling tests reject the GAD hypothesis in its canonical form. The extension of GAD to GGD with nonzero time-average quadrupole and octupole terms makes the paleointensity and paleoinclination data to comply with GGP model realizations; however, these models are mutually exclusive because of mutual inconsistency of their parameters. Testing the paleoinclination data against GDP model shows that a small correction to the purely dipole component of the geomagnetic field should be introduced. At the same time, the paleointensity data analysis suggests that these data highly probably agree with GGP models with a high quadrupole contribution making up 1/3 of the dipole coefficient, which is strongly at odds with the parameters of the model corresponding to paleoinclination data. This inconsistency is most likely to be due to the artifacts associated with incorrect paleointensity determinations; however, this interpretation does not explain the causes of the strong latitudinal dependence of the intensity of the Virtual Axial Dipole Moment (VADM) which follows from the empirical data.

About the authors

V. P. Scherbakov

Borok Geophysical Observatory, Schmidt Institute of Physics of the Earth; Kazan Federal University

Author for correspondence.
Russian Federation, Borok; 18, Kremliovskaya street, Kazan, 420008

A. V. Khokhlov

Borok Geophysical Observatory, Schmidt Institute of Physics of the Earth; Institute of Earthquake Prediction Theory and Mathematical Geophysics

Russian Federation, Borok; Institute of Earthquake Prediction Theory and Mathematical Geophysics

N. K. Sycheva

Borok Geophysical Observatory, Schmidt Institute of Physics of the Earth

Russian Federation, Borok


  1. Грибов С.К., Долотов А.В. Особенности поведения химической остаточной намагниченности при окислении природного титаномагнетита в изотермических условиях. «Палеомагнетизм и магнетизм горных пород: теория, практика, эксперимент». Всероссийская школа-семинар по проблемам палеомагнетизма и магнетизма горных пород, Санкт-Петербург, 3–7 октября 2016 г. [материалы] Ярославль: Филигрань. 2016. С. 35–39.
  2. Грибов С.К., Долотов А.В., Щербаков В.П. Экспериментальное моделирование химической остаточной намагниченности и методики Телье на титаномагнетитсодержащих базальтах // Физика Земли. 2017. № 2. С. 109–128. doi: 10.7868/S0002333717010069
  3. Хохлов А. Моделирование вековых геомагнитных вариаций. Принципы и реализация // Геофизические исследования. 2011. Т. 13. № 2. С. 50–61.
  4. Хохлов А.В., Люлье Ф., Щербаков В.П. Перемежаемость и особенности статистических характеристик геомагнитного поля в моделях геодинамо // Физика Земли. 2017. № 5. С. 81–88. doi: 10.7868/S0002333717050076
  5. Храмов А.Н., Гончаров Г.И., Коммисарова Р.А. и др. Палео¬магнитология. Л.: Недра. 1982. 321 с.
  6. Щербаков В.П., Сычева Н.К., Грибов С.К. Экспериментальное и численное моделирование процесса образования химической остаточной намагниченности и методики Телье // Физика Земли. 2017. № 5. С. 30–43. doi: 10.7868/S0002333717040081
  7. Щербаков В.П., Сычева Н.К., Щербакова В.В. Эволюция величины магнитного момента Земли в геологическом прошлом // Геофизические исследования. 2008. Т. 9. № 2. С. 7–24.
  8. Щербаков В.П., Хохлов А.В., Сычева Н.К. О функции распределения величины геомагнитного поля по модели Большого Гауссового Процесса и эмпирическим данным // Физика Земли. 2015. № 5. С. 179–192. doi: 10.7868/S0002333715050117
  9. Bouligand C., Gillet N., Jault D., Schaeffer N., Fournier A. et al. Frequency spectrum of the geomagnetic field harmonic co¬efficients from dynamo simulations // Geophysical Journal International. Oxford University Press (OUP). 2016. V. 207. P. 1142–1157.
  10. Constable C.G., Johnson, C.L. Anisotropic paleosecular variation models: implications for geomagnetic field observables // Earth Planet. Sci. Lett. 1999. V. 115. P. 35–51.
  11. Constable C.G., Parker R.L. Statistics of the Geomagnetic Secular Variation for the Past 5 m.y. // J. Geophys. Res. 1988. V. 93. № B10. P. 11569–11581.
  12. Draeger U., Prevot M., Poidras T., Riisager J. Single-domain chemical, thermochemical and thermal remanences in a basaltic rock // Geophys. J. Int. 2006. V. 166. P. 12–32.
  13. Fisher R. Dispersion on a sphere // Proc. R. Soc. Lond. 1953. A 217. P. 295–305.
  14. Guyodo Y., Valet J.P. Global changes in intensity of the Earth’s magnetic field during the past 800 kyr // Nature. 1999. V. 399. P. 249–252.
  15. Hospers J. Reversals of the main geomagnetic field, I, II. Proc. Kon. Neder. Akad. Welensch. 1953. B56. P. 467–491.
  16. Hospers J. Reversals of the main geomagnetic field, III, IV. Proc. Kon. Neder. Akad. Welensch. 1954. B57. P. 112–121.
  17. Hulot G., Le Mouel J-L. A statistical approach to the Earth’s main magnetic field // Phys. Earth Planet. Int. 1994. V. 82. P. 167–183.
  18. Johnson C., Constable C. Paleosecular variation recorded by lava flows over the last 5 Myr // Phil. Trans. R. Soc. Lond. 1996. V. 354. P. 89–141.
  19. Khokhlov A., Hulot G. Probability uniformization and application to statistical palaeomagnetic field models and directional data // Geophys. J. Int. 2013. V. 193. № 1. P. 110–121. doi: 10.1093/gji/ggs118
  20. Khokhlov A., Hulot G., Bouligand C. Testing statistical palaeomagnetic field models against directional data affected by measurement errors // Geophys. J. Int. 2006. V. 167. № 2. P. 635–648. doi: 10.1111/j.1365–246X.2006.03133.x
  21. Khokhlov A., Shcherbakov V., Palaeointensity and Brunhes palaeomagnetic field models // Geophys. J. Int. 2015. V. 202. № 2. P. 1419–1428. doi: 10.1093/gji/ggv236.
  22. Lawrence K P., Tauxe L., Staudigel H., Constable CG., Koppers A., McIntosh W., Johnson C.L. Paleomagnetic field properties at high southern latitude // Geochem. Geophys. Geosyst. 2009. V. 10. P. 1–27.
  23. McElhinny M.W., McFadden P.L., Merrill R.T. The time-averaged paleomagnetic field 0–5 Ma // J. Geophys. Res. 1996. V. 101. P. 25007–25027.
  24. McElhinny M.W. Paleomagnetism and Plate Tectonics. Cambridge Univ. Press. Cambridge. U. K. 1973. 357 p.
  25. Merrill R.T., McElhinny M.W. Anomalies in the time-averaged palcomagnetic feld and their implications for the lower mantle // Rev. Geophys. 1977. V. 15. P. 309–323.
  26. Merrill R.T., McElhinny M.W. The Earth’s Magnetic Field: Its History, Origin and Planetary Perspective. Academic. San Diego. 1983. 401 p.
  27. Merrill Ronald T. The magnetic field of the Earth: paleo¬magnetism, the core, and the deep mantle / By Ronald T. Merrill, Michael W. McElhinny, Phillip L. McFadden. Academic Press. International Geophysics Series. 1996. V. 63. 531 p.
  28. Muxworthy Adrian R. Considerations for Latitudinal Time-Averaged-Field Palaeointensity Analysis of the Last Five Million Years // Frontiers in Earth Science. 2017. V. 5. Article 79. doi: 10.3389/feart.2017.00079
  29. Perrin M., Shcherbakov V.P. Paleointensity of the Earth’s Magnetic Field for the Past 400 Ma: Evidence for a Dipole Structure during the Mesozoic Low // J. Geomag. Geoelectr. 1997. V. 49. P. 601–614.
  30. QuidellerX., Courtillot V. On low-degree spherical harmonic models of paleosecular variation // Phys. Earth Planet. Int. 1996. V.95. P. 55–77.
  31. Quidelleur X., Valet J.P., Courtillot V., Hulot G. Long¬term geometry of the geomagnetic field for the last five million years: an updated secular variation database // Geophys. Res. Lett. 1994. V. 15. P. 1639–1642. doi: 10.1029/94GL01105
  32. Smirnov A.V., Tarduno J.A. Thermochemical remanent magnetization in Precambria rocks Are we sure the geomagnetic field was weak? // J. Geophys. Res. 2005. V. 110. B06103. doi: 10.1029/2004JB003445
  33. Tauxe L., Kent D.V. A simplified statistical model for the geomagnetic field and the detection of shallow bias in paleomagnetic inclinations: was the ancient magnetic field dipolar? In Timescales of the Paleomagnetic field. 2004. V. 145. P. 101–115.
  34. Wang H., Kent D.V., Rochette P. Weaker axially dipolar time averaged paleomagnetic field based on multidomain-corrected paleointensities from Galapagos lavas // Proc. Natl. Acad. Sci. U.S.A. 2015. V. 112. P. 15036–15041. doi: 10.1073/pnas.1505450112
  35. Wilson R.L. Dipole offset-the time-averaged paleomagnetic field over the past 25 million years // Geophys. J.R. Astr. Soc. 1971. V. 22. P. 491–504.
  36. Wilson R.L. Permanent aspects of the Earth’s non-dipole magnetic field over upper Tertiary times // Geophys. J.R. Astr. Soc. 1970. V. 19. P. 417–437.
  37. Wilson R.L., Ade-Hall J.M., Paleomagnetic indications of a permanent aspect of the non-dipole field. In: Paleo¬geophysics / Ed.: Runcorn S.K. Academic Press. San Diego. 1970. P. 307–312.
  38. Wilson R.L., McElhinny M.W. Investigation of the large scale palaeomagnetic field over the past 25 million years; eastward shift of the Icelandic spreading ridge // Geophys. JR. Astron. Soc. 1974. V. 39. P. 570–586.

Copyright (c) 2019 Российская академия наук

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies