V. We, Courtillot for fruitful discussions and C. Constable for a very helpful review. This work was partly supported by grant INTAS/CNES 97-1048. INSU 'Interieur de la Terre' programme contribution No. 254 and IPGP contribution No, 1724.

C. Bingham, A series expansion for angular Gaussian distribution, Appendix C, Statistics on Spheres, pp.226-231, 1983.

J. Bloxham and A. Jackson, Time-dependent mapping of the magnetic field at the core-mantle boundary, Journal of Geophysical Research, vol.351, issue.B13, pp.19-537, 1992.
DOI : 10.1029/92JB01591

J. Carlut and V. Courtillot, How complex is the Earth's average magnetic field?, Geophys, J. Int, vol.134, pp.527-544, 1998.

C. Johnson and C. Constable, Anisotropic paleosecular variation models: implications for geomagnetic field observables, Earth planet. Sci. Lett, vol.115, pp.35-51, 1999.

C. G. Constable and R. L. Parker, Statistics of the geomagnetic secular variation for the past 5 Myr, J. geophys. Res, vol.93, pp.11-569, 1988.

D. H. Eckhardt, Correlations between global features of terrestrial fields, Journal of the International Association for Mathematical Geology, vol.82, issue.2, pp.155-171, 1984.
DOI : 10.1007/BF01032214

N. I. Fisher, T. Lewis, and B. J. Embleton, Statistical Analysis of Spherical Data, 1987.

D. Gubbins and P. Kelly, Persistent patterns in the geomagnetic field over the past 2.5 Myr, Nature, vol.365, issue.6449, pp.829-832, 1993.
DOI : 10.1038/365829a0

L. Hongre, G. Hulot, and A. Khokhlov, An analysis of the geomagnetic field over the past 2000 years, Physics of the Earth and Planetary Interiors, vol.106, issue.3-4, pp.311-315, 1998.
DOI : 10.1016/S0031-9201(97)00115-5

G. Hulot and Y. Gallet, On the interpretation of virtual geomagnetic pole (VGP) scatter curves, Physics of the Earth and Planetary Interiors, vol.95, issue.1-2, pp.37-53, 1996.
DOI : 10.1016/0031-9201(95)03106-5

G. Hulot and J. Le-mouël, A statistical approach to the Earth's main magnetic field, Physics of the Earth and Planetary Interiors, vol.82, issue.3-4, pp.167-183, 1994.
DOI : 10.1016/0031-9201(94)90070-1

C. Johnson and C. Constable, The time-averaged geomagnetic field as recorded by lava flows over the past 5 Myr, Geophysical Journal International, vol.122, issue.2, pp.489-519, 1995.
DOI : 10.1111/j.1365-246X.1995.tb07010.x

C. Johnson and C. Constable, Palaeosecular Variation Recorded by Lava Flows over the past Five Million Years, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.354, issue.1704, pp.89-141, 1996.
DOI : 10.1098/rsta.1996.0004

C. Johnson and C. Constable, The time-averaged geomagnetic field: global and regional biases for 0-5 Ma, Geophysical Journal International, vol.131, issue.3, pp.643-666, 1997.
DOI : 10.1111/j.1365-246X.1997.tb06604.x

P. Kelly and D. Gubbins, The geomagnetic field over the past 5 million years, Geophysical Journal International, vol.128, issue.2, pp.1-16, 1997.
DOI : 10.1111/j.1365-246X.1997.tb01557.x

J. T. Kent, The Fisher-Bingham distribution on the sphere, J. R. stat. Soc, vol.44, pp.71-80, 1982.

D. Knuth, The Art of Computer Programming, 1981.

M. Kono, Paleosecular Variation in Field Directions Due to Randomly Varying Gauss Coefficients., Journal of geomagnetism and geoelectricity, vol.49, issue.4, pp.615-631, 1997.
DOI : 10.5636/jgg.49.615

M. Kono and H. Tanaka, Mapping the Gauss Coefficients to the Pole and the Models of Paleosecular Variation., Journal of geomagnetism and geoelectricity, vol.47, issue.1, pp.115-130, 1995.
DOI : 10.5636/jgg.47.115

M. Kono, H. Tanaka, and H. Tsunakawa, Spherical harmonic analysis of paleomagnetic data: The case of linear mapping, Journal of Geophysical Research: Solid Earth, vol.22, issue.42, pp.5817-5833, 2000.
DOI : 10.1029/1999JB900050

S. Kullback, Information Theory and Statistics, 1968.

R. A. Langel, The main field, in Geomagnetism, pp.249-512, 1987.

S. Lee, A study of the time-averaged paleomagnetic field for the last 195 million years, 1983.

L. Goff and M. , Lissage et limites d'incertitude des courbes de migration polaire?pondération des données extension bivariate de la statistique de Fisher, C. R. Acad. Sci. Paris, pp.3111-1191, 1990.

M. Mcelhinny and P. Mcfadden, Palaeosecular variation over the past 5 Myr based on a new generalized database, Geophysical Journal International, vol.131, issue.2, pp.240-252, 1997.
DOI : 10.1111/j.1365-246X.1997.tb01219.x

M. Mcelhinny, P. Mcfadden, and R. Merrill, The timeaveraged paleomagnetic field 0-5My the Earth, J. geophys. Res, vol.101, pp.25-32, 1996.

R. Merrill, M. Mcelhinny, and P. Mcfadden, The Magnetic Field of the Earth, 1996.

X. Quidelleur and V. Courtillot, On low-degree spherical harmonic models of paleosecular variation, Physics of the Earth and Planetary Interiors, vol.95, issue.1-2, pp.55-77, 1996.
DOI : 10.1016/0031-9201(95)03115-4

X. Quidelleur, J. Valet, V. Courtillot, and G. Hulot, Longterm geometry of the geomagnetic field for the last five million years: an updated secular variation database, Geophys. Res. Lett, vol.15, pp.1639-1642, 1994.
URL : https://hal.archives-ouvertes.fr/insu-01405155

S. Schneider and D. Kent, The time-averaged paleomagnetic field, Reviews of Geophysics, vol.101, issue.824, pp.71-96, 1990.
DOI : 10.1029/RG028i001p00071

R. L. Wilson, Permanent Aspects of the Earth's Non-dipole Magnetic Field over Upper Tertiary Times, Geophysical Journal International, vol.19, issue.4, pp.417-437, 1970.
DOI : 10.1111/j.1365-246X.1970.tb06056.x

R. L. Wilson, Dipole Offset--The Time-Average Palaeomagnetic Field Over the Past 25 Million Years, Geophysical Journal International, vol.22, issue.5, pp.491-504, 1971.
DOI : 10.1111/j.1365-246X.1971.tb03616.x