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A representation function for a distribution of points on the unit sphere—with applications to analyses of the distribution of virtual geomagnetic poles
Earth, Planets and Space volume 55, pages 395–404 (2003)
Abstract
An arbitrary point distribution consisting of a finite number of points on a unit sphere may be completely and uniquely represented by an analytic function in the form of a spherical harmonic expansion. The applications of this representation function are illustrated in an analysis of the symmetries in the virtual geomagnetic pole (VGP) distribution of the polarity reversal records of the past 10 million years. We find that the longitudinal confinements in the VGP distribution are (a) persistent only in the equatorially symmetric part (of the non-zonal symmetries) of the VGP distribution and (b) strong along the east coast of the North American continent and weak along the longitudes of East Asia-Australia. We also find that the equatorially symmetric patterns in the VGP distribution appear to extend preferentially into the Pacific Ocean and are relatively depleted in the longitude band associated with Africa.
References
Backus, G., R. Parker, and C. Constable, Foundation of Geomagnetism, Cambridge University Press, Cambridge, 158 pp., 1996.
Channell, J. E. T. and B. Lehman, The last two geomagnetic polarity reversals recorded in high-deposition-rate sediment drifts, Nature, 389, 712–715, 1997.
Clement, B. M., Geographical distribution of transitional VGPs: Evidence for non-zonal equatorial symmetry during the Matuyama-Brunhes geomagnetic reversal, Earth planet. Sci. Lett., 104, 48–58, 1991.
Coe, R. S. and J. C. Liddicoat, Overprinting of natural magnetic remanence in lake sediments by a subsequent high-intensity field, Nature, 367, 57–59, 1994.
Fisher, N. I., T. Lewis, and B. J. J. Embleton, Statistical Analysis of Spherical Data, Cambridge University Press, Cambridge, 329 pp., 1987.
Laj, C., A. Mazaud, R. Weeks, M. Fuller, and E. Herrero-Bervera, Geomagnetic reversal paths, Nature, 351, 447, 1991.
Laj, C., A. Mazaud, R. Weeks, M. Fuller, and E. Herrero-Bervera, Geomagnetic reversal paths, Nature, 359, 111–112, 1992a.
Laj, C., A. Mazaud, R. Weeks, M. Fuller, and E. Herrero-Bervera, Statistical assessment of the preferred longitudinal bands for recent geomagnetic reversal records, Geophys. Res. Lett., 19, 2003–2006, 1992b.
Langereis, C. G., A. A. M. van Hoof, and P. Rochette, Longitudinal confinement of geomagnetic reversal paths as a possible sedimentary artefact, Nature, 358, 226–230, 1992.
McFadden, P. L., C. E. Barton, and R. T. Merrill, Do virtual geomagnetic poles follow preferred paths during geomagnetic reversals?, Nature, 361, 342–344, 1993.
Prévot, M. and P. Camps, Absence of preferred longitude sectors for poles from volcanic records of geomagnetic reversals, Nature, 366, 53–57, 1993.
Quidelleur, X. and J.-P. Valet, Paleomagnetic records of excursions and reversals: Possible biases caused by magnetization artefacts, Phys. Earth planet. Inter., 82, 27–48, 1994.
Valet, J.-P., P. Tucholka, V. Courtillot, and L. Meynadier, Palaeomagnetic constraints on the geometry of the geomagnetic field during reversals, Nature, 356, 400–407, 1992.
Weeks, R., M. Fuller, C. Laj, A. Mazaud, and E. Herrero-Bervera, Sedimentary records of reversal transitions—magnetization smoothing artefact or geomagnetic field behaviour?, Geophys. Res. Lett., 19, 2007–2010, 1992.
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Shao, JC., Hamano, Y., Bevis, M. et al. A representation function for a distribution of points on the unit sphere—with applications to analyses of the distribution of virtual geomagnetic poles. Earth Planet Sp 55, 395–404 (2003). https://doi.org/10.1186/BF03351773
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DOI: https://doi.org/10.1186/BF03351773