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

Earth, Planets and Space volume 53, pages 31–44 (2001)Cite this article

Abstract

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 03 ). We also show that the measurement errors do not induce biases in the mean field data, provided that they are random and isotropic.

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Authors and Affiliations

  1. Department of Earth and Planetary Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan

    Tadahiro Hatakeyama

  2. Institute for Study of the Earth’s Interior, Okayama University, 827 Yamada, Misasa, Tottori, 682-0193, Japan

    Tadahiro Hatakeyama & Masaru Kono

Authors
  1. Tadahiro Hatakeyama
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  2. Masaru Kono
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Correspondence to Tadahiro Hatakeyama.

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Hatakeyama, T., Kono, M. Shift of the mean magnetic field values: Effect of scatter due to secular variation and errors. Earth Planet Sp 53, 31–44 (2001). https://doi.org/10.1186/BF03352360

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