Statistics of the Geomagntic Seculariation for the Past 5-MY

Constable, CG, Parker RL.  1988.  Statistics of the Geomagntic Seculariation for the Past 5-MY. Journal of Geophysical Research-Solid Earth and Planets. 93:11569-11581.

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A new statistical model is proposed for the geomagnetic secular variation over the past 5 m.y. Unlike previous models, which have concentrated upon particular kinds of paleomagnetic observables, such as VGP or field direction, the new model provides a general probability density function from which the statistical distribution of any set of paleomagnetic measurements can be deduced. The spatial power spectrum of the present-day nondipole field is consistent with a white source near the core-mantle boundary with Gaussian distribution. After a suitable scaling, the spherical harmonic coefficients may be regarded as statistical samples from a single giant Gaussian process; this is our model of the nondipole field. Assuming that this characterization holds for the fields of the past, we can combine it with an arbitrary statistical description of the dipole. We compute the corresponding probability density functions and cumulative distribution functions for declination and inclination that would be observed at any site on the surface of the Earth. Global paleomagnetic data spanning the past 5 m.y. are used to constrain the free parameters of the model, i.e., those giving the dipole part of the field. The final model has these properties: (1) with two exceptions, each Gauss coefficient is independently normally distributed with zero mean and standard deviation for the nondipole terms commensurate with a white source at the core surface; (2) the exceptions are the axial dipole g1 and axial quadrupole g2 terms; the axial dipole distribution is bimodal and symmetric, resembling a combination of two normal distributions with centers close to the present-day value and its sign-reversed counterpart; (3) the standard deviations of the nonaxial dipole terms g11 and h11 and of the magnitude of the axial dipole are all about 10% of the present-day g1 component; and (4) the axial quadrupole reverses sign with the axial dipole and has a mean magnitude of 6% of its mean magnitude. The advantage of a model specified in terms of the spherical harmonic coefficients is that it is a complete statistical description of the geomagnetic field, capable of simultaneously satisfying many known properties of the field. Predictions about any measured field elements may be made to see if they satisfy the available data.