Paleosecular Variation in Field Directions Due to Randomly Varying Gauss Coefficients.

Kono, Michikata

doi:10.5636/jgg.49.615

Cited by 11 publications

(9 citation statements)

References 13 publications

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“… Johnson and Constable [1995], derived a time‐averaged model from a combination of lacustrine and archeomagnetic data for the past 3000 years. Similar exercises were extended over time periods as long as 5 Ma [ McElhinny et al , 1996; Kelly and Gubbins , 1997; Kono , 1997; Carlut and Courtillot , 1998]. There is now a large number of archeomagnetic records.…”

Section: Introductionmentioning

confidence: 99%

Secular variation of the geomagnetic dipole during the past 2000 years

Valet

Herrero‐Bervera

Lemouel

et al. 2008

Geochem Geophys Geosyst

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[1] We have constructed a very simple model of a time-varying geocentric dipole based on the archeomagnetic records obtained at four widely separated sites on the globe for the past 2 ka. The predictions of the model in terms of directional variations have been tested against actual archeomagnetic data from 12 sites distributed over the globe. They were also compared with the Hongre et al. (1998) timevarying spherical harmonic model and with the CALS7K-2 model by Korte et al. (2005). We find that the misfits between the predictions of our simple dipole model and the data are equivalent to those of the spherical harmonic models for the European sites and not strikingly larger for the rest of the world. Many discrepancies can be accounted for by uncertainties inherent to the archeomagnetic records, which, along with the small number and poor geographical distribution of sites, leads us to conclude that the present state of the database does not allow the extraction of secular variations described by terms going beyond degree 2. It appears also that dipole tilt could be responsible for the main part of the secular variation associated with time constants exceeding 10 2 years. In a second step, we used the paleointensity records contained in the same database to construct the curve depicting the variations of the true dipole moment. The present decrease of the dipole did not begin prior to 1000 years ago, and the dipole was actually increasing from 0 until A.D. 500. The dipole moment of CALS7K is lower than the present estimate, probably due to large repartition of energy to higher harmonics to minimize the misfit between the inversion and the data. The tilt and strength of the dipole can predict the dipole field at any site and were used to derive the contribution of the nondipole field to values of paleointensity at Paris during the past 2 ka. The results show that the ''archeomagnetic jerks'' are associated with various configurations depending on the phase relationship between the nondipolar and dipolar parts of the field.

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Section: Introductionmentioning

confidence: 99%

Secular variation of the geomagnetic dipole during the past 2000 years

Valet

Herrero‐Bervera

Lemouel

et al. 2008

Geochem Geophys Geosyst

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“…The projection of the unimodal, 3‐D Gaussian distribution onto the unit sphere, a marginalization obtained by integrating over all intensities, is the angular‐Gaussian distribution, which has been given in series form by Bingham (1983), and which has been revisited recently by Khokhlov et al (2001) in their analysis of palaeosecular directional variation. In the context of palaeosecular vectorial variation, the 3‐D Gaussian distributions considered here are related, at least mathematically, to the statistical models of Constable & Parker (1988), Hulot & LeMouël (1994), Kono (1997), and others, where spherical‐harmonic coefficients describing global geomagnetic secular variation are regarded as independent statistical samples from a giant‐Gaussian process. With such a global model, the palaeosecular variation at a particular geographic site can be described by a forward calculation.…”

Section: Introductionmentioning

confidence: 99%

Gaussian statistics for palaeomagnetic vectors

Love

Constable

2003

Geophysical Journal International

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SUMMARY With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three‐space of orthogonal magnetic‐field components consisting of a single (unimodal) non‐zero mean, spherically‐symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi‐Gaussian distributions, and in the spherical three‐space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off‐axis angle are closed‐form and especially manageable, with the intensity distribution being Rayleigh–Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi‐Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically‐uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum‐likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to formulate the inverse problem, and how to estimate the mean and variance of the magnetic vector field, even when the data consist of mixed combinations of directions and intensities. We examine palaeomagnetic secular‐variation data from Hawaii and Réunion, and although these two sites are on almost opposite latitudes, we find significant differences in the mean vector and differences in the local vectorial variances, with the Hawaiian data being particularly anisotropic. These observations are inconsistent with a description of the mean field as being a simple geocentric axial dipole and with secular variation being statistically symmetrical with respect to reflection through the equatorial plane. Finally, our analysis of palaeomagnetic acquisition data from the 1960 Kilauea flow in Hawaii and the Holocene Xitle flow in Mexico, is consistent with the widely held suspicion that directional data are more accurate than intensity data.

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“…Subsequent papers (e.g. Kono & Tanaka 1995;Hulot & Gallet 1996;Quidelleur & Courtillot 1996;Kono 1997;Constable & Johnson 1999) have generalized this approach by both relaxing the simple axisymmetric assumptions of the original GGP and producing additional statistical predictions to be compared with the data. These studies have highlighted the power of the GGP approach.…”

Section: Introductionmentioning

confidence: 99%

Towards a self-consistent approach to palaeomagnetic field modelling

Khokhlov

Hulot

Carlut

2001

Geophysical Journal International

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International audienceRecent studies of the palaeomagnetic field behaviour over the past 5 Myr rely on statistical analysis of mainly directional data. However, the data are quite sparse and ill-distributed, and directional parameters are non-linear functions of the local field, rendering such statistical analysis non-trivial. Up to now these difficulties have usually been ignored or removed by relying on simplifications (linearization, neglecting internal correlations, etc.) that are unfortunately not justified if the field contains some amount of complexity. The purpose of the present paper is to present a rigorous statistical forward approach to palaeomagnetic field modelling. Starting from a statistical model of the field defined in terms of the statistics of its Gauss coefficients (along the lines pioneered by Constable & Parker 1988), we show how such a model may be exactly tested against any given data set, either on a local regional or a global scale. A method to implement this approach is outlined and examples based on published models are provided. In particular we focus on the treatment of directional data, for which the method is most relevant. The corresponding local probability density functions are derived and shown to be non-Fisherian, which we note may be a significant source of artefacts for standard mean-field modelling. Although the method we propose is already useful in its present state, some slight improvements are possible in order to account for noise in the data better

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Paleosecular Variation in Field Directions Due to Randomly Varying Gauss Coefficients.

Cited by 11 publications

References 13 publications

Secular variation of the geomagnetic dipole during the past 2000 years

Secular variation of the geomagnetic dipole during the past 2000 years

Gaussian statistics for palaeomagnetic vectors

Towards a self-consistent approach to palaeomagnetic field modelling

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