2001
DOI: 10.1111/j.1365-246x.2001.01386.x
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Towards a self-consistent approach to palaeomagnetic field modelling

Abstract: 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 justifi… Show more

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Cited by 29 publications
(41 citation statements)
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“…The scalar mean of 1000 simulations of Δ calculated for the vector average of N site directional data is quite consistently estimated as between −1.42 and −1.5°. Note that it is nonzero because of the lack of intensity information available in averaging unit vectors as first predicted by Creer [1983] and more recently discussed by Khokhlov et al [2001] and by Love and Constable [2003]. The size of this bias in estimating the average field direction from unit vectors depends on the statistical properties of the PSV: we noted varying values depending on whether we used CJ98.GAD or either of the nonzonal versions of the PSV model (CJ98.nz.GAD) in which excess variance is concentrated in either the h 2 1 or g 2 1 spherical harmonic.…”
Section: Discussionmentioning
confidence: 71%
“…The scalar mean of 1000 simulations of Δ calculated for the vector average of N site directional data is quite consistently estimated as between −1.42 and −1.5°. Note that it is nonzero because of the lack of intensity information available in averaging unit vectors as first predicted by Creer [1983] and more recently discussed by Khokhlov et al [2001] and by Love and Constable [2003]. The size of this bias in estimating the average field direction from unit vectors depends on the statistical properties of the PSV: we noted varying values depending on whether we used CJ98.GAD or either of the nonzonal versions of the PSV model (CJ98.nz.GAD) in which excess variance is concentrated in either the h 2 1 or g 2 1 spherical harmonic.…”
Section: Discussionmentioning
confidence: 71%
“…Second, measurements of absolute declination provide important constraints on longitudinal structure in the field (see discussion by Johnson and Constable [1997]), and these are often unavailable from deep sea sediment cores. Third, such data are well‐suited to statistical investigations of the paleomagnetic field: they can be used to test the predictions of statistical models such as those pioneered by Constable and Parker [1988], the most recent refinement of which is that of Tauxe and Kent [2004]; to compare with the statistical properties of dynamo models [e.g., Bouligand et al , 2005]; or ultimately can be used to invert for both the time‐averaged field and its temporal variability (some progress in this area has been made by Khokhlov et al [2001, 2006]). Finally, from a practical perspective, data collection efforts by several groups over the past decade have resulted in many new high‐quality paleodirections, that can collectively be compared with those used to generate the models shown in Figures 1 and 2.…”
Section: Introductionmentioning
confidence: 99%
“…This can make the problem trickier, because those quantities are not linearly related to x ( t ). However, it turns out that the statistics predicted for such directional data by a given generalized GGP can also exactly be computed (Khokhlov et al 2001).…”
Section: Local Expression Of Ggpsmentioning
confidence: 99%
“…One approach in particular has proved successful in the recent years. The giant gaussian process (GGP) approach first introduced by Constable & Parker (1988) in a relatively restrictive form, next generalized by Kono & Tanaka (1995), and by Hulot & Le Mouël (1994) and Khokhlov et al (2001) to also account for possible temporal and spatial correlations. This approach is particularly attractive as its formalism can be used to simultaneously analyse the historical (Constable & Parker 1988; Hulot & Le Mouël 1994), the archeomagnetic (Hongre et al 1998) and the palaeomagnetic MF (Constable & Parker 1988 and many studies since, see e.g.…”
Section: Introductionmentioning
confidence: 99%
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