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| Titel |
Poisson goes, random walker comes: Explaining the power-law distribution of the durations of stable-polarity intervals |
| VerfasserIn |
Karl Fabian, Valera Shcherbakov |
| Konferenz |
EGU General Assembly 2010
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 12 (2010) |
| Datensatznummer |
250041993
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| Zusammenfassung |
| In contrast to the predominant paradigm, recent studies indicate that the lengths of
polarity intervals do not follow Poisson statistics, not even if non-stationary Poisson
processes are considered. It is here shown that first-passage time (FPT) statistics for a
one-dimensional random walk provides a good fit to the polarity time scale (PTS)
in the range of stable polarity durations between 10Â ka and 3000Â ka. This fit is
achieved by adjusting only a single diffusion time T , which comes to lie between
70Â ka and 100Â ka depending on the PTS chosen. A physical interpretation, why
the FPT distribution of a random-walk process applies to the geodynamo, could
relate to a balance between decay of stochastic turbulence and generation of the
magnetic field. A simplified picture assumes the field generation to occur from a
collection of 10-100 statistically independent dynamo processes, where each is
described, e.g., by a Rikitake equation in the chaotic regime. An interesting feature
of the random walk model is that it naturally introduces an internal variable, the
position of the walk, which could be linked to field intensity. This connection would
suggest that the variance of field intensity increases with the duration of the polarity
interval. It does not predict a strong correlation between the strength of the paleofield
and the duration of a chron. A further strength of the random walk model is that
superchrons are not outliers, but natural rare events within the system. The apparent
non-stationary nature of the geodynamo can be interpreted in the random walk
model by a continuous shift in the governing parameters, and does not require major
restructuring of the internal geodynamo process as in case of the Poisson picture. |
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