Mathematics – Probability
Scientific paper
Dec 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007agufmgp23a..03c&link_type=abstract
American Geophysical Union, Fall Meeting 2007, abstract #GP23A-03
Mathematics
Probability
1507 Core Processes (1213, 8115), 1510 Dynamo: Theories And Simulations, 1522 Paleomagnetic Secular Variation, 1595 Planetary Magnetism: All Frequencies And Wavelengths
Scientific paper
Paleomagnetic data are not easily assimilated into geodynamical models of Earth's core, but statistical descriptions of paleomagnetic field behavior can provide a basis for determining whether geodynamo models are basically compatible with long term observations of the geomagnetic field. Such statistical descriptions generally include some kind of average field state and variability about the mean, and have often been parameterized in terms of a so-called Giant Gaussian Process, in which spherical harmonic coefficients describing the poloidal part of the geomagnetic field are represented as samples from specific normal probability distributions. The time-averaged field at any location can be determined from the means, while the anticipated variability over time is reflected in the standard deviations of these statistical distributions, and the spherical harmonic representation in principle allows for arbitrary spatial complexity in the paleofield. In practice the number and quality of paleomagnetic data available limit the parameters that can be determined, along with simplifying hypotheses about overall field structure. Data used to assess field variability for these models are usually derived from lava flows and reflect instantaneous quasi-independent observations of the field at random times determined by the associated igneous processes. A two step process is presented for inverting globally distributed data to find a suitable Giant Gaussian Process, first discovering parameters to describe local or regional field variations, and then proceeding to a global inversion. Such models can be extended by using estimates of the geomagnetic power spectrum to accommodate temporal correlations in the spherical harmonic structures. A simplified model for frequency dependence of the geomagnetic dipole spectrum is derived from recent estimates of the paleomagnetic power spectrum, and could be merged with simple parametrizations for secular variation at higher spherical harmonic degree.
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