A seminar by Professor Cathy Constable from University of California at San Diego
Title: Gauss and Earth’s Magnetic Field: Statistics Meet Observations
Abstract: The use of paleomagnetic methods to study Earth’s magnetic field from the geological record has a venerable history, starting from Ronald Fisher’s use of the Von Mises-Fisher distribution to describe the dispersion of paleomagnetic directions. The Fisher distribution, as it is widely known in paleomagnetism, corresponds to the restriction of an isotropic Gaussian distribution to the surface of the unit 3-sphere. The first applications were targeted to recover reliable mean directions from lava flows, evolving to hierarchical situations where the mean directions recovered from multiple individual flows are themselves part of a distribution representing the time variations in the geomagnetic field known as paleosecular variation (PSV). Complete PSV distributions must also allow for temporal changes in intensity of the magnetic field so they are not limited to the unit sphere. They also depend on geographic location, requiring a consistent global statistical representation for the field, often provided in the form of a so-called Giant Gaussian Process (GGP), with the statistical distribution at any individual location represented as a 3-dimensional Gaussian distribution. The local GGP distributions are determined by an underlying statistical representation for a spherical harmonic expansion of the solution to Laplace’s equation. My talk will briefly outline methods for acquiring global paleomagnetic data, highlighting the geographic and temporal variability in GGP statistical distributions and ongoing challenges in estimating them from finite and noisy data sets.
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