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Statistical methods for paleovector analysis

January 1, 2007

Our concern is with the statistical description of paleomagnetic vectors and the estimation of their mean and variance. These vectors may come from a number of different rock units or archeological samples, representing a range of acquisition times, and be useful for studies of the mean paleomagnetic field and paleosecular variation; alternatively, the vectors may come from individual measurements taken from a given rock unit or archeological sample, representing the same moment of acquisition, and be useful for studying the acquisition process itself. Directional data of a particular polarity are usually analyzed with a Fisher distribution (1953), and data of mixed polarities are usually analyzed with a Bingham distribution (1964). Occasionally, other directional distributions are used. For example, Bingham (1983) considered the projection of a three‐dimensional (3D), scalar‐variance Gaussian distribution onto the unit sphere, something he called the “angular‐Gaussian” distribution. More recently, Khokhlov et al. (2001) considered a generalization of the angular‐Gaussian distribution, one with a covariance matrix, which they used to analyze directional data from a number of sites. With respect to intensity data, they have traditionally been treated separately from paleodirections, analyzed with normal, log‐normal, or gamma distributions. Here, for data of either a particular polarity or of mixed polarities, we summarize these works, and that of Love and Constable (2003), who developed a full‐vector, scalar‐variance, Gaussian‐statistical framework for treating directional and intensity data simultaneously and self‐consistently.

Publication Year 2007
Title Statistical methods for paleovector analysis
DOI 10.1007/978-1-4020-4423-6_295
Authors Jeffrey J. Love
Publication Type Book Chapter
Publication Subtype Book Chapter
Index ID 70200686
Record Source USGS Publications Warehouse
USGS Organization Geologic Hazards Science Center