On the shape of paleomagnetic data sets

A quick and easy method to analyze the shape of paleomagnetic data sets is described and illustrated. The elongation E of a set of directions of virtual geomagnetic poles VGP is defined as E = k(2)/k(3), where k(2) and k(3) are the second and third eigenvalues of the Bingham distribution. It is shown that E<3 or so indicates that the distribution is significantly elongate, although the size of the sample and the paleolatitude both affect this conclusion. Because the azimuth of k(2) gives the direction of elongation, it can be used to help determine why a particular distribution is elongate. It is shown that for most units from the craton both directions and VGP are nearly circular, except for units magnetized at very low latitudes. In general, poles are more circular than directions. Some units formed in plate margin locations also are circular, but many are highly elongate. Many units from the western Cordillera of North America have highly elongate distributions that are compatible with origin within a shear zone; others are obviously underformed internally. Units formed during extension are less commonly elongate, but some show the probably effects of normal faulting. It is hoped that shape analysis will be part of any complete paleomagnetic study in the future.