SAMPLING AND STATISTICS IN PALEOMAGNETIC STUDIES OF SEDIMENTARY ROCKS

Common paleomagnetic practice for determining pole positions from sedimentary units involves collecting and demagnetizing a suite of samples from a spatially-limited stratigraphic location, averaging the suite's individual sample directions, and then averaging site-mean directions from an appropriate number of these sampling localities. The theory behind this 'two-tier' practice makes assumptions about depositional and preservation conditions that are appropriate for volcanic and intrusive rocks but rarely valid for sediments. Use of this site-mean technique on sediments may exclude valid data and limits the resolution of magnetostratigraphic inference. Because many random events affect the natural remanent magnetization of sedimentary rocks, the most parsimonious sampling method is to sample densely through many layers in a vertical stratigraphic interval rather than across a horizontal exposure or bedding layer. For most sediments, the Central Limit Theorem of the calculus of probabilities applied directly to the principal magnetic components determined from demagnetization experiments justifies calculation of the mean direction of magnetization and associated errors in a 'one-tier' approach. Application of two-tier statistics in calculating poles may bias results by variable amounts in random directions, introducing unnecessary ambiguity into tectonic reconstructions.

Additionally, a minor problem exists with the McFadden and McElhinny (1988) technique for combination of linear and planar data in paleomagnetic analyses. When using samples with variable tilt corrections, the population of maximum likelihood directions from circle samples chosen before and after tilt correction will not be the same, minimizing the difference in dispersion statistics and potentially leading to a Type-II statistical error. Examples from the paleomagnetic literature will be examined to show differences in tectonic conclusions reached by changing these methodologies