Establishing a Statistical Framework for Assessing Paleomagnetic Data Quality: A Significance Test Based on Maximum Angular Deviation

Abstract

Paleomagnetic data underpin our understanding of Earth's ancient magnetic field and are essential to paleogeographic reconstructions. At the specimen level, paleomagnetic analysis relies upon stepwise demagnetization to enable isolation and quantification of magnetic remanence components in geological materials. This quantification is performed typically using principal component analysis (PCA) to fit a line to stepwise demagnetization data. The quality of such PCA fits is assessed via the so-called maximum angular deviation (MAD), which is used in a heuristic fashion to represent directional uncertainty and as a selection criterion for identifying poorly or well behaved specimens. We present here a significance test that employs MAD as a statistic to compare demagnetization data against a null hypothesis of random behavior. This places MAD within a formal statistical framework that can be used to test the quality of demagnetization data before undertaking more detailed analysis. Tables of numerically estimated significance levels are provided to enable ready application of the proposed test and recommendations are made concerning the number of demagnetization data needed for statistical inference.