Quantifying Inclination Shallowing and Representing Flattening Uncertainty in Sedimentary Paleomagnetic Poles

Abstract

Inclination is the angle of a magnetization vector from horizontal. Clastic sedimentary rocks often experience inclination shallowing whereby syn- to post-depositional processes result in flattened detrital remanent magnetizations relative to local geomagnetic field inclinations. The deviation of recorded inclinations from true values presents challenges for reconstructing paleolatitudes. A widespread approach for estimating flattening factors (f) compares the shape of an assemblage of magnetization vectors to that derived from a paleosecular variation model (the elongation/inclination [E/I] method). Few studies exist that compare the results of this statistical approach with empirically determined flattening factors and none in the Proterozoic Eon. In this study, we evaluate inclination shallowing within 1.1 billion-year-old, hematite-bearing red beds of the Cut Face Creek Sandstone that is bounded by lava flows of known inclination. Taking this inclination from the volcanics as the expected direction, we found that detrital hematite remanence is flattened with (Formula presented.) whereas the pigmentary hematite magnetization shares a common mean with the volcanics. Using the pigmentary hematite direction as the expected inclination results in (Formula presented.). These flattening factors are consistent with those estimated through the E/I method (Formula presented.) supporting its application in deep time. However, all methods have significant uncertainty associated with determining the flattening factor. This uncertainty can be incorporated into paleomagnetic poles with the resulting ellipse approximated with a Kent distribution. Rather than seeking to find “the flattening factor,” or assuming a single value, the inherent uncertainty in flattening factors should be recognized and incorporated into paleomagnetic syntheses.