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 the true
values presents challenges for reconstructing paleolatitudes. A
widespread approach for estimating the flattening factor ($f$)
compares the shape of an assemblage of magnetization vectors to that
derived from a paleosecular variation model (the elongation/inclination
[$E/I$] method). However, 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, interflow red beds of the Cut Face Creek Sandstone
that is bounded by lava flows of known inclination. We found that
detrital hematite remanence is flattened with f =
0.65{0.75}_{0.56}$ whereas the pigmentary hematite magnetization
shares a common mean with the volcanics. Comparison of detrital and
pigmentary hematite directions results in $f =
0.61^{0.67}_{0.55}$. These empirically determined flattening
factors are consistent with those estimated through the $E/I$ method
($f = 0.64^{0.85}_{0.51}$) supporting its application in deep
time. However, all methods have significant uncertainty associated with
determining the flattening factor. This uncertainty can be incorporated
into the calculation of 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.