Quantifying Inclination Shallowing and Representing Flattening Uncertainty in Sedimentary Paleomagnetic Poles

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........ = 0.650.75 0.56 whereas the pigmentary hematite magnetization shares a common mean with the volcanics. Using the pigmentary hematite direction as the expected inclination res....ults in.... = 0.610.67 0.55. These flattening factors are consistent with those estimated through the E/I m....ethod (.... = 0.640.85 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 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. Plain Language Summary The magnetization of ancient sedimentary rocks provides great insight into Earth's past. Earth scientists use these rocks to understand how Earth's magnetic field has flipped through time and to reconstruct how continents have moved. Hematite is a common mineral which gives many sandstones a red color-leading geologists to refer to them as red beds. While hematite is a reliable magnet through time, the magnetic directions recorded by hematite grains can be shallower than the geomagnetic field (i.e., they are flattened). Magnetization steepness is how Earth scientists determine the latitude where rocks were deposited as the magnetic field gets steeper toward the pole. We need ways to correct for magnetization shallowing in sedimentary rocks. In this study, we compared the steepness of magnetic directions held by hematite to that of lava flows that formed in the same time interval. Magnetic directions from lava flows are not flattened so this comparison allows us to determine the shallowing amount. We compare it to a statistical method and see that the results are indistinguishable within the appreciable uncertainty of the methods. Earth scientists should include the uncertainty associated with inclination shallowing when they report ancient pole positions determined from such flattened magnetic directions.

Automated summary

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........ = 0.650.75 0.56 whereas the pigmentary hematite magnetization shares a common mean with the volcanics. Using the pigmentary hematite direction as the expected inclination res....ults in.... = 0.610.67 0.55. These flattening factors are consistent with those estimated through the E/I m....ethod (.... = 0.640.85 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 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.