Inferences of Mantle Viscosity Based on Ice Age Data Sets: The Bias in Radial Viscosity Profiles Due to the Neglect of Laterally Heterogeneous Viscosity Structure

Abstract

Inferences of mantle viscosity using glacial isostatic adjustment (GIA) data are hampered by data sensitivity to the space‐time geometry of ice cover. A subset of GIA data is relatively insensitive to this ice history: the Fennoscandian relaxation spectrum (FRS), postglacial decay times in Canada and Scandinavia, and the rate of change of the degree‐2 zonal harmonic of the geopotential ( J̇2). These geographically limited data have been inverted to constrain the radial (one‐dimensional [1D]) mantle viscosity profile. We explore potential biases in these 1D inversions introduced by neglecting a three‐dimensional (3D) viscosity structure. We perform 1D Bayesian inversions of synthetic GIA data generated from Earth models with realistic 3D variations in mantle viscosity and lithospheric thickness and compare results to the 1D viscosity profile associated with the 3D model used to generate the synthetics. Differences between these two 1D profiles reflect GIA data resolution and biasing introduced by neglecting, in the inversions, a 3D viscosity structure. We focus on the second issue, demonstrating that the largest bias occurs within the upper mantle (in particular, the transition zone). This remains consistent when varying inversion parameters (e.g., prior/starting models) and the 1D/3D viscosity fields adopted in generating the synthetics. Inversions of individual data sets show 3D biasing increases for data exhibiting shallower (thus more localized) sensitivity to viscosity. Of the data considered herein, inversions of the FRS are subject to the largest bias followed by decay time data. The bias is minimal for J̇2, as its deeper sensitivity is accompanied by broader averaging of structure in radial and lateral directions.

Constraints on mantle viscosity and Laurentide ice sheet evolution from pluvial paleolake shorelines in the western United States

“…These elevated sublithospheric temperatures are consistent with body wave tomography results that reveal relatively high S-and P-wave speeds and a high P to S-wave speed ratio, which suggests the presence of sublithospheric melt (Schmandt and Humphreys, 2010). The low viscosity estimates derived from lake rebound studies is therefore consistent with the notion that Earth structure underneath the Western U.S. is significantly weaker than cratonic sites such as the Canadian and Fennoscandian shields from which rebound-based estimates of viscosity are normally obtained (Lau et al, 2018).…”

Uncertainties of Glacial Isostatic Adjustment Model Predictions in North America Associated With 3D Structure

“…Surface geology (e.g., Kennett & TkalČić, 2008) and seismic tomography (e.g., Bunge & Grand, 2000) show that Earth's material properties are laterally heterogeneous and many studies have revealed that the 3D structure has a significant influence on GIA predictions (e.g., Austermann et al, 2013; Li et al, 2018; Yousefi et al, 2018). Indeed, 3D structure has been invoked as a mechanism whereby GIA models may better fit late Quaternary RSL records (e.g., Clark et al, 2019; Kuchar et al, 2019; Love et al, 2016), while neglecting 3D structure could introduce bias in 1D viscosity inversions (Lau et al, 2018).…”

An investigation into the sensitivity of postglacial decay times to uncertainty in the adopted ice history

“…Mitrovica & Forte 2004;Lau et al 2016;Nakada et al 2016), and indicates that while there are regions of parameter space that are more sensitive to the input ice history than others, this sensitivity does not seem to extend to the regions of parameter space most favoured by the data. However, the Richmond Gulf andÅngerman River decay times are reflective of their own local viscosity structure, and while it is consistent in our modelling framework to combine these constraints for a 1-D spherically symmetric Earth, it may not reflect the real Earth where viscosity structure exhibits lateral variation that can significantly affect decay time calculations (Lau et al 2018;Kuchar et al 2019). For example, Paulson et al (2005) compare computed Hudson Bay decay times from a 3-D GIA model with those of 1-D models with viscous structure corresponding to global and regional averages identical to the 3-D model, and find nearly a 30 per cent misfit when comparing the 3-D model to its corresponding global average 1-D model, and a reduced but still significant 10 per cent misfit when comparing to the Hudson Bay regional average model.…”