Glacial Isostatic Adjustment Modelling for Crustal Motion in North America

Date

2023-04-27

Authors

Brierley-Green, Connor

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Abstract

Due to the expansion and retreat of the large ice sheets that covered most of Canada and parts of the northern United States during the Last Glacial Maximum (LGM), the surface of North America presently exhibits vertical and horizontal crustal motion due to glacial isostatic adjustment (GIA). The purpose of this study was to explore the effects that Earth rheology parameters have on this crustal motion and to find a model that best fits the observations. The Earth is assumed to be spherically symmetric, and this thesis explores the effects of varying the Earth-model parameters and the general limitations of the laterally homogeneous approximation. The GIA models used in this study are randomly generated from a wide range of Earth rheological parameters for a 3-layered mantle viscosity model with the spherically symmetric Preliminary Reference Earth Model (PREM) for continuous density and elastic parameters. The surface loading model is ICE6G_C. A new Earth response calculation method dubbed the hybrid method is presented to calculate as much of the normal mode response as possible while still being accurate and robust. The crustal motion predictions of the randomly generated GIA models were compared to the observed MIDAS velocity fields for selected Global Navigation Satellite System (GNSS) sites across North America. The goodness-of-fit was assessed through a Root-Mean-Square (RMS) calculation of the residual velocities. Three types of best models were produced: one for minimizing the vertical crustal response residuals, one for the horizontal crustal response, and one for the combined vertical and horizontal response. The horizontal and combined response exhibited two optimal viscosity profile ranges that produced small residuals, with the global optimum transitioning between these two optimal ranges between 100 and 120 km thick lithospheres, while the vertical response’s optimal viscosity profile range was relatively consistent across all tested lithosphere thicknesses. The optimal viscosity profile for the vertical response was close to other previously published viscosity profiles like VM5a and VM7, and it was most similar to VM1. The horizontal and combined response viscosity profile before the 100 – 120 km transition was also similar to VM1, but after the transition the viscosity profile shifted substantially, with the parts of the viscosity profile changing by more than an order of magnitude. The best vertical response was for a lithospheric thickness of 100 km. The horizontal and combined responses did not show a well-defined minimum until the viscosity profiles across the 100 – 120 km transition were extrapolated before and after the transition. With this extrapolation, both the horizontal and combined showed a minimum RMS residual at 100 km akin to the vertical response. Using 100 km thickness as the best model for all responses, the RMS of the residuals were 1.012 and 0.684 mm/yr for the vertical and horizontal response respectively and 1.303 (vertical) and 0.791 (horizontal) mm/yr for the combined response. For the null hypothesis (no GIA model), the RMS values of the observations were 3.244 and 1.321 mm/yr for the vertical and horizontal responses, respectively. The vertical and horizontal crustal motions of the best combined response model are more similar to the crustal motions of the best horizontal response model than to the crustal motions of the best vertical response model, suggesting that the combined model favours the horizontal constraints over the vertical constraints. Despite the extensive search through Earth rheology, the residuals of the best models are still relatively large. This indicates the potential limitation of the spherically symmetric approximation and the need to incorporate lateral heterogeneity to produce an improved fit to the observations. It may also indicate that other processes, such as surface hydrological change, contribute significantly to the GNSS-observed crustal motion signal and would need to be considered in a future joint analysis.

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Keywords

Post-glacial rebound, Glacial isostatic adjustment, North America, Mantle viscosity, Lateral homogeneity, Hybrid method

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