A fast surrogate model for 3D Earth glacial isostatic adjustment using Tensorflow (v2.8.0) artificial neural networks

Abstract

Models of glacial isostatic adjustment (GIA) play a central role in the interpretation of various geologic and geodetic data to understand and simulate past and future changes in ice sheets and sea level, as well as to infer rheological properties of the deep Earth. During the past few decades, a major advance has been the development of models that include 3D Earth structure, as opposed to 1D spherically symmetric (SS) structure. However, a major limitation in employing 3D GIA models is their high computational expense. As such, we have developed a method using artificial neural networks (ANNs) and the Tensorflow library to predict the influence of 3D Earth models with the goal of more affordably exploring the parameter space of these models, specifically the radial (1D) viscosity profile to which the lateral variations are added. Our goal is to test whether the use of an ANN to produce a fast surrogate model can accurately predict the difference in GIA model outputs (i.e., relative sea level (RSL) and uplift rates) for the 3D case relative to the SS case. If so, the surrogate model can be used with a computationally efficient SS (Earth) GIA model to generate output that replicates that from a 3D (Earth) GIA model. Evaluation of the surrogate model performance for deglacial RSL indicates that it is able to provide useful estimates of this field throughout the parameter space when trained on only ≈15 % (≈50) of the parameter vectors considered (330 in total). We applied the surrogate model in a model–data comparison exercise using RSL data distributed along the North American coasts from the Canadian Arctic to the US Gulf Coast. We found that the surrogate model is able to successfully reproduce the model–data misfit values such that the region of minimum misfit either generally overlaps the 3D GIA model results or is within two increments of the radial viscosity model parameter space (defined here as lithosphere thickness, upper-mantle viscosity, and lower-mantle viscosity). The surrogate model can, therefore, be used to accurately explore this aspect of the 3D Earth model parameter space. In summary, this work demonstrates the utility of machine learning in 3D Earth GIA modelling, and so future work to expand on this initial proof-of-concept analysis is warranted.