A Fast Surrogate Model for 3D-Earth Glacial Isostatic Adjustment using Tensorflow (v2.8.10) 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, and infer rheological properties of the deep Earth. A relatively recent advance has been the development of models that include 3D Earth structure, as opposed to 1D, spherically symmetric 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 emulate the influence of 3D Earth models with the goal of more affordably constraining the parameter space of these models: specifically the radial (1D) viscosity profile upon which the lateral variations are added.

This study provides an initial “proof of concept” assessment of using ANNs to emulate the influence of lateral Earth structure on GIA model output. Our goal is to test whether the fast surrogate model can accurately predict the difference in these outputs (i.e., 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 reproduces output 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). Our results indicate that the ANN:model misfits, while not negligible, are of a scale such that useful predictions of deglacial RSL changes can be made.

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 find that the surrogate model is able to successfully reproduce the data:model misfit values such that the region of minimum misfit either overlaps the 3D GIA model results, or is within two increments in the parameter space. The surrogate model can, therefore, be used to accurately explore this aspect of the 3D Earth model parameter space. While the 3D Earth models can outperform the SS Earth models for some regional subsets of the RSL data set, the SS Earth models still produce better fits overall. In summary, this work demonstrates the utility of machine learning in 3D Earth GIA modelling and so future work to expand on this analysis is warranted.