Applying machine learning to characterize and extrapolate the relationship between seismic structure and surface heat flow

Abstract

SUMMARY Geothermal heat flow beneath the Greenland and Antarctic ice sheets is an important boundary condition for ice sheet dynamics, but is rarely measured directly and therefore is inferred indirectly from proxies (e.g. seismic structure, magnetic Curie depth, surface topography). We seek to improve the understanding of the relationship between heat flow and one such proxy—seismic structure—and determine how well heat flow data can be predicted from the structure (the characterization problem). We also seek to quantify the extent to which this relationship can be extrapolated from one continent to another (the transportability problem). To address these problems, we use direct heat flow observations and new seismic structural information in the contiguous United States and Europe, and construct three Machine Learning models of the relationship with different levels of complexity (Linear Regression, Decision Tree and Random Forest). We compare these models in terms of their interpretability, the predicted heat flow accuracy within a continent and the accuracy of the extrapolation between Europe and the United States. The Random Forest and Decision Tree models are the most accurate within a continent, while the Linear Regression and Decision Tree models are the most accurate upon extrapolation between continents. The Decision Tree model uniquely illuminates the regional variations of the relationship between heat flow and seismic structure. From the Decision Tree model, uppermost mantle shear wave speed, crustal shear wave speed and Moho depth together explain more than half of the observed heat flow variations in both the United States [$r^2 \approx 0.6$ (coefficient of determination), $\mathrm{RMSE} \approx 8\, {\rm mW}\,{\rm m}^{-2}$ (Root Mean Squared Error)] and Europe ($r^2 \approx 0.5, \mathrm{RMSE} \approx 13\, {\rm mW}\,{\rm m}^{-2}$), such that uppermost mantle shear wave speed is the most important. Extrapolating the U.S.-trained models to Europe reasonably predicts the geographical distribution of heat flow [$\rho = 0.48$ (correlation coefficient)], but not the absolute amplitude of the variations ($r^2 = 0.17$), similarly from Europe to the United States ($\rho = 0.66, r^2 = 0.24$). The deterioration of accuracy upon extrapolation is caused by differences between the continents in how seismic structure is imaged, the heat flow data and intrinsic crustal radiogenic heat production. Our methods have the potential to improve the reliability and resolution of heat flow inferences across Antarctica and the validation and cross-validation procedures we present can be applied to heat flow proxies other than seismic structure, which may help resolve inconsistencies between existing subglacial heat flow values inferred using different proxies.