Heteroscedastic uncertainty quantification for GGM-inverted bathymetry: A zero-mean Laplace distribution framework

Abstract

The Gravity-Geologic Method (GGM) is widely used to predict bathymetry from satellite-derived gravity anomalies, yet a robust framework for quantifying the uncertainty of its predictions is lacking. Traditional approaches often assume homoscedastic, Gaussian-distributed errors, which do not hold in complex terrains. This study introduces a novel heteroscedastic uncertainty quantification framework for GGM-derived bathymetry by assuming that the prediction residuals follow a zero-mean Laplace distribution rather than a Gaussian one. Noting that the scale parameter of this distribution depends clearly on both predicted water depth and topographic roughness, we parameterize this relationship using a fully connected neural network to model spatially varying uncertainty. The proposed method generates spatially explicit 95% confidence intervals, providing a more reliable and interpretable measure of prediction reliability. Validation across three distinct topographic provinces (trenches, seamounts, and plains) in the Western Pacific confirms the superiority of the zero-mean Laplace distribution assumption and the effectiveness of the heteroscedastic modeling approach. This framework significantly enhances the practical utility of GGM predictions for applications requiring risk assessment, such as marine engineering and navigation safety.