Simulation-based inference of depth-resolved radar attenuation rates 

Radar attenuation rates are required to infer basal properties, to identify subglacial water and to characterise the thermal state of ice sheets. However, existing methods of estimating attenuation rates from radar measurements only provide depth-averaged values and rely on simplifying assumptions such as spatially constant reflectivity along the bed reflector or near-constant reflectivity of internal reflection horizons (IRHs) within the ice column. Comparisons of these methods on the same radar data set clearly show that depth-averaged attenuation rate estimates are strongly method-dependent and exhibit significant biases, which hinder the full interpretation of radar data.Here, we present a novel approach that provides improved depth-averaged attenuation rate estimates and, unlike previous works, can estimate depth-resolved attenuation rate profiles. We cast the problem of estimating attenuation rates as a Bayesian inference problem. To solve for the posterior distribution of attenuation rates underlying radar data, we first design a radar forward model that can generate realistic radar traces given depth profiles of attenuation rates. Subsequently, we apply Neural Posterior Estimation, a machine learning technique for estimating Bayesian posterior distributions, and train it on pairs of simulated radar traces and attenuation rate profiles. For synthetic radar data, our approach robustly infers both depth-averaged and depth-resolved attenuation rates and outperforms existing methods. We further demonstrate its transferability to ground-penetrating radar data collected at two distinct ice-dynamic settings in Antarctica: South Pole Lake and Rutford Ice Stream. In both cases, the temperature profiles derived from the inferred depth-resolved attenuation rates match in-situ borehole temperature measurements. This is a significant step forward in recovering englacial temperatures from ground-penetrating radar data, as well as in achieving an uncertainty-constrained interpretation of the basal reflection power.