Methodology:

The misfit between measured and predicted acoustic impedance is used to infer the most probable basal sliding law, as described in Hank et al. (2025). This methodology utilizes the dependence of predicted acoustic impedance on effective pressure, as described by the Viscous Grain-Shearing theory (VGS; Buckingham, 1997, 2000, 2005, 2007).

The effective pressure is determined based on the basal sliding laws. Usually, these laws are expressed so that basal drag is a function of sliding speed and effective pressure. To compute effective pressure, these relationships must be inverted, either by explicitly rearranging the equations or by numerical root-finding. For all sliding laws, we ensure the effective pressure does not exceed the ice overburden pressure.

The VGS provides a model of acoustic propagation in granular material. Substituting the estimated effective pressure (from the basal sliding law) into this model and using independent estimates for the grain diameter and porosity from sediment cores provides an estimate of acoustic impedance for each sliding law. The predicted acoustic impedance is then compared to acoustic impedance measurements collected at five sites on Pine Island Glacier (PIG) in Antarctica (Brisbourne et al., 2017).

More specifically, the different models (VGS + sliding laws) are compared using Bayesian model selection. We assume the error of the data follows a Gaussian distribution and consider each model equally probable at the beginning. Since the parameter space differs between the models (number of individual parameters (dimensions) as well as number of tested parameter values), we apply Occam's razor, penalizing models with a larger parameter space.

Details of all other data sets, including the basal drag and sliding speed inversion (Arthern et al., 2015) as well as the prior distributions, can be found in Hank et al. (2025).

The contributing datasets used to constrain the model and parameter ranges are listed by Hank et al. (2025). The model was run between Nov 13, 2024 and Mar 11, 2025. The output is from the same date range.

Data collection:

The misfit calculations were performed using Julia version 1.8.3. The Bayesian model selection and all other data processing was done using Python version 3.13.2.

Data quality:

Key experiments were repeated with (log-)uniform prior distributions for all parameters to examine the sensitivity to the choice of the prior. Furthermore, experiments with a sub-sampled data set (every 10th acoustic impedance measurement) were carried out. A value of NaN indicates there is no data there.