Simulation and characterization of fracture patterns in glaciers

During drainage of subglacial lakes the surface of the glacier subsides and fractures, generating a homogeneous, circular fracture pattern on the rim of the resulting depression. We have analyzed several fracture patterns around the Skafta cauldron on Iceland. A regular fracture spacing was observed on the cauldron rim, indicating that the region was subjected to a uniform strain. In this region, standard image analysis techniques were applied to find the lengths L and open areas A of the fractures. We demonstrate that an understanding of sampling biases allows a scaling relation L ∝ Aβ to be established and the exponent β to be determined. This relation provides a quantitative characterization of interactions between fractures in the population. The value of β is higher for that observed for laboratory experiments on clay, but the uncertainties do not rule out a universal behavior, which applies to ice, rock, and all other solids. The size distribution of fractures did not display a similarly simple crossover behavior, and a power law scaling relation could not be established without a better understanding of the crossovers for large fractures. We introduce a simple simulation model that reproduces the most important visual and statistical properties of the glacier fracture pattern. The direct comparison validates the use of the model to simulate geological fracturing processes.