A story about distributions of dimensions and locations of boulders

The topic concerns the density of occurrence of boulders and the joint distribution of the primary boulder dimensions in the till deposits of the Great Belt region in Denmark. The investigation was made in 1987–1988 on the initiative of A/S Storebæltsforbindelsen in order to prepare the tendering for making a bored tunnel through the till deposit. Geographical universality was discovered through the statistical analysis of observations of boulder coordinates and dimension measures from widespread cliff beach locations. One conclusion is that the joint size distribution up to some degree of modeling approximation has a surprisingly simple structure. In particular, the maximal dimension has an exponential distribution while the ratios between maximal and intermediate dimension and between the intermediate dimension and the smallest dimension are independent and identically distributed according to a beta-distribution. Moreover, these ratios are independent of the maximal dimension. The random point field structure of the boulder coordinates as isolated points or as clusters of points makes Poisson fields reasonable modeling candidates for the fields of both single points and cluster points. The cluster size distributions are well modeled by a Markov chain type of model. Different details of the data and their statistical analysis support several modeling conjectures concerning the glacial history of boulder deposition. In a companion paper, it is described how the results of this beach boulder investigation are used for interpretation of the results from seismic scanning of the till deposits along the planned tunnel line, and for prediction of the density of boulders of maximal dimension above any specified length.