TY - JOUR
T1 - A story about distributions of dimensions and locations of boulders
AU - Ditlevsen, Ove Dalager
PY - 2006
Y1 - 2006
N2 - 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 1987-88 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 wide spread 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.
AB - 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 1987-88 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 wide spread 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.
KW - Boulders; Boulder size; Data analysis; Geologic processes; Glacier till; Poisson field;
M3 - Journal article
SN - 0266-8920
VL - 21
SP - 9
EP - 17
JO - Probabilistic Engineering Mechanics
JF - Probabilistic Engineering Mechanics
IS - 1
ER -