A story about estimation of a random field of boulders from incomplete seismic measurements

This paper reports on the statistical interpretation of seismic diffraction measurements of boulder locations. The measurements are made in a corridor along the planned tunnel line for the later realized bored tunnel through the till deposits under the East Channel of the Great Belt in Denmark. The investigation was made in 1987-88 on the initiative of A/S Storebæltsforbindelsen in order to prepare its tendering for the bored tunnel. The purpose was to make a prediction of the density of boulders of maximal dimension above any specified length. The properties of the seismic measuring device and its graphical registrations on seismograms do not make a proper interpretation possible without detailed knowledge about the joint distribution of the primary dimensions of the boulders. Therefore separate measurements were made of the dimensions of boulders deposited visibly on the cliff beaches of the Great Belt. The surprisingly simple results from the analysis of the data from this separate measuring program are reported in a companion paper. Based on the revealed geographical universality of the joint dimension distribution it is anticipated that the same distribution is applicable for the till deposits along the tunnel line. By use of this important distribution information and of the observed homogeneity of the seismic point source field together with the physical properties of diffraction it became possible to make the wanted prediction. During the excavation the found boulders were counted and measured. These direct observations on site confirmed that the prediction was quite good.