Determination of Discontinuity Size Distributions from Scanline Data

Abstract

The paper outlines a new method for estimating the distribution form, and mean size, of discontinuities from scanline data. By assuming that the discontinuities are circular discs it has been possible to apply existing solutions for the distributions of censored semi-trace lengths sampled by a scanline at an exposed rock face. These solutions have been implemented by numerical quadrature in a standard Excel spreadsheet, with solution optimisation achieved with Solver. Problems caused by a singularity in the integration were overcome by applying an integration offset parameter. A trigonometrical substitution for removing this singularity is also outlined. The numerical quadrature strategy was validated by comparison with the analytical solution for the uniform distribution, and by comparison with the results of an extensive geometrical simulation of the stereological process. A new distribution, here named the Wicksell distribution, has been identified. This distribution is characterised by the fact that the distribution of disc diameters and the distribution of complete traces on a cutting plane are identical. Two examples, based on real scanline data, are presented to illustrate the practical application of the new methods.