Estimating the mean length of discontinuity traces

Abstract A technique is proposed for estimating the mean trace length of discontinuities observed in mine drive walls. The method is distribution-free, i.e. independent of the assumed functional form of the statistical distribution of trace lengths, and no knowledge of the actual lengths of the observed traces is required. Under the very general assumption that trace midpoints are randomly and homogeneously distributed, all that needs to be known about each trace observed is whether it is censored (at one or both ends) or not. The method is restricted to a set of parallel traces of arbitrary direction. It is shown that, if the joint survey imposes a cut off at some length below which traces are ignored (i.e. truncation of small traces), the method provides an exact solution if the trace length distribution can be assumed to be exponential. The technique is illustrated by data from the Dolphin Mine of King Island Scheelite in Tasmania, Australia. In order to derive confidence limits for the sampling estimate of the trace length mean, it is necessary to assume that trace midpoints are distributed as a Poisson field; this requires that the distribution of spacings between traces conforms to the exponential model.