A general procedure to correct sampling bias on joint orientation using a vector approach

Observed relative frequencies of joints should be corrected for sampling bias before inferring statistical distributions for orientations. The procedure available for sampling bias correction when finite size joints intersect finite size sampling domains is directly applicable only for vertical sampling planes [1-3]. Thus, a general procedure applicable for sampling domains of any orientation is developed in the present study. The corrected frequency of a joint is obtained by assigning a weight to each joint through a weighting function which is inversely propotional to the probability of intersection between the joint and the sampling plane. This probability of intersection is determined from a hypothesis indicating "the probability of intersection is proportional to the volume in which the center of the sampling domain should lie in order to intersect the joint". A vector approach to find this volume is described herein, followed by applications of this method to study the influence of the sampling bias correction on orientation frequency and to find statistical distributions for orientation data.