About the determination of the joint set intensity

摘要

In a previous paper (Grossmann 1988), the general expressions giving the intensity of a joint set as a function of the sum of the trace lengths of its joints on an observation surface, as well as the formulas for the usual types of observation surfaces were already deduced. However, those expressions and formulas were based on the simplifying assumption that all joints of the considered joint set had the same attitude, namely, the mean attitude of the joint set. This simplification can lead to very incorrect estimates of the joint set intensity, especially in the cases in which the observation surface has an attitude which is very near to the mean attitude of that joint set. This paper presents the theoretical background for the correct formulation of the problem, assuming that the attitudes of the joints of the considered joint set follow a bivariate normal distribution on the tangent plane at the mean attitude, and gives also formulas for the practical use.