Simple graphical methods for estimating the confidence region about the orientation of the intersection of two planes

Abstract

We give a simple graphical method for the construction on a stereonet of the confidence region for the orientation of the line of intersection of two planes. The method applies when the poles to the planes have been estimated by large and approximately equal numbers of measurements which may be treated as samples from two Fisher distributions of equal and large precision parameters. The method requires the estimation of the acute angle between poles to the planes and the range of the plunges of the poles.When the samples of poles are samples of large size from two Bingham distributions tightly clustered about their common plane, a more complex graphical construction is available. It requires the estimation of scatter of the poles in and perpendicular to the common plane and some simple calculations.The methods are applicable to a variety of problems in structural geology and rock mechanics.