The orientation distribution of single joint sets

Poles from line samples of systematic joint sets scatter about a mean pole because joints are neither perfectly planar nor parallel, and because measurement instruments are imprecise. Definition of a single joint set can be based solely on its orientation distribution and this distribution is assessed using two statistical parameters: Square root of the circular variance (approximately equal to the standard deviation σ for two-dimensional (2D) data) and cone of confidence (α ₉₅ for 3D data). The distribution for joints generated in the absence of tectonic deformation is well clustered with σ = 1.7° and α ₉₅ = 0.48° based on a bootstrap sample of 50. Jointing associated with various fold styles show less clustering: The kink of a fault-bend fold (σ = 6.1° and α ₉₅ = 1.7°), basement cored anticline (σ = 3.5° and σ ₉₅ = 1.5°), regional joint set transected by a basement-cored anticline (σ = 5.2° and α ₉₅ = 1.8°) and a buttress anticline (σ = 4.3° and α ₉₅ = 1.7°). Jointing associated with local faulting tends to show even less clustering: a Cretaceous marl (σ = 8.3° and α ₉₅ = 2.4°) and a glauconitic sandstone (σ = 8.6° and α ₉₅ = 2.2°). The latter sample was drawn from two overlapping joint sets, indicating that distribution data greater than a α ₉₅ = 2.2° may signal overlapping joint sets.