Estimating Densities in Contoured Orientation Diagrams

INTRODUCTION; The contoured orientation diagram is widely used as a method of displaying three-dimensional orientation data. However progress toward a quantitative understanding of the diagram has been slow. We attempt here to carry this understanding a step further by a theoretical and experimental investigation of the statistical properties of densities observed in the diagrams. The density of orientation data in a direction on the orientation diagram has been used in two way: first, to infer that the fabric studied departs significantly from a random fabric (Kamb, 1959); second, to characterize the degree of preferred orientation the fabric shows (Hopwood, 1968; Voll, 1960). While qualitative descriptions of a fabric as containing “strong” or “weak” preferred orientations are common, little use has been made of the more precise information the contoured orientation diagram contains. Practical applications of this information to rock mechanics (McMahon, 1967; Goodman, 1976) have prompted our study.