Confidence regions for fabric shape diagrams

Fabric shape is often quantified using the three eigenvalues from the ‘orientation tensor’ method applied to a sample of directions. Several studies have used eigenvalues plotted on fabric shape diagrams to distinguish sedimentary facies or strain histories. However, such studies seldom consider how well the sample eigenvalues represent the true fabric shape. In this paper, we use ‘bootstrapping’ techniques to define confidence regions for sample eigenvalues, and show that sample and population eigenvalues may differ substantially. Confidence regions are often very large for small sample sizes, and we recommend that sample sizes should be at least 50.