RANDOM VARIATION OF FABRIC EIGENVALUES: IMPLICATIONS FOR THE USE OF A-AXIS FABRIC DATA TO DIFFERENTIATE TILL FACIES² DOUGLAS I. BENN 1 * AND TREVOR J. RINGROSE 2 1 School of Geography and Geosciences, University of St Andrews, St Andrews, Fife, KY16 9ST, UK 2 Applied Mathematics and OR Group, Cranfield University, RMCS Shrivenham, Swindon, SN6 8LA, UK Received 18 November 1999; Revised 19 July 2000; Accepted 24 July 2000 ABSTRACT Fabric ‘shape’, based on the relative values of three eigenvalues calculated from fabric data, has been used to differentiate sediment facies and infer deformation histories. The eigenvalues are based on samples drawn from parent populations, and as such are subject to statistical variance due to sampling effects. In this paper, the degree of statistical variance in fabric data for two types of subglacial till from Breidamerkurjøkull, Iceland, is investigated using ‘bootstrapping’ techniques, in which empirical ‘confidence regions’ are built up by repeated resampling of the original data. The experiments show that, for each till type, the observed between-sample variability in the fabrics lies within the boundaries associated with random variations, indicating that the observed range of fabric shapes within each till type is likely to be entirely the product of sampling effects. Differences in fabric shape between till types are generally greater than that associated with random variations, indicating that their fabric shape characteristics, as measured by eigenvalues, are significantly different. Nevertheless, the results suggest that great care should be exercised when using a-axis fabric data to differentiate sedimentary facies, or to infer subtle differences in physical processes or conditions. Copyright # 2001 John Wiley & Sons, Ltd. KEY WORDS: clast fabric; fabric shape; deformation till; Breidamerkurjøkull INTRODUCTION The calculation of eigenvalues has been widely adopted as a standard method of summarizing sedimentary fabrics, particularly by sedimentologists working on glacigenic deposits (e.g. Mark, 1974; Lawson 1979; Domack and Lawson 1985; Rappol 1985; Dowdeswell and Sharp 1986; Hart 1994; Benn 1994a,b, 1995; Benn and Evans 1996; Bennett et al., 1999). Eigenvalues reduce large data sets to simple descriptive statistics describing the strength and orientation of directional properties of a sediment, thus allowing the ready comparison of fabric data from many localities. Furthermore, facies with contrasting depositional and deformational histories may have distinct fabric characteristics, and eigenvalues determined for deposits of known origin have been used to guide the interpretation of sedimentary facies, and to infer depositional processes and strain histories (Hart 1994; Benn 1994a,b, 1995; Evans et al., 1995; Benn and Evans 1996). Most studies of fabric data tacitly assume that eigenvalues faithfully represent the ‘true’ fabric of the parent deposit. In practice, however, fabric eigenvalues are derived from one or a few of the many possible samples that could have been taken from the parent deposit, and are therefore subject to statistical variance about the ‘true’ population values. The existence of such variance introduces an important source of uncertainty to the interpretation of fabric eigenvalues, and may limit the accuracy of conclusions that may be drawn from them. There is no guarantee that fabric eigenvalues are particularly representative of the facies under investigation, or that differences between eigenvalues for any two samples are due to true differences or merely sampling Earth Surface Processes and Landforms Earth Surf. Process. Landforms 26, 295–306 (2001) Copyright # 2001 John Wiley & Sons, Ltd. * Correspondence to: D. I. Benn, School of Geography and Geosciences, University of St Andrews, St Andrews, Fife, KY16 9ST, UK. E-mail: doug@st-andrews.ac.uk. ² Calculations were performed using the numerical mathematics package MATLAB. Copies of the program used are freely available by email from the authors at T.J.Ringrose@rmcs.cranfield.ac.uk