Summary. The singular value decomposition and its interpretation as a linear biplot have proved to be a powerful tool for analysing many forms of multivariate data. Here we adapt biplot methodology to the specific case of compositional data consisting of positive vectors each of which is constrained to have unit sum. These relative variation biplots have properties relating to the special features of compositional data: the study of ratios, subcompositions and models of compositional relationships. The methodology is applied to a data set consisting of six-part colour compositions in 22 abstract paintings, showing how the singular value decomposition can achieve an accurate biplot of the colour ratios and how possible models interrelating the colours can be diagnosed.

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Biplots of compositional data

Pebble fabric data are available from several facies of glacigenic sediments deposited by modern glaciers, where sedimentary processes can be observed or inferred with relatively little ambiguity. Over 100 samples from contemporary environments illustrate fabrics characterizing melt-out till, deformed and undeformed lodgement till, sediment flow deposits and ice slope colluvium. Lodgement till fabric variability is related to the two-layer structure of these sediments; a structureless, friable upper layer with low shear strength and high consolidation coefficient, overlying a very compact material of horizontal platy structure. Fabric strength (assessed by eigenvalue analysis) is weaker and pebble dip is more dispersed in the upper structureless horizon. Stronger fabrics in the lower platy horizon may be primary depositional fabrics which are destroyed by subglacial shearing to give weaker fabrics in the upper horizon. Alternatively, upper horizon fabrics may be characteristic of all recently-deposited lodgement tills, with stronger fabrics developing at depth by dewatering and consolidation. There is a general reduction in fabric strength and an increase in particle dip associated with the transition from melt-out tills, through undeformed and deformed lodgement tills, to sediment flow deposits and ice slope colluvium. There is, however, considerable overlap in the fabric strengths characteristic of sediment flow deposits and deformed lodgement tills. Fabric data from modern glacial sedimentary facies are used to assist in interpreting the mode of deposition of some Quaternary glacial sediments. Relatively strong fabrics characteristic of melt-out tills and undeformed lodgement tills are more likely to be diagnostic of genesis than weaker fabrics associated with deformed sediments.

Characterization of pebble fabrics in modern terrestrial glacigenic sediments

Till—as a glacial “tectomict”, its internal architecture, and the development of a “typing” method for till differentiation

The interpretation of glacigenic diamictons is a subjective process, for which quantitative support is frequently sought from parameters such as clast shape and fabric. It has been widely suggested that different glacigenic diamicton facies possess distinct clast-fabric signatures. This paper examines this concept using a data set of 111 clast fabrics, and a synthesis of published results. Eigenvalues are calculated and compared for a variety sedimentary facies. It is concluded that clast fabric alone is not able to discriminate between different glacigenic facies, and it is argued that clast fabric offers little quantitative support in the interpretation of glacigenic sediments. It is suggested, therefore, that although clast fabric may continue to have a role as an indicator of relative strain at specific sites, its use in the discrimination of glacigenic facies is limited. Consequently, we should be much more selective in undertaking such analyses in the future. Copyright © 1999 John Wiley & Sons, Ltd.

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Glacigenic clast fabrics: genetic fingerprint or wishful thinking?

Terrestrial or waterlain glacial diamictites? Three case studies from the late Precambrian and late Ordovician glacial drifts in West Africa

The analysis of the orientation of the long axis of clasts in till (till fabric) is used to assess aspects of its depositional history. The till fabric of the Catfish Creek Till has been analyzed in two sections located on Lake Erie for three particle sizes: 0.3–0.6 cm, 1–5 cm, and +5 cm, at approximately 1 m intervals within each section. Data were analyzed using Bingham9s distribution. Results indicate different depositional histories for the upper and lower units of the till. There are also differences between the two sections.Comparison of the results from this fabric study with those of other investigators, both qualitatively and quantitatively, when combined with other local geological criteria, indicate a complex subglacial environment of deposition, probably involving meltout, debris flows, and lodgement. This complexity of processes would account for the poorly developed fabrics.

Quantitative evaluation of clast fabrics within the Catfish Creek Till, Bradtville, Ontario

David et al. (1974a, b) present a different approach to factor analysis and are to be commended for bringing to the attention of the geological community the existence of a method of data analysis called Correspondence Analysis. However, before the utility of the technique can be properly evaluated on the basis of the set of data used in the paper, a number of points should be clarified. Principal Components Analysis (PCA) is not synonymous with Ror Q-mode factor analysis (Mulaik 1972; Davis 1973). The usual procedure (Klovan 1968 ; Rummel 1970; Davis 1973) is to begin with a PCA and then rotate a subset of the principal component axes according to some substantive criterion (for example, simple structure: Harmon 1967; Rummel 1970). The most common method of orthogonal rotation is the varimax procedure (Kaiser 1958). Oblique rotational methods (Hakstian 1969; Rummel 1970; Mulaik 1972) where the orthogonality constraints of the varimax scheme are relaxed are also utilized (Hitchon et al. 1971). The authors state (p. 13 1) that the 'technique' (correspondence analysis) is designed to extract the maximum of information from an array of positive numbers. They also emphasize the saving of computer time and storage (and by inference money). The latter aspect may be the most redeeming quality of their Correspondence Analysis. The transformation which they employ (p. 134) is a bounding type of data matrix transformation (Rummel 1970) and not standardization. Standardization in the strict sense involves subtracting the mean of a variable from each original observation and dividing the resultant

Ronald W. May

Papers

Quantitative evaluation of clast fabrics within the Catfish Creek Till, Bradtville, Ontario

Progresses in R- and Q-Mode Analysis: Correspondence Analysis and its Application to the Study of Geological Processes: Discussion