ABSTRACT

This paper describes a mathematical method of classifying limestones. The technique offers many advantages over other numerical methods of classification, particularly in that qualitative data can be utilised. This removes the necessity for point counting, speeds up the description of samples and allows the inclusion of rock properties of a non-parametric nature. The method could be used in many branches of geology and is of particular interest to the oil geologist.

The technique involves the numerical description of rock samples, followed by cluster analysis. Samples are described in terms of several two-state attributes (e.g. presence of absence of quartz), and/or several multistate attributes (e.g. quartz abundant, present, rare, or not present). Multistate attributes are subsequently recoded into two-state form, using numerical methods devised for use in biological taxonomy. Similarity coefficients are then computed between all possible pairs of samples, and cluster analysis groups together those samples most similar to one another. These groups can be mapped or charted as facies units.

Dendrograms (graphic representations of the output of cluster analysis) of two hypothetical cases illustrate and provide a rough test of the method.

Quantitative data collected from modern Bahamian carbonates (Purdy, 1960) provide a further test of the method. Formerly these samples had been grouped by a numerical technique into five facies on the basis of accurately determined quantitative variables; these groups were extensively studied and shown to be geologically significant (Purdy, 1963a, b). In the present test, each quantitative variable is divided into the coarse categories, `abundant,'`present' and `not present.' Cluster analysis using these data produces 5 groups of samples that correspond closely (86 percent) with Purdy's original facies. Anomalous samples are either close to mapped facies boundaries, or marginal in composition between two of the five groups, and do not materially affect the final map.