One of the vexing problems of geology is recognizing boundaries between facies that intergrade. For example, if a shale facies grades laterally into sandstone, where do you draw the line between the two facies? No matter where the boundary is placed, it is partly subjective and depends on what you consider to be important criteria--color, lithological proportions, thickness of beds, kinds of fossils, and so on. Factor analysis, a statistical technique, can help in determining facies boundaries by objectively establishing where major changes occur, once the criteria have been decided.

As an experiment, a thin, continuous limestone unit within the Lower Permian Americus limestone was sampled at 27 localities along a 250-mile-long outcrop belt in Kansas and Oklahoma. The problem was to interpret variations along the outcrop belt and to decide where facies changes occur. Specimens from each of the localities were point-counted and were also analyzed chemically. As a result, 14 different constituents (percentages of bryozoans, fusulinids, crinoids, shells, intraclasts, visibly crystalline calcite, microcrystalline calcite, silica, magnesia, the R₂O₃ group, manganese, titanium, strontium, and vanadium) were quantitatively determined, and permitted comparisons between each of the 27 localities in terms of each of the 14 constituents. Factor analysis brought about a great simplification by showing that two basic variables, or factors, were sufficient to mark where major changes occur and where boundaries between four different facies should be placed. Thus, 2 factors substituted for 14 constituents.

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