The theory of canonical correlation analysis has been combined with that of trend-surface analysis in order to construct a multivariate trend surface that is called a canonical trend surface. A canonical trend surface is a parsimonious summarization of areal variations of a set of geologic variates. This trend has a property of maximum correlation between variates and geographic coordinates. It does not show the absolute value of each variate, but it shows the nature of variation of a linear function of the variates. By use of this type of trend, it is possible to reveal the underlying pattern of geographic variation common to a set of variates. The Permian system in western Kansas and eastern Colorado was studied as a numerical example to illustrate the general procedures in solving practical problems and also to demonstrate the validity of this technique.
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P. J. Lee (1969) studied this question.
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