<p> The theory of canonical correlation analysis has been combined with that of trend surface analysis in order to construct a multivariate trend surface which is called a canonical trend surface. </p> <p> A canonical trend surface is a parsimonious summarization of areal variations of a set of geological 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 the variation of a linear combination of the 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. By use of this type of trend it is possible to reveal the underlying pattern of geographic variation common to a set of variates. </p> <p> Other applications of canonical correlation analysis in geology have been explained with illustrative geological examples, namely: the relationships between two sets of variates, matching two factor patterns, Q-technique canonical correlation, and discriminatory analysis. </p> <p> Comparison of canonical correlation analysis and principal factor solution in factor analysis suggests that factor analysis may be more appropriate for suggesting interrelationships among variables, while canonical correlation analysis may be a suitable tool for prediction problems. </p> <p> FORTRAN IV programs for these computations are listed in appendices with instructions for using them. </p> / Thesis / Doctor of Philosophy (PhD)