THE FOURIER SERIES MODEL IN MAP ANALYSIS.
NORTHWESTERN UNIV EVANSTON ILL DEPT OF GEOLOGY
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During the past several years the double Fourier Series has been applied to the analysis of contour-type maps as an alternative to the more commonly used polynomial model. The double Fourier Series has high potential in the study of areal variations, inasmuch as a succession of trend maps based on decreasing wavelengths of the harmonic function can readily be prepared. Such maps are useful in distinguishing broad-scale regional effects from smaller-scale local fluctuations superimposed on the larger-scale trends. This report reviews some aspects of Fourier analysis, and shows the relation of the Fourier model to the general linear model in terms of the coefficient array and the sq Z array that expresses the variance contributions of the individual coefficients. The analogy between trend analysis and analysis of variance designs nested models and rowcolumn models is pointed out, and it is shown that the double Fourier Series can be used to summarize the directional properties of areally-distributed data. An Appendix lists computer programs for double Fourier analysis of gridded map data, and for continuous symbol maps of double Fourier trends and residuals. Author
- Cartography and Aerial Photography
- Numerical Mathematics