Trend surface analysis of contour-type maps with irregular control-point spacing

Trend surface analysis is a procedure for separating the relatively large-scale systematic changes in mapped data from essentially non-systematic small-scale variations due to local effects. The method can be applied to any contour-type map, and has been used for analysis of gravity maps, isopach maps, facies maps, and maps of igneous and sedimentary rock attributes. When observations can be collected on a rectangular grid, orthogonal polynomial analysis permits convenient separation of the trend from the residuals. When observations are limited in number or are irregularly distributed over the map, non-orthogonal polynomial analysis can be used to determine at least the linear and quadratic components of the trend. These surfaces and deviations from them have value in geological interpretation, and they suggest that even when the complete trend is known, maps of selected trend components may be useful for examining special problems. Polynomial analysis of maps is facilitated by use of high speed computers. Organization of an IBM 650 program is outlined in this paper.