The problem is to analyze mapped data into components which may be termed "trend" and "residual." The approach used is polynomial fitting by least squares, following the method of DeLury when the data are evenly distributed (or sampled), and of Kendall when they are not. The DeLury method, however, is extended somewhat in scope to include missing values. A number of statistical tests are discussed which should assist in determining the optimum amount of complexity to ascribe to "trend." The attitude taken throughout this paper is unbiased in the sense that positive and negative residuals are held a priori to be equally likely. An example is given of the regional correction of a gravity survey designed to explore for sulfides near Val d'Or, Quebec. In conclusion, a brief discussion is given of the advantages of polynomial fitting over smoothing and "gridding" methods from the point of view of labor and costs.