Direct method for determining constant corrections to geophysical survey lines for reducing mis‐ties

Abstract

A least‐squares method of minimizing mis‐ties in geophysical surveys yields a simple, direct method for determining constant corrections along each crossing survey line. This “direct method” is a special case of the more general, orthogonal polynomial method of Foster et al. (1970). The constant corrections are determined directly from the observed data, eliminating the need to iterate or invert a matrix to determine the corrections as in previously published, constant‐correction algorithms. The magnitude of the constant correction to the field values along a particular line equals the difference between the mean mis‐tie value for that line and one‐half the mean mis‐tie for the entire survey. The method minimizes both the mis‐ties and the distortion of the original survey; namely, the mean squared mis‐tie for the entire survey and the mean squared corrections are both minimized. Application of the direct method to test cases in which known errors are added to known “true” field values along survey lines in an (x, y) plane indicates that (1) the mis‐ties are completely eliminated if their functional form contains only terms which are functions of either x or y, regardless of the functional form of the errors themselves, (2) the method preserves both the relative field values along the survey lines and the original mean error of the survey, (3) the corrections are independent of the true field, (4) errors common to both intersecting lines will remain in the final map, and (5) the resulting corrected field is not necessarily a more accurate representation of the “true” field even when the mis‐ties are completely eliminated.