MINIMUM VARIANCE IN GRAVITY ANALYSIS PART II: TWO‐DIMENSIONAL

Abstract

The principles developed in Part 1 apply whether the data points are located on a line or distributed over a plane. The practical calculation problem, however, is more complicated in two dimensions than in one. There are two steps: (1) deciding what terms to keep in the polynomial approximation; (2) estimating second vertical derivatives and the like on the basis of the chosen approximation. For (1) we can use two‐dimensional orthogonal polynomials; but complete tables of them would be bulky, and therefore several alternative procedures are outlined. For (2) we can easily derive “best” estimation formulas by the minimum‐variance method; but these usually involve many‐digit multipliers, and therefore “near‐best” coefficients, with fewer digits, are also derived. The specific problems solved here start with uncorrelated data at points of a square grid. In practice, data are taken at irregularly distributed stations: then the minimum‐variance principle and orthogonalization still apply, but the calculations are more complex, and grid values computed from the station values are correlated.