A CONTRIBUTION TO THE COMPUTATION OF THE “SECOND DERIVATIVE” FROM GRAVITY DATA

Abstract

The theory and practical application of the second derivative method of gravity interpretation have been discussed by Elkins (1951) in a very interesting paper based partly on an earlier paper by Peters (1949). In this paper, Elkins shows how the second derivative may be computed at the center of a series of concentric circles using the arithmetic means of the gravity values, assumed to be continuous, around each circle. A method is here proposed which does not use a continuum of gravity values but instead requires only a series development. The approximation formulas needed for the routine calculations can be derived by a method different from that of Elkins and the least squares adjustments he used can be dispensed with. Two hypothetical examples using the formulas derived by the series method are given and the results are compared with those computed by Elkins’ formula.