Considerable attention has been directed recently to applications of gravity gradients, e.g., Hammer and Anzoleaga (1975), Stanley and Green (1976), Fajklewicz (1976), Butler (1979), Hammer (1979), Ager and Liard (1982), and Butler et al. (1982). Gravity-gradient interpretive procedures are developed from properties of true or differential gradients, while gradients are determined in an interval or finite-difference sense from field gravity data. The relations of the interval gravity gradients to the true or differential gravity gradients are examined in this paper.
Figure 1 illustrates the concepts of finite-difference procedures for gravity-gradient determinations. In Figure 1a, a tower structure is illustrated schematically for determining vertical gradients. Gravity measurements are made at two or more elevations on the tower, and various finite-difference or interval values of vertical gradient can be determined. For measurements at three elevations on the tower, for example, three interval gradient determinations are possible: Δg′13/Δz13; Δg′12/Δz12; Δg′23/Δz23; where Δg′13 = gz(h1)−gz(h3) and Δz13 = h1−h3, etc. For a positive downward z-;axis, these definitions for Δg′ij and Δzij will result in positive values for the vertical gradient. Relations of the interval gradients to each other and to the true or differential gradient are examined in this paper.