Residual anomalies and depth estimation

The residual gravity anomaly at a point is defined as the difference between the average anomalies along two concentric circles whose center is at the point, divided by the difference between the two radii or R(g)=-g¯(r1)-g¯(r2)r1-r2. It is shown that the residual anomalies previously determined by the average circle or the average polygon method (Griffin, 1949) are included in the present definition. The second vertical derivative of g and, to some extent, the fourth vertical derivative of g (Peters, 1949) are also included. The relation between the residual anomalies and the depth of the subterranean masses is examined. It has been pointed out that the gravitational effect originating from a body with mass m is clearly apparent when the center of mass of the body has the depth z=2r=r1+r2. The influence from masses at a greater or lesser depth is almost eliminated. By avoiding the use of the center point in the figuring of the residual anomalies the influence of random errors is minimized.