Abstract

The maximum gradient which can be caused by a simple mass is that of a spherical body. The equation for the vertical gradient at the point P above the center of a spherical mass of density contrast σ (see insert on Figure 1) can be written in the form  
gh=(8/3)πGσ/(1+h/R)3,
where G is the universal gravity constant 6.672×10−8cgs. Expressing the gradient in the E”tv”s units, we have  
gh=559σ/(1+h/R)3E
In terms of percentage of the earth's normal vertical gradient, the anomaly is  
gh=18.11σ/(1+h/R)3%of 3086 E.
At the surface of the sphere (h = 0), we have the maximum value  
gh=18.11σ%of 3086E
which is independent of the radius R.
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