Chap. 7] GRAVITATIONAL METHODS 253 



Contrary to semiquantitative analysis, quantitative analysis requires 

 an evaluation of the anomalies by calculation in each particular case. The 

 approach may be direct or indirect. The direct methods are applicable 

 only where one geologic feature exists, where the geologic situation is 

 simple, and where the geologic features have or approach the shape of 

 simple geometric bodies. Direct methods make use of the magnitude of 

 the anomalies in gradients, curvatures, and relative gravity at the points 

 of symmetry or maximum anomaly; or they utilize the abscissas of zero, 

 maximum, minimum, or half-value anomalies to calculate depth, dimen- 

 sions, and disposition of geologic bodies. The application of direct 

 methods of interpretation is confined largely to mining problems and to 

 ore bodies of simple character. Its application in oil exploration problems 

 is the exception rather than the rule. 



Indirect interpretation methods are applicable in all interpretation 

 problems. Their principle is as follows: From the results of qualitative 

 and semiquantitative analysis the assumption is made that a gravitating 

 body has a definite shape, depth, and density. The anomalies of this body 

 are then calculated and the results of such calculations are compared with 

 the field data. The assumed body is then changed with regard to its 

 different parameters until a reasonable agreement between field data and 

 calculated anomalies is secured. This is a trial-and-error method, and 

 fairly laborious; however, it has been very successful when applied with 

 patience and supplemented by geologic data. It is the only interpreta- 

 tion method that can be used when a number of geologic bodies or forma- 

 tions are effective. It is superior to qualitative analysis where sufficient 

 geologic or geophysical information is available to limit the number of 

 possible combinations of bodies capable of producing a given anomaly. 



In all semiquantitative and quantitative torsion balance interpretation 

 methods, it is necessary to know what type anomalies are produced by 

 geologic bodies of a given shape, density, and depth. They may be cal- 

 culated (1) analytically, (2) graphically, or (3) by integration machines. 

 Regardless of calculation method, the fundamental relations are the same 

 in all methods, but they differ depending upon whether they apply to two- 

 or three-dimensional bodies and are derived from the expressions for the 

 Newtonian and logarithmic gravity potentials given in eqs. (7-396) and 

 (7-39e). It was shown before that gravity was obtained from these po- 

 tentials by differentiation with respect to z. Likewise, the horizontal 

 gravity component would be obtainable by differentiation with respect to 

 X, Therefore, the gravity gradients and curvature values follow by dif- 

 ferentiation with respect to x and y, respectively, of the vertical (eqs. 



