416 EXPLORATION GEOPHYSICS 



lation procedure in a gravity survey, and in itself provides a considerable 

 simplification. 



After correcting for the first five effects listed above, it is often neces- 

 sary to consider the sixth, which in many cases can be separated into two 

 parts, namely, the regional and the local or residual gravity components. In 

 exploratory geophysics we are interested primarily in the residual gravity 

 values and, to obtain a picture wherein they stand out more clearly, it is 

 necessary to remove the masking effect of the regional gravity. 



This separation is accomplished by constructing a residual gravity map, 

 showing only the gravitational field due to local structure. The residual 

 values are obtained by removing the regional gravity effects from the 

 Bouguer station values. To express this mathematically,! 



Ag = g(o)-g(r) (130) 



where Ag is the residual gravity value, 



g(o) is the station gravity value, and 



g(r) is the average gravity value for the area within a radius of r 

 from the point where the station value g(o) was obtained. 



The average gravity value may be expressed by 



gir)=-:t\ g(.r,6)d6 (131) 



ZttJ 



which may be considered as the average value obtained at a series of read- 

 ing points around a circle of radius r, with the station g{o) as its center, 

 in increments of dO. 



In general, an integrable form of g{r, 6) is not known, and a close 

 approximation may be had by obtaining the arithmetical average at a finite 

 number of stations located on the circumference of the circle. This average, 

 for a series of n points, may be expressed by the relationship! 



g(r) = [gi(r) + g2 (r) + gs(r) + . . . gn (r)]/n (132) 



The value of w may be any whole number. The resultant residual gravity 

 Ag may be positive, zero, or negative, depending upon the relative gravity 

 value of the point under study compared to the regional or background 

 value of ^(r). 



Average Value Method. — The number and position of the points on 

 a map at which gravity values are selected to find the regional, or average, 

 value to be applied at a station can be varied to suit the problem at hand. 

 These points may be chosen at an equal spacing on a circle of given radius 



t W. R. Griffin, "Residual Gravity in Theory and Practice," Geophysics, Vol. XIV, No. 1, 

 January, 1949. 



t W. R. Griffin, loc. cit. 



