408 EXPLORATION GEOPHYSICS 



cylinder and in the plane through one end. This formula where Vi and r^ 

 are the inner and outer radii of the cylinder is : 



= -2^Gd \r2-n + Vi^ + h^- S/r^^ + ^' 1 



• A^ = -l-nGd r2-ri + V^i^ + h^- S/ri" + /iM (129) 



In the above, G = the gravitational constant and d = the density. 



The tables do not give the correction for zone A, the area within 6.56 

 feet (2 meters) radius around the station. This is because only exceptional 

 terrain conditions would give significant effects in this small area, or the 

 terrain could be controlled by leveling it, as in torsion balance work. In 

 practically all cases, a sufficiently level spot can be found on which to set 

 a gravimeter. A terrain effect of 0.01 mg. (for d = 2.0) within zone A 

 requires a slope of 27y2°, which establishes a practical working limit for 

 slope in locating stations in the field. 



The terrain correction supplements the Bouguer correction described 

 in the section on pendulum gravity corrections (p. 257). It has been 

 shown that the Bouguer and the elevation corrections taken together reduced 

 the gravity observations to what they would be if the gravimeter had been 

 on the datum plane established for the survey. 



The Bouguer correction intentionally treats the section of material 

 between the ground surface at the station and the datum as if it were a flat 

 circular slab of infinite radius bounded by two plane surfaces. These 

 surfaces are a horizontal plane through the station and the horizontal datum 

 plane. This assumption makes no allowance for any hills or hollows in 

 the ground and therefore, so to speak, ignores the terrain. All depressions 

 are treated as if they were filled up with material of a certain assumed 

 density and hills are not considered. This is a valid process where the 

 terrain is essentially flat. The terrain correction measures the gravity effect 

 of existing undulations of the top surface of the slab, thereby determining 

 the error inherent in the Bouguer correction and correcting for it. 



The Bouguer correction, as applied, is always too great in those cases 

 where either hills or depressions affect a gravity station. Gravimeter read- 

 ings due to the presence of a hill or a valley are less than they would be if 

 these terrain features were absent. The Bouguer correction therefore, by 

 over-correcting, gives reduced (on datum) gravity values that are too 

 small. 



This can be explained as follows. A hill adjacent to a gravity station 

 places a mass of material above the station and gives rise to a gravity 

 component opposed to the downward gravity force. This results in a 

 lower gravity value than would exist if the hill were not present, as is 

 assumed in the Bouguer correction. The actual gravity effect of the hill 

 (which tends to decrease the effective gravity) is shown by the terrain 

 tables, and hence is added to the reduced gravity value in order to correct 

 it. The Bouguer correction applied on the basis of no hill being present 

 was, obviously, an over-correction of the reading or gravity value obtained. 



