Chap. 7] GRAVITATIONAL METHODS 213 



The planetary variation of the curvature value is shown in Fig. 7-73a. 

 Uxy is zero, since X was assumed to be zero. The maximum value of 

 (t^A)norm. occurs at the equator; it is zero at both poles. 



2. Terrain corrections. Since the torsion balance is a very sensitive 

 instrument for the detection of certain types of subsurface mass irregulari- 

 ties, it is readily understood why it also reacts very perceptibly to the 

 visible, that is, topographic masses around it. As it measures variations in 

 gravity components rather than gravity itself, it is seen that it must be 

 more sensitive to terrain variations than is the pendulum or the gravi- 

 meter. Finally, the variations of the horizontal gravity components 

 (curvature values) are much more affected by terrain than are the varia- 

 tions of the vertical components (gradients). 



In order to correct for terrain effects, it is necessary to know the shape of 

 the topography surrounding the instrument. This is done for close 

 distances (up to about 200 or 300 feet) by leveling. For greater distances, 

 existing contour maps may be used with sufficient accuracy. It is cus- 

 tomary to refer to the correction for the short distances as terrain or topo- 

 graphic correction and to the correction for the greater distances as carto- 

 graphic correction. 



It is obviously impossible to survey in detail all the small terrain irregu- 

 larities around the instrument. As will be shown below, any method of 

 terrain correction can do no more than substitute a more or less idealized 

 surface for the actual terrain surface. Hence, the field survey need not 

 be carried beyond the limits of accuracy inherent to the mathematical 

 representation of terrain eflFects. The principal requirement is that the 

 calculation of the terrain effects be within the limits of error with which 

 gradients and curvature values can be read on the instrument and inter- 

 preted. Terrain effects are therefore calculated in flat country (oil explora- 

 tion) with a probable error of several tenths to one E.U., while in hilly 

 country (mining applications) the probable error is several to 5 or even 

 10 E.U. In any event, there is no need for carrying the accuracy of terrain 

 surveys to extremes, since most analytical terrain methods are based on 

 the assumption of uniform densities. This assumption is not always 

 correct for the surface' layer, to say nothing of the effect of a denser medium 

 beneath the weathered layer. 



Experience has shown that it is generally sufficient to smooth out the 

 ground immediately adjacent to the instrument (out to 1.5 m radius) as 

 much as possible and to measure elevations in eight azimuths from the 

 setup, along circles whose radii depend on terrain and correction method 

 used. In most terrain methods the radii are fixed ; and, in very unfavorable 

 terrain, elevations are determined in sixteen instead of eight azimuths. 



Terrain correction procedures may be divided into (a) analytical, (6) 



