Chap. 7] GRAVITATIONAL METHODS 137 



The sign of the correction is positive; the effect of the latitude term is 

 very small. In gravimeter surveys requiring an accuracy of ±0.1 milligal, 

 elevations must be determined with an accuracy of one foot, and free-air 

 and Bouguer corrections are usually combined (see eq. [7-376]). 



2. Bouguer' s reduction is concerned with the effect of the rocks between 

 station level and sea level not included in the free-air reduction. It lessens 

 the amount of the free-air correction and is calculated from the attraction 

 of an infinite horizontal plate between station and sea level since the topo- 

 graphic correction (see paragraph 3) "fills up" all mass deficiencies to 

 station level. The attraction of an infinite plate of thickness h and 

 density 5 is Ag = 2T-k-8-h (see eq. [7-40]). Since g is approximately 

 equal to' kM/R^ = ikirRSm, (M = earth's mass; 8m = mean density), 

 k = Zg/AirRbm. Thus, 



^^ = 9 ^~ • p • ^- (7-37o) 



Therefore, Bouguer's reduction, combined with the free-air reduction, is 



g'^ = g + H^eter. (0.0003086 - 0.00004215) gals. (7-376) 



The last coefficient in this equation is also used in the form 0.0128-5 milli- 

 gals per foot. 



It follows from eq. (7-376) that in Bouguer's reduction the attraction 

 of a plate of 10 m thickness and 2.4 density corresponds to a gravity 

 anomaly of about 1 milligal. Therefore, in the combined free-air and 

 Bouguer's reductions, a difference in elevation of 1 m (for a density of 

 2.5) corresponds to a gravity anomaly of about 0.20 milligal. With the 

 density variations encountered in practice, the correction varies between 

 0.06 to 0.08 milligal per foot. Surface densities are usually determined 

 by trial and error as discussed on page 71. 



3. Terrain correction is of appreciable value only in very hilly country. 

 It may be computed from elevations obtained by leveling around the sta- 

 tion and from contour maps. The surrounding terrain is divided into 

 sectors bounded by radial lines from and concentric circles about the 

 station. The effect of a sector with the notation employed in Fig. 7-37 is 



Agsector = k.8.<p(ri + Vrl + h' - Vr\ + h' - r,). (7-38a) 



The derivation of this relation is given in the next section on interpreta- 

 tion of gravity anomalies. By selecting zones of suitable radii and divid- 

 ing them into a predetermined number of compartments, eq. (7-38a) 

 may be solved for h. Thus, the attraction of each compartment may be 

 determined for unit elevation. A chart and tables for twelve zones ranging 



