136 GRAVITATIONAL METHODS [Chap. 7 



in which the second order terms are usually neglected. The following 

 corrections are then applied: (1) free-air correction (the symbol for gravity 

 thus corrected is go) ; (2) Bougucr's reduction (the symbol for gravity thus 

 corrected is g'o); (3) terrain correction (the symbol for gravity supplied 

 with all three corrections is go); (4) isostatic correction; (5) correction for 

 normal gravity (yo)- The symbol for the fully corrected gravity anomaly 

 is Ago. Corrections (1) and (2) are generally combined; reductions (3) 

 and (4) are combined only if pendulum observations are made for the 

 purpose of geodetic investigations. In gravimeter exploration the iso- 

 static correction is generally omitted, correction (5) is applied in the form of 

 a latitude reduction, and provision is made for a base correction previously 

 discussed. 



1. The free-air reduction. In a gravity survey all stations must be re- 

 duced to sea level (or another reference level). The change of the gravity 

 with elevation may be obtained with sufficient accuracy by differentiating 

 the Clairaut equation (7-lOa) with respect to r, so that the vertical gradient 

 of gravity is 



d^ ^dg ^ _ 



32' ~ dz ^ 



2n2 



•]■ 



where R (substituted for r) is the earth's radius. From eq. (7-36a), we 

 have, with sufficient accuracy, 



dg _ 2g 



„ (1 -h 0.00071 cos 2 ^) 

 dz R 



(7-366) 



= -0.3086(1 + 0.00071 cos 2(^) milligals-m ^ 



and gravity (in gals), as reduced to sea level, is 



go = g -{- 0.0003086 (1 + 0.00071 cos 2<p) H^eters , (7-36c) 



where H is absolute elevation. Table 20 gives some values for the eleva- 

 tion correction in milligals {(p = 45°). 



Table 20^ 



ELEV.A.TION H FrEE-.\IR CORRECTION 



(Meters) (Milligals) 







100 +30.9 



200 +61.7 



300 +92.6 



400 + 123.4 



500 +154.3 



600 +185.2 



700 +216.0 



800 +246.9 



900 +277.7 



1000 +308.6 



