Subsurface Methods as Applied in Geophysics 1065 



lying rocks, it becomes necessary to remove from the observed gravity all 

 influencing factors except those due to density irregularities. 



Variation of Gravity with Latitude — If the earth were not rotating 

 about its axis, it is quite possible that we would be living on a perfect 

 sphere. However, owing to this rotation, centrifugal force has increased 

 the equatorial radius some thirteen miles over the polar radius, thus 

 forming an oblate spheroid. The acceleration of gravity at the equator 

 is about five gals less than at the poles because (1) centrifugal force, 

 which acts to oppose the gravitational force, is a maximum at the equator, 

 and (2) the earth's surface at the equator is about thirteen miles farther 

 from the center of mass than at the poles. 



Equations have been developed ^^ that indicate the normal gravita- 

 tional force at sea level as a function of latitude for a homogeneous earth. 

 Since the force of gravity varies from north to south, corrections are 

 applied to all regional gravity surveys eliminating this normal variation 

 from consideration. In the state of Oklahoma the normal increase of 

 gravity to the north is roughly 1.1 milligals per mile. 



Variation of Gravity with Elevation — An elevation correction must 

 be applied to all relative-gravity data to compensate for the normal 

 decrease in the force of gravity as the distance to the center of the earth 

 increases. As an example, if a gravity-meter observation were made 

 on the earth's surface and if another observation could be made in a 

 balloon located one hundred feet above the earth's surface, it would be 

 found that gravity had decreased by 9.4 milligals. This normal decrease 

 of gravity with increase in distance to the earth's center is known as the 

 "free-air effect." 



If we could fill in the space between the balloon and the ground 

 with a soil layer of infinite extent, we should find that our original 

 gravity difference of 9.4 milligals has diminished to about 7.0 milligals, 

 depending upon the density of the intervening soil layer. The attraction 

 of the soil layer, which opposes the decrease of gravity with altitude, is 

 known as the "Bouguer effect." The Bouguer attraction varies with the 

 density of the soil and the thickness as follows: 



Attraction in mg. = 0.01276S/i 



where h is thickness in feet and 8 is density. 



The elevation correction as ordinarily used in gravity surveys com- 

 bines both the free-air and Bouguer corrections with due regard for the 

 density of the surface rocks within the topographic extremes. The com- 

 bined correction is usually carried to a sea-level datum plane for conven- 

 ience. This correction equals (0.094 - 0.01276S) h milligals per foot and 

 has a value of 0.070 milligals per foot for a surface density of about 1.9 

 grams per cm.^ In rugged terrain where the assumption of an infinite 



" Heiland, C. A., op. cit., p. 97. 



