Variations in Gravity Due to Excess Mass
The free-air correction accounts for elevation differences between observation locations. Although observation locations may have differing elevations, these differences usually result from topographic changes along the earth's surface. Thus, unlike the motivation given for deriving the elevation correction, the reason the elevations of the observation points differ is because additional mass has been placed underneath the gravimeter in the form of topography. Therefore, in addition to the gravity readings differing at two stations because of elevation differences, the readings will also contain a difference because there is more mass below the reading taken at a higher elevation than there is of one taken at a lower elevation.
As a first-order correction for this additional mass, we will assume that the excess mass underneath the observation point at higher elevation, point B in the figure below, can be approximated by a slab of uniform density and thickness. Obviously, this description does not accurately describe the nature of the mass below point B. The topography is not of uniform thickness around point B and the density of the rocks probably varies with location. At this stage, however, we are only attempting to make a first-order correction. More detailed corrections will be considered next.