GRAVITY METHOD - Field Geophysics - page 50

the Earth's centre of mass and the effect is therefore negative (i.e. the free-
air correction is positive) for stations above sea level. It varies slightly with
latitude and elevation, according to the equation:

δ g = (0 . 308 769 1 − 0 . 000 439 8 sin 2 λ )h + 0 . 000 000 072 125 h 2 mGal

An average value of 0.3086 mGal m − 1 is often used, regardless of latitude.
The quantity obtained after applying both the latitude and free-air corrections
is termed the free-air anomaly or free-air gravity .

2.3.3 Bouguer correction
Since topographic masses are irregularly distributed, their effects are difficult
to calculate precisely and approximation is necessary. The simplest approach
assumes that topography can be represented by a flat plate, with constant
density and thickness equal to the height of the gravity station above the
reference surface, extending to infinity in all directions. This Bouguer plate
produces a gravity field equal to 2 πρ Gh ,where h is the plate thickness and
ρ the density. The correction is equal to 0.1119 mGal m − 1

at the standard

2.67 Mg m − 3 density.
The Bouguer effect is positive and the correction is therefore negative.
Since it is only about one-third of the free-air correction, the net effect of an
increase in height is a reduction in field. The combined correction is positive
and equal to about 0.2 mGal m − 1 , so elevations must be known to 0.5 cm to
make full use of the microGal sensitivity of the CG-5 gravity meter.
Because Bouguer corrections depend on assumed densities as well as
measured heights, they are fundamentally different from free-air corrections,
and combining the two into unified elevation corrections can be misleading.
It is also sometimes stated that the combined corrections reduce gravity
values to those that would have been obtained had the readings been made
on the reference surface, with all the topography removed. This is not true. In
Figure 2.5, the effect of the mass 'M' recorded at the observation point P is
not altered by these corrections. It remains the effect of a body a distance 1.5 h
below P, not a distance 0.5 h below P . Still more obviously, the corrections
do not eliminate the effect of the mass 'm', which is above the reference
surface, since the Bouguer correction assumes constant density. Bouguer
gravity is determined at the points where measurements are made, and this
fact must be taken into account during interpretation.

2.3.4 Terrain corrections
In areas of high relief, detailed topographic corrections must be made.
Although it would be possible to correct directly for the entire topography
above the reference surface in one pass without first making the Bouguer