Gravity reduction - Physical Geodesy - page 135

dividing the terrain by means of a template. Note the difference between
A T , the attraction of the topographic masses, and the terrain correction A t !
Then

= ∆ A,

A T (3-37)

where we now have b = H , c = H P . Use (3-13) with b = H P for the

innermost circle.
Instead of (3-35), we now have

g B = g − A T + F. (3-38)

The Bouguer reduction may be still further refined by the consider-
ation of density anomalies, anomalies in the free-air gradient of gravity
(Sect. 2.20), and spherical effects. More computational formulas may be
found in Jung (1961: Sect. 6.4).

3.5 Poincare and Prey reduction

Suppose we need the gravity g inside the earth. Since g cannot be measured,
it must be computed from the surface gravity. This is done by reducing the
measured values of gravity according to the method of Poincar´eandPrey.
We denote the point at which g is to be computed by Q ,sothat g = g Q .
Let P be the corresponding surface point so that P and Q are situated on
the same plumb line (Fig. 3.8). Gravity at P , denoted by g P ,ismeasured.
The direct way of computing g Q would be to use the formula

P

∂g
∂H dH ,

g Q = g P − (3-39)

Q

plumb line

P

Q

H= P

earth's surface

z= Q

geoid
W= 0

P 0

Fig. 3.8. Prey reduction