Statistical methods in physical geodesy - Physical Geodesy - page 360

% =2.2 g/cm 3

% =2.4 g/cm 3

% =2.6 g/cm 3

distance along profile

Fig. 9.5. Bouguer anomalies corresponding to different densities :the
best density is =2 . 4 g/cm 3 (no correlation); for other densities the
Bouguer anomalies are correlated with height (positive correlation for
=2 . 2 g/cm 3 , negative correlation for =2 . 6 g/cm 3 )

It may be shown that this is equivalent to the condition that the points of
Fig. 9.4 lie approximately on a straight line. The coecient b is then given
by

b =tan α (9-85)

as the inclination of the line towards the h -axis.
In practice these conditions are very often fulfilled to a good approx-
imation. Furthermore, by computing b from Eq. (9-84) or determining it
graphically by means of (9-85), we often get a value that is close to the
normal Bouguer gradient (9-81).
If we assume that b depends only on the rock density , then we obtain a
means for determining the average density, which is often dicult to measure
directly. This is the “ Nettleton method ”, used in geophysical prospecting: the
coecient b is found statistically by means of Eqs. (9-84) or (9-85), and
the rock density is then computed from (9-80). Figure 9.5 illustrates the
principle of this method; see also Jung (1956: p. 600).
If the condition (9-83) is fulfilled, then we may consider the “Bouguer
anomaly” z as a gravity anomaly that is completely uncorrelated with height;
we can directly apply to it the whole theory of the preceding sections. But
even when this condition is not quite satisfied, Bouguer anomalies will in
general be far less correlated with height than free-air anomalies. The fact
that in (9-79) gravity is reduced to a mean height and not to sea level,
is quite irrelevant in this connection because this is only a question of an