Gravity surveying - An Introduction to Geophysical Exploration - page 125

6

Gravity surveying

where G is the Gravitational Constant (6.67 ¥ 10 -11
m 3 kg -1 s -2 ).
Consider the gravitational attraction of a spherical,
non-rotating, homogeneous Earth of mass M and radius
R on a small mass m on its surface. It is relatively simple to
show that the mass of a sphere acts as though it were con-
centrated at the centre of the sphere and by substitution
in equation (6.1)

6.1 Introduction

In gravity surveying, subsurface geology is investigated
on the basis of variations in the Earth's gravitational field
arising from differences of density between subsurface
rocks. An underlying concept is the idea of a causative
body , which is a rock unit of different density from its sur-
roundings.A causative body represents a subsurface zone
of anomalous mass and causes a localized perturbation in
the gravitational field known as a gravity anomaly.A very
wide range of geological situations give rise to zones of
anomalous mass that produce significant gravity anoma-
lies. On a small scale, buried relief on a bedrock surface,
such as a buried valley, can give rise to measurable anom-
alies. On a larger scale, small negative anomalies are asso-
ciated with salt domes, as discussed in Chapter 1. On a
larger scale still, major gravity anomalies are generated
by granite plutons or sedimentary basins. Interpreta-
tion of gravity anomalies allows an assessment to be
made of the probable depth and shape of the causative
body.
The ability to carry out gravity surveys in marine areas
or, to a lesser extent, from the air extends the scope of the
method so that the technique may be employed in most
areas of the world.

GM
R

F = mmg = (6.2)

2

Force is related to mass by an acceleration and the
term g = GM / R 2 is known as the gravitational accelera-
tion or, simply, gravity . The weight of the mass is given
by mg.
On such an Earth, gravity would be constant. How-
ever, the Earth's ellipsoidal shape, rotation, irregular sur-
face relief and internal mass distribution cause gravity to
vary over its surface.
The gravitational field is most usefully defined in
terms of the gravitational potential U :

GM
r

U = (6.3)

Whereas the gravitational acceleration g is a vector quan-
tity, having both magnitude and direction (vertically
downwards), the gravitational potential U is a scalar, hav-
ing magnitude only. The first derivative of U in any di-
rection gives the component of gravity in that direction.
Consequently, a potential field approach provides com-
putational flexibility. Equipotential surfaces can be
defined on which U is constant.The sea-level surface, or
geoid , is the most easily recognized equipotential surface,
which is everywhere horizontal, that is, at right angles to
the direction of gravity.

6.2 Basic theory
The basis of the gravity survey method is Newton's Law
of Gravitation, which states that the force of attraction F
between two masses m 1 and m 2 , whose dimensions are
small with respect to the distance r between them, is
given by

Gm m
r

12
2

F = (6.1)