Gravity and magnetic methods - Geophysics for the Mineral Exploration Geoscientist - page 168

Horizontal layering Vertical step Sphere

a) b) c)

Relative
gravity

Relative
gravity

Relative
gravity

r r r

1 1 1

r

2

r

r

r

2

2

3

r

r

1

2

r

r

2

3

r

r

1

3

r

r 1

1

r

2

r

r 3

2

r

3

r

3

rrr >

2 > 3 1

Figure 3.68 Equivalent gravity models for
three common geological sections: (a) gravity
anomaly, (b) some possible density cross-
sections that produce the gravity anomaly,
and (c) equivalent model.

r = Background r = Background

r = Background

Z

H Point mass

geophysics. As shown in Fig. 3.68a , laterally continuous
horizontal layers do not cause relative changes in
gravity on a surface above them, so the structure of a
horizontally layered sequence cannot be determined from
measurements made from above. The response is the same
as a homogeneous half-space. This is a simpler geometrical
form and is, therefore, the equivalent gravity model.
Consider the models in Fig. 3.68b . Only lateral changes
in density will cause variation in the gravity response.
Careful examination of the models shows that in terms of
lateral density change these models are equivalent. In all
cases there is a lateral density contrast (

In these three examples the gravity response is identical
even though the subsurface density models are different. It
goes without saying that the gravity response cannot be
used to tell them apart.

3.10.6.2 Non-uniqueness
In Section 2.11.4 we described the phenomenon of non-
uniqueness in geophysical modelling, whereby many dif-
ferent physical property distributions can produce the
same geophysical response, and strategies for dealing with
it.

ρ 3 - ρ 2 ) which has a
vertical thickness H and depth to top Z.
For the case of spherical density distributions
( Fig. 3.68c ), where the mass is distributed radially and
evenly around the centre of the sphere, the gravity effect
is the same as if its mass was concentrated at a point at its
centre. The same gravity effect is obtained when the mass
is distributed homogeneously as a sphere of larger volume
and smaller density contrast, or as a spherical shell, or as a
multiple spherical density zonation. In all cases the total
excess mass (see Section 3.2.1.3 ) and depth to centre are
the same, but the densities and radii varying accordingly.
The solid homogeneous sphere, being the simplest form, is
the equivalent model for all spherical distributions.

Physical property/geometry ambiguity, as it relates to
gravity data, is illustrated in Fig. 2.49a . Here, a broad low
density feature at shallow depth produces the same gravity
response as a range of more compact bodies, of increasing
density, at progressively greater depths. They all have the
same excess mass (see Section 3.2.1.3 ) . The shallowest,
widest and least dense body, and the deepest, smallest
and most dense compact body, represent end-members
of an in nite number of solutions to the measured
response. As shown in Section 3.10.1 , amplitude increases
when the body is shallower or its density contrast
increased, whilst wavelength increases as the body is made
deeper or wider. So long as the excess mass of the solutions
is the same, the same gravity response will be obtained.