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size. So for very deep sources, a simple sphere, having only
depth and diameter, can be an appropriate model to use.
Philosophically it is very important to apply Occam
a)
s
razor when modelling geophysical data. The simplest pos-
sible source geometry should be used despite being some-
times criticised for being
'
Location
Least contrast
'
'
. Simple
geometry is geophysically appropriate when it conveys the
actual level of information that the data is capable of
providing.
geologically unrealistic
Greatest contrast
2.11.4
Non-uniqueness
b)
It is crucial to understand when modelling most kinds of
geophysical data that there is no single mathematical solu-
tion, i.e. no unique model, for an observed response. Many
models can be found with computed responses matching
the observed data; a particular model is not necessarily the
only possibility and not necessarily the correct one.
A geological analogy is cross-section balancing as used to
test structural interpretations. If the section does not bal-
ance, this is equivalent to the computed responses not
matching the observed data. In this case the interpretation
is de
nitely wrong. Successfully balancing the section is
equivalent to creating a geophysical model that honours
the observations. In either case, the interpretation could be
right, but is not necessarily so, i.e. it is subject to ambiguity
or non-uniqueness.
Non-uniqueness occurs because the fundamental char-
acteristics of an anomaly, i.e. amplitude and wavelength
which together control the gradients of the flanks of the
anomaly, are reproduced by different combinations of the
source
Location
Least contrast,
largest thickness
Greatest contrast,
smallest thickness
c)
Location
2
3
1
Physical-property
vector
s location, geometry/shape and its physical property
the body is shallower or its physical property contrast
increased, whilst wavelength increases as the body is made
deeper or wider. This ability to
'
d)
Location
1
2
'
trade off
'
different model
characteristics occurs in several ways:
Both body width (thickness) and depth affect the wave-
length of the geophysical response; so adjusting either
parameter allows a match to be found to the data
(
Fig. 2.49a
)
.
Apparent source
Figure 2.49
Forms of source ambiguity: (a) depth versus width/
volume. Redrawn, with permission, from Grif
For sheet-like sources, only the product of the physical
property contrast and the thickness can be resolved from
a model (
Fig. 2.49b
)
. This means that it is impossible to
resolve one parameter without knowing the other, e.g.
increasing the thickness has the same effect as increasing
the physical property contrast. This effect
(b) thickness versus property contrast, and (c) dip versus
directionally dependent physical property (such as magnetism). Note
the various drillhole lengths needed to test the various dip directions.
(d) Misinterpretation due to lack of resolution. Note how drillhole
(1) tests the modelled source but misses the actual source.
is quite
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