Geology Reference
In-Depth Information
N
1
N - 1
x n
V =
GAUSSIAN
CURVE
n =1
where x n is the difference
between the n th sample
and the mean of
N samples
3SD
2SD
SD
Mean
SD
2SD
3SD
Figure 1.9 Gaussian distribution. The curve is symmetric, and approxi-
mately two-thirds of the area beneath it lies within one standard deviation
(SD) of the mean. V = variance.
number of values) and a variance ( V , defined in Figure 1.9) or its square
root, the standard deviation (SD). About two-thirds of the readings in a nor-
mal distribution lie within 1 SD of the mean, and less than 0.3% differ from
it by more than 3 SDs. The SD is popular with contractors when quoting
survey reliability, since a small value can efficiently conceal several major
errors. However, it is rare, in many types of geophysical survey, for enough
field data to be obtained for statistical methods to be validly applied, and
distributions are often assumed to be normal when they cannot be shown to
be so.
Gaussian and more sophisticated statistical summaries of data (both
background and target-related) are recommended for unexploded ordnance
(UXO) surveys, where confidence is essential, to quantify the detection as-
surance level (the distance from a sensor within which a target of a certain
size can be detected with 100% confidence). This measure will vary from
site to site, and within a site, depending on the variable composition of made
ground or geology, as well as on target size.
1.5.8 Anomalies
Only rarely is a single geophysical observation significant. Usually, many
readings are needed, and regional background levels must be determined,
 
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