Geology Reference
In-Depth Information
10.1.4 Decibels
The performance of a radar system is often described in terms of processes
involving amplifications and attenuations ( gains and losses ) measured in
decibels (dB). If the power input to a system is I and the power output
is J , then the gain, in dB, is equal to 10.log 10 ( J / I ). A gain of 10 dB thus
corresponds to a ten-fold, and a 20 dB gain to a hundred-fold, increase in
signal power. Negative values indicate losses. The logarithmic unit allows
the effect of passing a signal through a number of stages to be obtained by
straightforward addition of the gains at each stage.
Log 10 2 is equal to 0.301, and doubling the power is thus almost equivalent
to a gain of 3 dB. This convenient approximation is so widely quoted that it
sometimes seems to have become the (apparently totally arbitrary) definition
of the decibel. Almost equally confusing is the popular use of decibels to
measure absolute levels of sound. This conceals a seldom stated threshold
(dB = 0) of 10 12 Wm 2 , the commonly accepted minimum level of sound
perceptible to the human ear. This acoustic decibel is, of course, irrelevant
in radar work.
10.1.5 The radar range equation
Predicting, without an on-site test survey, whether useful results are likely
to be obtained is probably no more difficult with GPR than with any other
geophysical method (which means that it is very difficult) but, because the
method is relatively new, the principles are less widely understood. The
constraints can be divided into those related to instrument performance and
those dependent on site conditions.
Instrument performance is dominated by the ratio between the power
supplied by the transmitter and the minimum level of signal resolvable by
the receiver. The signal loss during transmission through the ground, which
is governed by the attenuation constant, is the most important factor but
losses in the cables or optical fibres linking transmitters and receivers to their
respective aerials, and due to the directional characteristics of the aerials,
are significant. These are entered separately into the equations because they
depend on the frequencies and aerials used, which can be changed in virtually
all GPR units. If the sum, in dB, of all the instrumental factors is equal to
F , then the radar range equation can be written as:
2 e 4 ar
2 r 4 ]
F =− 10 · log 10 [ A λ
/ 16 π
where λ is the radar wavelength, a is the attenuation constant, A is a shape
factor, with the dimensions of area, that characterises the target, and r
is the range , i.e. the theoretical maximum depth at which the target can
be detected. The logarithmic form, which makes the equation appear more
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