Geology Reference
In-Depth Information
Figure 10.3
'Typical' nomogram relating radar range to attenuation con-
stant for various fixed values of system gain and spreading and attenuation
losses.
formidable than it really is, arises simply from the use of decibels. The factor
log
10
[
λ
2
/
4
π
] is often included in the system parameters but the quantity
remaining then has dimensions and care must be taken in choosing units.
For specular reflection from, respectively, a smooth plane and a rough
surface, the shape factors are equal to
π
r
2
(RC)
2
and
πλ
r
(RC)
2
,whereRC
is the reflection coefficient. The range equations become:
=−
10 log
10
[(RC)
2
2
e
−
4
ar
/
16
π
r
2
]and
F
λ
10 log
10
[(RC)
2
3
e
−
4
ar
r
3
]
F
=−
λ
/
32
π
Neither can be solved directly for the range, which appears in both the
exponent and the divisor. Computers can obtain numerical solutions but
graphs provide another practical way of dealing with the problem (Fig-
ure 10.3). A rough rule that is sometimes applied where conductivity and/or
attenuation are known is that the maximum depth of investigation will
be somewhat less than 30 divided by the attenuation or 35 divided by
the conductivity. The range equation usually provides a rather optimistic
prediction of how a radar system will perform.
Noise in GPR work is caused by unwanted signal from various sources
internal and external to the system. The ratio of the power received by an
antenna to the power of the noise defines the signal to noise ratio (SNR).
