GPR Fundamental equations used and its
relation to physics
Pulse-mode GPR systems radiate short
pulses of high frequency (200 MHz) electromagnetic energy into the ground from
the transmitting antenna. The propagation of the radar signal depends on the electrical
properties of the ground. Electrical conductivity of the soil or rock materials
along the propagation paths primarily, dependents on the moisture content and
mineralization present on the subsurface. The radiated energy with an amplitude
A goes trough the ground and enconters
the dielectric constant (ε) , part of the incident energy with an
amplitude AR is reflected back to the radar antenna(Olhoeft 1992). The
dielectric constant is a property of certain materials. It is used to calculate
velocity of the signals send to the ground. Reflected signals are amplified,
transformed to the audio-frequency range, recorded, processed and displayed.
From the recorded display, subsurface features such as soil/soil, soil/rock and
unsaturated/saturated interfaces can be identified (Samsudin, 2008).
Basic setup of the SIRveyor with one channel receiver
(Huang, 2009)
1)
Radar velocity equation:
v = c / q(μεr) ~ c / qεr =
0.3/ qεr , in m/nsec
Where
C: 3x108 m/s;
μ: relative magnetic permeability
(~1.0 for most rock)
2)
Dielectric constant equation
Topp’s equation
εr
= 3.03 + 9.3θ + 146.0θ2 − 76.7θ3
&
α
= 1.69 σ/ qεr
where θ: volumetric water content of
soil
α: attenuation, db/m
σ: electric conductivity, mS
The
value ϴ was obtained from the laboratory data after testing samples
collected at the site see table 2.2 for the ϴ value to be used to
calculate our dielectric constant. Table 4.1 summarizes the dielectric and
velocities of certain material. This table was used to approximate the
dielectric value that we used by the time we setup the data collection
parameters in the computer before performing the test.
EM properties of some materials (Huang,
2009)
3)
Thickness of the layer equation:
Z = Vt/2 V= velocity t =
Time