ωκε ωκε 5.11 Ground Penetrating Radar (GPR)

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Derrick Briggs
5 years ago
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1 5. Ground Penetrating Radar (GPR) The plane wave solutions we have studied so far have been valid for frequencies and conductivities such that the conduction currents dominate the displacement currents ( > ε). If the displacement currents dominate it would seem that the propagation constant µ µε i =, would simply become pure real and equal to µε. However, we now that there will still be attenuation because there still is conduction current and so there will be energy loss. There must therefore be an imaginary component of. Doing the algebra carefully we find: R = κε µκε and I = κε µκε Now, when κε >> the phase velocity, / R, is essentially independent of conductivity and depends only on µ and ε.

2 In free space when is zero, the phase velocity, V ph, becomes / µ ε, which is the velocity of light, c, (c = 3x 8 m/sec). In a non-magnetic material the velocity varies as / κ. The wavelength for such a propagating field is, V ph /f. The attenuation term, the imaginary part of the propagation constant, is found to be independent of frequency, and strongly dependant on conductivity. From the above expression we find: I µ µ = = 377 ε κ ε κ In terms of sin-depth we find that: κ δ = 377 The following table summarizes the useful range of radar penetration depths for typical values of ground conductivity and dielectric constant. κ m.7 m.7 m.7 m 3.46 m.46 m.46 m 4.6 m.84 m.84 m.84 m 8.4 m 3.45 m.45 m.45 m 4.5 m 8.37 m.37 m.37 m 3.7 m

3 In practice, modern radar can detect objects at a depth of about 4 sin depths. Peter Annan has a practical rule for the depth of detection: D max = 35/ (ms/m) Thus in Ohm m ground the maximum detection depth is about 3.5 m when the sin depth is.84 m. Field radar system In ground penetrating radar a pulse of current in an antenna produces an electric field and associated magnetic field which propagates away from the source. The frequency is chosen so that κε >> (that maes it radar). At these frequencies the field travels radially from the source along ray paths which behave lie light rays. The amplitude decreases with distance from the source due to spherical spreading and to the attenuation due to the conductivity. If the conductivity is too high the fields may attenuate so rapidly that there is no appreciable wave field to measure after a few centimeters. The rays reflect and transmit at boundaries following Snell s Law. A practical radar system emits a pulse such as: 3

4 which is said to have a center frequency, f c, of /T. The pulse travels down into the ground, reflects off a buried layer or object (if there is a velocity (κ) contrast) and comes bac to be detected at the receiver antenna which is either co-located with the transmitter (monostatic system) or located a short distance away (bistatic system). The total travel time for the pulse is: t = L h Vph If the travel time is measured for several offsets, L, both the velocity and depth can be recovered. In many applications it is assumed that the velocity is constant and profiles of monostatic travel times are plotted which reveal a time section rather than a depth section. The performance of a GPR system is expressed by its dynamic range the range between the smallest signal it can detect and the direct signal it has to accommodate when the transmitter fires. 4

5 The role of the center frequency is much more subtle. We have seen that the attenuation due to conductivity is independent of frequency. However another effective attenuation is caused by the scattering of the wave field by inhomogeneities in the ground (rocs, cobbles, pebbles etc). This generally leads to increased attenuation with frequency. The remaining factor is resolution, usually expressed as the minimum separation of two point scatterers or diffractors that can be resolved with a given wave length of field. The usual standard is that the resolution is λ/4. In a ground of κ = 3 this translates to resolutions of:.4 m at 3 MHz.43 m at MHz.4 m at 3 MHz.43 m at. GHz Obviously one would lie to have the highest resolution but practically the high frequencies may have a high scattering attenuation and no useful penetration. 5

7. Consider the following common offset gather collected with GPR.

7. Consider the following common offset gather collected with GPR. Questions: GPR 1. Which of the following statements is incorrect when considering skin depth in GPR a. Skin depth is the distance at which the signal amplitude has decreased by a factor of 1/e b. Skin