Q345 : Transient Behavior in High Resistivity Soils

Question
I am running a study of the transient behavior of counterpoises buried in a high resistivity soil (20 000 Ohm-m, relative permittivity = 4) using HIFREQ and FFTSES. The length of the counterpoise is 90 meters. I observe unexpectd oscillations of the GPR along the counterpoise. What is wrong?

An often used formula (which is quoted in the FFTSES User's Manual) gives the propagation wavelength in a conductive medium as a function of the resistivity of the medium and the frequency, namely:

Wavelength (in meters) = 3160 * sqrt(Resistivity / Frequency)

For a 20 000 Ohm-m soil at, say, 2 MHz, the wavelength calculated with this formula is 316 meters.

However, this formula is applicable only when the frequency is such that conduction currents dominate over capacitive currents. The precise condition is:

2 * PI * Frequency * Resistivity * Permittivity << 1

or

Frequency * Resistivity * (Relative Permittivity) * 10^-9 << 18

With a resistivity of 20 000 Ohm-m and a relative permittivity of 4, this gives

Frequency << 220 kHz

Therefore, for frequencies larger than about 50 kHz, the simple formula above can't be used. The wavelength computed using the full formula is available in the HIFREQ's F09 file (search for the string "wavelength"). At 1.46 MHz, for instance, the wavelength in the 20 000 Ohm-m soil layer reaches about 100 m, which is comparable to the size of the counterpoises. This is the reason behind the oscillations that you observed in the GPR of the counterpoises.

Moreover, the real part of the propagation constant is considerably larger than its imaginary part for those values of the frequency and soil parameters. This means that the GPR doesn't decay very fast and has to go through several oscillations before being dissipated.

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