Constant dielectric losses of ground-penetrating radar waves

The attenuation of ground-penetrating radar (GPR) energy by the subsurface shifts the amplitude spectrum of the radar pulse to lower frequencies (absorption) with increasing traveltime and also causes a distortion of wavelet phase (dispersion). Accounting for dielectric losses (or attenuation), the permittivity is, in general, a complex quantity. Absorption is introduced via the imaginary part of dielectric permittivity, while the frequency dependence of the real part introduces the dispersion. The radar attenuation is characterized by the quality factor Q, which is a measure of the energy stored to the energy lost per radian and can be estimated from the ratio of the real to imaginary parts of permittivity. In order to model for both effects of attenuation (absorption and dispersion), a complex power law of frequency for dielectric permittivity is introduced into the wavenumber. We also show that this approach corresponds to a constant-Q model, and is valid for any positive value of Q. Using this wavenumber we propagate the radar pulse to find theoretical deformed pulses transmitted at any distance. By comparing the theoretical synthetic data with the real radar transmission data, we can obtain the quality factor Q. Real radar data transmitted (and recorded) into granite and salt are shown to illustrate the reliability of the proposed method.