In the early 1990s, it was established empirically that, in many materials, ground-penetrating radar (GPR) attenuation is approximately linear with frequency over the bandwidth of a typical pulse. Further, a frequency-independent Q* parameter characterizes the slope of the band-limited attenuation versus frequency curve. Here, I derive the band-limited Q* function from a first-order Taylor expansion of the attenuation coefficient. This approach provides a basis for computing Q* from any arbitrary dielectric permittivity model. For Cole-Cole relaxation, I find good correlation between the first-order Q* approximation and Q* computed from linear fits to the attenuation coefficient curve over two-octave bands. The correlation holds over the primary relaxation frequency. For some materials, this relaxation occurs between 10 and 200 MHz, a typical frequency range for many GPR applications. Frequency-dependent losses caused by scattering and by the commonly overlooked problem of frequency-dependent reflection make it difficult or impossible to measure Q* from reflection data without a priori understanding of the materials. Despite these complications, frequency-dependent attenuation analysis of reflection data can provide valuable subsurface information. At two field sites, I find well-defined frequency-dependent attenuation anomalies associated with nonaqueous-phase liquid contaminants.
Bradford, John H.. (2007). "Frequency-Dependent Attenuation Analysis of Ground-Penetrating Radar Data". Geophysics, 72(3), . http://dx.doi.org/10.1190/1.2710183