Conductivity and scattering Q in GPR data: Example from the Ellenburger dolomite, central Texas

Abstract

Total attenuation ([Formula: see text]) in ground-penetrating radar (GPR) data is a composite of intrinsic and scattering attenuations ([Formula: see text] and [Formula: see text]). For nonmagnetic materials, [Formula: see text] is a combination of the effects of real conductivity and dielectric relaxation. The attenuation for real conductivity [Formula: see text] in the GPR frequency band is a function of frequency while the dielectric relaxation is frequency-independent. These frequency behaviors allow separation of the attenuation types by attributing and fitting the [Formula: see text] decay shape with frequency to the conductivity, and by attributing the magnitude of [Formula: see text] to the sum of conductivity and dielectric relaxation attenuations at each frequency. Total attenuation is calculated from GPR data using spectral ratios, and [Formula: see text] is obtained by fitting a smooth lower bound to [Formula: see text]; the difference between [Formula: see text] and [Formula: see text] estimates the scattering contribution [Formula: see text]. Scatterer size spectra are evaluated using [Formula: see text] for 2D, and [Formula: see text] for 3D, propagation (where [Formula: see text] is wavenumber and [Formula: see text] is the scatterer size). We illustrate with 2D synthetic data and three field 2D crosshole profiles from an outcrop of an Ellenburger collapsed paleocave environment in central Texas. Between the three pairs of holes, we estimate the breccia sizes from the scattering spectra [Formula: see text]. To image the anisotropic electrical conductivity distributions, we use simultaneous iterative reconstruction tomography. There is a correlation between the low wavenumber features of the results of the current conductivity tomography and those in previous velocity tomography, and with surface data results that are predicted and calculated from GPR data attributes. Low- and high-conductivity zones tend to follow either the GPR facies distributions, lithological boundaries, or the larger of the fractures. Correlations are not visible where the breccias are finer because these tend to be more randomly oriented, and/or below the resolution of the GPR data.