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Abstract

Resolution of the ground-penetrating-radar (GPR) method largely depends on the wavelength of the propagated electromagnetic waves, the depth, and the dimensions of the investigated targets. Locating small-scale targets such as fractures can be difficult, especially when the size of the fractures themselves and the spacing between them are smaller than the wavelength of the EM waves. In such cases, fractures will not be resolved individually in the time domain. Examining the frequency (spectral) content of GPR time series might provide additional information that can improve fracture location relative to the results from conventional examination of the time series alone. The S-transform, a powerful time-frequency analysis tool, can be applied to GPR time series extracted from synthetic data over 1D and 2D models of fractured limestone as well as to a data set collected at a fractured limestone site in Egypt. In synthetic scenarios, the value of the S-transform analysis can be investigated under two conditions: (1) discrete fractures spaced at distances greater than one-quarter wavelength and (2) closely spaced fractures separated by distances less than one-quarter wavelength. The synthetic studies include analysis of the dependence of S-transform results on the dielectric properties of a fracture, by simulating both air-and water-filled fractures. Time-frequency analysis can aid in determining the location of discrete, closely spaced fractures when fractures are separated by distances greater than one-quarter wavelength. However, the clarity of fracture expressions from the S-transform depends on the dielectric contrast between the fracture and the host material, so air-filled fractures are not always identified. In the case of fractures smaller than one-quarter wavelength, boundaries where fracture spacing (density) changes abruptly do not result in diagnostic shifts in the frequency content of the S-transform along the time series. However, diagnostic frequency shifts do occur when the dielectric properties of closely spaced fractures change between air-filled and water-filled fractures, with water-filled fractures displaying a higher-frequency content. This frequency-spectrum dependence on dielectric properties of fractures can be used to infer locations of water-filled fractures. In addition, this dependence can help to locate possible localized moisture transport between fracture zones, via capillary effects, at a field site.

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