Constant-Q model can reproduce the frequency-dependent dispersion of GPR signals in sedimentary rocks

We measured the complex dielectric permittivities of sandstone and carbonate samples from the Rio do Peixe and Potiguar basins, respectively, in the frequency range of 50-800 MHz, which is the relevant frequency content of a Ground Penetrating Radar (GPR) signal measured with a 200 MHz antenna. The sandstone samples can be clean or affected by deformation bands, whilst the carbonate samples might be impacted by dissolution or stylolite formation processes. We show that the measured amplitude spectra of the dielectric permittivities can be fitted with the Jonscher power-law model. In addition, we investigate the reliability of the constant-Q model to reproduce the dispersion effects on a synthetic Ricker GPR signal propagated in dispersive media described by the obtained Jonscher model parameters. We show that a constant-Q model can satisfactorily describe the dispersion effect in the case the equivalent constant Q values are chosen in order to reproduce the centroid frequency shift and the time-domain shape of the pulse. As part of our approach, we show how to estimate a window of propagation distances inside which the equivalent $Q$ estimate is valid.