Modelos de Q constante podem reproduzir a dispersão dependente da frequência dos sinais de GPR em rochas sedimentares

Abstract

We measured the complex dielectric constants of sandstone and carbonate samples from the Rio do Peixe and Potiguar basins, respectively presenting deformation bands and karstification features. The measurements were modeled using the Jonscher power-law model, which is able to represent the frequency-dependent behavior of these samples. We investigate the applicability of constant-Q models to describe the dispersion of Ground Penetrating Radar (GPR) signals in sedimentary rocks. GPR data is often affected by signal dispersion, which can make difficult the interpretation of events in GPR sections, especially in complex sedimentary environments. We then estimated an equivalent constant quality factor (Q) model, under the criterion of matching the frequency centroid shift of the GPR signal, using a line search approach. Equivalent Q estimates are possible to obtain using our approach, but they depend on the chosen propagation distances when the distances are small. Additionally, we obtain an analytical upper bound for the propagation distance that produces small phase shifts as a function of the Jonscher model parameters and the wavelength.