Incorporando atenuação na modelagem de GPR no domínio do tempo através do modelo de Q constante, usando múltiplos polos de Debye: teoria e aplicação em rochas carbonáticas carstificadas

Abstract

Dispersion and absorption are important effects contributing to attenuate real GPR (Ground Penetrating Radar) signals and must be incorporated in wave propagation. The constant-Q model (Quality Factor Q) is valid for most rocks for typical GPR frequency ranges. In time-domain wave modeling, to simulate a constant-Q model, using a superposition of multiple Debye poles, the number of poles and their parameters must be previously specified, given target values for Q and velocity and the useful frequency band of the wavelet. For electromagnetic (and also viscoelastic) waves, this problem is usually formulated as a highly nonlinear optimization problem presenting several solutions, which is solved using global optimization methods. An efficient linear approach to estimate multiple Debye poles to simulate constant-Q models in GPR data is presented. The resulting inverse problem is easy to solve because the number of demanded poles is quite small. For the usual GPR frequency bands, just two or three poles are necessary. The gain in efficiency is particularly high because the approach allows to obtain a rescaled solution that depends just on the frequency band and number of poles. Specific solutions satisfying target values for velocity and Q are obtained from the rescaled solution. Choosing the number of poles is tentatively done so that both velocity and Q curves, as function of frequency, are approximately constant in the specified frequency band. To minimize computational costs in time-domain modeling, as few poles as possible should be used. The importance of introducing attenuation effects is exemplified by presenting a trial-and-error modeling approach to reproduce, as close as possible, a 200 MHz field GPR section acquired in fractured and karstified carbonate rocks.