Inversion and sensitivity analysis of Ground Penetrating Radar data with waveguide dispersion using deterministic and Markov Chain Monte Carlo methods

Ground Penetrating Radar (GPR) has found widespread application for the non-invasive characterization of the subsurface. Nevertheless, the interpretation of GPR measurements remains difficult in some cases, particularly when the subsurface contains thin horizontal layers with contrasting dielectric properties that might act as waveguides for electromagnetic wave propagation. GPR data affected by waveguide dispersion are typically interpreted using the socalled dispersion curve, which describes the phase velocity as a function of frequency. These dispersion curves are commonly analyzed with deterministic optimization algorithms and which return dielectric properties of the subsurface as well as the location and depth of the respective soil layers. Unfortunately, current state-of-the-artinversion methods do not provide estimates of the associated uncertainty of the inferred subsurface properties. Here, we apply a Bayesian inversion methodology using the recently developed DiffeRential Evolution Adaptive Metropolis DREAM(ZS) algorithm. This Markov Chain Monte Carlo simulation method is admirably suited to estimate (nonlinear) parameter uncertainty and treat measurement error explicitly. Analysis of synthetic GPR data showed that the frequency range used in the inversion has an important influence on the estimated values of the parameters. This is related to the parameter sensitivity that varies with frequency. Our results also demonstrate that measurement errors of the dispersion curve are frequency dependent, and that the estimated model parameters become severely biased if this error is not properly treated. We demonstrate how frequency dependent measurement errors can be estimated jointly with the model parameters using the DREAM(ZS) algorithm. The posterior distribution of the model parameters derived this way compared well with inversion results for a reduced frequency bandwidth which is another method to reduce the bias introduce through measurement error. Altogether, the inversion procedure presented herein provides an objective methodology for analysis of dispersive GPR data, and appropriately treats measurement error and