Inversion and sensitivity analysis of ground penetrating radar data with waveguide dispersion using deterministic and Markov chain Monte Carlo methods

Ground-penetrating radar (GPR) data affected by waveguide dispersion are not straightforward to analyse. Therefore, waveguide dispersed common midpoint measurements are typically interpreted using so-called dispersion curves, which describe the phase velocity as a function of frequency. These dispersion curves are typically evaluated with deterministic optimization algorithms that derive the dielectric properties of the subsurface as well as the location and depth of the respective layers. However, these methods do not provide estimates of the uncertainty of the inferred subsurface properties. Here, we applied a formal Bayesian inversion methodology using the recently developed DiffeRential Evolution Adaptive Metropolis DREAM(zs) algorithm. This Markov Chain Monte Carlo simulation method rapidly estimates the (non-linear) parameter uncertainty and helps to treat the measurement error explicitly. We found that the frequency range used in the inversion has an important influence on the posterior parameter estimates, essentially because parameter sensitivity varies with measurement frequency. Moreover, we established that the measurement error associated with the dispersion curve is frequency dependent and that the estimated model parameters become severely biased if this frequency-dependent nature of the measurement error is not properly accounted for. We estimated these frequency-dependent measurement errors together with the model parameters using the DREAM(zs) algorithm. The posterior distribution of the model parameters derived in this way compared well with inversion results for a reduced frequency bandwidth which is an alternative, yet subjective method to reduce the bias introduced by this frequency-dependent measurement error. Altogether, our inversion procedure provides an integrated and objective methodology for the analysis of dispersive GPR data and appropriately treats the measurement error and parameter uncertainty.