Integrated analysis of waveguide dispersed GPR pulses using deterministic and Bayesian inversion methods

Abstract

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.

Waveguide properties recovered from shallow diffractions in common offset GPR

“…Key inputs for effective inversion of waveguide dispersion data are the range and density of frequencies selected [ Bikowski et al ., ]. We have presented inversion results based on best fit to all data points that could reasonably be extracted from the field experiments (see Figure ).…”

Analysis of ground penetrating radar data using hierarchical Markov Chain Monte Carlo simulation

“…The aim herein is to obtain a set of model parameters that minimize the discrepancy between the model outcome and the actual data (Bikowski et al 2012). Traditionally models analyzing ambiguities are deterministic and estimate only a "best" set of model parameters without consideration for parameter uncertainty (Pettinelli et al 2007;Steelman and Endres 2010).…”

Improved characterization of underground structure defects from two-stage Bayesian inversion using crosshole GPR data

“…This realization exhibits the closest match between the observed and simulated EM waves but does not appropriately communicate measurement and modeling uncertainties [32]. Probabilistic inversion methods allow for the treatment of different sources of error and return to the user an ensemble of realizations deemed statistically acceptable [33][34][35][36][37][38][39][40]. Among these methods, Bayesian inference coupled with Markov chain Monte Carlo (MCMC) simulation has found widespread application and use in GPR inversion.…”