Jutta Bikowski

Integrated analysis of waveguide dispersed GPR pulses using deterministic and Bayesian inversion 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 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. This more subjective method is an alternative to reduce the bias introduced by this frequencydependent 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.

Inversion and sensitivity analysis of GPR data with waveguide dispersion using Markov Chain Monte Carlo simulation

GPR data with waveguide dispersion are known to be very difficult to interpret using traditional inversion methods. Recently, an algorithm was developed that inverts dispersive GPR data using dispersion curves. Here we analyze the sensitivity of this algorithm, and determine posterior probability density functions of the inverted parameters using Markov Chain Monte Carlo simulation. This method is especially designed to work well in the presence of measurement and model error, and is applied to measured CMP data assuming a two layered subsurface. Lower frequencies determine the inverted permittivity of the lower halfspace, whereas higher frequencies contain information about the waveguide height and its permittivity. Removing the beginning or end of the dispersion curve significantly increases parameter uncertainty.

Full-waveform inversion of GPR data in frequency-domain

A new full-waveform inversion scheme is developed to obtain high-resolution images of cross-hole ground penetrating radar (GPR) data. The inversion is formulated as a non-linear least squares problem which minimizes errors between synthetic and observed data. The full-waveform modeling is implemented in frequency domain using the finite-difference (FDFD) solution of Maxwell equation. Here, we are using an iterative gradient method (Gauss-Newton) where the gradient is determined by using the forward vector wavefield and the backward-propagated vectorial residual wavefield. The algorithm inverts sequentially from low to high frequencies and permittivity and conductivity distributions can be obtained simultaneously. Preliminary inversion results of a synthetic example for a homogeneous background model with embedded high contrast parameters anomalies show that the permittivity result is comparable with time domain full-waveform inversion that uses an expanding bandwidth for increasing iterations.

Full-waveform inversion of multi-offset surface GPR data

Common ray-based techniques for analysing common midpoint (CMP) ground penetrating radar (GPR) data use only part of the measured traces and return results with limited resolution and non-quantitative values for conductivity. Due to the fact that full-waveform inversion uses all information of the measured traces, a higher resolution image of the subsurface and quantitative conductivity values can be obtained. Using an experimental dispersive CMP dataset, the results of dispersion analysis, i.e. permittivity and thickness, define the start model parameters for full-waveform inversion. After estimating an effective source wavelet, the full-waveform inversion based on a simplex search algorithm returns reliable permittivity and conductivity values of the subsurface.

Explicit consideration of measurement uncertainty during Bayesian inversion of dispersive GPR data

Thin layers in the shallow subsurface can act as waveguides and result in dispersive common midpoint (CMP) data. Recently developed algorithms, similar to those used for seismic Rayleigh inversion, are able to successfully solve the inversion problem and obtain values of the waveguide properties. Despite this progress made, parameter uncertainty has not yet been appropriately considered. In this study, we investigate the influence of measurement uncertainty on the final parameter values using a Markov Chain Monte Carlo scheme with synthetic and experimental data. Explicit consideration of measurement uncertainty increases the uncertainty of the inferred waveguide parameters, but improves the reliability of the parameter estimates. The results of this study advocate the use of an explicit definition of the measurement uncertainty in the likelihood function when inverting for waveguide properties.

GPR full-waveform inversion of chloride gradients in concrete

The use of salt for deicing roads is a major problem for reinforced concrete structures. With time chlorides migrate within concrete pores and causes reinforcement to corrode, which leads to the reduction of the structures load carrying capacity. Due to alternating wet and dry climates, chlorides are distributed in gradients within concrete. Here, an experiment was carried out where concrete specimens were exposed to controlled wetting-drying cycles using different saline solutions for different exposure times to generate chloride gradients. During this experiment repeated off-ground GPR measurements were made. In this paper, two GPR processing methodologies, enabling chloride content determination, are developed to provide an assessment tool for structural engineers. A ray-based forward model provides average permittivity and conductivity values and a novel full-waveform method enables the reconstruction of conductivity gradients within concrete slabs. The destructive determination of chloride gradients distribution confirmed the obtained results. Finally, the obtained results indicate that the chloride solution concentration is dominating the chloride gradient distribution, whereas the exposure time has a minor influence.

Two-layer inversion of dispersive GPR data due to freezing induced waveguides — A synthetic study

A large permittivity contrast between a thin surface layer and the underlying substratum, caused by rapid changing dynamic processes in the subsurface, can result in waveguide dispersion. In some cases, a single-layer waveguide cannot explain the measured electromagnetic waves. Here, we show an analysis of four synthetic dispersive datasets of two-layer leaky waveguides which have large and small permittivity contrasts between the layers as well as an increasing and a decreasing permittivity with depth. The four synthetic datasets are inverted with a multi-layer inversion algorithm for leaky waveguides and with different single-layer inversion algorithms. For the two-layer waveguides with a large increasing permittivity with depth, it is not possible to reliably reconstruct the model parameters of the lowest layer. For small contrasts within the waveguide, the single-layer inversion algorithm resulted in an arithmetic mean value for the permittivity and a total waveguide thickness.