Ground Penetrating Radar Full-waveform Inversion Research Articles

Evaluation of starting model approaches and effective source wavelet variations for high-frequency ground-penetrating radar full-waveform inversion

High-frequency ground-penetrating radar (GPR) full-waveform inversion (FWI) can enhance the characterization of small-scale structures in the subsurface below the decimeter scale. We have investigated the potential and requirements to use FWI for higher-frequency data. Thereby, we focus on the two most important criteria to achieve reliable FWI results: adequate starting models that fulfill the half-wavelength criterion and the accuracy of the effective source wavelet. Therefore, we have defined a realistic reference model, generated synthetic GPR data sets (200, 450, and 700 MHz), and tested different standard ray-based starting model methods and frequency-hopping approaches to derive results close to our reference model. Although standard starting models provide good parameter reconstruction for lower-frequency data, a frequency-hopping approach is required for the 700 MHz data. In addition, we have seen that the reconstruction of the conductivity results is more sensitive to the presence of noise (25 dB) than the permittivity tomograms. The definition of the effective source wavelets is directly linked to the accuracy of the starting models; therefore, we investigate the effect on the FWI results for high-frequency data by varying the source wavelets in terms of starting time and/or amplitude. Considering the multiparameter nature of FWI, we observe that time shifts have a greater influence on the performance of the FWI than amplitude variations. Large time shifts of approximately 0.1 ns for the 700 MHz data may lead to the failure of the inversion, whereas amplitude variations (±5% of the maximum amplitude) affect the quantitative conductivity results only (no effect on permittivity) with an increased root-mean-square error of the data of up to 20%. Using a stochastically perturbed synthetic model, we determine an improved parameter reconstruction for higher frequencies. On the basis of our findings, we develop a workflow to obtain reliable results for high-frequency GPR FWI for future users.

Full waveform inversion of common-offset ground-penetrating radar based on a special source wavelet and multiple integral wave-field transform

Ground-penetrating radar (GPR) can obtain the geological information by using the electrical difference between the abnormal body and the background field. Full waveform inversion (FWI) can process radar data and obtain a more accurate distribution of relative permittivity. However, when the electrical parameters between the anomalous body and the background field are quite different, the wavefield information is seriously disturbed. In that case, the FWI method can not obtain accurate physical parameters, which is worse for common-offset GPR because of the lack of illumination angles and of wavenumber coverage. To solve this problem, a novel GPR FWI method is proposed to improve the stability of inversion using a special source wavelet and multiple integral wave-field transform. The manuscript is composed as follows: first, a special wavelet is used to improve the gradient in FWI. Then the integral wave-field transform can provide low-frequency information of data. This process can make full use of the low-frequency components hidden in the original data, obtain the large-scale relative permittivity distribution structure, and reduce the instability of the full waveform inversion. Finally, three simulation examples and a practical example verify the effectiveness of the method. Especially when there is a large difference between the dielectric parameters of the abnormal body and the background field (more than ten times or even dozens of times), the proposed FWI algorithm can still obtain stable results.

Detection of Tracer Plumes Using Full‐Waveform Inversion of Time‐Lapse Ground Penetrating Radar Data: A Numerical Study in a High‐Resolution Aquifer Model

AbstractImaging subsurface small‐scale features and monitoring transport of tracer plumes at a fine resolution is of interest to characterize transport processes in aquifers. Full‐waveform inversion (FWI) of crosshole ground penetrating radar (GPR) measurements enables aquifer characterization at decimeter‐scale resolution. The method produces images of both relative dielectric permittivity (εr) and bulk electrical conductivity (σb) that can be related to hydraulic aquifer properties and tracer distributions. To test the potential of time‐lapse GPR FWI for imaging tracer plumes, we conducted a numerical tracer experiment by injecting saline water, desalinated water, and ethanol in a heterogeneous aquifer. The saline and desalinated tracers only changed σb, whereas ethanol changed both εr and σb. Tracer concentrations were retrieved from the inverted εr and σb models using information about petrophysical parameters. GPR FWI εr and σb tracer images could recover preferential paths of ∼0.2 m width, while the derived σb structures are smoother. FWI of 50 time‐lapse data sets demonstrated the potential of the FWI to derive spatially resolved breakthrough curves of the saline and ethanol tracer in the image plane between the boreholes. Thus, high‐resolution imaging with GPR FWI of tracers that produce a high permittivity contrast against the background has a great potential for characterization of heterogeneous transport in aquifers.

Coupled full-waveform inversion of horizontal borehole ground penetrating radar data to estimate soil hydraulic parameters: A synthetic study

Coupled inversion is a promising technique for determining soil hydraulic properties from time-lapse geophysical measurements. In this inversion approach, a hydrological model is coupled with ground penetrating radar (GPR) forward modelling to avoid interpretation errors from data processing. In this study, a workflow for coupled GPR full-waveform inversion (CFWI) is proposed that combines the benefits of coupled inversion and full-waveform inversion (FWI) to estimate soil hydraulic properties from time-lapse horizontal borehole GPR measurements. In particular, a synthetic modelling study is presented that compares the performance of coupled inversion of full waveforms and first arrival time data from zero-offset profile (ZOP) borehole measurements obtained during an infiltration event for estimating hydraulic parameters and the thickness of the first layer for a 2-layer soil profile. It was found that the thickness of the first layer could be more accurately estimated by CFWI because of the additional information contained in reflected and refracted waves from the air–soil layer boundary. Furthermore, the hydraulic parameters estimated by the coupled inversion of GPR travel times slightly deviated from true values and showed a relatively large uncertainty, whereas the results of CFWI precisely matched the known water retention and hydraulic conductivity functions. Despite these promising results, several challenges should be solved before CFWI can be applied to experimental GPR data. First, conducting CFWI needs accurate conceptual setups for the hydro(geo-)logical model. Furthermore, a robust approach should be developed to accurately estimate an effective source wavelet from the experimental ZOP data, and a more sophisticated hydrological modelling approach has to be considered to better estimate the distribution of soil electrical conductivity during the infiltration event. Finally, the accuracy and efficiency of current GPR modelling methods may need to be improved.

A Deep Learning Enhanced Full Waveform Inversion Scheme

Due to the device limitation, the observed ground penetrating radar (GPR) or seismic data are usually band-limited and do not contain reliable low-frequency components. Without the low-frequency data, the full waveform inversion (FWI) is easy to be trapped in local minima. This work presents a deep learning method for recovering the absent low-frequency data during the inversion. To improve the robustness and the generalization ability of the neural network, we adopt an accelerated self-supervised learning method and propose a training set initialization technique. The proposed method is validated by seismic and GPR FWI. Experiment results show that our method converges fast and the low-frequency data could be reconstructed successfully.

Attribute Recognition of Buried Pipes Based on Multi-Trace Phase Features Using K-means Clustering for GPR Data Interpretation

Accurate location and depth determination of underground pipes, especially the attribute recognition, are of great importance yet remake a challenging issue in municipal environments. Single-trace phase difference analysis remains a bottleneck due to its inherent and strong randomness in object identification. This paper developed a multi-trace phase difference analysis framework for ground-penetrating radar (GPR) data based on K-means cluster analysis technique and the theory of region of interest (ROI), which could serve as a new criterion for successful pipe attribute recognition. After improving signal-to-noise ratio of GPR data by using the preprocessing techniques, the connected components algorithms (CCA) based on image segmentation and morphological operation is performed to delineate the ROI. The K-means cluster analysis technique is further employed to efficiently extract the multi-trace phase statistical features for comprehensively evaluating the attributes of ROI. We verify this proposed framework by simulated GPR signals, laboratory data and field datasets. Results demonstrate that the proposed method can not only facilitate the attribute recognition of pipes, but also reduce the interpretation ambiguity of the pipe material even in the field site environment. Specifically, if the phase difference of pipe turns out to be even multiples of π, the target can be automatically identified as metallic-category pipes, whereas odd multiples of π, point to non-metallic-category pipes with a lower permittivity than that of the background. This criterion presents promising applicability in subsurface pipeline identification and attributes recognition, especially in constructing a more appropriate initial model of GPR full waveform inversion for survey in pipes.

3D aquifer characterization of the Hermalle-sous-Argenteau test site using crosshole ground-penetrating radar amplitude analysis and full-waveform inversion

To improve the understanding of flow and transport processes in the critical zone, high-resolution and accurate estimation of the small-scale heterogeneity is essential. Preferential flow paths related to high-porosity layers and clay lenses in gravel aquifers greatly affect flow and transport processes in the subsurface, and their high electrical contrast to their surrounding matrix and limited extent can act as low-velocity electromagnetic waveguides. In the past decade, time-domain full-waveform inversion (FWI) of crosshole ground-penetrating radar (GPR) data has shown to provide 2D decimeter-scale resolution images of relative permittivity and electrical conductivity of the subsurface, which can be related to porosity and soil texture. Most studies using crosshole GPR FWI resolved high-porosity zones that were identified by an amplitude analysis approach. But clay lenses or zones with higher electrical conductivity that act as low-velocity waveguides are hard to distinguish in the measured data and amplitude analysis because of the absence of characteristic wave-propagation features. We have investigated a set of nine crosshole GPR data sets from a test site in Hermalle-sous-Argenteau near the Meuse River in Belgium to characterize the aquifer within a decimeter-scale resolution and to improve the understanding of a previously performed heat tracer experiment. Thereby, we extend the amplitude analysis to identify two different types of low-velocity waveguides either caused by an increased porosity or a higher electrical conductivity (and higher porosity). Combining the GPR amplitude analysis for low-velocity waveguide zones with the standard FWI results provided information on waveguide zones, which modified the starting models and further improved the FWI results. Moreover, an updated effective source wavelet is estimated based on the updated permittivity starting models. In comparison with the traditional FWI results, the updated FWI results present smaller gradient of the medium properties and smaller root-mean-squared error values in the final inversion results. The nine crosshole sections are used to generate a 3D image of the aquifer and allowed a detailed analysis of the porosity distribution along the different sections. Consistent structures of the permittivity and electrical conductivity show the robustness of the updated FWI results. The aquifer structures obtained by the FWI results agree with those results of the heat tracer experiment.

2.5D crosshole GPR full-waveform inversion with synthetic and measured data

Full-waveform inversion (FWI) of cross-borehole ground-penetrating radar (GPR) data is a technique with the potential to investigate subsurface structures. Typical FWI applications transform 3D measurements into a 2D domain via an asymptotic 3D to 2D data transformation, widely known as a Bleistein filter. Despite the broad use of such a transformation, it requires some assumptions that make it prone to errors. Although the existence of the errors is known, previous studies have failed to quantify the inaccuracies introduced on permittivity and electrical conductivity estimation. Based on a comparison of 3D and 2D modeling, errors could reach up to 30% of the original amplitudes in layered structures with high-contrast zones. These inaccuracies can significantly affect the performance of crosshole GPR FWI in estimating permittivity and especially electrical conductivity. We have addressed these potential inaccuracies by introducing a novel 2.5D crosshole GPR FWI that uses a 3D finite-difference time-domain forward solver (gprMax3D). This allows us to model GPR data in 3D, whereas carrying out FWI in the 2D plane. Synthetic results showed that 2.5D crosshole GPR FWI outperformed 2D FWI by achieving higher resolution and lower average errors for permittivity and conductivity models. The average model errors in the whole domain were reduced by approximately 2% for permittivity and conductivity, whereas zone-specific errors in high-contrast layers were reduced by approximately 20%. We verified our approach using crosshole 2.5D FWI measured data, and the results showed good agreement with previous 2D FWI results and geologic studies. Moreover, we analyzed various approaches and found an adequate trade-off between computational complexity and accuracy of the results, i.e., reducing the computational effort while maintaining the superior performance of our 2.5D FWI scheme.

Review of crosshole ground-penetrating radar full-waveform inversion of experimental data: Recent developments, challenges, and pitfalls

Heterogeneous small-scale high-contrast layers and spatial variabilities of soil properties can have a large impact on flow and transport processes in the critical zone. Because their characterization is difficult and critical, high-resolution methods are required. Standard ray-based approaches for imaging the subsurface consider only a small amount of the measured data and suffer from limited resolution. In contrast, full-waveform inversion (FWI) considers the full information content of the measured data and could yield higher resolution images in the subwavelength scale. In the past few decades, ground-penetrating radar (GPR) FWI and its application to experimental data have matured, which makes GPR FWI an established approach to significantly improve resolution. Several theoretical developments were achieved to improve the application to experimental data from crosshole GPR FWI. We have determined the necessary steps to perform FWI for experimental data to obtain reliable and reproducible high-resolution images. We concentrate on experimental crosshole GPR data from a test site in Switzerland to illustrate the challenges of applying FWI to experimental data and discuss the obtained results for different development steps including possible pitfalls. Thereby, we acknowledge out the importance of a correct time-zero correction of the data, the estimation of the effective source wavelet, and the effect of the choice of starting models. The reliability of the FWI results is investigated by analyzing the fit of the measured and modeled traces, the remaining gradients of the final models, and validating with independently measured logging data. Thereby, we found that special care needs to be taken to define the optimal inversion parameters to avoid overshooting of the inversion or truncation errors.

Application of Laplace Domain Waveform Inversion to Cross-Hole Radar Data

Full waveform inversion (FWI) can yield high resolution images and has been applied in Ground Penetrating Radar (GPR) for around 20 years. However, appropriate selection of the initial models is important in FWI because such an inversion is highly nonlinear. The conventional way to obtain the initial models for GPR FWI is ray-based tomogram inversion which suffers from several inherent shortcomings. In this paper, we develop a Laplace domain waveform inversion to obtain initial models for the time domain FWI. The gradient expression of the Laplace domain waveform inversion is deduced via the derivation of a logarithmic object function. Permittivity and conductivity are updated by using the conjugate gradient method. Using synthetic examples, we found that the value of the damping constant in the inversion cannot be too large or too small compared to the dominant frequency of the radar data. The synthetic examples demonstrate that the Laplace domain waveform inversion provide slightly better initial models for the time domain FWI than the ray-based inversion. Finally, we successfully applied the algorithm to one field data set, and the inverted results of the Laplace-based FWI show more details than that of the ray-based FWI.

Radius estimation of subsurface cylindrical objects from ground-penetrating-radar data using full-waveform inversion

Ray-based radius estimations of subsurface cylindrical objects such as rebars and pipes from ground-penetrating-radar (GPR) measurements are not accurate because of their approximations. We have developed a novel full-waveform inversion (FWI) approach that uses a full-waveform 3D finite-difference time-domain (FDTD) forward-modeling program to estimate the radius including other object parameters. By using the full waveform of the common-offset GPR data, the shuffled complex evolution (SCE) approach is able to reliably extract the radius of the subsurface cylindrical objects. A combined optimization of radius, medium properties, and the effective source wavelet is necessary. Synthetic and experimental data inversion returns an accurate reconstruction of the cylinder properties, medium properties, and the effective source wavelet. Combining FWI of GPR data using SCE and a 3D FDTD forward model makes the approach easily adaptable for a wide range of other GPR FWI approaches.

Inverts permittivity and conductivity with structural constraint in GPR FWI based on truncated Newton method

Full waveform inversion (FWI) of ground penetrating radar (GPR) is a promising technique to quantitatively evaluate the permittivity and conductivity of near subsurface. However, these two parameters are simultaneously inverted in the GPR FWI, increasing the difficulty to obtain accurate inversion results for both parameters. In this study, I present a structural constrained GPR FWI procedure to jointly invert the two parameters, aiming to force a structural relationship between permittivity and conductivity in the process of model reconstruction. The structural constraint is enforced by a cross-gradient function. In this procedure, the permittivity and conductivity models are inverted alternately at each iteration and updated with hierarchical frequency components in the frequency domain. The joint inverse problem is solved by the truncated Newton method which considering the effect of Hessian operator and using the approximated solution of Newton equation to be the perturbation model in the updating process. The joint inversion procedure is tested by three synthetic examples. The results show that jointly inverting permittivity and conductivity in GPR FWI effectively increases the structural similarities between the two parameters, corrects the structures of parameter models, and significantly improves the accuracy of conductivity model, resulting in a better inversion result than the individual inversion.

Joint acoustic full-waveform inversion of crosshole seismic and ground-penetrating radar data in the frequency domain

Integrating crosshole ground-penetrating radar (GPR) with seismic methods is an efficient way to reduce the uncertainty and ambiguity of data interpretation in shallow geophysical investigations. We have developed a new approach for joint full-waveform inversion (FWI) of crosshole seismic and GPR data in the frequency domain to improve the inversion results of both FWI methods. In a joint objective function, three geophysical parameters (P-wave velocity, permittivity, and conductivity) are effectively connected by three weighted cross-gradient terms that enforce the structural similarity between parameter models. Simulation of acoustic seismic and scalar electromagnetic problems is implemented using 2D finite-difference frequency-domain methods, and the inverse problems of seismic FWI and GPR FWI are solved using a matrix-free truncated Newton algorithm. The joint inversion procedure is performed in several hierarchical frequencies, and the three parameter models are sequentially inverted at each frequency. The joint FWI approach is illustrated using three numerical examples. The results indicate that the joint FWI approach can effectively enhance the structural similarity among the models, modify the structure of each model, and improve the accuracy of inversion results compared with those of individual FWI approaches. Moreover, joint inversion can reduce the trade-off between permittivity and conductivity in GPR FWI, leading to an improved conductivity model in which artifacts are significantly decreased.

Quantitative imaging for civil engineering by joint full waveform inversion of surface-based GPR and shallow seismic reflection data

Full waveform inversion (FWI) of ground penetrating radar (GPR) and seismic data is a promising imaging tool for the detailed characterization of latent cavities and tunnels. In this study, surface-based GPR FWI and seismic FWI are combined to quantitatively image the geometry and geophysical attributes of the subsurface. These two FWI methods are integrated into a joint procedure and linked by cross-gradient functions which can provide structural constraints between the parameters. The elastic and electromagnetic properties of the medium (P-wave velocity, permittivity, and conductivity) are linked and simultaneously inverted in the joint FWI approach. This joint FWI approach is tested using three numerical examples. In the first two examples, target objects with various shapes are contained in both homogeneous and inhomogeneous media. In the third example, two sediment-filled cavities and a fractured area are analyzed in the calcarenite layers. The results show that the joint FWI approach can integrate the common structure of models and correct the model structures that are inaccurately reconstructed in the individual FWI methods, providing a comprehensive structural interpretation of the study areas.

Quantitative multi-layer electromagnetic induction inversion and full-waveform inversion of crosshole ground penetrating radar data

Due to the recent system developments for the electromagnetic characterization of the subsurface, fast and easy acquisition is made feasible due to the fast measurement speed, easy coupling with GPS systems, and the availability of multi-channel electromagnetic induction (EMI) and ground penetrating radar (GPR) systems. Moreover, the increasing computer power enables the use of accurate forward modeling programs in advanced inversion algorithms where no approximations are used and the full information content of the measured data can be exploited. Here, recent developments of large-scale quantitative EMI inversion and full-waveform GPR inversion are discussed that yield higher resolution of quantitative medium properties compared to conventional approaches. In both cases a detailed forward model is used in the inversion procedure that is based on Maxwell’s equations. The multi-channel EMI data that have different sensing depths for the different source-receiver offset are calibrated using a short electrical resistivity tomography (ERT) calibration line which makes it possible to invert for electrical conductivity changes with depth over large areas. The crosshole GPR full-waveform inversion yields significant higher resolution of the permittivity and conductivity images compared to ray-based inversion results.

Imaging and characterization of facies heterogeneity in an alluvial aquifer using GPR full-waveform inversion and cone penetration tests

Summary Spatially highly resolved mapping of aquifer heterogeneities is critical for the accurate prediction of groundwater flow and contaminant transport. Here, we demonstrate the value of using full-waveform inversion of crosshole ground penetrating radar (GPR) data for aquifer characterization. We analyze field data from the Krauthausen test site, where crosshole GPR data were acquired along a transect of 20 m length and 10 m depth. Densely spaced cone penetration tests (CPT), located close to the GPR transect, were used to validate and interpret the tomographic images obtained from GPR. A strong correlation was observed between CPT porosity logs and porosity estimates derived from GPR using the Complex Refractive Index Model (CRIM). A less pronounced correlation was observed between electrical conductivity data derived from GPR and CPT. Cluster analysis of the GPR data defined three different subsurface facies, which were found to correspond to sediments with different grain size and porosity. In conclusion, our study suggests that full-waveform inversion of crosshole GPR data followed by cluster analysis is an applicable approach to identify hydrogeological facies in alluvial aquifers and to map their architecture and connectivity. Such facies maps provide valuable information about the subsurface heterogeneity and can be used to construct geologically realistic subsurface models for numerical flow and transport prediction.

Improved Characterization of Fine-Texture Soils Using On-Ground GPR Full-Waveform Inversion

Ground-penetrating radar (GPR) uses the recording of electromagnetic waves and is increasingly applied for a wide range of applications. Traditionally, the main focus was on the analysis of the medium permittivity since estimates of the conductivity using the far-field approximation contain relatively large errors and cannot be interpreted quantitatively. Recently, a full-waveform inversion (FWI) scheme has been developed that is able to reliably estimate permittivity and conductivity values by analyzing reflected waves present in on-ground GPR data. It is based on a frequency-domain solution of Maxwell's equations including far, intermediate, and near fields assuming a 3-D subsurface. Here, we adapt the FWI scheme for on-ground GPR to invert the direct ground wave traveling through the shallow subsurface. Due to possible interference with the airwaves and other reflections, an automated time-domain filter needed to be included in the inversion. In addition to the obtained permittivity and conductivity values, also the wavelet center frequency and amplitude return valuable information that can be used for soil characterization. Combined geophysical measurements were carried out over a silty loam with significant variability in the soil texture. The obtained medium properties are consistent with Theta probe, electromagnetic resistivity tomography, and electromagnetic induction results and enable the formulation of an empirical relationship between soil texture and soil properties. The permittivities and conductivities increase with increasing clay and silt and decreasing skeleton content. Moreover, with increasing permittivities and conductivities, the wavelet center frequency decreases, whereas the wavelet amplitude increases, which is consistent with the radiation pattern and the antenna coupling characteristics.

Improvements in crosshole GPR full-waveform inversion and application on data measured at the Boise Hydrogeophysics Research Site

Abstract Crosshole ground penetrating radar (GPR) tomography has been widely used and has the potential to improve the obtained subsurface models due to its high spatial resolution compared to other methods. Recent advances in full-waveform inversion of crosshole GPR data show that higher resolution images can be obtained compared to conventional ray-based GPR inversion because it can exploit all information present in the observed data. Since the first application of full-waveform inversion on synthetic and experimental GPR data, the algorithm has been significantly improved by extending the scalar to a vectorial approach, and changing the stepped permittivity and conductivity update into a simultaneous update. Here, we introduce new normalized gradients that do not depend on the number of sources and receivers which enable a comparison of the gradients and step lengths for different crosshole survey layouts. An experimental data set acquired at the Boise Hydrogeophysics Research Site is inverted using different source–receiver setups and the obtained permittivity and conductivity images, remaining gradients and final misfits are compared for the different versions of the full-waveform inversion. Moreover, different versions of the full-waveform inversion are applied to obtain an overview of all improvements. Most improvements result in a reducing final misfit between the measured and synthetic data and a reducing remaining gradient at the final iteration. Regions with relatively high remaining gradient amplitudes indicate less reliable inversion results. Comparison of the final full-waveform inversion results with Neutron–Neutron porosity log data and capacitive resistivity log data show considerably higher spatial frequencies for the logging data compared to the full-waveform inversion results. To enable a better comparison, we estimated a simple wavenumber filter and the full-waveform inversion results show an improved fit with the logging data. This work shows the potential of full-waveform inversion as an advanced method that can provide high resolution images to improve hydrological models.

Validation of ground penetrating radar full-waveform inversion for field scale soil moisture mapping

Ground penetrating radar (GPR) is an efficient method for soil moisture mapping at the field scale, bridging the scale gap between small-scale invasive sensors and large-scale remote sensing instruments. Nevertheless, commonly-used GPR approaches for soil moisture characterization suffer from several limitations and the determination of the uncertainties in GPR soil moisture sensing has been poorly addressed. Herein, we used a proximal GPR method based on full-waveform inversion of ultra-wideband radar data for mapping soil moisture and we evaluated uncertainties in the soil moisture maps by three methods. First, GPR-derived soil moisture uncertainties were computed from GPR data inversions, according to measurements and modeling errors, and to the sensitivity of the electromagnetic model to soil moisture. Second, the repeatability of soil moisture mapping was evaluated. Third, GPR-derived soil moisture was compared with ground-truth measurements (soil core sampling). The proposed GPR method appeared to be highly precise and accurate, with a spatially averaged GPR inversion uncertainty of 0.0039 m3 m-3, a repetition uncertainty of 0.0169 m3 m-3, and an uncertainty of 0.0233 m3 m-3 when compared with ground-truth measurements. These uncertainties were mapped and appeared to be related to some local model inadequacies and to small-scale variability of soil moisture. In a soil moisture mapping framework, the interpolation was found to be the main source of the observed uncertainties. The proposed GPR method was proven to be largely reliable in terms of accuracy and precision and appeared to be highly efficient for soil moisture mapping at the field scale.

Taming the non-linearity problem in GPR full-waveform inversion for high contrast media

We present a new algorithm for the inversion of full-waveform ground-penetrating radar (GPR) data. It is designed to tame the non-linearity issue that afflicts inverse scattering problems, especially in high contrast media. We first investigate the limitations of current full-waveform time-domain inversion schemes for GPR data and then introduce a much-improved approach based on a combined frequency-time-domain analysis. We show by means of several synthetic tests and theoretical considerations that local minima trapping (common in full bandwidth time-domain inversion) can be avoided by starting the inversion with only the low frequency content of the data. Resolution associated with the high frequencies can then be achieved by progressively expanding to wider bandwidths as the iterations proceed. Although based on a frequency analysis of the data, the new method is entirely implemented by means of a time-domain forward solver, thus combining the benefits of both frequency-domain (low frequency inversion conveys stability and avoids convergence to a local minimum; whereas high frequency inversion conveys resolution) and time-domain methods (simplicity of interpretation and recognition of events; ready availability of FDTD simulation tools).