Crosshole Ground-penetrating Radar Data Research Articles

Three-Dimensional Reconstruction of Retaining Structure Defects from Crosshole Ground Penetrating Radar Data Using a Generative Adversarial Network

Crosshole ground penetrating radar (GPR) is an efficient method for ensuring the quality of retaining structures without the need for excavation. However, interpreting crosshole GPR data is time-consuming and prone to inaccuracies. To address this challenge, we proposed a novel three-dimensional (3D) reconstruction method based on a generative adversarial network (GAN) to recover 3D permittivity distributions from crosshole GPR images. The established framework, named CGPR2VOX, integrates a fully connected layer, a residual network, and a specialized 3D decoder in the generator to effectively translate crosshole GPR data into 3D permittivity voxels. The discriminator was designed to enhance the generator’s performance by ensuring the physical plausibility and accuracy of the reconstructed models. This adversarial training mechanism enables the network to learn non-linear relationships between crosshole GPR data and subsurface permittivity distributions. CGPR2VOX was trained using a dataset generated through finite-difference time-domain (FDTD) simulations, achieving precision, recall and F1-score of 91.43%, 96.97% and 94.12%, respectively. Model experiments validate that the relative errors of the estimated positions of the defects were 1.67%, 1.65%, and 1.30% in the X-, Y-, and Z-direction, respectively. Meanwhile, the method exhibits noteworthy generalization capabilities under complex conditions, including condition variations, heterogeneous materials and electromagnetic noise, highlighting its reliability and effectiveness for practical quality assurance of retaining structures.

Monte Carlo Full-Waveform Inversion of Cross-Hole Ground-Penetrating Radar Data Based on Improved Residual Network

A full-waveform inversion (FWI) of ground-penetrating radar (GPR) data can be used to effectively obtain the parameters of a shallow subsurface. Introducing the Markov chain Monte Carlo (MCMC) algorithm into the FWI can reduce the dependence on the initial model and obtain the global optimal solution, but it requires a large number of computations. In order to better detect underground targets based on ground-penetrating radar data, this paper proposes a joint scheme of an improved ResNet and an MCMC full-waveform inversion. This scheme combines the Bayesian MCMC algorithm and an improved ResNet to accurately invert the target dielectric permittivity. The introduction of deep learning networks into the forward calculation part of the MCMC inversion algorithm replaced the complex forward simulation process, greatly improving the inversion speed. It is worth noting that the neural network model was an approximation of complex forward modeling, and, therefore, it contained modeling errors. The MCMC method could quantify and explain modeling errors during the inversion process, reducing the impact of modeling errors on the inversion results. Finally, a simulation dataset was constructed for training and testing, and the errors were statistically analyzed. The results showed that this method can accurately reconstruct underground medium targets, and it has strong robustness and efficiency.

GAN-Based Inversion of Crosshole GPR Data to Characterize Subsurface Structures

The crosshole ground-penetrating radar (GPR) technique is widely used to characterize subsurface structures, yet the interpretation of crosshole GPR data involves solving non-linear and ill-posed inverse problems. In this work, we developed a generative adversarial network (GAN)-based inversion framework to translate crosshole GPR images to their corresponding 2D defect reconstruction images automatically. This approach uses fully connected layers to extract global features from crosshole GPR images and employs a series of cascaded U-Net structures to produce high-resolution defect reconstruction results. The feasibility of the proposed framework was demonstrated on a synthetic crosshole GPR dataset created with the finite-difference time-domain (FDTD) method and real-world data from a field experiment. Our inversion network obtained recognition accuracy of 91.36%, structural similarity index measure (SSIM) of 0.93, and RAscore of 91.77 on the test dataset. Furthermore, comparisons with ray-based tomography and full-waveform inversion (FWI) suggest that the proposed method provides a good balance between inversion accuracy and efficiency and has the best generalization when inverting actual measured crosshole GPR data.

Crosshole Ground‐Penetrating Radar in Clay‐Rich Quaternary Deposits: Toward Characterization of High‐Loss Media

AbstractKnowing the centimeter‐to meter‐scale distribution of sand in clayey deposits is important for determining the dominating water flow pathways. Borehole information has a high vertical resolution, on the millimeter‐ to centimeter‐scale, but provides poor lateral coverage. For highly heterogeneous deposits, such as glacial diamicts, this detailed borehole information may not be sufficient for creating reliable geological models. Crosshole ground‐penetrating radar (GPR) can provide information on the decimeter‐ to meter‐scale variation between boreholes, but has mainly been used in sandy environments. In this study, we investigate whether crosshole GPR can provide information on the structural relationship of diamicts and their material properties, such as water content, bulk density, and clay content. To achieve ground truth, we compare the crosshole GPR data with geological information from boreholes and an excavation at the field site. The GPR data was analyzed comprehensively using several radar wave attributes in both time‐ and frequency domain, describing the signal velocity, strength, and shape. We found small variations in signal velocity (between 0.06 and 0.07 m/ns) but large variations in both amplitude and shape (either order of magnitude variation or doubling/tripling of attribute values). We see that the GPR response from wetter and more clayey diamicts have both lower amplitudes and lower centroid frequencies than the response from their drier and sandier counterparts. Lastly, we find that the variation in amplitude and shape attributes is better correlated to the diamicts' material properties than the signal velocity.

Hydrogeophysical characterization and determination of petrophysical parameters by integrating geophysical and hydrogeological data at the limestone vadose zone of the Beauce aquifer

The hydrological characterization of the vadose zone remains a major challenge considering the spatiotemporal variability of its properties and the limitations associated with hydrological measurements techniques. Geophysical methods, in particular the DC-resistivity and ground penetrating radar, can provide large scale images of hydrogeological structures and a non-invasive assessment of the subsurface dynamic processes. However, these approaches rely on the accuracy of the petrophysical relationships connecting the geophysical parameters to hydrogeological ones, where the site-specific determination of the associated petrophysical parameters is considered crucial. The first objective of this study was to investigate the relationship between the water content, geological properties, and geophysical attributes at the vadose zone of a vulnerable limestone aquifer. The second objective aimed to obtain the Archie’s and Complex Refractive Index Model (CRIM) petrophysical parameters by using borehole electrical resistivity and cross-hole ground penetrating radar data. For this purpose, we adopted a grid search inversion algorithm where the field geophysical data were integrated with water content profiles simulated by using HYDRUS-1D. The vadose zone profile was divided into three layers, and the inversion was carried out for the petrophysical parameters in each of the model layers. The electrical resistivity and relative dielectric permittivity data showed a very good correspondence with the simulated and experimental water content distributions along the vadose zone profile. The petrophysical parameters estimated by the inversion showed values that fall in the ranges reported in the literature. Similar values have been observed in the different model layers, with slight differences that were attributed to the vertical heterogeneities associated with the alteration and fracturation features of the limestone vadose zone. This study showed a very good correlation between geophysical, hydrogeological and geological data, and highlighted the presence of heterogeneities that can have profound effects on the vadose zone water dynamics.

MCMC Method of Inverse Problems Using a Neural Network—Application in GPR Crosshole Full Waveform Inversion: A Numerical Simulation Study

Ground-penetrating radar (GPR) crosshole tomography is widely applied to subsurface media images. However, the inadequacies of ray methods may limit the resolution of crosshole radar images, since the ray method is a type of high-frequency approximation. To solve this problem, the full waveform method is introduced for GPR inversion. However, full waveform inversion is computationally expensive. In this paper, we introduce a trained neural network that can be evaluated very quickly to replace a computationally intensive forward model. Additionally, the forward error of the trained neural network can be statistically analyzed. We demonstrate a methodology for a full waveform inversion of crosshole ground-penetrating radar data using the Markov chain Monte Carlo (MCMC) method. An accurate forward model based on Maxwell’s equations is replaced by a quickly trained neural network. This method achieves a high computation efficiency, which is four orders of magnitude faster than the accurate forward model. The inversion result of the synthetic waveform data shows a good performance of the trained neural network, which greatly improves the calculation efficiency.

Practical data acquisition strategy for time-lapse experiments using crosshole GPR and full-waveform inversion

Crosshole ground penetrating radar (GPR) methods are increasingly used in time-lapse studies of flow in the uppermost near subsurface with important implications for our understanding of e.g., water infiltration in the unsaturated zone, and fluid flow in the saturated zone. A particular challenge in such time-lapse crosshole studies is the trade-off between collecting sufficient data to be able to resolve how a tracer moves, and, minimizing the data acquisition time such that the data approximates a static state. We test how dense recording geometries are needed for resolving a gas bubble injected in a highly heterogeneous chalk reservoir analogue using a full-waveform inversion (FWI) approach for modelling the crosshole GPR data. We show that even relatively sparse geometries provide sufficient resolution of the permittivity contrast caused by the gas bubble, provided that the detailed background permittivity structure is known from prior (before gas injection) FWI analysis of densely recorded high-resolution data. The conductivity contrast caused by the gas is more challenging to recover and the resolution suffers to a higher degree when reducing the survey geometry or at higher noise levels. As long as the permittivity change during the time-lapse experiment is the main target, a significant reduction in acquisition time is therefore possible as compared to the time needed to record the background permittivity structure. This reduced acquisition time has important practical implications for time-lapse experiments under realistic conditions. Our results are based on synthetic analysis based on a realistic subsurface scenario closely linked to characterization of heterogeneous chalk reservoirs. However, our findings also have important implications for planning of future time-lapse studies in other settings.

Improvement of ground-penetrating radar full-waveform inversion images using cone penetration test data

Detailed characterization of aquifers is critical and challenging due to the existence of heterogeneous small-scale high-contrast layers. For an improved characterization of subsurface hydrologic characteristics, crosshole ground-penetrating radar (GPR) and cone penetration test (CPT) measurements are performed. In comparison to the CPT approach, which can only provide 1D high-resolution data along vertical profiles, crosshole GPR enables measuring 2D cross sections between two boreholes. In general, a standard inversion method for GPR data is the ray-based approach, which considers only a small amount of information and can therefore only provide limited resolution. In the past few decades, full-waveform inversion (FWI) of crosshole GPR data in the time domain has matured, and it provides inversion results with higher resolution by exploiting the full-recorded waveform information. However, FWI results are limited due to complex underground structures and the nonlinear nature of the method. A new approach that uses CPT data in the inversion process is applied to enhance the resolution of the final relative permittivity FWI results by updating the effective source wavelet. The updated effective source wavelet possesses a priori CPT information and a larger bandwidth. Using the same starting models, a synthetic model comparison between the conventional and updated FWI results demonstrates that the updated FWI method provides reliable and more consistent structures. To test the method, five experimental GPR cross section results are analyzed with the standard FWI and the new proposed updated approach. The synthetic and experimental results indicate the potential of improving the reconstruction of subsurface aquifer structures by combining conventional 2D FWI results and 1D CPT data.

Analysis of Forward Model, Data Type, and Prior Information in Probabilistic Inversion of Crosshole GPR Data

The crosshole ground penetrating radar (GPR) is a widely used tool to map subsurface properties, and inversion methods are used to derive electrical parameters from crosshole GPR data. In this paper, a probabilistic inversion algorithm that uses Markov chain Monte Carlo (MCMC) simulations within the Bayesian framework is implemented to infer the posterior distribution of the relative permittivity of the subsurface medium. Close attention is paid to the critical elements of this method, including the forward model, data type and prior information, and their influence on the inversion results are investigated. First, a uniform prior distribution is used to reflect the lack of prior knowledge of model parameters, and inversions are performed using the straight-ray model with first-arrival traveltime data, the finite-difference time-domain (FDTD) model with first-arrival traveltime data, and the FDTD model with waveform data, respectively. The cases using first-arrival traveltime data require an unreasonable number of model evaluations to converge, yet are not able to recover the real relative permittivity field. In contrast, the inversion using the FDTD model with waveform data successfully infers the correct model parameters. Then, the smooth constraint of model parameters is employed as the prior distribution. The inversion results demonstrate that the prior information barely affects the inversion results using the FDTD model with waveform data, but significantly improves the inversion results using first-arrival traveltime data by decreasing the computing time and reducing uncertainties of the posterior distribution of model parameters.

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.

Two-dimensional Time-domain Full Waveform Inversion of On-ground Common-offset GPR Data Based on Integral Preprocessing

Full waveform inversion (FWI) is an advanced inversion technique for ground penetrating radar (GPR), which could provide quantitative, high-resolution subsurface imaging. FWI has been used widely to process crosshole and on-ground multi-offset GPR data, but its application to on-ground common-offset GPR data is more difficult and being developed. This is mainly because that on-ground common-offset GPR has much less coverage of the subsurface and mainly includes reflective information. The application of conventional FWI to pure reflection data in the absence of a highly accurate starting velocity model is difficult. Here, we demonstrate a means of achieving this successfully by preprocessing the observed data and the residual fields with an integral algorithm, which could produce a more reasonable gradient and therefore lead to better inversion results. Several cases verify the effectiveness of this method. We achieve the simultaneous inversion of relative permittivity and conductivity for on-ground common-offset GPR, and discuss the trade-off between permittivity and conductivity in details. According to the inversion results of test models, it seems that the inversion result of relative permittivity is more credible in most cases.

Crosshole reflection imaging with ground-penetrating radar data: Applications in near-surface sedimentary settings

Crosshole ground-penetrating radar (GPR) is applied in areas that require a very detailed subsurface characterization. Analysis of such data typically relies on tomographic inversion approaches providing an image of subsurface parameters. We have developed an approach for processing the reflected energy in crosshole GPR data and applied it on GPR data acquired in different sedimentary settings. Our approach includes muting of the first arrivals, separating the up- and the downgoing wavefield components, and backpropagating the reflected energy by a generalized Kirchhoff migration scheme. We obtain a reflection image that contains information on the location of electromagnetic property contrasts, thus outlining subsurface architecture in the interborehole plane. In combination with velocity models derived from different tomographic approaches, these images allow for a more detailed interpretation of subsurface structures without the need to acquire additional field data. In particular, a combined interpretation of the reflection image and the tomographic velocity model improves the ability to locate layer boundaries and to distinguish different subsurface units. To support our interpretations of our field data examples, we compare our crosshole reflection results with independent information, including borehole logs and surface GPR data.

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.

Evaluation of a Straight-Ray Forward Model for Bayesian Inversion of Crosshole Ground Penetrating Radar Data

Bayesian inversion of crosshole ground penetrating radar (GPR) data is capable of characterizing the subsurface dielectric properties and qualifying the associated uncertainties. Markov chain Monte Carlo (MCMC) simulations within the Bayesian inversion usually require thousands to millions of forward model evaluations for the parameters to hit their posterior distributions. Therefore, the CPU cost of the forward model is a key issue that influences the efficiency of the Bayesian inversion method. In this paper we implement a widely used straight-ray forward model within our Bayesian inversion framework. Based on a synthetic unit square relative permittivity model, we simulate the crosshole GPR first-arrival traveltime data using the finite-difference time-domain (FDTD) and straight-ray solver, respectively, and find that the straight-ray simulator runs 450 times faster than its FDTD counterpart, yet suffers from a modeling error that is more than 7 times larger. We also perform a series of numerical experiments to evaluate the performance of the straight-ray model within the Bayesian inversion framework. With modeling error disregarded, the inverted posterior models fit the measurement data nicely, yet converge to the wrong set of parameters at the expense of unreasonably large number of iterations. When the modeling error is accounted for, with a quarter of the computational burden, the main features of the true model can be identified from the posterior realizations although there still exist some unwanted artifacts. Finally, a smooth constraint on the model structure improves the inversion results considerably, to the extent that it enhances the inversion accuracy approximating to those of the FDTD model, and further reduces the CPU demand. Our results demonstrate that the use of the straight-ray forward model in the Bayesian inversion saves computational cost tremendously, and the modeling error correction together with the model structure constraint are the necessary amendments that ensure that the model parameters converge correctly.

Bayesian full-waveform tomography with application to crosshole ground penetrating radar data

We present a probabilistic full-waveform inversion (FWI) approach that infers a geostatistical model along with the subsurface structure. Probabilistic FWI with Markov chain Monte Carlo (MCMC) allows for uncertainty quantification and removes the requirement of having a starting model in the cone of attraction of the assumed correct global minimum. We demonstrate our approach on a synthetic and a field data set. For the latter, we compare the results with deterministic FWI and a cone penetration test. Our results compare equally well with the cone penetration test as the deterministic results do. This is a positive result as for the deterministic inversion almost seven times more data were used than for the probabilistic inversion. Furthermore, the probabilistic FWI was able to converge to the posterior distribution starting from randomly drawn models. However, our uncertainty estimates are too narrow, because the necessarily short Markov chains implied by a computationally costly forward problem and the global nature of the model proposal scheme prevented a full exploration of the posterior probability density function. Without prior information such as borehole logs, the algorithm is only able to infer relative electric conductivity values, because the unknown amplitude of the wavelet and the mean of the conductivity are strongly correlated. This study clearly demonstrates the feasibility of probabilistic FWI and highlights the advantages and disadvantages of the approach.

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

Abstract Crosshole ground-penetrating radar (GPR) is a widely used measurement technique to help inspect the structural integrity of man-made underground structures. In a previous paper, we have introduced a Bayesian framework for inversion of crosshole GPR experiments to help back out defects in concrete underground structures. Here, we evaluate the practical usefulness of our inversion framework by application to waveform data from a real-world GPR survey of a diaphragm wall panel with two embedded structure defects. We also use this case study to further refine our methodology by introducing the elements of a two-stage inversion method to help delineate the exact location and shape of small structure defects. Herein, a low-resolution inversion composed of relatively few inversion coefficients (stage-1) is used to determine roughly the presence of structure defects, followed by a second inversion (stage-2) with much enhanced spatial resolution in those areas classified with anomalous or suspicious permittivity values. This two-stage inversion approach uses more wisely CPU-resources by focusing primarily on those areas of the concrete structure that have been classified as anomalies. We investigate the benefits of this two-stage inversion scheme using a synthetic and real-world case study involving waveform data of a diaphragm wall panel measured with crosshole GPR. Our results demonstrate that the proposed two-stage inversion method recovers successfully the location and shape of structure defects, at a computational cost that is considerably lower than the original inversion framework.

Soil moisture estimation using tomographic ground penetrating radar in a MCMC\u2013Bayesian framework

In this study, we focus on a hydrogeological inverse problem specifically targeting monitoring soil moisture variations using tomographic ground penetrating radar (GPR) travel time data. Technical challenges exist in the inversion of GPR tomographic data for handling non-uniqueness, nonlinearity and high-dimensionality of unknowns. We have developed a new method for estimating soil moisture fields from crosshole GPR data. It uses a pilot-point method to provide a low-dimensional representation of the relative dielectric permittivity field of the soil, which is the primary object of inference: the field can be converted to soil moisture using a petrophysical model. We integrate a multi-chain Markov chain Monte Carlo (MCMC)–Bayesian inversion framework with the pilot point concept, a curved-ray GPR travel time model, and a sequential Gaussian simulation algorithm, for estimating the dielectric permittivity at pilot point locations distributed within the tomogram, as well as the corresponding geostatistical parameters (i.e., spatial correlation range). We infer the dielectric permittivity as a probability density function, thus capturing the uncertainty in the inference. The multi-chain MCMC enables addressing high-dimensional inverse problems as required in the inversion setup. The method is scalable in terms of number of chains and processors, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. The proposed inversion approach can successfully approximate the posterior density distributions of the pilot points, and capture the true values. The computational efficiency, accuracy, and convergence behaviors of the inversion approach were also systematically evaluated, by comparing the inversion results obtained with different levels of noises in the observations, increased observational data, as well as increased number of pilot points.

Mapping sand layers in clayey till using crosshole ground-penetrating radar

Fluid transport through clayey tills governs the quantity and quality of groundwater resources in the Northern Hemisphere. This transport is often controlled by a 3D network of macropores (biopores, fractures, and sand lenses) within the clayey till. At present, a nondestructive technique that can map and characterize the sand-lens network does not exist, and full excavation or extensive drilling is therefore the only solution. Acquisition and modeling of crosshole ground-penetrating radar (GPR) may provide the answer to this problem. We collected 1D and 2D crosshole GPR data at a field site in Denmark from four 8 m deep boreholes with horizontal distances varying between 2.64 and 5.05 m. We find that the depth, thickness, and tilt of a coherent sand layer within the clayey till (approximately 0.4–0.6 m thick), as well as the underlying sand formation, can be mapped accurately using GPR data. We efficiently identify the sand as a highly resistive section with high electromagnetic (EM) wave velocities, whereas the clayey till is conductive with lower EM wave velocities. We find that the exact location of the sand occurrences is better delineated by the increase in amplitude than the increase in EM wave velocity. We believe that crosshole GPR may contribute significantly to groundwater protection and contaminant remediation initiatives.

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.

Inference of multi-Gaussian relative permittivity fields by probabilistic inversion of crosshole ground-penetrating radar data

In contrast to deterministic inversion, probabilistic Bayesian inversion provides an ensemble of solutions that can be used to quantify model uncertainty. We have developed a probabilistic inversion approach that uses crosshole first-arrival traveltimes to estimate an underlying geostatistical model, the subsurface structure, and the standard deviation of the data error simultaneously. The subsurface is assumed to be represented by a multi-Gaussian field, which allows us to reduce the dimensionality of the problem significantly. Compared with previous applications in hydrogeology, novelties of this study include an improvement of the dimensionality reduction algorithm to avoid streaking artifacts, it is the first application to geophysics and the first application to field data. The results of a synthetic example show that the model domain enclosed by one borehole pair is generally too small to provide reliable estimates of geostatistical variables. A real-data example based on two borehole pairs confirms these findings and demonstrates that the inversion procedure also works under realistic conditions with, for example, unknown measurement errors.