References of "Nguyen, Frédéric"
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See detailRegularized focusing inversion of time-lapse electrical resistivity data: an approach to parametrize the minimum gradient support functional
Nguyen, Frédéric ULg; Hermans, Thomas ULg

Poster (2015, April 15)

Inversion of time-lapse resistivity data allows obtaining ‘snapshots’ of changes occurring in monitored systems for applications such as aquifer storage, geothermal heat exchange, site remediation or ... [more ▼]

Inversion of time-lapse resistivity data allows obtaining ‘snapshots’ of changes occurring in monitored systems for applications such as aquifer storage, geothermal heat exchange, site remediation or tracer tests. Based on these snapshots, one can infer qualitative information on the location and morphology of changes occurring in the subsurface but also quantitative estimates on the degree of changes in certain property such as temperature or total dissolved solid content. Analysis of these changes can provide direct insight into flow and transport and associated processes and controlling parameters. However, the reliability of the analysis is dependent on survey geometry, measurement schemes, data error, and regularization. Survey design parameters may be optimized prior to the monitoring survey. Regularization, on the other hand, may be chosen depending on available information collected during the monitoring. Common approaches consider smoothing model changes both in space and time but it is often needed to obtain a sharp temporal anomaly, for example in fractured aquifers. We here propose to use the alternative regularization approach based on minimum gradient support (MGS) (Zhdanov, 2002) for time-lapse surveys which will focus the changes in tomograms snapshots. MGS will limit the occurrences of changes in electrical resistivity but will also restrict the variations of these changes inside the different zones. A common difficulty encountered by practitioners in this type of regularization is the choice of an additional parameter, the so-called , required to define the MGS functional. To the best of our knowledge, there is no commonly accepted or standard methodology to optimize the MGS parameter . The inversion algorithm used in this study is CRTomo (Kemna 2000). It uses a Gauss-Newton scheme to iteratively minimize an objective function which consists of a data misfit functional and a model constraint functional. A univariate line search is performed at each Gauss-Newton iteration step to find the optimum value of the regularization parameter  which minimizes the data misfit as a function of  while the data misfit is above the desired value and yields the desired target misfit (root-mean square value of error-weighted data misfit equal to 1) at the last iteration for a maximum value of . We propose here to optimize the  of the MGS functional by considering a univariate line search at the first iteration to find the  that minimizes the data misfit. The parameter is then kept constant during the Gauss-Newton iterative scheme. In this contribution, we validate our approach on a numerical benchmark and apply it successfully on a case study in the context of salt tracers in fractured aquifers. Zhdanov M.S. 2002. Geophysical Inverse Theory and Regularization Problems. Elsevier, Amsterdam, 628 p. Kemna A. 2000. Tomographic Inversion of Complex Resistivity - Theory and Application. PhD Thesis, Ruhr University Bochum. [less ▲]

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See detailVariogram-based inversion of time-lapse electrical resistivity data: development and application to a thermal tracing experiment
Hermans, Thomas ULg; Nguyen, Frédéric ULg

Poster (2015, April 15)

Electrical resistivity tomography (ERT) has become a popular imaging methodology in a broad range of applications given its large sensitivity to subsurface parameters and its relative simplicity to ... [more ▼]

Electrical resistivity tomography (ERT) has become a popular imaging methodology in a broad range of applications given its large sensitivity to subsurface parameters and its relative simplicity to implement. More particularly, time-lapse ERT is now increasingly used for monitoring purposes in many contexts such as water content, permafrost, landslide, seawater intrusion, solute transport or heat transport experiments. Specific inversion schemes have been developed for time-lapse data sets. However, in contrast with static inversions for which many techniques including geostatistical, minimum support or structural inversion are commonly applied, most of the methodologies for time-lapse inversion still rely on non-physically based spatial and/or temporal smoothing of the parameters or parameter changes. In this work, we propose a time-lapse ERT inversion scheme based on the difference inversion scheme. We replace the standard smoothness-constraint regularization operator by the parameter change covariance matrix. This operator takes into account the correlation between changes in resistivity at different locations through a variogram computed using independent data (e.g., electromagnetic logs). It may vary for subsequent time-steps if the correlation length is time-dependent. The methodology is first validated and compared to the standard smoothness-constraint inversion using a synthetic benchmark simulating the injection of a conductive tracer into a homogeneous aquifer inducing changes in resistivity values of known correlation length. We analyze the influence of the assumed correlation length on inversion results. Globally, the method yields better results than the traditional smoothness constraint inversion. Even if a wrong correlation length is assumed, the method performs as well as the smoothness constraint since the regularization operator balances the weight given to the model constraint functional in the objective function. Then the methodology is successfully applied to a heat injection and pumping experiment in an alluvial aquifer. The comparison with direct measurements in boreholes (temperature loggers and distributed temperature sensing optic fibres) shows that ERT-derived temperatures and breakthrough curves image reliably the heat plume through time (increasing part of the curve, maximum and tail are correctly retrieved) and space (lateral variations of temperature are observed) with less spatial smoothing than standard methods. The development of new regularization operators for time-lapse inversion of ERT data is necessary given the broad range of applications where ERT monitoring is used. In many studies, independent data are available to derive geostatistical parameters that can be subsequently used to regularize geophysical inversions. In the future, the integration of spatio-temporal variograms into existing 4D inversion schemes should further improve ERT time-lapse imaging. [less ▲]

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See detailQuantitative temperature monitoring of a heat tracing experiment using cross-borehole ERT
Hermans, Thomas ULg; Wildemeersch, Samuel ULg; Jamin, Pierre ULg et al

in Geothermics (2015), 53

The growing demand for renewable energy leads to an increase in the development of geothermal energy projects and heat has become a common tracer in hydrology and hydrogeology. Designing geothermal ... [more ▼]

The growing demand for renewable energy leads to an increase in the development of geothermal energy projects and heat has become a common tracer in hydrology and hydrogeology. Designing geothermal systems requires a multidisciplinary approach including geological and hydrogeological aspects. In this context, electrical resistivity tomography (ERT) can bring relevant, qualitative and quantitative information on the temperature distribution in operating shallow geothermal systems or during heat tracing experiments. We followed a heat tracing experiment in an alluvial aquifer using cross-borehole time-lapse ERT. Heated water was injected in a well while water of the aquifer was extracted at another well. An ERT section was set up across the main flow direction. The results of ERT were transformed into temperature using calibrated petrophysical relationships. These ERT-derived temperatures were then compared to direct temperature measurements in control piezometers collected with distributed temperature sensing (DTS) and groundwater temperature loggers. Spatially, it enabled to map the horizontal and vertical extent of the heated water plume, as well as the zones where maximum temperatures occurred. Quantitatively, the temperatures and breakthrough curves estimated from ERT were in good agreement with the ones observed directly during the rise and maximum of the curve. An overestimation, likely related to 3D effects, was observed for the tail of the heat breakthrough curve. The error made on temperature can be estimated to be between 10 to 20 %, which is a fair value for indirect measurements. From our data, we estimated a quantification threshold for temperature variation of 1.2°C. These results suggest that ERT should be considered when designing heat tracing experiments or geothermal systems. It could help also to assess the geometrical complexity of the concerned reservoirs. It also appears that ERT could be a useful tool to monitor and control geothermal systems once they are in operation. [less ▲]

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See detailUncertainty in Training-Image Based Inversion of Hydraulic Head Data Constrained to ERT Data: Workflow and Case Study
Hermans, Thomas ULg; Nguyen, Frédéric ULg; Caers, Jef

Conference (2014, December 18)

In inverse problems, investigating the relationship between data and prior models and the uncertainty related to the posterior distribution of model parameters are as important as matching the data. In ... [more ▼]

In inverse problems, investigating the relationship between data and prior models and the uncertainty related to the posterior distribution of model parameters are as important as matching the data. In recent years, many efforts have been done to assess the posterior distribution of a given problem with reasonable computational costs through inversion techniques such as McMC. The derived posterior distribution is always dependent on the prior distribution. However, most of the studies ignore modeling the prior with realistic uncertainty. In this paper, we propose a workflow to assess the uncertainty of inversion of hydraulic heads data through the addition of electrical resistivity tomography (ERT) constraining data. The workflow is divided in three successive steps: 1) Construction of prior: we generate multiple alternative geological scenarios from literature data (architecture of facies) as well as site specific data (proportions of facies). Spatial uncertainty within each scenario is integrated hierarchically through geostatistics (multiple-point statistics simulation of facies constrained by ERT data as soft data). 2) Validation of prior scenarios: we transform prior facies scenarios into resistivity distribution scenarios through forward and inverse modeling. The scenarios are validated by comparison with field ERT data. The comparison is made through distance calculation and projection into a low dimensional space to calculate the probability of each scenario given field ERT data. 3) Matching dynamical data: we use the probability perturbation method, within each scenario, to integrate hydraulic heads to our models. We account for scenario probabilities, calculated in 2, in determining how many models per scenario we have to consider for building a reliable posterior distribution. As an illustration, the method is applied on a field case study in an alluvial aquifer (Belgium) where we consider prior uncertainty related to the type of elements (gravel channels or bars) and to their size. This study shows the importance of considering the uncertainty of the prior in inverse problems as it has a strong influence on model predictions and decision-making problems. [less ▲]

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See detailProspection géophysique de la zone faillée de Hockai dans la région de Malmedy: Rapport des tomographies de résistivité électrique
Hermans, Thomas ULg; Nguyen, Frédéric ULg

Report (2014)

Ce rapport consiste en la présentation des résultats des prospections géophysiques par tomographie de résistivité électrique (ERT) menées sur la zone faillée de Hockai dans la région de Malmedy. Le but ... [more ▼]

Ce rapport consiste en la présentation des résultats des prospections géophysiques par tomographie de résistivité électrique (ERT) menées sur la zone faillée de Hockai dans la région de Malmedy. Le but principal de ces investigations est de juger de la fracturation de la roche dans et en dehors de la Zone de Faille de Hockai (ZFH) et de mettre en évidence les structures liées à cette zone de failles. [less ▲]

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See detailVADOSE ZONE STUDIES AT AN INDUSTRIAL CONTAMINATED SITE: THE VADOSE ZONE MONITORING SYSTEM AND CROSS-HOLE GEOPHYSICS
Fernandez de Vera, Natalia ULg; Beaujean, Jean ULg; Jamin, Pierre ULg et al

Conference (2014, September 03)

In situ vadose zone characterization is essential to improve risk characterization and remediation measures for soil and groundwater contamination. However, most available technologies have been developed ... [more ▼]

In situ vadose zone characterization is essential to improve risk characterization and remediation measures for soil and groundwater contamination. However, most available technologies have been developed in the context of agricultural soils. Most of these methodologies are not applicable at industrial sites, where soils and contamination differ in origin and composition. In addition, they are applicable only in the first meters of soils, leaving deeper vadose zones with lack of information, in particular on field scale heterogeneity. To overcome such difficulties, a vadose zone experiment has been setup at a former industrial site in Belgium. Industrial activities carried out on site left a legacy of soil and groundwater contamination in BTEX, PAH, cyanide and heavy metals. The experiment involves the combination of two techniques: the Vadose Zone Monitoring System (VMS) and cross-hole geophysics. The VMS allows continuous measurements of water content at different depths of the vadose zone (Dahan et al., 2009). In addition, it provides the possibility of pore water sampling at different depths. The system is formed by a flexible sleeve installed in a slanted borehole (Fig. 1) and containing monitoring units along its depth (Fig. 2). The flexible sleeve contains three types of monitoring units in the vadose zone: Time Domain Transmissometry (TDT), which allows water content measurements; Vadose Sampling Ports (VSP), used for collecting water samples coming from the matrix; and the Fracture Samplers (FS), which are used for retrieving water samples from the fractures. Cross-hole electrical tomography measurements are carried providing detailed spatial patterns about electrical properties of the subsurface. Such properties are related with subsurface heterogeneities, water content and solute concentrations. Two VMS were installed on site, together with four vertical boreholes containing electrodes for geophysical measurements. The site has been monitored under natural recharge conditions during the summer, autumn and winter. Results show reactions in the soil at depths up to 6m as a consequence of rainfall infiltration and groundwater level fluctuations. In addition, the chemistry of the soil water changes with depth and water infiltration. Background images obtained from geophysical measurements show a highly conductive subsurface due to the lithologies and the high mineralization of the water in the vadose zone. The combination of cross-hole geophysics with the VMS has provided an effective tool for characterizing the chemistry and the structure of the vadose zone. [less ▲]

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See detailCase studies of incorporation of prior information in electrical resistivity tomography: comparison of different approaches
Caterina, David ULg; Hermans, Thomas ULg; Nguyen, Frédéric ULg

in Near Surface Geophysics (2014), 12(4), 451-465

Many geophysical inverse problems are ill-posed and their solution non-unique. It is thus important to reduce the amount of mathematical solutions to more geologically plausible models by regularizing the ... [more ▼]

Many geophysical inverse problems are ill-posed and their solution non-unique. It is thus important to reduce the amount of mathematical solutions to more geologically plausible models by regularizing the inverse problem and incorporating all available prior information in the inversion process. We compare three different ways to incorporate prior information for electrical resistivity tomography (ERT): using a simple reference model or adding structural constraints to Occam's inversion and using geostatistical constraints. We made the comparison on four real cases representing different field applications in terms of scales of investigation and level of heterogeneities. In those cases, when electromagnetic logging data are available in boreholes to control the solution, it appears that incorporating prior information clearly improves the correspondence with logging data compared to the standard smoothness constrain. However, the way to incorporate it may have a major impact on the solution. A reference model can often be used to constrain the inversion; however, it can lead to misinterpretation if its weight is too strong or the resistivity values inappropriate. When the computation of the vertical and/or horizontal correlation length is possible, the geostatistical inversion gives reliable results everywhere in the section. However, adding geostatistical constraints can be difficult when there is not enough data to compute correlation lengths. When a known limit between two layers exists, the use of structural constrain seems to be more indicated particularly when the limit is located in zones of low sensitivity for ERT. This work should help interpreters to include their prior information directly into the inversion process through an appropriate way. [less ▲]

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See detailInverting Hydraulic Heads In An Alluvial Aquifer Constrained With Electrical Resistivity Tomography Data Through Multiple-Point Statistics And Probability Perturbation Method: A Case Study
Hermans, Thomas ULg; Scheidt, Celine; Caers, Jef et al

Conference (2014, July)

Solving spatial inverse problems in the Earth Sciences remains a considerable challenge given the large number of parameters to invert for, the non-linearity of forward models and as a result the ill ... [more ▼]

Solving spatial inverse problems in the Earth Sciences remains a considerable challenge given the large number of parameters to invert for, the non-linearity of forward models and as a result the ill-posedness of the problem. Geostatistics is therefore needed to specify prior models, more particularly, information to control the spatial features of the inverse solutions. We used multiple-point statistics (MPS) to build models of pre-defined hydrofacies: clay, sand and gravel facies constrained to geological data (hard data) and geophysical data (soft data). The electrical resistivity tomography method was chosen to bring relevant spatially distributed information on the presence of the facies, given its sensitivity to variations in lithology and porosity. The comparison of the geophysical signature of the deposits with direct observations in boreholes enables to derive the conditional probability of observing a facies given its electrical resistivity. This is used to produce probability maps for each facies and constrain stochastic simulations of the alluvial aquifer. Then, the probability perturbation method (PPM) is used to integrate hydraulic heads data, using MPS to generate models. This process enables us to obtain calibrated models of the aquifer. The PPM algorithm will automatically seek solutions fitting both hydrogeological data and training-image based geostatistical constraints. Only geometrical features of the model are affected by the perturbation, i.e. we do not attempt to directly find the optimal value of hydrogeological parameters (chosen a priori), but the optimal spatial distribution of facies whose prior distribution is quantified in a training image. The methodology is first tested with a synthetic benchmark. The tests performed show that the choice of the training image is a major source of uncertainty. Therefore, one first needs to select those training images consistent with the geophysical data (and hence reject the inconsistent ones). Then, we proceed with them to hydrogeological inversions. Geophysical data (soft constraints) acts as an accelerator of convergence by reducing prior uncertainty. The hydraulic conductivity of each facies is a sensitive parameter, but it can be easily optimized prior to the PPM process. The stochastic method is then successfully applied within the context of an alluvial aquifer submitted to a pumping experiment. We show how the integration of various sources of data (borehole logs, geophysics, hydraulic heads) aids in calibrating hydrogeological models, locating high hydraulic conductivity zones and reducing uncertainty. The developed methodology proposes a common framework (multiple-point statistics) to integrate various information sources with variable resolutions relevant for hydrogeology: geological, geophysical and hydrogeological data. The method can be extended to integrate tracer tests to enable the calibration of transport parameters as well. The originality of the method is to use geophysical data both to refine the choice of the training image and to constrain the inversion of hydrogeological models. [less ▲]

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See detailVadose zone studies at an industrial contaminated site: the vadose zone monitoring system and cross-hole geophysics
Fernandez de Vera, Natalia ULg; Beaujean, Jean ULg; Jamin, Pierre ULg et al

Poster (2014, April 29)

Poster presented at the European Geoscience Union General Assembly 2014. In this poster, the installation of the vadose zone experimental set up is presented along with first results

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See detailVadose zone studies at an industrial contaminated site: the vadose zone monitoring system and cross-hole geophysics
Fernandez de Vera, Natalia ULg; Pena Hernandez, Juan Angel; Beaujean, Jean ULg et al

Scientific conference (2014, March 05)

Oral presentation of the PhD project at the ENVITAM PhD day in Louvain-la-Neuve

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See detailVadose zone studies at an industrial contaminated site: the vadose zone monitoring system and cross-hole geophysics
Fernandez de Vera, Natalia ULg; Pena Hernandez, Juan; Beaujean, Jean ULg et al

Scientific conference (2014, January 15)

Oral presentation for the PhD geoscience day at the University of Liege.

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See detailUtilisation de la géostatistique multi-points pour l'intégration de données de tomographie de résistivité électrique aux modèles hydrogéologiques
Hermans, Thomas ULg; Scheidt, Céline; Caers, Jef et al

Scientific conference (2014, January 15)

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See detailDétermination des propriétés de couches dans le béton à l'aide d'un géoradar commercial à hautes fréquences: approche pic-à-pic et analyse fréquentielle du coefficient de réflexion
Van der Wielen, Audrey ULg; Nguyen, Frédéric ULg; Courard, Luc ULg

in Annales du Bâtiment et des Travaux Publics (2014)

The Ground Penetrating Radar (GPR) is an efficient tool for the non-destructive inspection of concrete structures. It is widely used for the detection of rebars or humid zones or for evaluating the ... [more ▼]

The Ground Penetrating Radar (GPR) is an efficient tool for the non-destructive inspection of concrete structures. It is widely used for the detection of rebars or humid zones or for evaluating the thickness of elements. But when an element contains a thin layer, the radar waves are submitted to multiple reflections on the interfaces and the layer appears in the radargram as a single reflection, whose detailed analysis can allow determining the thickness and the permittivity of the thin layer. Two approaches were considered in this paper. In the first one, the analysis is based on the peak-to-peak reflection amplitude. The second approach uses a frequency analysis of the reflection coefficient, whose amplitude and phase can then be calculated for several frequencies. With this method, the thickness and permittivity of the layer can in theory be simultaneously determined. Both methods were numerically validated through finite difference simulations and experimentally tested on concrete samples containing an air layer of variable thickness. We showed that the frequency analysis allowed to reach a higher precision in the parameters estimation for a limited additional computing cost. The method efficiency depends on the conditions and is optimal for layers with a high permittivity presenting a large contrast with the matrix. [less ▲]

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See detailCoupling heat and chemical tracer experiments for estimating heat transfer parameters in shallow alluvial aquifers
Wildemeersch, Samuel ULg; Jamin, Pierre ULg; Orban, Philippe ULg et al

in Journal of Contaminant Hydrology (2014), 169

Geothermal energy systems, closed or open, are increasingly considered for heating and/or cooling buildings. The efficiency of such systems depends on the thermal properties of the subsurface. Therefore ... [more ▼]

Geothermal energy systems, closed or open, are increasingly considered for heating and/or cooling buildings. The efficiency of such systems depends on the thermal properties of the subsurface. Therefore, feasibility and impact studies performed prior to their installation should include a field characterization of thermal properties and a heat transfer model using parameter values measured in situ. However, there is a lack of in situ experiments and methodology for performing such a field characterization, especially for open systems. This study presents an in situ experiment designed for estimating heat transfer parameters in shallow alluvial aquifers with focus on the specific heat capacity. This experiment consists in simultaneously injecting hot water and a chemical tracer into the aquifer and monitoring the evolution of groundwater temperature and concentration in the recovery well (and possibly in other piezometers located down gradient). Temperature and concentrations are then used for estimating the specific heat capacity. The first method for estimating this parameter is based on a modeling in series of the chemical tracer and temperature breakthrough curves at the recovery well. The second method is based on an energy balance. The values of specific heat capacity estimated for both methods (2.30 and 2.54 MJ/m3/K) for the experimental site in the alluvial aquifer of the Meuse River (Belgium) are almost identical and consistent with values found in the literature. Temperature breakthrough curves in other piezometers are not required for estimating the specific heat capacity. However, they highlight that heat transfer in the alluvial aquifer of the Meuse River is complex and contrasted with different dominant process depending on the depth leading to significant vertical heat exchange between upper and lower part of the aquifer. Furthermore, these temperature breakthrough curves could be included in the calibration of a complex heat transfer model for estimating the entire set of heat transfer parameters and their spatial distribution by inverse modeling. [less ▲]

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See detailGeophysical Methods for Monitoring Temperature Changes in Shallow Low Enthalpy Geothermal Systems
Hermans, Thomas ULg; Nguyen, Frédéric ULg; Robert, Tanguy et al

in Energies (2014), 7

Low enthalpy geothermal systems exploited with ground source heat pumps or groundwater heat pumps present many advantages within the context of sustainable energy use. Designing, monitoring and ... [more ▼]

Low enthalpy geothermal systems exploited with ground source heat pumps or groundwater heat pumps present many advantages within the context of sustainable energy use. Designing, monitoring and controlling such systems requires the measurement of spatially distributed temperature fields and the knowledge of the parameters governing groundwater flow (permeability and specific storage) and heat transport (thermal conductivity and volumetric thermal capacity). Such data are often scarce or not available. In recent years, the ability of electrical resistivity tomography (ERT), self-potential method (SP) and distributed temperature sensing (DTS) to monitor spatially and temporally temperature changes in the subsurface has been investigated. We review the recent advances in using these three methods for this type of shallow applications. A special focus is made regarding the petrophysical relationships and on underlying assumptions generally needed for a quantitative interpretation of these geophysical data. We show that those geophysical methods are mature to be used within the context of temperature monitoring and that a combination of them may be the best choice regarding control and validation issues. [less ▲]

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See detailDetection of near-field, low permittivity layers with Ground Penetrating Radar: analytical estimation of the reflection coefficient
Van der Wielen, Audrey; Courard, Luc ULg; Nguyen, Frédéric ULg

in LAMBOT, Sébastien (Ed.) Proceedings of 15th International Conference on ground Penetrating Radar (2014)

The reflection coefficient of GPR waves encountering embedded thin layers is commonly estimated using a plane wave, far field approximation. But when the thin layer is situated in the near field of the ... [more ▼]

The reflection coefficient of GPR waves encountering embedded thin layers is commonly estimated using a plane wave, far field approximation. But when the thin layer is situated in the near field of the antenna, the spherical nature of the waves and the possible propagation of a lateral wave into the layer may have a strong influence on the measured reflected amplitude. In this work, we studied through 2D FDTD simulations the behavior of a radar wave interacting with thin layers of different thicknesses. The snapshots and radargrams showed a large influence of the layer thickness on the wave propagation. For the very thin layers, the evanescent wave plays a major role and the plane wave approximation gives a good estimation of the reflection coefficient. For thicker layers, the specific inclination of each multiple reflection has to be taken into account, as well as the lateral wave propagation. On the basis of these observations, we determined which analytical method should be used for the analytical prediction of the reflection coefficient, as a function of the layer thickness. [less ▲]

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See detailDétermination des propriétés de couches minces dans le béton à l’aide d’un géoradar commercial à hautes fréquences: approche pic-à-pic et analyse fréquentielle du coefficient de réflexion
Van der Wielen, Audrey; Courard, Luc ULg; Nguyen, Frédéric ULg

in Balayssac, Jean-Paul (Ed.) Compte-rendus de Diagnobeton 2014 (2014)

The Ground Penetrating Radar (GPR) is an efficient tool for the non-destructive inspection of concrete structures. It is widely used for the detection of rebars or humid zones or for evaluating the ... [more ▼]

The Ground Penetrating Radar (GPR) is an efficient tool for the non-destructive inspection of concrete structures. It is widely used for the detection of rebars or humid zones or for evaluating the thickness of elements. But when an element contains a thin layer, the radar waves are submitted to multiple reflections on the interfaces and the layer appears in the radargram as a single reflection, whose detailed analysis can allow determining the thickness and the permittivity of the thin layer. Two approaches were considered in this paper. In the first one, the analysis is based on the peak-to-peak reflection amplitude. The second approach uses a frequency analysis of the reflection coefficient, whose amplitude and phase can then be calculated for several frequencies. With this method, the thickness and permittivity of the layer can in theory be simultaneously determined. Both methods were numerically validated through finite difference simulations and experimentally tested on concrete samples containing an air layer of variable thickness. We showed that the frequency analysis allowed to reach a higher precision in the parameters estimation for a limited additional computing cost. The method efficiency depends on the conditions and is optimal for layers with a high permittivity presenting a large contrast with the matrix. [less ▲]

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See detailAssessing the Probability of Training Image-Based Geological Scenarios Using Geophysical Data
Hermans, Thomas ULg; Caers, Jef; Nguyen, Frédéric ULg

in Pardo-Iguzquiza, Eulogio; Guardiola-Albert, Carolina; Heredia, Javier (Eds.) et al Mathematics of Planet Earth - Proceedings of the 15th Annual Conference of the International Association for Mathematical Geosciences (2014)

In multiple-point statistics (MPS), the construction of training im-ages (TIs) is one of the most critical steps. Reliable geological studies may not always be available to depict with certainty what ... [more ▼]

In multiple-point statistics (MPS), the construction of training im-ages (TIs) is one of the most critical steps. Reliable geological studies may not always be available to depict with certainty what geological patterns or heterogeneity are present. In this context, geophysical techniques may provide additional information to reduce the possible large uncertainty in the understanding of prior geological scenarios. To overcome this problem, we developed a methodology to verify the consistency of geophysical data with independently-built TIs representing different plausible geological scenarios. If a TI is deemed consistent with the field geophysical survey, then in a sec-ond step we calculate a likelihood probability for each consistent TI. Our methodology starts by creating subsurface models with each TI. From these models we create synthetic geophysical data and from this synthetic data, synthetic inverted models. These models are now compared with a single inverted model obtained from the field sur-vey, allowing for our definition of what is “consistent”. To that ex-tent, we calculate the Euclidean distance between any two inverted models as well as field data and visualize the results in a 2D or 3D space using multidimensional scaling (MDS). With this technique, it is possible to verify if field cases fall in the distribution represented by synthetic cases, and thus are consistent with them. In a second step, we present a cluster analysis on the MDS-map to highlight which parameters are the most sensitive for the construction of TI. Based on this analysis, a probability of each geological scenario is computed through kernel smoothing of the densities in reduced pro-jected metric space. This approach was tested using electrical resistivity tomography as geophysical data to analyze TI scenarios for the Meuse alluvial aqui-fer (Belgium), where the lack of reliable sedimentological data lead to the definition of a multitude of geological scenarios, hence TIs. [less ▲]

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