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Proper description of antenna effects on ground-penetrating radar (GPR) data generally relies on numerical methods such as the Method of Moments (MoM) or Finite-Difference Time-Domain (FDTD) modeling approaches. Yet, numerical methods are computationally expensive and accurate reproduction of real measurements has remained a major challenge for many years. Recently, intrinsic modeling approaches, through which radar antennas are effectively described using their fundamental features, have demonstrated great promise for near-field radar antenna modeling. Although such approaches are not suited for designing radar antennas, they are particularly powerful for fast and accurate modeling, which is a prerequisite when full-wave inversion is applied, e.g., for estimating medium electrical properties. These approaches are also of great interest for filtering out antenna effects from measured radar data for improved subsurface imaging.

Soils play an important role in the carbon (C) cycle. They constitute an important part of the global C pool, by storing C in de forms of organic matter and carbonates. The soil micro-organisms respiration transforms organic carbon (OC) into CO2. Two considerable concerns exist in relation with this: the global climate change due to the greenhouse gas warming potential of CO2 and the decrease of soil quality.

We present validation results of a new groundpenetrating radar (GPR) near-field model for determining the electrical properties and correlated water content of a sand using both frequency- and time-domain radars. The radar antennas are intrinsically characterized using an equivalent set of infinitesimal source/field points and characteristic functions of antennas, which were determined using measurements with the antenna at different distances from a copper plane. The antenna radiation was modeled using six source and field points, which was found to be a good compromise between high modeling accuracy and computing efficiency. We validated our model by inverting GPR data to predict the water content of a sand layer subject to seven levels of saturation. A soil dielectric mixing model was integrated into the full-wave GPR inverse modeling to directly estimate the water content and to account for the frequency dependence of the electrical properties. Although the quality of the fit slightly decreased as the antenna approached the sand surface, the results showed a close agreement between measured and modeled data, resulting in accurate estimation of the water content. The average errors of all water content estimates were 0.012 cm3/cm3 for the frequency domain and 0.016 cm3/cm3 for the time-domain GPR. However, the accuracy reduced when the sand became wet. By performing numerical simulations, we found that it is due to the vertical heterogeneity of soil moisture under the effect of the hydrostatic pressure.We also showed that the GPR inversion with the multilayered soil model could account for this heterogeneity and improved the agreement between the modeled and measured GPR data as well as the accuracy of soil moisture estimation. As for the frequency dependence of the electrical properties, in the frequency ranges of bothGPR systems, while the dielectric permittivity was approximately constant, the apparent conductivity exponentially increased with increasing frequ

Water lost through leaks can represent high percentages of the total production in water supply systems and constitutes an important issue. Leak detection can be tackled with various techniques such as the ground-penetrating radar (GPR). Based on this technology, various procedures have been elaborated to characterize a leak and its evolution. In this study, we focus on a new full-wave radar modelling approach for near-field conditions, which takes into account the antenna effects as well as the interactions between the antenna(s) and the medium through frequency-dependent global transmission and reflection coefficients. This approach is applied to layered media for which 3-D Green’s functions can be calculated. The model allows for a quantitative estimation of the properties of multilayered media by using full-wave inversion. This method, however, proves to be limited to provide users with an on-demand assessment as it is generally computationally demanding and time consuming, depending on the medium configuration as well as the number of unknown parameters to retrieve. In that respect, we propose two leads in order to enhance the parameter retrieval step. The first one consists in analyzing the impact of the reduction of the number of frequencies on the information content. For both numerical and laboratory experiments, this operation has been achieved by investigating the response surface topography of objective functions arising from the comparison between measured and modelled data. The second one involves the numerical implementation of multistatic antenna configurations with constant and variable offsets in the model. These two kinds of analyses are then combined in numerical experiments. To perform the numerical analyses, synthetic Green’s functions were simulated for different multilayered medium configurations. The results show that an antenna offset increase leads to an improvement in the response surface topography, which is more or less marked according

Ground-penetrating radar (GPR) has recently become a powerful geophysical technique to characterize soil moisture at the field scale. Compared to the airborne/spaceborne remote sensing techniques, GPR can provide soil moisture data with a much higher spatial resolution (around 0.1- 1 m). Its characterization depth is also larger for the fact that GPR works near the soil surface. We developed a data assimilation scheme to simultaneously estimate the vertical soil moisture profile and hydraulic parameters from time-lapse GPR measurements. The assimilation scheme includes a soil hydrodynamic model to simulate the soil moisture dynamics, a full-wave electromagnetic wave propagation model and petrophysical relationship to link the state variable with the GPR data, and a maximum likelihood ensemble assimilation algorithm. The hydraulic parameters are estimated jointly with the soil moisture using a state augmentation technique. The approach allows for the direct assimilation of GPR data, thus maximizing the use of the information. The proposed approach was validated by numerical experiments assuming wrong initial conditions and hydraulic parameters. We compared three scenarios: open-loop (without assimilation), surface soil moisture assimilation and GPR assimilation. The synthetic soil moisture profiles were generated by the Hydrus-1D model, which then were used by the electromagnetic model and petrophysical Relationship to create "observed" GPR data. The results show that the data assimilation significantly improves the accuracy of the hydrodynamic model prediction. Compared with the surface soil moisture assimilation, the GPR data assimilation better corrects the soil moisture profile and hydraulic parameters. The results also show that the estimated soil moisture profile in the coarse soil converges to the "true" state more rapidly than in the fine one. Of the three unknown parameters of the Mualem-van Genuchten model, the estimation of n is more accurate than that of

Root water uptake dynamics at local scale can be studied in laboratory conditions by growing plants in rhizotron containing sand and by imaging the water content evolution of the medium using light transmission. This technique allows to accurately retrieve the water content with high resolution but cannot be applied in opaque medium as leaf-mold or clay, which is a major limitation for more realistic applications. Recently, ground-penetrating radar (GPR) has proven to be one of the most promising techniques for high-resolution digital soil mapping at intermediate scale. Particularly, by using a full-wave inverse modeling of near-field GPR with a high frequency antenna, the electrical properties of soil and their correlated water content with high spatiotemporal resolution can be reconstruct. In this study, we applied the approach by using an ultra-wideband frequency-domain radar with a transmitting and receiving horn antenna operating in the frequency range 3-6 GHz for imaging, in near-field conditions, a rhizotron containing sand subject to different water contents. Synthetic radar data were also generated to examine the well-posedness of the full-waveform inverse problem at high frequencies. Finally, we compared the water content obtained by GPR and light transmission measurements. The results have shown that the near-field modeled and measured GPR data perfectly match in the frequency and time domain for both dry and wet sand. In the case of dry sand, the estimated water content based on GPR and light transmission data was retrieved with small differences. Indeed, the thinness of the sand layer in the rhizotron involves a biggest influence of the air in the GPR signal leading to an underestimate value of the water content. This research shows the potential of the GPR system and the near-field model to accurately estimate the water content of different soils with a high spatial resolution. Future studies will focus on the use of GPR to monitor root water uptake dy

Accurate quantification of soil moisture is crucial for hydrology, meteorology, and environment. Recently, GPR has become a popular technique to characterize soil moisture. Although there have been intensive studies on applications of GPR for soil moisture estimation, significant efforts are still needed to improve its accuracy. In addition, in many applications, knowledge of the soil moisture profile is essential, which has remained a major challenge for many years. For increasing the accuracy of soil moisture estimation, we improved the GPR modeling and petrophysical relationships. For the GPR model, we further developed the near-field antenna model introduced by Lambot and Andre (2013). We successfully calibrated and validated the model using both numerical and laboratory experiments. Then, we improved the petrophysical relationship by coupling full-wave GPR inversion, dielectric mixing model and Debye's equation to account for the frequency dependence of electric properties and directly estimate soil moisture. For estimating the soil hydraulic properties and moisture profile, the GPR model was integrated into the hydrodynamic model in an assimilation framework. The hydrodynamic model was employed to simulate the spatiotemporal dynamics of soil moisture in the unsaturated zone, while the GPR model and petrophysical relationships were used to link the soil moisture profile with GPR data. The assimilation was performed using the Maximum Likelihood Ensemble Filter algorithm. Instead of using the surface soil moisture only, the approach allows us to use the information of the whole soil moisture profile for the assimilation. This thesis opens a new development and application avenue for digital soil mapping and soil water resources monitoring., (AGRO - Sciences agronomiques et ingénierie biologique) -- UCL, 2014

Root water uptake dynamics at local scale can be studied in laboratory conditions by growing plants in rhizotron containing sand and by imaging the water content evolution of the medium using light transmission. This technique allows to retrieve the water content with high resolution but cannot be applied in opaque media such as leaf-mold or clay, which is a major limitation for more realistic applications. Recently, ground-penetrating radar (GPR) has proven to be one of the most promising techniques for high-resolution digital soil mapping at the field scale. Particularly, by using full-wave inverse modeling of near-field GPR data with a high frequency antenna, the electrical properties of soil and their correlated water content can be reconstructed with a high spatiotemporal resolution. In this study, we applied the approach by using an ultra-wideband frequency-domain radar with a transmitting and receiving horn antenna operating in the frequency range 3-6 GHz for imaging, in near-field conditions, a rhizotron containing sand subject to different water content conditions. Synthetic radar data were also generated to examine the well-posedness of the full-waveform inverse problem at high frequencies. Finally, we compared the water content obtained by GPR and light transmission measurements. The results have shown that the near-field modeled and measured GPR data match very well in the frequency and time domains for both dry and wet sands. In the case of the dry sand, the estimated water content based on GPR and light transmission data was retrieved with small differences. This research shows the potential of the GPR system and near-field full-wave antenna-medium model to accurately estimate the water content of soils with a high spatial resolution. Future studies will focus on the use of GPR to monitor root water uptake dynamics of plants in field conditions.

In this paper, we synthesize the main outcomes of a collaborative project (2009-2014) initiated at the UCL (Belgium). The main objective of the project was to increase our understanding of soil organic matter dynamics in complex landscapes and use this to improve predictions of regional scale soil carbon balances. In a first phase, the project characterized the emergent spatial variability in soil organic matter storage and key soil properties at the regional scale. Based on the integration of remote sensing, geomorphological and soil analysis techniques, we quantified the temporal and spatial variability of soil carbon stock and pool distribution at the local and regional scales. This work showed a linkage between lateral fluxes of C in relation with sediment transport and the spatial variation in carbon storage at multiple spatial scales.

Time and amplitude drift is a common problem for some time-domain radars. Some corrections have been suggested for far-field radar data, but due to the coupling effect, there is no equivalent for near-field radar data. In this paper we first quantified, considering the occurrence of the first reflection peak, the time drift of a 900 MHz center-frequency pulse radar system over a certain time period (28 hours non consecutive in identical situation). The maximum time drift was 0.0978 ns. Second, in the frequency-domain, we characterized the maximum time and amplitude drift via the calculation of a frequencydependent ratio to multiply to the original signal to illustrate the effects of the drift. Third, we measured the sensitivity of the soil material characterization by full-wave inversion in response to a drift. For the inversion problem, we used a new near-field model taking particularly into account the antennamedium coupling through antenna characteristic global reflection and transmission coefficient functions. The overestimation of the dielectric permittivity may reach 50% for low values of the dielectric permittivities, and the underestimation 25% for higher values, following a gradient. The errors on the estimation of the electric conductivity is much higher reaching an extreme 105:4% for the lowest original values, with an average of 102:5%. The differences in the estimation of these two parameters have been explained through a sensitivity analysis. Indeed, the lower sensitivity of the electric conductivity leads to higher errors than for the dielectric permittivity.

Full-wave inverse modeling of low-frequency, nearfield ground-penetrating radar (GPR) data was used for simultaneously reconstructing both the electric permittivity and conductivity of the soil. Low GPR frequencies provide a significant sensitivity of the reflection coefficient to electrical conductivity and are less affected by soil roughness and local heterogeneities. Based on the near-field model, several numerical experiments were conducted to simultaneously retrieve ground electrical conductivities and dielectrical permittivities in the range 10-180 MHz for different water contents. We calibrated a time-domain GPR system equipped with transmitting and receiving 80 MHz unshielded dipoles antennas using measurements collected at different heights over a water layer of known electrical conductivity. Then, the GPR model was validated for measurements collected over water subject to a range of electrical conductivities. A good agreement was obtained between the radar data and the fullwave electromagnetic model for the different antenna heights but the water layer properties were not accurately retrieved. These differences were attributed to errors in the transfer functions of the antenna mainly due to the instability of the radar system. The future challenge in this research will focus on an accurate determination of the antenna transfer functions of a stable radar system for improved medium reconstruction.

Antenna arrays have been increasingly used in many civil engineering and geoscience applications as they allow collecting multi-offset measurements simultaneously, thereby providing additional information for subsurface imaging and characterization. We extended a new near-field intrinsic antenna modeling approach to antenna arrays. The array was considered as a combination of couples of transmitting-receiving antennas with different offsets. Each couple of antennas was characterized using an equivalent set of infinitesimal source/field points and reflection/transmission transfer functions. We proposed an iterative approach to calibrate the model through which the antenna model was progressively completed. To reduce the number of simultaneous unknown parameters, linear and nonlinear optimization algorithms were combined together. We also applied the time gain for both modeled and measured array data to compensate for the wave attenuation, which is expected to improve the accuracy of the calibration. We validated the proposed calibration approach to an antenna array with two-Vivaldi antenna elements operating in the frequency range 0.8- 3 GHz. The offsets between the two antennas were 20 and 40cm, respectively. Calibration data consisted of 100 measurements corresponding to the antenna array at 100 different distances from a copper plane. The calibrated and measured antenna array data closely agree, with correlation coefficients larger than 0.9979 and root mean square error less than 2.3×10−5. These results open a new development avenue to apply the antenna array for digital soil mapping and non-destructive testing of materials using full-wave inverse modeling.

In this study, we numerically evaluated a full-wave antenna model for near-field conditions using a Finite-Difference Time-Domain (FDTD) antenna model. The antenna is effectively characterized by a series of source and field points and global reflection/transmission coefficients, which by using analytical solutions of Maxwell’s equations, enable us to significantly reduce computation times compared to numerical approaches. The full-wave GPR model was calibrated by a series of radar data from numerical measurements performed above an infinite perfect electrical conductor (PEC). The calibration results provided a very good agreement with data from the FDTD antenna model giving a correlation coefficient of 0.9995. The model was subsequently verified by using it to invert responses from the FDTD antenna model to reconstruct the electrical properties of an artificial medium subject to 8 scenarios of layering, thickness and electrical properties. Full-wave inverse modelling enabled us to very well reproduce the GPR data both in time and frequency domains, resulting in accurate estimations of the dielectric permittivity even with a two-layered medium with highly contrasting electrical properties. The relative errors of the permittivity estimation were less than 5% for all medium scenarios and antenna heights. Inversion also provided very good estimations of the electrical conductivity when this parameter was relatively high but poor results were obtained for low conductivities. Surface response analysis showed that the model was more sensitive to permittivity than conductivity and more sensitive to high than low conductivities. Our modelling approach shows great potential to apply full-wave inversion for retrieving the electrical properties of the subsurface from near- and far-field radar measurements.

The root zone soil moisture has been long recognized as important information for hydrological, meteorological and agricultural research. In this study, we propose a closed-loop data assimilation procedure to update the vertical soil moisture profile from time-lapse ground-penetrating radar (GPR) data. The hydrodynamic model, Hydrus-1D (Simunek et al., 2009), is used to propagate the system state in time and a radar electromagnetic model (Lambot et al., 2004) to link the state variable (soil moisture profile) with the observation data (GPR data), which enables us to update the soil moisture profile by directly assimilating the GPR data. The assimilation was performed within the maximum likelihood ensemble filter (MLEF) framework developed by Zupanski et al., (2005), for which the problem of nonlinear observation operator is solved much more effectively than the Ensemble Kalman filter (EnKF) techniques. The method estimates the optimal state as the maximum of the probability density function (PDF) instead of the minimum variance like in most of the other ensemble data assimilation methods. Direct assimilation of GPR data is a prominent advantage of our approach. It avoids solving the timeconsuming inverse problem as well as the estimation errors of the soil moisture caused by inversion. In addition, instead of using only surface soil moisture, the approach allows to use the information of the whole soil moisture profile, which is reflected via the ultra wideband (UWB) GPR data, for the assimilation. The use of the UWB antenna in this study is also an advantage as it provides more information about soil moisture profile with a better depth resolution compared to other classical remote sensing techniques. Our approach was validated by a synthetic study. We constructed a synthetic soil column with a depth of 80 cm and analyzed the effects of the soil type on the data assimilation by considering 3 soil types, namely, loamy sand, silt and clay. The assimilation of GPR dat

We developed a closed-form equation for intrinsic modeling of near-field ground-penetrating radar (GPR) and electromagnetic induction (EMI) antennas for reconstructing the electrical properties of planar layered media. Resorting to plane wave decomposition, the antennas operating on the ground or in near-field conditions are modeled using a set of infinitesimal dipoles and characteristic, frequency-dependent, global reflection and transmission coefficients. Wave propagation and diffusion in the medium are described using a set of three-dimensional planar layered media Green’s functions. Both GPR and EMI antennas were calibrated using measurements collected at different heights, ranging from near-field to far-field conditions, over a perfect electrical conductor. The GPR and EMI models were then validated for measurements collected over water subject to different salinity levels. The models showed a high degree of accuracy for reproducing the observed data and model inversion provided good estimates of the medium electrical properties. Yet, for EMI, discrepancies between measured and estimated electrical conductivity values were observed for the lowest salinity levels, resulting mainly from the limited sensitivity of the prototype EMI system used for this study. Technical possibilities for increasing the sensitivity of the EMI system are currently under examination. In addition, in order to further improve the model performances for EMI, we also investigate different configurations for the set of infinitesimal dipoles used to model the EMI antenna. The proposed approach is applicable to any GPR and EMI system, either prototypes or commercially available sensors and operating either in the time domain or in the frequency domain. It is in particular promising for joint analysis of GPR and EMI data in an inverse data fusion framework, especially as the modeling procedures are identical for both instruments.

Knowledge of the temporal and spatial variations of soil moisture at different scales is essential for environmental and agricultural research and engineering. In that respect, there is an urgent demand for developing novel techniques to quantitatively characterize this key variable. Over this last decade, ground‐penetrating radar (GPR) has known an increasing interest to provide soil moisture data with a high spatial resolution at the field scale.

Physically-based filtering of antenna effects in farfield conditions, including antenna-ground interactions, can be performed using intrinsic antenna modeling based on antenna global reflection and transmission coefficients. This has been in particular validated for frequency domain radars for quantitative reconstruction of layered media using full-wave inversion and improved subsurface imaging. In this paper, we further extend the concept to time domain radars for which the source is not separated from the antenna characteristics. Then, we provide insights on the application of the method to near-field conditions. Radar measurements were performed with the antenna at different heights over a perfect electrical conductor (PEC) and on a sandy soil with buried targets. For the PEC measurements, far-field filtering performed very well and also provided relatively good results in near-field conditions, except for the shortest range. Far-field measurements for the sand also provided good results, although the antenna transfer functions had to be corrected to account for the varying time domain radar source (drift). The radar image was not improved for the on-ground radar configuration. Future research will focus on near-field filtering of antenna effects using a recent generalization of the far-field model to near-field conditions.

In this research, full-wave modeling of near-field ground-penetrating radar (GPR) data is used for reconstructing the electrical properties of a reference water layer. Based on the three-dimensional multilayered media Green's functions from the near-field model, several numerical experiments were conducted to simultaneously retrieve the water electrical conductivities, water thickness and antenna heights at relatively low frequencies (i.e., 10-710 MHz). We calibrated a homemade bowtie antenna using measurements collected at different heights over a water layer of known electrical conductivity. Once the global transmission and reflection coefficients of the antenna were known, synthetic radar data could be simulated to test the well-posedness of the inverse problem. The GPR model was then validated for measurements collected over water subject to a range of electrical conductivities. A good agreement was obtained between the radar data and the full-wave electromagnetic model and the water layer properties were accurately retrieved. Yet, some discrepancies were observed between the inversely estimated and measured water electrical conductivities. This was attributed to a lower sensitivity of the model to electrical conductivity for this particular setup. The proposed methods present promising perspectives for digital soil mapping.

For years, the need to develop techniques able to characterize soil layer properties at relevant scales has increased continuously to appraise dynamic subsurface phenomena and conceive optimal exploitation and remediation strategies. Amongst existing geophysical techniques, ground-penetrating radar (GPR) is of particular interest for providing high-resolution subsurface images and especially addressing water-related questions. Yet, the retrieval of quantitative information regarding the soil physical properties has remained a challenge. In order to maximize information retrieval from GPR, full-wave inverse modeling should be performed, which requires an accurate forward electromagnetic radar-medium model. For the specific case of far-field GPR, an efficient and accurate model was developed and successfully used to retrieved soil water content in many applications. Yet, this model is limited to far-field applications and thus soil information retrieval is limited to relatively shallow depths. In this research, a new near-field radar modeling approach is used to analyze the soil properties by GPR. This model inherently takes into account the effects of interactions between antenna and the medium, allowing us to operate in near-field conditions (e.g., with the antenna in contact with the soil) and thereby increase the penetration depth and resolution. The main objective of the presented research is modeling and calibration of a low frequency radar antenna and focus inversion on the antenna-soil coupling to simultaneously retrieve the soil electrical conductivity and dielectric permittivity, which are correlated to physical properties of interest such as soil water content. The model was calibrated using near- and far-field measurements with the radar antenna at different heights above a copper sheet. For the validation, we preformed several measurements with the antenna on the surface of a water layer whose frequency-dependent electrical properties were described using

Knowledge of temporal surface soil moisture variability is an useful key in agriculture, surface hydrology and meteorology. In that respect, ground-penetrating radar (GPR) is a non-invasive and promising tool for high resolution and large scale characterization. In the case of quantitative analysis, off-ground GPR signal modeling and full-waveform inversion has shown a great potential during the last decade. In this research, we applied GPR in an agricultural field with different hillslopes along a 300 m single transect for more than 6 months. The 200-2000 MHz TEM-horn antenna situated 1.1 m above the ground, connected to a VNA was used as an off-ground frequency domain GPR. The accurate positioning was done using a differential GPS. All the systems were mounted on a 4-wheel vehicle for continuous scanning. Calibration the antenna and using the GPR signal inversion permitted to the ground surface relative dielectric permittivity. Topp’s model was used for transformation of the relative dielectric permittivity to the soil moisture. The temporal stability of the field-average soil moisture was computed by indicators based on the relative difference of the soil moisture to the field-average. The results showed a good correlation (-0.754) for temporal stability of soil moisture and slope variability.

We used a new integrated modeling procedure for analyzing near-field ground-penetrating radar (GPR) and electromagnetic induction (EMI) data for reconstructing the electrical properties of multilayered media. Both GPR and EMI systems are set up using vector network analyzer technology and operate with the antennas on the ground or in near-field conditions. The antennas are modeled using a set of infinitesimal dipoles and characteristic, frequency-dependent, global reflection and transmission coefficients. Wave propagation and diffusion in the medium are described using a set of three-dimensional multilayered media Green’s functions. GPR and EMI antennas were calibrated using measurements collected at different heights over water of know electrical conductivity. The GPR and EMI models were then validated for measurements collected over water subject to different salinity levels. The models showed a high degree of accuracy for reproducing the observed data and model inversion provided good estimates of the medium electrical properties, though discrepancies between measured and estimated water electrical conductivity values were observed in some cases due to a lack of sensitivity. The proposed approach is in particular promising for joint analysis of GPR and EMI data in an inverse data fusion framework, especially as the calibration and modeling procedures are identical for both instruments.

Characterization of the electrical properties of a medium using ground-penetrating radar (GPR) appeals to inverse modeling, which has remained a major challenge in applied geophysics in particular due to antenna modeling limitations. In this paper, we present far-field and near-field radar forward and inverse modeling approaches for wave propagation in layered media in a digital soil mapping context. Radar antennas are modeled using an equivalent set of infinitesimal electric dipoles and characteristic, frequency-dependent, global reflection and transmission coefficients. These coefficients determine through a plane wave decomposition wave propagation between the radar reference plane, point sources, and field points. The interactions between the antenna and the medium are thereby inherently accounted for. The fields are calculated using three-dimensional Green's functions. We validated the model using both time and frequency domain radars. The antennas were calibrated using measurements at different heights above a copper plane. The proposed model provided unprecedented results for describing far-field and near-field radar data collected over water, whose frequency-dependent electrical properties were described using the Debye model. Very good agreements were also obtained for measurements collected over sand subject to a range of water contents. Model inversion further permitted to estimate the medium electrical properties. The proposed modeling approaches are fast and show great promise for digital soil mapping an non-destructive material characterization. We show field application examples where GPR is used to map soil moisture with a high spatial resolution.

Characterization of the electrical properties of a medium using ground-penetrating radar (GPR) appeals to inverse modeling, which has remained a major challenge in applied geophysics in particular due to antenna modeling limitations. In this paper, we propose a new near-field radar modeling approach for wave propagation in layered media. Radar antennas are modeled using an equivalent set of infinitesimal electric dipoles and characteristic, frequency-dependent, global reflection and transmission coefficients. These coefficients determine, through a plane wave decomposition, wave propagation between the radar reference plane, point sources, and field points. The interactions between the antenna and the medium are thereby inherently accounted for. The fields are calculated using three-dimensional Green’s functions. We validated the model using both time and frequency domain radars. The antennas were calibrated using measurements at different heights above a copper plane. The proposed model provided unprecedented results for describing nearfield radar data collected over water, whose frequency-dependent electrical properties were described using the Debye model. Very good agreements were also obtained for measurements collected over water as validating medium for the inversions. The proposed modeling approach is fast and shows great promise for digital soil mapping or non-destructive material characterization.

We coupled dielectric mixing models with a full-wave ground-penetrating-radar (GPR) model to estimate the soil water content by inversion. Two mixing models were taken into account in this study, namely, a power law model and the Wang and Schmugge model.With this combination, we could account for the frequency dependence of the dielectric permittivity and apparent conductivity in the inverse algorithm and directly estimate the soil water content without using an empirical petrophysical formula or a priori knowledge on soil porosity. The approach was validated by a series of experiments with sandy soil in controlled laboratory conditions. The results showed that the performance of our approach is better than the common approach, which assumes a linear dependence of apparent conductivity on frequency and uses Topp’s equation to transform permittivity to water content. GPR data were perfectly reproduced in the time and frequency domains, leading to very accurate water-content estimates with an average absolute error of less than 0.013 cm3∕cm3. However, the accuracy was reduced as the water content increased. Sensitivity analysis indicated that the Green’s function was most sensitive to the water content and sand-layer thickness but much less so with DC conductivity. The results also revealed that as the frequency increased, although the permittivity was nearly constant, the apparent electrical conductivity and the attenuation increased remarkably, especially for wet sands due to dielectric losses. The successful validation of the proposed approach opens a promising avenue of development to use dielectric mixing models for soil-moisture mapping from GPR measurements.

Physically-based ground-penetrating radar (GPR) data processing is essential for quantitative characterization of soils and materials. A novel near-field GPR antenna model coupled with layered media Green's functions was used to investigate the effect of antenna-medium coupling in the analysis of GPR data. The radar antennas are modeled using an equivalent set of infinitesimal electric dipoles and characteristic, frequency-dependent, global reflection and transmission coefficients. These coefficients determine through a plane wave decomposition, wave propagation between the radar reference plane, point sources, and field points. We calibrated in laboratory conditions a 400 MHz centerfrequency time-domain antenna, from which synthetic GPR data sets were generated. We observed that, depending on the model configuration, antenna effects may affect the topography of the objective function in fullwaveform inverse problems. In addition, antenna-medium coupling has a significant impact on the medium surface reflection, whether in terms of amplitude or propagation time (which usually defines the so-called time zero). We also showed that an effective source cannot be used for simulating near-field radar data as the antenna-medium coupling strongly depends on the medium properties. Numerical and laboratory experiments demonstrated that the proposed modeling approach shows great promise for non-destructive testing of planar materials and soils, e.g., using ground-penetrating radar.

A closed form near-field radar modeling approach for wave propagation in planar layered media is presented. The radar antennas are modeled using an equivalent set of infinitesimal electric dipoles and characteristic, frequency-dependent, global reflection and transmission coefficients. These coefficients determine through a plane wave decomposition wave propagation between the radar reference plane, point sources, and field points. Coupling between the antenna and layered medium is thereby inherently accounted for. The fields are calculated using threedimensional Green's functions. We validated the model using frequency and time-domain radars with antennas operating in different frequency ranges. The antenna characteristic coefficients were obtained from nearand far-field measurements over a copper plane. The proposed model provided unprecedented accuracy for describing near-field radar measurements collected over water and sand layers with frequencydependent electrical properties. Medium properties could be retrieved through full-wave inversion. The proposed approach shows great promise for non-destructive testing of planar materials and soils, e.g., using ground-penetrating radar.

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