Sébastien Lambot

Modeling of ground-penetrating Radar for accurate characterization of subsurface electric properties

The possibility to estimate accurately the subsurface electric properties from ground-penetrating radar (GPR) signals using inverse modeling is obstructed by the appropriateness of the forward model describing the GPR subsurface system. In this paper, we improved the recently developed approach of Lambot et al. whose success relies on a stepped-frequency continuous-wave (SFCW) radar combined with an off-ground monostatic transverse electromagnetic horn antenna. This radar configuration enables realistic and efficient forward modeling. We included in the initial model: 1) the multiple reflections occurring between the antenna and the soil surface using a positive feedback loop in the antenna block diagram and 2) the frequency dependence of the electric properties using a local linear approximation of the Debye model. The model was validated in laboratory conditions on a tank filled with a two-layered sand subject to different water contents. Results showed remarkable agreement between the measured and modeled Greens functions. Model inversion for the dielectric permittivity further demonstrated the accuracy of the method. Inversion for the electric conductivity led to less satisfactory results. However, a sensitivity analysis demonstrated the good stability properties of the inverse solution and put forward the necessity to reduce the remaining clutter by a factor 10. This may partly be achieved through a better characterization of the antenna transfer functions and by performing measurements in an environment without close extraneous scatterers.

Analysis of air-launched ground-penetrating radar techniques to measure the soil surface water content

We analyze the common surface reflection and full-wave inversion methods to retrieve the soil surface dielectric permittivity and correlated water content from air-launched ground-penetrating radar (GPR) measurements. In the full-wave approach, antenna effects are filtered out from the raw radar data in the frequency domain, and full-wave inversion is performed in the time domain, on a time window focused on the surface reflection. Synthetic experiments are performed to investigate the most critical hypotheses on which both techniques rely, namely, the negligible effects of the soil electric conductivity (?) and layering. In the frequency range 1–2 GHz we show that for ? > 0.1 Sm?1, significant errors are made on the estimated parameters, e.g., an absolute error of 0.10 in water content may be observed for ? = 1 Sm?1. This threshold is more stringent with decreasing frequency. Contrasting surface layering may proportionally lead to significant errors when the thickness of the surface layer is close to one fourth the wavelength in the medium, which corresponds to the depth resolution. Absolute errors may be >0.10 in water content for large contrasts. Yet we show that full-wave inversion presents valuable advantages compared to the common surface reflection method. First, filtering antenna effects may prevent absolute errors >0.04 in water content, depending of the antenna height. Second, the critical reference measurements above a perfect electric conductor (PEC) are not required, and the height of the antenna does not need to be known a priori. This averts absolute errors of 0.02–0.09 in water content when antenna height differences of 1–5 cm occur between the soil and the PEC. A laboratory experiment is finally presented to analyze the stability of the estimates with respect to actual measurement and modeling errors. While the conditions were particularly well suited for applying the common reflection method, better results were obtained using full-wave inversion.

A global multilevel coordinate search procedure for estimating the unsaturated soil hydraulic properties

We present a new inverse modeling procedure to characterize the hydraulic properties of partially saturated soils from soil moisture measurements during a natural transient flow experiment. The inversion of the governing one-dimensional Richards equation is carried out using the Global Multilevel Coordinate Search optimization algorithm in sequential combination with the local Nelder-Mead Simplex algorithm (GMCS-NMS). We introduce this optimization method in the area of unsaturated zone hydrology since it is adapted for solving accurately and efficiently complex nonlinear problems. Several numerical experiments have been conducted to evaluate the proposed inversion method using synthetic error-free and error-contaminated data for different textured soils. Inversion of the simulated error-free data and examination of the related response surfaces demonstrated the uniqueness of the inverse solution and the suitability of the GMCS-NMS strategy when identifying four key parameters of the hydraulic functions described by the Mualem-van Genuchten model. Inversion of the error-contaminated data proved further the good stability of the inverse solution that is consistent with the needs required by real experiments.

Filtering Soil Surface and Antenna Effects From GPR Data to Enhance Landmine Detection

The detection of antipersonnel landmines using ground-penetrating radar (GPR) is particularly hindered by the predominant soil surface and antenna reflections. In this paper, we propose a novel approach to filter out these effects from 2-D off-ground monostatic GPR data by adapting and combining the radar antenna subsurface model of Lambot with phase-shift migration. First, the antenna multiple reflections originating from the antenna itself and from the interaction between the antenna and the ground are removed using linear transfer functions. Second, a simulated Greens function accounting for the surface reflection is subtracted. The Greens function is derived from the estimated soil surface dielectric permittivity using full-wave inversion of the radar signal for a measurement taken in a local landmine-free area. Third, off-ground phase-shift migration is performed on the 2-D data to filter the effect of the antenna radiation pattern. We validate the approach in laboratory conditions for four differently detectable landmines embedded in a sandy soil. Compared to traditional background subtraction, this new filtering method permits a better differentiation of the landmine and estimation of its depth and geometrical properties. This is particularly beneficial for the detection of landmines in low-contrast conditions

Estimating soil electric properties from monostatic ground‐penetrating radar signal inversion in the frequency domain

[1] A new integrated approach for identifying the shallow subsurface electric properties from ground-penetrating radar (GPR) signal is proposed. It is based on an ultrawide band (UWB) stepped frequency continuous wave (SFCW) radar combined with a dielectric filled transverse electric and magnetic (TEM) horn antenna to be used off the ground in monostatic mode; that is, a single antenna is used as emitter and receiver. This radar configuration is appropriate for subsurface mapping and allows for an efficient and more realistic modeling of the radar-antenna-subsurface system. Forward modeling is based on linear system response functions and on the exact solution of the three-dimensional Maxwell equations for wave propagation in a horizontally multilayered medium representing the subsurface. Subsurface electric properties, i.e., dielectric permittivity and electric conductivity, are estimated by model inversion using the global multilevel coordinate search optimization algorithm combined sequentially with the local Nelder-Mead simplex algorithm (GMCS-NMS). Inversion of synthetic data and analysis of the corresponding response surfaces proved the uniqueness of the inverse solution. Laboratory experiments on a tank filled with a homogeneous sand subject to different water content levels further demonstrated the stability and accuracy of the solution toward measurement and modeling errors, particularly those associated with the dielectric permittivity. Inversion for the electric conductivity led to less satisfactory results. This was mainly attributed to the characterization of the frequency response of the antenna and to the high frequency dependence of the electric conductivity.

Electromagnetic inversion of GPR signals and subsequent hydrodynamic inversion to estimate effective vadose zone hydraulic properties

We combine electromagnetic inversion of ground penetrating radar (GPR) signals with hydrodynamic inverse modeling to identify the effective soil hydraulic properties of a sand in laboratory conditions. Ground penetrating radar provides soil moisture time series that are subsequently used as input in the hydrodynamic inverse procedure. The technique relies on an ultrawide band (UWB) stepped frequency continuous wave (SFCW) radar combined with an off-ground monostatic transverse electromagnetic (TEM) horn antenna. Ground penetrating radar signal forward modeling is based on the exact solution of the three-dimensional Maxwell equations for describing free wave propagation and on linear systems in series and parallel for describing wave propagation in the antenna. Water flow in the sand is described by the one-dimensional Richards equation using the Mualem-van Genuchten parameterization. Both model inversions are formulated by the classical least-squares problem and are performed iteratively using advanced global optimization techniques. Compared with time domain reflectometry (TDR), results demonstrated the appropriateness the GPR integrated approach to measure soil moisture remotely. In particular, the approach was found to be less sensitive to the inherent small-scale heterogeneities. Hydrodynamic inversion of soil moisture data led to hydraulic parameters agreeing reasonably well with direct measurements. The observed discrepancies were attributed to the different characterization scales and samples. The overall integrated approach offers great promise to map the effective hydraulic properties of the shallow subsurface at a high spatial resolution.

Electromagnetic induction calibration using apparent electrical conductivity modelling based on electrical resistivity tomography

Electromagnetic parameters of the subsurface such as electrical conductivity are of great interest for non-destructive determination of soil properties (e.g., clay content) or hydrologic state variables (e.g., soil water content). In the past decade, several non-invasive geophysical methods have been developed to measure subsurface parameters in situ . Among these methods, electromagnetic (EM) induction appears to be the most efficient one that is able to cover large areas in a short time. However, this method currently does not provide absolute values of electrical conductivity due to calibration problems, which hinders a quantitative analysis of the measurement. In this study, we propose to calibrate EM induction measurements with electrical conductivity values measured with electrical resistivity tomography (ERT). EM induction measures an apparent electrical conductivity at the surface, which represents a weighted average of the electrical conductivity distribution over a certain depth range, whereas ERT inversion can provide absolute values for local conductivities as a function of depth. EM induction and ERT measurements were collected along a 120-metre-long transect. To reconstruct the apparent electrical conductivity measured with EM induction, the inverted ERT data were used as input in an electromagnetic forward modelling tool for magnetic dipoles over a horizontally layered medium considering the frequencies and offsets used by the EM induction instruments. Comparison of the calculated and measured apparent electrical conductivities shows very similar trends but a shift in absolute values, which is attributed to system calibration problems. The observed shift can be corrected for by linear regression. This new calibration strategy for EM induction measurements now enables the quantitative mapping of electrical conductivity values over large areas.

Effect of soil roughness on the inversion of off-ground monostatic GPR signal for noninvasive quantification of soil properties

We report on a laboratory experiment that investigates the effect of soil surface roughness on the identification of the soil electromagnetic properties from full-wave inversion of ground-penetrating radar (GPR) data in the frequency domain. The GPR system consists of an ultrawide band stepped-frequency continuous-wave radar combined with an off-ground monostatic horn antenna. Radar measurements were performed above a rectangular container filled with a loose sandy soil subject to seven water contents and four random surface roughnesses, including a smooth surface as reference. Compared to previous studies, we have reduced the modeling error of the GPR signal for the smooth surface case thanks to improved antenna transfer functions by solving an overdetermined system of equations based on six model configurations instead of only three. Then, the continuously increasing effect of surface roughness on the radar signal with respect to frequency is clearly observed. In close accordance with Rayleighs criterion, both the radar signal and the inversely estimated parameters are not significantly affected if the surface protuberances are smaller than one eighth of a wavelength. In addition, when this criterion is not respected, errors are made in the estimated parameters, but the inverse solution remains stable. This demonstrates the promising perspectives for application of GPR for noninvasive water content estimation in agricultural and environmental field applications.

Fast evaluation of zero-offset Green's function for layered media with application to ground-penetrating radar

We propose an efficient integration path for the fast evaluation of the three?dimensional spatial?domain Greens function for electromagnetic wave propagation in layered media for the particular case of zero?offset, source?receiver proximal ground?penetrating radar (GPR) applications. The integration path is deformed in the complex plane of the integration variable k? so that the oscillations of the dominant exponential term in the spectral Greens function are minimized. The contour does not need to be closed back on the real k? axis as the complex integrand rapidly damps. The accuracy and efficiency of the technique have been confirmed by comparison with traditional elliptic integration contours. The proposed algorithm appears to be promising development for fast, full?wave modeling and inversion of GPR data

Full-Wave Modeling of Near-Field Radar Data for Planar Layered Media Reconstruction

A new near-field radar modeling approach for wave propagation in planar layered media is presented. The radar antennas are intrinsically 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 layered medium are thereby inherently accounted for. The fields are calculated using 3-D Greens functions. We validated the model using an ultrawideband frequency-domain radar with a transmitting and receiving Vivaldi antenna operating in the range 0.8-4 GHz. The antenna characteristic coefficients are obtained from near- and far-field measurements over a copper plane. The proposed model provides unprecedented accuracy for describing near-field radar measurements collected over a water layer, the frequency-dependent electrical properties of which were described using the Debye model. Layer thicknesses could be retrieved through full-wave inversion. The proposed approach demonstrated great promise for nondestructive testing of planar materials and digital soil mapping using ground-penetrating radar.