Evert Slob

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.

Tutorial on seismic interferometry: Part 2-Underlying theory and new advances

In the 1990s, the method of time-reversed acoustics was developed. This method exploits the fact that the acoustic wave equation for a lossless medium is invariant for time reversal. When ultrasonic responses recorded by piezoelectric transducers are reversed in time and fed simultaneously as source signals to the transducers, they focus at the position of the original source, even when the medium is very complex. In seismic interferometry the time-reversed responses are not physically sent into the earth, but they are convolved with other measured responses. The effect is essentially the same: The time-reversed signals focus and create a virtual source which radiates waves into the medium that are subsequently recorded by receivers. A mathematical derivation, based on reciprocity theory, formalizes this principle: The crosscorrelation of responses at two receivers, integrated over different sources, gives the Green’s function emitted by a virtual source at the position of one of the receivers and observed by the other receiver. This Green’s function representation for seismic interferometry is based on the assumption that the medium is lossless and nonmoving. Recent developments, circumventing these assumptions, include interferometric representations for attenuating and/or moving media, as well as unified representations for waves and diffusion phenomena, bending waves, quantum mechanical scattering, potential fields, elastodynamic, electromagnetic, poroelastic, and electroseismic waves. Significant improvements in the quality of the retrieved Green’s functions have been obtained with interferometry by deconvolution. A trace-by-trace deconvolution process compensates for complex source functions and the attenuation of the medium. Interferometry by multidimensional deconvolution also compensates for the effects of one-sided and/or irregular illumination.

Surface and borehole ground-penetrating-radar developments

During the past 80 years, ground-penetrating radar (GPR) has evolved from a skeptically received glacier sounder to a full multicomponent 3D volume-imaging and characterization device. The tool can be calibrated to allow for quantitative estimates of physical properties such as water content. Because of its high resolution, GPR is a valuable tool for quantifying subsurface heterogeneity, and its ability to see nonmetallic and metallic objects makes it a useful mapping tool to detect, localize, and characterize buried objects. No tool solves all problems; so to determine whether GPR is appropriate for a given problem, studying the reasons for failure can provide an understanding of the basics, which in turn can help determine whether GPR is appropriate for a given problem. We discuss the specific aspects of borehole radar and describe recent developments to become more sensitiveto orientation and to exploit the supplementary information in different components in polarimetric uses of radar data. Multicomponent GPR data contain more diverse geometric information than single-channel data, and this is exploited in developed dedicated imaging algorithms. The evolution of these imaging schemes is discussed for ground-coupled and air-coupled antennas. For air-coupled antennas, the measured radiated wavefield can be used as the basis for the wavefield extrapolator in linear-inversion schemes with an imaging condition, which eliminates the source-time function and corrects for the measured radiation pattern. A handheld GPR system coupled with a metal detector is ready for routine use in mine fields. Recent advances in modeling, tomography, and full-waveform inversion, as well as Greens function extraction through correlation and deconvolution, show much promise in this field.

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

Controlled-source interferometric redatuming by crosscorrelation and multidimensional deconvolution in elastic media

Various researchers have shown that accurate redatuming of controlled seismic sources to downhole receiver locations can be achieved without requiring a velocity model. By placing receivers in a horizontal or deviated well and turning them into virtual sources, accurate images can be obtained even below a complex near-subsurface. Examples include controlled-source interferometry and the virtual-source method, both based on crosscorrelated signals at two downhole receiver locations, stacked over source locations at the surface. Because the required redatuming operators are taken directly from the data, even multiple scattered waveforms can be focused at the virtual-source location, and accurate redatuming can be achieved. To reach such precision in a solid earth, representations for elastic wave propagation that require multicomponent sources and receivers must be implemented. Wavefield decomposition prior to crosscorrelation allows us to enforce virtual sources to radiate only downward or only upward. Virtual-source focusing and undesired multiples from the overburden can be diagnosed with the interferometric point-spread function (PSF), which can be obtained directly from the data if an array of subsurface receivers is deployed. The quality of retrieved responses can be improved by filtering with the inverse of the PSF, a methodology referred to as multidimensional deconvolution.

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.

Stochastic joint inversion of 2D seismic and seismoelectric signals in linear poroelastic materials: A numerical investigation

The interpretation of seismoelectrical signals is a difficult task because coseismic and seismoelectric converted signals are recorded simultaneously and the seismoelectric conversions are typically several orders of magnitude smaller than the coseismic electrical signals. The seismic and seismoelectric signals are modeled using a finite-element code with perfectly matched layer boundary conditions assuming a linear poroelastic body. We present a stochastic joint inversion of the seismic and seismoelectrical data based on the adaptive Metropolis algorithm, to obtain the posterior probability density functions of the material properties of each geologic unit. This includes the permeability, porosity, electrical conductivity, bulk modulus of the dry porous frame, bulk modulus of the fluid, bulk modulus of the solid phase, and shear modulus of the formations. A test of this approach is performed with a synthetic model comprising two horizontal layers and a reservoir partially saturated with oil, which is embedded in the second layer. The result of the joint inversion shows that we can invert the permeability of the reservoir and its mechanical properties.

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.