Ground penetrating radar inversion in 1-D: an approach for the estimation of electrical conductivity, dielectric permittivity and magnetic permeability

This paper presents a method for inverting ground penetrating radargrams in terms of one-dimensional profiles. We resort to a special type of linearization of the damped E-field wave equation to solve the inverse problem. The numerical algorithm for the inversion is iterative and requires the solution of several forward problems, which we evaluate using the matrix propagation approach. Analytical expressions for the derivatives with respect to physical properties are obtained using the self-adjoint Green's function method. We consider three physical properties of materials; namely dielectrical permittivity, magnetic permeability and electrical conductivity. The inverse problem is solved minimizing the quadratic norm of the residuals using quadratic programming optimization. In the iterative process to speed up convergence we use the Levenberg–Mardquardt method. The special type of linearization is based on an integral equation that involves derivatives of the electric field with respect to magnetic permeability, electrical conductivity and dielectric permittivity; this equation is the result of analyzing the implication of the scaling properties of the electromagnetic field. The ground is modeled using thin horizontal layers to approximate general variations of the physical properties. We show that standard synthetic radargrams due to dielectric permittivity contrasts can be matched using electrical conductivity or magnetic permeability variations. The results indicate that it is impossible to differentiate one property from the other using GPR data.     

Soil moisture estimation using tomographic ground penetrating radar in a MCMC–Bayesian framework

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

Simulation and analysis of GPR signal based on stochastic media model with an ellipsoidal autocorrelation function

Target detection using ground penetrating radar (GPR) is based on the contrast between the electrical parameters of the target and the background medium, such as dielectric permittivity, conductivity and permeability. The application mainly concentrates on the detection of the medium interface and the target shape. In any theoretical study, a simulation model is built with a homogeneous medium. However, real detection encounters heterogeneous media which might produce scattering and diffraction at electrical interfaces and distort the radar pulse shape and affect the detection resolution. In this paper, we build multi-scale random media model with an ellipsoidal autocorrelation function and use FDTD method to simulate the GPR signal response. We then estimate and analyze the arrival time, layer thickness, permittivity and the physics relation in different scale random models according to the S transform method and the transmission wave method. The results demonstrate that we can use GPR to obtain geophysical information of multi-scale heterogeneous media, and provide a foundation for real media detection and complex media inversion.     

一种新的实时电磁逆散射方法

为解决介质圆柱体逆散射问题,提出一种新的在线逆散射方法,通过支持向量机将逆散射问题转化成一个回归估计问题. 该方法可应用于各种逆散射方面, 尤其是目标的几何与电磁参数重构和埋地目标探测. 文中首次将支持向量机方法应用到该领域,设置多个散射场的观测点,通过提取散射场的不同信息作为样本信息训练支持向量机, 建立了介质圆柱体的逆散射模型, 利用该模型重构了介质圆柱体的电磁参数,同时探测了埋地位置. 数值结果显示了该方法的有效性和准确性,为目标的实时逆散射研究提供了一种有效方法.     

Effect of medium electrophysical parameters and their temperature dependences on wideband electromagnetic pulse propagation

The dielectric permittivity of fiery spoil tips (Shakhty town, Rostov Region) is studied with the use of a GROT 12E remote-controlled ground-penetrating radar (GPR). An anomalous zone in a combustion source is shown to be clearly pronounced in GPR data due to the temperature dependence of the dielectric permittivity of these spoil tips. To substantiate this statement, the GPR data are compared with direct measurements of soil temperatures at depths from 1.5 to 2.5 m. The experimental results are compared with the variable spectral range of a GPR sounding pulse. GPR is shown to be a promising tool for the mapping of temperature-contrast underground objects.     

Synthetic radargrams from electrical conductivity and magnetic permeability variations

The objective of this work is to assess the importance of electrical conductivity and magnetic permeability variations in ground penetrating radar (GPR) reflections commonly interpreted only in terms of permittivity variations. We use the matrix propagator approach to obtain the surface electric field associated with a horizontally layered model whose three electromagnetic properties vary from layer to layer. The solution is based on the plane wave boundary value problem using inverse Fourier transformation to accommodate particular GPR pulses. Our results indicate that while magnetic permeability is unimportant, reflections from electrical conductivity variations can be of the same order as those associated with electrical permittivity boundaries. In particular, we show that a realistic ground model composed of thin conductive layers can produce radargrams similar to those caused by a lossless permittivity contrast.     

Two Brazilian archaeological sites investigated by GPR: Serrano and Morro Grande

The application of the ground penetrating radar (GPR) at two archaeological sites, Serrano and Morro Grande, situated in Araruama County, Rio de Janeiro, Brazil, aids the study of a prehistoric indigenous culture, associated with the “Tupinambá” that inhabited the region during prehistoric times.The archaeological remains of the study area are mainly characterized by pottery artifacts for several uses, including funerary urns, which were buried within layers of sand and clay. Several profiles were acquired using a RAMAC system, with a 200 and 400 MHz frequency antennae. At the Serrano site, the profiles were acquired around some partially exposed pottery shards, due to sand exploitation. The resultant profiles provided a response model to guide the interpretation of new profiles acquired at other sites in the area, which present similar characteristics.The results showed the great importance of the dielectric permittivity contrast which exists between the targets and the host media, in order for possibly significant features to be identified in radar data.     

Application of the Brewster angle to quantify the dielectric properties of ground ice formations

Previous studies of ground ice using moveout type ground-penetrating radar (GPR) surveys indicate that the dielectric permittivity can constrain the type of ground ice present in the subsurface. Due to the high-loss nature of the active layer over permafrost targets, however, the signal strength of GPR signals is often insufficient to resolve the basal boundary required for determining the dielectric permittivity of an underlying unit. We apply a non-conventional antenna orientation and post-processing method to determine the dielectric permittivity of the unit underlying the lowest resolvable boundary. We conduct moveout surveys using a 450 MHz GPR with collinear parallel oriented antennas on two adjacent ground ice formations in the region of Thomas Lee Inlet, Devon Island, Nunavut. We exploit the Brewster angle to calculate the approximate dielectric permittivity of ground ice formations below the active layer. The results agree within 1 dielectric unit with on-ice permittivity measurements made during a complementary study of the site.     

基于改进全变差正则化的GPR多尺度全波形双参数同步反演

针对探地雷达（GPR）双参数全波形反演中电导率反演精度差、双参数存在串扰现象、反演计算量大、易陷入局部极值等问题.作者将具有多参数调节功能的L-BFGS算法引入到GPR时间域全波形反演中,它避免了对Hessian矩阵的直接存储与精确求解,减小了存储量和计算量.结合参数调节因子的选取,有效减小了同步反演时介电常数与电导率的串扰影响,在不降低介电常数反演精度的前提下,提高电导率参数的反演精度.通过在反演目标函数中加载改进全变差正则化方法,提高了反演的稳定性,使目标体边缘轮廓更加清晰.首先以简单模型为例,对比了单尺度反演与多尺度串行反演策略的优劣,说明多尺度串行反演有利于逐步搜索全局最优解;而开展参数调节因子的选取实验,说明合适的参数调节因子可以有效改善介质电导率的反演精度;测试了不同正则化的反演效果,表明改进全变差正则化能提高反演稳定性,显著降低模型重构误差.最后,分别对含噪合成数据和实测数据进行了反演测试,说明本文提出的多尺度、双参数反演具有较强的鲁棒性,能提供更丰富的信息约束,重构图像界面清晰、反演效果好.     

Modelling of GPR waves for lossy media obeying a complex power law of frequency for dielectric permittivity

The attenuation of ground‐penetrating radar (GPR) energy in the subsurface decreases and shifts the amplitude spectrum of the radar pulse to lower frequencies (absorption) with increasing traveltime and causes also a distortion of wavelet phase (dispersion). The attenuation is often expressed by the quality factor Q. For GPR studies, Q can be estimated from the ratio of the real part to the imaginary part of the dielectric permittivity. We consider a complex power function of frequency for the dielectric permittivity, and show that this dielectric response corresponds to a frequency‐independent‐Q or simply a constant‐Q model. The phase velocity (dispersion relationship) and the absorption coefficient of electromagnetic waves also obey a frequency power law. This approach is easy to use in the frequency domain and the wave propagation can be described by two parameters only, for example Q and the phase velocity at an arbitrary reference frequency. This simplicity makes it practical for any inversion technique. Furthermore, by using the Hilbert transform relating the velocity and the absorption coefficient (which obeys a frequency power law), we find the same dispersion relationship for the phase velocity. Both approaches are valid for a constant value of Q over a restricted frequency‐bandwidth, and are applicable in a material that is assumed to have no instantaneous dielectric response. Many GPR profiles acquired in a dry aeolian environment have shown a strong reflectivity inside dunes. Changes in water content are believed to be the origin of this reflectivity. We model the radar reflections from the bottom of a dry aeolian dune using the 1D wavelet modelling method. We discuss the choice of the reference wavelet in this modelling approach. A trial‐and‐error match of modelled and observed data was performed to estimate the optimum set of parameters characterizing the materials composing the site. Additionally, by combining the complex refractive index method (CRIM) and/or Topp equations for the bulk permittivity (dielectric constant) of moist sandy soils with a frequency power law for the dielectric response, we introduce them into the expression for the reflection coefficient. Using this method, we can estimate the water content and explain its effect on the reflection coefficient and on wavelet modelling.     

Location and Characterization of Subsurface Anomalies Using a Soil Conductivity Probe

An electrical conductivity probe, designed for use with "direct push" technology, has been successfully used to locate buried drums, contaminant plumes, and to precisely locate and characterize a previously installed permeable reactive iron wall. The conductivity probe was designed to characterize various soil and sediment types as it was driven through the dry and saturated soil matrix; however, its ability to locate and characterize subsurface anomalies may also prove to be a valuable asset. The probe uses an electrical field that works like and mimics the results from an oilfield engineering tool called the Wenner array. This electrical field array penetrates into the soil matrix to measure the electrical conductivity of the soil matrix surrounding the probe to a radius of about two to four inches. This tool has allowed operating personnel to verify the location of manmade or natural subsurface anomalies with precision.     

不依赖源子波的跨孔雷达时间域波形反演

波形反演是近年来较热门的反演方法,其分辨率可以达到亚波长级别.在波形反演的实际应用中,源子波的估计十分重要.传统方法使用反褶积来估计源子波并随着反演过程更新,该方法在合成数据波形反演中效果较好,但在实际数据反演过程中存在一系列的问题.由于实际数据信噪比较低,在源子波估计过程中需要大量的人为干涉,且结果并不一定可靠.本文使用一种基于褶积波场的新型目标函数,令反演过程不再依赖源子波.详细推导了针对跨孔雷达波形反演的梯度及步长公式,实现介电常数和电导率的同步反演.针对一个合成数据模型同时反演介电常数和电导率,结果表明该方法能够反演出亚波长尺寸异常体的形状和位置.接着,将该方法应用到两组实际数据中,并与基于估计源子波的时间域波形反演结果进行比较.结果表明不依赖源子波的时间域波形反演结果分辨率更高,也更准确.     

Integrated Electrical Resistivity Tomography and Ground Penetrating Radar Measurements Applied to Tomb Detection

The integrated use of electrical resistivity tomography (ERT) and ground penetrating radar (GPR) measurements, and in particular the joint analysis of 2D and 3D data, can represent a valid solution for target identification at complex archaeological sites. A good example, in this respect, is given by the case study of a Phoenician–Punic necropolis in the archaeological site of Nora, in southern Sardinia (Italy), where GPR and ERT measurements were collected before site excavation. In this specific case, the mix of soil and air in the buried chambers, as well as the orientation and the complex spatial distribution of these structures into the sandstone bedrock, generated a number of anomalies difficult to interpret only using 2D results. Only the integration of all GPR and ERT data in a 3D view, and the comparison with archaeological evidence after the excavation, allowed a solid interpretation of geophysical anomalies visible in the 2D sections. Overall, this case study demonstrates the efficiency of the combined use of GPR and ERT acquisitions and shows how, in general, only the joint analysis of 2D data and in a 3D view can help the interpretation of the real distribution of the buried archaeological remains at similar archaeological complex sites.     

Time domain reflectometry measurement principles and applications

Time domain reflectometry (TDR) is a highly accurate and automatable method for determination of porous media water content and electrical conductivity. Water content is inferred from the dielectric permittivity of the medium, whereas electrical conductivity is inferred from TDR signal attenuation. Empirical and dielectric mixing models are used to relate water content to measured dielectric permittivity. Clay and organic matter bind substantial amounts of water, such that measured bulk dielectric constant is reduced and the relationship with total water content requires individual calibration. A variety of TDR probe configurations provide users with site‐ and media‐specific options. Advances in TDR technology and in other dielectric methods offer the promise not only for less expensive and more accurate tools for electrical determination of water and solute contents, but also a host of other properties such as specific surface area, and retention properties of porous media. Copyright © 2002 John Wiley & Sons, Ltd.     

Simulation for ground penetrating radar (GPR) study of the subsurface structure of the Moon

Ground penetrating radar (GPR) is currently within the scope of China's Chang-E 3 lunar mission, to study the shallow subsurface of the Moon. In this study, key factors that could affect a lunar GPR performance, such as frequency, range resolution, and antenna directivity, are discussed firstly. Geometrical optics and ray tracing techniques are used to model GPR echoes, considering the transmission, attenuation, reflection, geometrical spreading of radar waves, and the antenna directivity. The influence on A-scope GPR echoes and on the simulated radargrams for the Sinus Iridum region by surface and subsurface roughness, dielectric loss of the lunar regolith, radar frequency and bandwidth, and the distance between the transmit and receive antennas are discussed. Finally, potential scientific return about lunar subsurface properties from GPR echoes is also discussed. Simulation results suggest that subsurface structure from several to hundreds of meters can be studied from GPR echoes at P and VHF bands, and information about dielectric permittivity and thickness of subsurface layers can be estimated from GPR echoes in combination with regolith composition data.     

Improvements in crosshole GPR full-waveform inversion and application on data measured at the Boise Hydrogeophysics Research Site

Crosshole ground penetrating radar (GPR) tomography has been widely used and has the potential to improve the obtained subsurface models due to its high spatial resolution compared to other methods. Recent advances in full-waveform inversion of crosshole GPR data show that higher resolution images can be obtained compared to conventional ray-based GPR inversion because it can exploit all information present in the observed data. Since the first application of full-waveform inversion on synthetic and experimental GPR data, the algorithm has been significantly improved by extending the scalar to a vectorial approach, and changing the stepped permittivity and conductivity update into a simultaneous update. Here, we introduce new normalized gradients that do not depend on the number of sources and receivers which enable a comparison of the gradients and step lengths for different crosshole survey layouts. An experimental data set acquired at the Boise Hydrogeophysics Research Site is inverted using different source–receiver setups and the obtained permittivity and conductivity images, remaining gradients and final misfits are compared for the different versions of the full-waveform inversion. Moreover, different versions of the full-waveform inversion are applied to obtain an overview of all improvements. Most improvements result in a reducing final misfit between the measured and synthetic data and a reducing remaining gradient at the final iteration. Regions with relatively high remaining gradient amplitudes indicate less reliable inversion results. Comparison of the final full-waveform inversion results with Neutron–Neutron porosity log data and capacitive resistivity log data show considerably higher spatial frequencies for the logging data compared to the full-waveform inversion results. To enable a better comparison, we estimated a simple wavenumber filter and the full-waveform inversion results show an improved fit with the logging data. This work shows the potential of full-waveform inversion as an advanced method that can provide high resolution images to improve hydrological models.     

An electromagnetic modelling tool for the detection of hydrocarbons in the subsoil

Electromagnetic geophysical methods, such as ground-penetrating radar (GPR), have proved to be optimal tools for detecting and mapping near-surface contaminants. GPR has the capability of mapping the location of hydrocarbon pools on the basis of contrasts in the effective permittivity and conductivity of the subsoil. At radar frequencies (50 MHz to 1 GHz), hydrocarbons have a relative permittivity ranging from 2 to 30, compared with a permittivity for water of 80. Moreover, their conductivity ranges from zero to 10 mS/m, against values of 200 mS/m and more for salt water. These differences indicate that water/hydrocarbon interfaces in a porous medium are electromagnetically 'visible'. In order to quantify the hydrocarbon saturation we developed a model for the electromagnetic properties of a subsoil composed of sand and clay/silt, and partially saturated with air, water and hydrocarbon. A self-similar theory is used for the sandy component and a transversely isotropic constitutive equation for the shaly component, which is assumed to possess a laminated structure. The model is first verified with experimental data and then used to obtain the properties of soils partially saturated with methanol and aviation gasoline. Finally, a GPR forward-modelling method computes the radargrams of a typical hydrocarbon spill, illustrating the sensitivity of the technique to the type of pore-fluid. The model and the simulation algorithm provide an interpretation methodology to distinguish different pore-fluids and to quantify their degree of saturation.     

Application of sub-image multiresolution analysis of Ground-penetrating radar data in a study of shallow structures

Fourier-based algorithms originally developed for the processing of seismic data are applied routinely in the Ground-penetrating radar (GPR) data processing, but these conventional methods of data processing may result in an abundance of spurious harmonics without any geological meaning. We propose a new approach in this study based essentially on multiresolution wavelet analysis (MRA) for GPR noise suppression. The 2D GPR section is similar to an image in all aspects if we consider each data point of the GPR section to be an image pixel in general. This technique is an image analysis with sub-image decomposition. We start from the basic image decomposition procedure using conventional MRA approach and establish the filter bank accordingly. With reasonable knowledge of data and noise and the basic assumption of the target, it is possible to determine the components with high S/N ratio and eliminate noisy components. The MRA procedure is performed further for the components containing both signal and noise. We treated the selected component as an original image and applied the MRA procedure again to that single component with a mother wavelet of higher resolution. This recursive procedure with finer input allows us to extract features or noise events from GPR data more effectively than conventional process.To assess the performance of the MRA filtering method, we first test this method on a simple synthetic model and then on experimental data acquired from a control site using 400 MHz GPR system. A comparison of results from our method and from conventional filtering techniques demonstrates the effectiveness of the sub-image MRA method, particularly in removing ringing noise and scattering events. Field study was carried out in a trenched fault zone where a faulting structure was present at shallow depths ready for understanding the feasibility of improving the data S/N ratio by applying the sub-image multiresolution analysis. In contrast to the conventional methods, the MRA sub-image filtering technique provides an overall improvement in image quality of the data as shown in the field study.