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Ground Penetrating Radar (GPR) is a non-destructive geophysical technique utilizing electromagnetic pulses to detect subsurface material properties. The analysis of regions of interest (ROIs) in GPR images often entails the identification of hyperbolic reflection regions of underground targets through accurate segmentation, a crucial preprocessing step. Currently, this represents a research gap. In the hyperbolic reflection region, manual segmentation not only demands professional expertise but is also time-consuming and error-prone. Automatic segmentation can aid in accurately determining the location and depth of the reflection region, thereby enhancing data interpretation and analysis. This study presents a deep residual Convolutional Neural Network (Res-CNN) that integrates skip connections within an encoder-decoder framework for ROI-binarized hyperbolic segmentation. The proposed framework includes designed downsampling and upsampling modules that facilitate feature computation sharing between these two modules through skip connections within network blocks. In the evaluation of both simple and complex models, our method attained PSNR, SSIM, and FSIM values of 57.1894, 0.9933, and 0.9336, and 58.4759, 0.9958, and 0.9677, respectively. Compared to traditional segmentation methods, the proposed approach demonstrated clearer segmentation results, enabling intelligent and effective identification of the ROI region containing abnormal hyperbolic reflection waves in GPR images. [ABSTRACT FROM AUTHOR]

A reliable inspection of the tree trunk internal defects is often considered vital in the health condition assessment for the living tree. There has been a desire to reconstruct the internal structure quantitatively using a non-destructive testing technology. This paper intends to apply wavefield reconstruction inversion (WRI) to obtain high-precision information from tree trunk detection using ground penetrating radar data. The variational projection method and the grouped multi-frequency strategy are adopted to strengthen the algorithm stability and adaptability by inverting frequency components sequentially. Through an irregular trunk model test, the influence of the penalty parameter, initial model, frequency strategy, and grid generation methods are investigated on WRI. Additionally, the comparison between full waveform inversion and WRI is discussed in detail. This synthetic case indicates that WRI is efficient and for a reasonable result, a proper multi-frequency strategy and an accurate mesh closer to reality are important. Furthermore, a field case of a historical tree is used to prove the validity and reliability of the algorithm. The success in this case indicates that our algorithm can characterize the distribution of media parameters of tree trunks accurately, which could provide data support for the rejuvenation and maintenance of living trees. [ABSTRACT FROM AUTHOR]

Ground penetrating radar (GPR), geophysics exploring technology, could non-destructively acquire high-precision information about the shallow subsurface. This Special Issue aims to introduce and report on recent advancements in GPR, encompassing aspects such as numerical simulation, inversion imaging, data processing methodologies, and various domains of GPR application. In the modern epoch, equipment for GPR data acquisition is well established, but the explication of GPR data still relies on artificial judgment and experience, lacking automation. [Extracted from the article]

High-precision detection of the underground pipelines is an indispensable part of the development and construction of cities. At present, the inversion technology for ground-penetrating radar (GPR) data is an effective means of realizing shallow-underground-space visualization in the field of geophysical exploration. However, the traditional full-waveform inversion (FWI) method usually faces the problems of strong nonlinearity of the objective function, high dependence on the initial model, and huge calculation cost. For improving the accuracy and efficiency of GPR data inversion, a wavefield reconstruction inversion (WRI) strategy is used for GPR data imaging to reduce the nonlinearity of the inversion problem and the dependence on the initial model. Then, the frequency weighting strategy and the multi-scale method are adopted to avoid the high-frequency component data dominating the optimization process and enhance the stability of inversion. In this paper, two numerical experiments of pipeline models with different materials and spacing or buried depths verified that the proposed method can effectively reconstruct the subsurface pipelines, and further performance of our algorithm on the field data verified the reliability of high-precision imaging of urban underground pipelines, which shows great potential of application in the field of high-precision detection of the urban underground pipelines. [ABSTRACT FROM AUTHOR]

The full-waveform inversion (FWI) of ground-penetrating radar (GPR) data yields promise for quantitatively characterizing the parameters of the Earth’s shallow subsurface. However, conventional FWI is highly nonlinear and suffers from cycle skipping once the low-frequency data are missed or the initial model is poor. Furthermore, having limited prior knowledge of the subsurface in GPR measurements increases the ill-posedness of the inverse problem. Wavefield reconstruction inversion (WRI), which mitigates cycle skipping, extends the FWI search space by relaxing the wave equation constraint, reduces the nonlinearity, and is less sensitive to the initial model. In this article, we extend WRI to the 2-D frequency-domain imaging of on-ground GPR data. To improve the inversion stability and mitigate the ill-posedness, we utilize modified total variation (MTV) regularization to constrain the inverted models. With a simple numerical example, we first investigate the effects of the penalty parameter, initial models, and MTV regularization on WRI and further discuss the differences between WRI and FWI. Then, we analyze the sensitivity of the proposed approach to the frequency component and noise in a multiple-targets model. Furthermore, we assess our method with a complex synthetic example containing noise-contaminated data, showing that our proposed approach works efficiently even given noisy GPR data. Therefore, the reasonable combination of WRI and MTV regularization can improve the accuracy and efficiency of imaging for on-ground GPR data. This joint approach for the multiparameter quantitative reconstruction of GPR data ultimately exhibits good applicability and strong robustness and is worthy of promotion. [ABSTRACT FROM AUTHOR]

Full waveform inversion (FWI) of ground-penetrating radar (GPR) data is becoming a promising technique to facilitate the interpretation of surface-GPR data and the mapping of the subsurface. However, more general FWIs still require a sufficient amount of RAM memory, and it is difficult to produce an accurate and representative reconstruction result due to a large amount of the Hessian matrix calculations and singular value decomposition (SVD). In this article, we developed a novel full-waveform approach of the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm for surface-GPR data that is based on a quasi-Newton framework and the total variation (TV) regularization. The proposed approach uses an L-BFGS algorithm and combines a scale-transformation regularization technique to mitigate the ill-posed problem of inversion, which can impose a biparameter preinformation constraint to ensure the stability of inversion, and adaptive regularization weights are applied to improve the convergence efficiency of inversion. To demonstrate the novelty and effectiveness of the proposed scheme, we tested our FWI algorithm using synthetic data and in-site field data. In the testing, we focus on analyzing the influence of different aspects of the FWI results, including different scale factors, regularization weights, inversion strategies, acquisition configurations, initial models, and the noisy data set. In particular, the FWI experiment is performed to demonstrate the applicability of the proposed algorithm. The results show that the proposed algorithm can effectively reconstruct the biparameter near the subsurface with high accuracy, which makes our approach very attractive for attribute analysis applications and makes the surface-GPR FWI commercially viable. [ABSTRACT FROM AUTHOR]

Ground-penetrating radar (GPR) full-waveform inversion (FWI) is an emerging near-surface high-resolution imaging technology that has been widely used in GPR 2-D imaging to better quantitatively evaluate the permittivity and conductivity of the subsurface. However, the 2-D imaging method limits the applicability and accuracy of FWI for the 3-D object cases. In this letter, we develop a 3-D FWI algorithm involving permittivity and conductivity for GPR in the frequency domain. The method employs the edge-based finite element method to solve the forward problem and the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method to solve the inverse problem, which avoids the calculation of the Hessian matrix. In particular, by using the parameter scaling and scaling factor, it is convenient to carry out the simultaneous inversion of permittivity and conductivity with high efficiency. In addition, a modified total variation regularization scheme is utilized for ensuring the stability of the inversion, as well as identifying the abnormal body boundary more effectively. As a demonstration, a synthetic 3-D model experiment is presented to test the proposed algorithm. The results show that the proposed inversion strategy can accurately reconstruct the permittivity structure together with the conductivity distribution from the 3-D on-ground GPR data. [ABSTRACT FROM AUTHOR]

Full-waveform inversion (FWI) in the time domain of ground-penetrating radar (GPR) data involves a vast number of calculations; thus, it requires a large amount of memory and is difficult to calculate on a personal computer (PC). In this paper, GPR data are analyzed with multiscale FWI using two parameters (permittivity and conductivity) based on total variation (TV) regularization, which is implemented on a PC using a graphics processing unit (GPU) parallel acceleration strategy. The inverse problem is considered to be a nonlinear optimization problem and is solved with limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) process, which is a quasi-Newton method. The gradient of the objective function is calculated using the adjoint-state method, and the finite-difference method is required to solve the forward problem many times. A multiscale serial inversion strategy is applied to optimize the inversion algorithm and to decompose the inversion problem into 2–3 frequency bands to search in the direction of the global minimum point instead of local minimums. Taking the complex model as an example, experiments are carried out to assess the parameter adjustment factor and regularization parameter. The appropriate parameter adjustment factor and regularization parameter can effectively guarantee the convergence speed and stability of dual-parameter inversion method and improve the accuracy of GPR data inversion. Finally, FWI of the noise-free and 25-dB signal-to-noise ratio (SNR) noise data of the overthrust model is performed. The results show that the multiscale and dual-parameter inversion method proposed in this paper can provide reliable constraints, has better adaptability to noisy data, and can reliably and accurately reconstruct the dielectric properties distribution of the subsurface. [ABSTRACT FROM AUTHOR]

Efficient and accurate simulation of ground penetrating radar (GPR) in the open region helps immensely in both grasping the features of echoes and facilitating the interpretation of real GPR data. Due to the limitation of the computer model, however, the strong artificial boundary reflections, especially the low-frequency propagating waves encountered at the late stage of simulation greatly affect the simulation accuracy of GPR. This paper presents an innovative optimized unsplit-field convolutional perfectly matched layer (UCPML) based on rotated staggered grid (RSG) scheme to truncate the finite-difference time-domain (FDTD) lattices. Rather than obey the sharp variation based on an ${m}$ th-order polynomial, the optimized approach employs a novel optimized term and an adjustment factor to seek a gentle variation on optimal constitutive coefficients. This guarantees that the determination of optimal constitutive coefficients can be less influenced by the order of polynomial and especially, to improve the absorptive performance on low-frequency propagating waves. The calculating efficiency and accuracy of the RSG-FDTD scheme, as well as the absorbing performance of the optimized UCPML, are verified by two numerical examples. In particular, the analysis of the amplitude-frequency features of low-frequency clutters at steady state of the electromagnetic (EM) field and the corresponding global reflection error in the time–frequency domain is also presented. [ABSTRACT FROM AUTHOR]

Investigation into the electromagnetic response of porous media and the porosity distribution is a key for improved porous material. However, current ground penetrating radar (GPR) simulation techniques based on the finite difference method (FDM) or even finite element method (FEM) are mainly focused on describing macro characteristics of porous property. In this regard a novel methodology combining the FEM and B-spline wavelet on the interval (BSWI) is proposed to specify the propagation characteristics of GPR echoes in a micro-perspective way. A line current radiation model is first introduced to validate the high precision and multi-scale trait of BSWI. In addition, two representative models with different porosity distributions are established using the spectral decomposition and hybrid auto-correlation functions based on the stochastic process. By using this technique, specifically, can reduce the uncertainty of model error, making the models built more in line with the actual circumstances. Next, the multi-scale technique is developed based on the scaling function using tensor product of BSWI, by which the porous model can be split into multi-resolution space both temporally and spatially. Through this integration of parameter-oriented porous modeling and multi-resolution calculation technique, a set of examples and comparisons are presented, which validates the effectiveness and reliability of the proposed methodology for analyzing complex kinematic nature of diffraction and corresponding electromagnetic characteristics to different porosity distributions. • Proposing an approach to construct the model with specifiable porosity distributions for GPR testing. • Comparing the electromagnetic response of porous media using the proposed approach with that of the finite element method. • Investigating the kinematic nature of diffracted waves under different porosity distributions. • Presenting the shape function and element matrix of the B-spline wavelet on the interval. [ABSTRACT FROM AUTHOR]

Full waveform inversion (FWI) of common-offset ground penetrating radar (GPR) data can make up for the defects of the traditional prospecting technology such as destructive, cumbersome, and low efficiency, which also provides a robust and high-precision tool for quantitative assessment of subsurface prospecting. Nonetheless, conventional GPR-FWI is of limited practicality since the deficiency of accurate source wavelet and tremendous computational cost. We develop an efficient source-independent inversion algorithm based on the convolution method to eliminate the influence of source wavelet and enhance the algorithm efficiency to inverse field data. To suppress the noises induced by the convolution and cross-correlation operations, the time window is introduced in the reference trace which is selected automatically by singular value decomposition (SVD). The stochastic strategy reduces the computational cost by source subsampling. The synthetic model of a complex lens body demonstrates that source-independent FWI with time window has more tolerant to the initial model and noise, and the stochastic strategy improves the efficiency with ensured inversion accuracy. In the field GPR data of a sand trough containing two anomalous bodies, our algorithm has good adaptability and can accurately reconstruct the distribution of the permittivity and conductivity of the subsurface media without accurate estimation of the source wavelet. The results above indicate that the proposed algorithm in this study is valid for common-offset GPR data and improves the inversion efficiency by 1.24 to 3.10 times, which shows great potential to promote qualitative assessment in real-time subsurface exploration. • Develop an efficient source-independent GPR-FWI algorithm based on convolution • Automatical selections of the reference trace and time window suppress the noises • The stochastic strategy improves the inversion efficiency by 1.24 to 3.10 times • Validate the proposed algorithm through synthesis and field tests • Reconstruct details of the target body accurately without estimate of source wavelet [ABSTRACT FROM AUTHOR]

We introduce a novel implementation of a rotated staggered grid (RSG) finite difference (FD) method based on the unsplit convolutional perfectly matched layer (UCPML). The method is carried out using rotated staggered FD operators and a general complex frequency shifted stretching factor. It can offer a number of advantages over the RSG with split convolutional perfectly matched layer (SCPML), such as improving computational efficiency, overcoming the numerical dispersions resulting from the high-frequency propagation and strong contrasts in material, and specifically absorbing the evanescent modes at grazing incidence. A half-space numerical example with a lossy medium attached demonstrates that large-scale spurious reflections and evanescent modes at grazing incidence are absorbed efficiently by the UCPML in RSG scheme. Meanwhile, the comparison of the reflection error between the proposed algorithm and traditional approaches [using time-dependent reflection error (TDRE) and frequency-dependent reflection error (FDRE)] suggests that the proposed algorithm of RSG provides a preferable improvement in absorbing low-frequency coda wave of evanescent modes, particularly in the lossy medium that possesses inhomogeneous discontinuities. [ABSTRACT FROM PUBLISHER]

The finite element time-domain (FETD) method is an appealing electromagnetic (EM) field-solving procedure for the derivation of high-resolution field distribution of complex geological models. However, the arising computational burden has become a main bottleneck restricting the efficient implementation of ground penetrating radar (GPR) simulation at a high speed and large scale. In this research, we developed a high-efficiency EM solver to discretize the partial differential equations on unstructured triangular meshes, using a high-order graphics processing unit (GPU)-finite element discontinuous Galerkin time-domain (DGTD) method. By introducing a semi-discrete strong format instead of solving large stiffness matrices, and by employing the Runge-Kutta temporal integration scheme, the DGTD method can effectively overcome the problem of memory shortage and thereby solves the issue of instability. Besides, the uniaxial perfectly matched layer (UPML) is extended to match the lossy medium and used as an absorbing boundary condition to simulate an open space. Three models were manufactured to compare the DGTD method with the state-of-art methods (FDTD, FETD) of different grids in terms of computing accuracy, the dispersion degree of the rough interface, and memory occupied. To be specific, we explored the detailed effect of both the grid sizes and the order of basis functions on the modeling accuracy for the proposed GPU-DGTD method. We finally verified the numerical solution and demonstrated its applications by simulating a complex model for tunnel geological forecast. The experimental results reveal the order of basic function N and the size of the grid d are closely concerned with the wavelength λ of EM waves, for example, an appropriate definition is d / N ≈ λ /15. • The unstructured-grid high-order GPU-DGTD is developed for GPR. • GPU-DGTD can be applied to complex models and have high accuracy and efficiency. • d / N ≈ λ /15 is the recommended formula for grid sizes and order of basis functions. • A high-order DGTD with large grid is better than a low-order one with small grid. [ABSTRACT FROM AUTHOR]

Reverse time migration (RTM) is the important intermediate step for focusing the radar diffracted energy of the targets in ground penetrating radar imaging. The conventional RTM algorithm demands a large number of iterative trial experiments and depends on the experts' decision on the estimation of the velocity or relative permittivity of the subsurface medium. Meanwhile, the RTM profile is vulnerable to artifacts, which are composed of noise interference, multiple interferences, arc-shaped clutter, and crosstalk, so it is difficult to inspect visually. Therefore, we propose a RTM method based on accurate velocity estimation and total variation (TV) de-noising to improve the accuracy of the RTM imaging. Firstly, the appropriate migration velocity is obtained automatically by autofocusing metrics to reduce the number of visual inspection times and corrections in the migration processing. Secondly, the TV de-noising strategy based on split Bregman iterative is applied to the RTM profile with the cross-correlation imaging condition, so that the edge of the target can be obvious and the position can be accurate. Then, we apply the proposed method to the simulation data of the pipeline model and the tunnel lining model. All results show that the selected three different autofocusing metrics have unimodality and unbiasedness, which can focus on a single relative permittivity to obtain appropriate migration velocity. Furthermore, the TV de-noising strategy successfully eliminates artifacts, reconstructs contours, enhances the edge sharpness, and improves the quality and accuracy of the radar profile. Finally, we take the field data of the LiuYang River tunnel to verify the applicability of our method, we choose 2–30 as a wider range of relative permittivity based on prior information. Considering the different lateral velocity of the field data, we adopt lateral segmentation processing to improve the quality of the GPR profile. The tests of simulation data and the field data indicate that the proposed method can provide a scientific and effective way for accurate interpretation of GPR data. • Autofocusing techniques obtain the appropriate velocity model automatically. • Total variation de-noises and improves the accuracy of GPR imaging. • This strategy was successfully applied to the simulation data and the field data. • The split Bregman iterative method converges to an accurate solution. [ABSTRACT FROM AUTHOR]

The high-fidelity attenuation of random ground penetrating radar (GPR) noise is important for enhancing the signal-noise ratio (SNR). In this paper, a novel network structure for convolutional denoising autoencoders (CDAEs) was proposed to effectively resolve various problems in the noise attenuation process, including overfitting, the size of the local receptive field, and representational bottlenecks and vanishing gradients in deep learning; this approach also significantly improves the noise attenuation performance. We described the noise attenuation process of conventional CDAEs, and then presented the output feature map of each convolutional layer to analyze the role of convolutional layers and their impacts on GPR data. Furthermore, we focused on the problems of overfitting, the local receptive field size, and the occurrence of representational bottlenecks and vanishing gradients in deep learning. Subsequently, a network structure optimization strategy, including a dropout regularization layer, an atrous convolution layer, and a residual-connection structure, was proposed, namely convolutional denoising autoencoders with network structure optimization (CDAEsNSO), comprising an intermediate version, called atrous-dropout CDAEs (AD-CDAEs), and a final version, called residual-connection CDAEs (ResCDAEs), all of which effectively improve the performance of conventional CDAEs. Finally, CDAEsNSO was applied to attenuate noise for the H-beam model, tunnel lining model, and field pipeline data, confirming that the algorithm adapts well to both synthetic and field data. The experiments verified that CDAEsNSO not only effectively attenuates strong Gaussian noise, Gaussian spike impulse noise, and mixed noise, but it also causes less damage to the original waveform data and maintains high-fidelity information. [ABSTRACT FROM AUTHOR]

Accurate and efficient 3D simulation is extremely important for both grasping the features of radar wave propagation in realistic models and the high-resolution inversion. In this paper, we propose a new numerical algorithm called the low-storage five-stage fourth-order explicit Runge-Kutta interpolation scaling function method (LSERK-ISFM) and apply it into the 3D simulation of ground penetrating radar (GPR). Firstly, we derive the auxiliary differential equation (ADE) of the 3D Maxwell's equations based on the complex-frequency shifted perfectly matched layer (CFS-PML), discretize the spatial derivative of the Maxwell equation by ISFM, and integrate the temporal dimension through the LSERK scheme. Compared with the traditional finite-difference time-domain (FDTD) method, the LSERK-ISFM algorithm can effectively improve the precision of space-time dispersion of the Maxwell's equations. Specifically, by the homogeneous vacuum medium model, we compare the forward modeling results of the different number of grids per wavelength, the comparison results prove that a smaller number of grids per wavelength can be selected in the LSERK-ISFM scheme, which can greatly contribute to reducing the consumption of memory. Then we build a simple 3D model to properly compare the proposed algorithm with the coarse-mesh FDTD and the fine-mesh FDTD, the results show that, with the same mesh generation, the LSERK-ISFM algorithm outperforms the conventional FDTD algorithms in terms of both accuracy and efficiency. Finally, we test the algorithm on a 3D complex model by a series of 3D forward profiles and the corresponding slices, both simulated reflections and diffractions clearly depict the shape and location of the anomalous bodies, which shows great potential of application in the field of 3D exploration and interpretation for GPR community. • A new numerical simulation algorithm LSERK-ISFM is developed in the simulation of 3D GPR. • The LSERK method allows a larger stable time step, which in general has a better dispersion characteristic. • LSERK-ISFM methodology effectively reduces the high memory consumption and improves the simulation efficiency. [ABSTRACT FROM AUTHOR]

We present a new approach of unstructured grid adaptive finite element in the frequency domain (AFEFD) based on exact perfect matching layer (EPML) boundary condition for Ground penetrating radar (GPR) simulation. The discrete equations of transverse magnetic mode are derived by using the unstructured Delaunay mesh coupled with linear interpolation basis functions. For the trade off between the computational efficiency and the accuracy of simulation, an h-type adaptive finite element method (AFEM) is employed and, in particular, with less layer thickness and fewer parameters setting, an EPML boundary condition is developed to truncate the AFEM lattices. In addition, the Zienkiewicz-Zhu posterior error estimation, the mesh refinement scheme and the implementation process of AFEM are also elaborated in detail. To testify the validity and practicability of this methodology, a homogeneous medium model of line current radiation field with analytical solution and a complex model of lining fracture disease are considered. The results of frequency-domain slices, transformed time-domain forward profile, together with wavefield snapshots demonstrated that the reflections, diffractions and other codas caused by non-physical factors at the boundary are effectively absorbed, subsequently, the absorbing performance of simulation with AFEM in frequency domain is greatly improved. More importantly, the proposed methodology can automatically control its mesh density according to the features of the complex object, which significantly economize the computing resource of simulation when AFEM is employed. • The unstructured grid AFEFD method based on exact PML is developed in the forward modelling of GPR. • EPML makes the simulation can be performed efficiently and rapidly with less layer thickness and fewer parameters setting. • The proposed methodology can automatically control its mesh density according to the features of the complex object. • Verification of the practicability with AFEFD based on exact PML in complex medium. [ABSTRACT FROM AUTHOR]

Complex irregular defects of tunnel linings under complicated geological conditions cannot be accurately reconstructed with the traditional full-waveform inversion (FWI) method due to their irregular geometrical characteristics and complex dielectric properties. Because of extensive inversion calculations and high memory requirements, the traditional FWI method is very sensitive to the initial model and plunge into a local minimum or cycle skipping. To solve this problem, a novel ground-penetrating radar (GPR) FWI method involving two parameters (i.e. permittivity and conductivity) is proposed for improving reconstruction accuracy of lining defects using the total variation (TV) regularization. First, the Delaunay unstructured triangular mesh in finite element time-domain (FETD) method is employed to perform GPR forward modeling, and then the total-variation model constraint and multi-scale inversion strategy are implemented during execution of the conjugate gradient (CG) algorithm, which facilitates the quick search for the global optimal minimum value, thus guaranteeing the avoidance of the ill-posed problem during the inversion process. Accordingly, the detailed features of lining defects can be characterized and reconstructed even for those complicated geological conditions, more specifically, the results show that, with fewer iterations (up to 59 times less), the proposed method present a lower reconstruction error both on permittivity (up to 12.05% lower) and conductivity (up to 7.35% lower). From a comparison of the inversion results and the model, it can be concluded that the proposed FWI algorithm can effectively eliminate the non-physical oscillation and artifacts in the image reconstruction, which may significantly improving the accuracy of defects interpretation and assessing the severity of complex defects. [ABSTRACT FROM AUTHOR]