Ground Penetrating Radar (GPR) is a powerful tool for exploring the shallow subsurface due to its effective and noninvasive features. Recently, accurate and high-resolution characterization of subsurface properties in three-dimensional (3D) GPR investigations calls for a quantitative and high-resolution imaging approach. However, the full-waveform inversion (FWI) method for GPR data was performed mostly in 2D and rarely discussed the polarizations. To fully utilize 3D GPR polarization data, this letter proposes a frequency-domain FWI algorithm for simultaneous inversion of both the co-polarized and cross-polarized data. Detail derivations and vital processes in our inversion workflow were described in detail, before applying it to the numerical experiments and analyzing the potential impacts of the polarizations on inversion results with a synthetic model. Results showed that the cross-polarized data is more sensitive than the co-polarized data in inversion, and the behaviors in the inversion of the multi-polarized data with different values in the weighting matrix suggests that larger weights for co-polarized data is of benefit to a better inversion result.

Theoretical advancements in full waveform inversion (FWI) of ground-penetrating radar (GPR) data have shown promising potential for enhancing the accuracy of GPR data interpretation. However, the widespread implementation of FWI faces significant challenges due to its low-computational efficiency and high memory consumption, primarily attributed to the gradient operation stage. To address these issues, we propose a spatiotemporal optimization approach for GPR FWI based on super-resolution (SR) technology. The proposed method focuses on three optimization directions: adopting a storage strategy that only preserves the forward wavefield while synchronizing the gradient operation and adjoint wavefield operation, compressing the time dimension of the GPR wavefield based on the Nyquist sampling law, and obtaining a fuzzy gradient in the spatial dimension by sampling the wavefield at each moment and restoring it using an SR network to complete the FWI. Experimental results demonstrate that the proposed optimization method achieves a nearly 50% acceleration in computational efficiency without compromising the original inversion architecture. Moreover, it reduces the memory usage to approximately 4.17% of the original memory, while maintaining the effectiveness of the inversion process. This method exhibits practicality and effectiveness through several numerical and measured data experiments, providing a solid foundation for the widespread application of FWI on commonly available microcomputers.

Ground penetrating radar (GPR) inversion is a well-accepted technique for tunnel geological prediction by reconstructing the permittivity distribution in front of the tunnel face. However, full waveform inversion (FWI) still retains practical obstacle mainly due to the limited illumination in the common-offset gathering mode. Moreover, the narrow width of tunnel face, initial model sensitivity, together with unaffordable computational cost could exacerbate the ill-posedness problem of the FWI for real-time prediction. The conventional U-Net network typically uses skip connections to directly fuse shallow and deep features, without differentiating the weight of each feature channel, and lacks an effective constraint mechanism. Consequently, the featural extraction capability of U-Net is rather limited, especially for the EM response details concerning small-scale geological anomalies. To mitigate this, we propose a novel TGPInvNet framework for real-time GPR inversion in tunnel geological prediction. The network is an improved U-Net for adaptive focus on small-scale features by incorporating the attention gate (AG) mechanism, convolution block attention module (CBAM). More importantly, the multi-task learning (MTL) module is introduced to provide constraints and information for the inversion. Both synthetic and field experiments are conducted to assess the performance of the proposed network against state-of-the-art methods, include GPRNet, PINet, and TV-regularized FWI. For field validation, four quantitative metrics (i.e., MSE, MAE, SSIM, and MSSIM with values of 0.0047, 0.0495, 0.7467, and 0.7469, respectively) demonstrate the potential application and visible practicality of the proposed TGPInvNet.

Reverse time migration (RTM) is an important technology for imaging ground penetrating radar (GPR) data. To address the problem of artifacts flooding of imaging results and high memory consumption of RTM, we propose an optimized multitraces cross correlation window (MCW) to increase the order of magnitude difference between the signals and artifacts for more obvious separation effect, but it also exacerbates the problem of computational cost. With the high sampling rate and high efficiency of collection method, common offset GPR is convenient to acquire large amounts of data, which consumes more numerous cost for RTM. Due to the attenuation property of high-frequency radar waves, most of the signals of common offset GPR originate from a small region below the antenna. Inspired by the footprint in airborne electromagnetic method, we propose the finite domain (FD) strategy, which limits the calculation of single trace to FD, and combine it with optimized MCW. It can reduce the computational cost of RTM and MCW significantly at the same time, especially for long profile data. Numerical experiments show that the FD reduces the computation by 77.22% with speedup 11.01. The optimized MCW retains the effective information separated from artifacts. The migration of the measured data proves the advantages and practicality of this method in engineering practical exploration.

Ground penetrating radar (GPR) migration is a crucial imaging method to obtain the spatial position, size, and shape of the underground structures. However, Kirchhoff migration, finite-difference migration, F-K migration, and reverse time migration (RTM) focus on geometric structure imaging and cannot provide realistic reflection coefficients. Least-squares reverse time migration (LSRTM) regards imaging as an inversion problem in the sense of least squares. It continuously corrects the imaging results by minimizing the residual between the simulated data and the observed data to obtain realistic reflection coefficients. In order to enhance the accuracy of the LSRTM result, we introduce the cross-correlation window to suppress artifacts and noise. Although the non-interface information in the gradient is effectively suppressed, the cross-correlation window will cause new noise to appear. This makes the LSRTM result unsatisfactory because the window is used multiple times in the calculation. Therefore, we proposed the improved cross-correlation window that utilizes the Block-matching and 3D Filtering (BM3D). This improvement preserves the ability of eliminating artifacts while preventing the window from introducing new noise. Experiments results with the synthetic data and the measured data demonstrate that compared with the traditional methods, the LSRTM based on the improved cross-correlation window suppresses noise, reduces artifacts, enhances clarity of the interfaces, and achieves higher imaging accuracy.

Ground penetrating radar (GPR) full waveform inversion (FWI) can make full use of kinematics information and dynamics information to achieve the highest theoretical resolution, serving as a promising tool for reconstructing subsurface structures and the physical properties of the medium. However, conventional FWI is constrained by strong nonlinearity, easily falls into the local minimum, and requires multiple forward simulations coupled with intensive adjoint wavefield calculations, which cannot satisfy the requirements of engineering exploration. To mitigate the nonlinearity of the inversion and improve computational efficiency, this paper designs a FWI framework based on deep learning, featuring a multi-frequency and multiscale fusion strategy. Utilizing a multi-output convolutional neural network (CNN) constructed by the hybrid dilated convolution, the receptive field is expanded without incurring additional computational complexity and memory consumption. The dilated CNN predicts multiple sets of available low-frequency data from its respective higher-frequency components of GPR data and integrates the multi-frequency strategy to guide FWI to converge the global minimum. The sizes of computational models are selected according to distinct electromagnetic wave frequencies, and the very deep super-resolution (VDSR) model facilitates the automatic mapping of grids at different scales which reduces unnecessary calculation and boosts inversion efficiency. The synthetic and field cases prove that the proposed framework significantly enhances the spatial resolution, robustness, and efficiency of FWI. The dilated CNN and VDSR constructed have demonstrated robust generalization and noise tolerance abilities, which are suitable for geophysical tasks.

Aiming at solving the clutter flooding problem in the traditional cross-correlation reverse time migration (RTM) of ground penetrating radar (GPR), we proposed an improved RTM method based on multi-traces cross-correlation window (MCW) imaging condition. The main difference between the proposed method and the traditional direct stacking is that it can effectively enhance the effective signal while weakening the clutter by performing MC calculation on the single trace imaging results, avoiding the enhancement of both clutter interference and effective signal concurrently by direct stacking. Secondly, the window threshold is set according to the GPR observation accuracy, and the effective signal in the MC result is retained as the abnormal region window, while the imaging results in the non-abnormal region are discarded, so as to suppress the clutter and retain the abnormal region information. Numerical experiments show that, compared with the traditional RTM and total variation de-noising method with cross-correlation imaging conditions, the MCW imaging condition can accurately locate abnormal region, suppress clutter interference, and have the advantage of no loss of effective information, which greatly improves the imaging quality. Finally, the proposed method is applied to the measured data to verify the practicability and effectiveness in practical engineering applications.

Reverse time migration (RTM) has the advantage of high-precision imaging, and it can converge the radar wave back to its actual position, making it widely used in radar exploration. However, there are artifacts, low-frequency noise and fuzzy deep imaging in RTM results. Researchers have proposed full wavefield separation imaging condition and total variation (TV) technique, both of which could suppress noise and artifacts. However, the original wavefield separation method was considerably limited by its extensive calculation, and it cannot solve the problem of weak energy of imaging in the deep zone; the conventional TV technique was likely to be affected by artifacts due to the inevitable over-smoothing-suppression of anomaly edges. To address these issues, this paper improves the RTM methodology by combining an optimized full wavefield separation based on Poynting vector imaging condition and TV-L1 based artifacts suppressing technique. Specifically, the physical significance of the Poynting vector is introduced to separate the wavefield for reducing the calculation burden; the compensation function is integrated with the imaging condition to compensate for the deep energy; the TV-L1 based artifacts suppressing method is used to resolve the imaging problem of loss of specific and edge details. Synthetic data and laboratory data experiments are carried out to verify the effectiveness and practicability of the proposed RTM methodology.

Ground penetrating radar (GPR) is an important shallow electromagnetic non-destructive detection technology. The full waveform inversion (FWI) of GPR data utilizes all information including dynamics and kinematics, theoretically has the highest imaging accuracy, and meets the increasingly sophisticated needs of engineering exploration imaging. However, the bottleneck restricting the FWI is the low calculation efficiency, which cannot meet the requirements of rapid reconstruction of underground medium in actual engineering. In order to improve the calculation efficiency, we introduce the data encoding into the GPR dual-parameter FWI. Data encoding often brings crosstalk noise, and the noise is closely related to the encoding methods and data types. For this reason, we select the encoding of the crosshole data, wide-angle reflection and refraction data, and common-offset data for inversion. Experiments show that data encoding can effectively reduce computing time, and three different GPR data require different encoding methods due to their different redundancies. Total variation (TV) regularization can suppress the noise caused by data encoding. Although it will slightly increase the calculation time, it can significantly improve the inversion quality.

Multi-parameter elastic full waveform inversion (FWI) makes full use of the dynamic and kinematic information of all seismic wavefield. Through the mutual constraint and verification of the three parameters of P-wave velocity, S-wave velocity, and density, the joint evaluation is carried out, which is helpful to understand the structural and lithologic information of underground media more comprehensively. The bottleneck restricting the multi-parameter FWI is the large amount of calculation and low efficiency. To improve this problem, multiple shots are directly superimposed to form super shots. While it usually results in an unstable inversion due to that a large amount of crosstalk noise will be easily generated between adjacent shots. In this paper, we introduce the random source-encoding strategy to improve the inversion efficiency and load the total-variation (TV) regularization term to suppress the crosstalk noise, but it also brings the problem of regularization parameters selection for multi-parameter FWI. Thus, the projection method is applied to directly load the regularization term into the model as a constraint, which avoids the unsatisfactory results caused by the improper selection of regularization parameters and effectively improves the ill-posedness of inversion. Finally, three examples of the graben, the 1994BP, and the overthrust model are used to prove that the proposed algorithm based on random source-encoding and projection regularization can effectively improve the inversion efficiency, suppress noise, and has good practicability and adaptability.

Ground-penetrating radar (GPR) has been regarded as a potentially efficient way of evaluating the growth status of trees and preventing deterioration associated with trunk defects. The majority of current GPR data inversions, however, focused on imaging the macroscale location of defects. As the first attempt to seek a preferable quantitative inversion methodology for specifying tree protection and remedies, this article proposes a full-waveform inversion (FWI) approach involving dual-parameter attributes applied to common-offset GPR data from a commercial antenna. Specifically, the synchronous inversion of both dielectric constant and conductivity improves the identification accuracy of certain defect types. In particular, both a multifrequency strategy and total-variation (TV) regularization are seamlessly introduced to assure inversion stability by overcoming local minima and cycle skipping. Through an irregular trunk model test, the effectiveness of the optimized inversion is initially verified by presenting the precise features of the crack, hollow, and decay with the dual-parameter inversion results. In addition, several other synthetic trunk models and in-site trunk model tests further demonstrate the robustness and practicability of the proposed algorithm, which can offer more specific and comprehensive guidance for the formulation of tree protection and restoration measures.

We investigate an algorithm for the 3-D inversion of frequency-domain airborne electromagnetic (AEM) data based on the forward modeling and sensitivity calculation by footprint-guided compact finite element method (CFEM). Unlike the conventional approach, the modeling volume in our algorithm for each transmitter–receiver pair is a regular hexahedral that encloses the footprint, rather than a large mesh for the entire survey area or the local mesh with a number of grids extending from the footprint. After the electric fields in the modeling volume are solved by vector finite element method (FEM) with an integral equation boundary condition, the response and sensitivity are explicitly calculated by employing the product of the prepared Green’s functions and the vector of electric fields. The accuracy of this footprint-guided CFEM is validated by comparing it against conventional CFEM, and different synthetic models are tested by our inversion algorithm. The inversion tests of synthetic models show the feasibility of the combination of footprint-guided CFEM and Gauss–Newton optimization in recovering models within an acceptable error level, and the inversion results show a good agreement with the true models on both the model geometry and recovered conductivity.

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.

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.

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.

To address problems, such as the computationally intensive inversion requirements, low inversion efficiency, and inadequate inversion accuracy caused by multiparameter crosstalk in a synchronous inversion, a new dynamic stochastic source encoding strategy combined with minmax-concave total variation (MCTV) regularization model constraints was proposed. This strategy avoids crosstalk noise between shots caused by the algorithm and greatly improves the inversion efficiency without affecting the inversion accuracy. By comparing a “cross”-shaped model with the multiparameter inversion results, we found that the MCTV regularization strategy boasts the best inversion effect. We further showed that dynamic stochastic source encoding can increase the inversion efficiency threefold by applying the 1994 British Petroleum (BP) migration international standard topography model and establishing a function to evaluate the most efficient inversion strategy from among seven options. Compared with the traditional stochastic source encoding strategies, dynamic stochastic source encoding was shown to better suppress crosstalk noise. The proposed strategy also presented a higher acceleration ratio; additionally, combining this strategy with MCTV regularization model constraints provided the clearest reconstructed image with the highest inversion precision and obtained the best evaluation score among the considered inversion strategies, albeit with a slight reduction in the total elapsed time-acceleration ratio.

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.

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.