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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]

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]

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]

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]