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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]

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]