Due to the unevenness of ground surface, mismatch between trig interval and sampling speed, or other electromagnetic interferences, traces missing is a quite typical occurrence during the on-ground ground penetrating radar (GPR) testing. Effective reconstruction of GPR missing traces has been regarded a crucial link to improve both the signal-to-noise ratio of raw data and the resolution of GPR imaging. In this paper, we propose a novel deep-learning framework based on the residual feature distillation block U-Net (RFDB-U-Net) to mitigate the transmission loss problem of the conventional U-Net. To be specific, by employing the information distillation network based on the multiple feature extraction connections, RFDB is capable of utilizing the adequate residual information of each layer for feature learning. Moreover, a skip connection is additional patched on the residual units to properly compensate the missing features in the convolution process. In particular, the merging of lightweight U-Net ensures the lightness of RFDB. The outperformance of the proposed framework is verified in detail through the reconstruction accuracy and evaluation metrics in the test of synthetic data, laboratorial data and in-site field data.

Data assimilation for unconfined seepage analysis has faced significant challenges due to hybrid causes, such as sparse measurements, heterogeneity of porous media, and computationally expensive forward models. To address these bottlenecks, this paper introduces a physics-informed neural network (PINN) model to resolve the data assimilation problem for seepage analysis of unsaturated earth–rockfill dams. This strategy offers a solution that decreases the reliance on numerical models and enables an accurate and efficient prediction of seepage parameters for complex models in the case of sparse observational data. For the first attempt in this study, the observed values are obtained by random sampling of numerical solutions, which are then contributed to the synchronous constraints in the loss function by informing both the seepage control equations and boundary conditions. To minimize the effects of sharp gradient shifts in seepage parameters within the research domain, a residual adaptive refinement (RAR) constraint is introduced to strategically allocate training points around positions with significant residuals in partial differential equations (PDEs), which could facilitate enhancing the prediction accuracy. The model’s effectiveness and precision are evaluated by analyzing the proposed strategy against the numerical solutions. The results indicate that even with limited sparse data, the PINN model has great potential to predict seepage data and identify complex structures and anomalies inside the dam. By incorporating coupling constraints, the validity of our PINN model could lead to theoretically viable applications of hydrogeophysical inversion or multi-parameter seepage inversion. The results show that the proposed framework can predict the seepage parameters for the entire research domain with only a small amount of observation data. Furthermore, with a small amount of observation data, PINNs are able to obtain more accurate results than purely data-driven DNNs.

Diffraction separation is considered of great importance for the full-wavefront reconstruction (FWR) of ground penetrating radar (GPR) and its delicate data processing. In contrast to reflections, GPR diffraction events encode the fully dynamic feature and subwavelength information to identify small-scale heterogeneities, thereby offering enhanced illumination and resolution for GPR imaging. However, fully extracting these faint diffraction components remains a very challenging task. These components are usually ignored because of the strong interference and masking effect of the more dominant reflective components, and in particular, the attenuation of GPR waves accelerates almost exponentially with the frequency. In this article, we developed a coherence analysis (CA) framework for extracting GPR diffractions by considering the kinematic attributes and discontinuity features of GPR wavefronts, as well as the dispersion and attenuation effects of GPR responses. To be specific, the compensation preprocessing and semblance summation are performed sequentially for coherence acquisition, after which a multiscale subtraction is designed toward the coherent fields. In particular, we concentrated on analyzing media losses and multiparameter impacts on diffraction separation performance. To demonstrate the feasibility and practicality of the proposed framework, we tested our algorithm using synthetic and field datasets, both results with quantified metrics showing the elimination of continuities. The comparative results reveal the performance of the framework in preserving the edge components of GPR diffractions, making it potentially attractive for microscopic velocity analysis, refined full wavefield migration (FWM), and well-constrained full waveform inversion in terms of small-scale heterogeneities and discontinuities.

As a fundamental part of ground penetrating radar (GPR) data processing, reverse time migration (RTM) can correctly position reflection waves and focusing diffraction waves on the proper spatial position. Least-squares reverse-time migration (LSRTM) is widely used in the seismic field for its ability to suppress artifacts and generate high-resolution images in comparison to conventional RTM. However, in the particular case of GPR detection methods, LSRTM is extremely susceptible to aliasing artifacts caused by under-sampling. In pursuit of enhanced precision in underground structure characterization, this paper presents the development of a new LSRTM based on modified total variation (MTV) regularization to improve imaging resolution. Initially, the objective function of LSRTM is derived by combining the Born approximation in 2-D transversal magnetic mode. Next, the adjoint equations and their gradients are solved using the Lagrange multiplier method. The objective function is then constrained by MTV regularization to ensure the precision and convergence of the LSRTM, which delivers a refined edge with reconstruction details. In the numerical experiments, in comparison to the conventional LSRTM method, the LSRTM-MTV algorithm demonstrated a 30.4% increase in computational speed and a 21.1% reduction in mean squared error (MSE). The outperformance of the proposed method is verified in detail through the image resolution and amplitude preservation in the test of synthetic data and laboratory data. Future research efforts will center on applying the proposed method to models featuring dispersive or anisotropic media that closely mimic real-world conditions and extending the application to various imaging techniques involving objective function minimization.

Magnetotellurics (MT) is an important geophysical method for resource exploration and mineral evaluation. As a direct and effective form of data interpretation, MT inversion is usually considered to be a penalty-function constraint-based optimization strategy. However, conventional MT inversion involves a large number of calculations in penalty terms and causes difficulties in selecting exact regularization factors. For this reason, we propose a multiplier-based MT inversion scheme, which is implemented by introducing the incremental Lagrangian function. In this case, it can avoid the exact solution of the primal-dual subproblem in the penalty function and further reduce the sensitivity of the regularization factors, thus achieving the goal of improving the convergence efficiency and accelerating the optimization calculation of the inverse algorithm. In this study, two models were used to verify the performance of the multiplier method in the regularized MT inversion. The first experiment, with an undulating two-layer model of metal ore, verified that the multiplier method could effectively avoid the MT inversion falling into local minimal. The second experiment, with a wedge model, showed that the multiplier method has strong robustness, due to which it can expand the selection range and reduce the difficulty of the regularization factors. We tested the feasibility of the multiplier method in field data. We compared the results of the multiplier method with those of conventional inversion methods in order to verify the accuracy of the multiplier method.