Seepage dynamics in earth dams are greatly influenced by the spatial heterogeneity of dam material, which governs hydrological state variables and affects overall dam stability. This study develops a three-dimensional (3D) framework integrating the van Genuchten model for unsaturated hydraulic conductivity and the Signorini condition to transform outflow boundaries into hydraulic-head constraints. This paradigm shift enables full volumetric flow redistribution, lateral bypassing, and anisotropic seepage patterns that cannot be captured in two-dimensional (2D) simulations. Validation against rectangular dams shows mean absolute percentage errors of 0.14–1.04

Time-lapse electrical resistivity tomography (TL-ERT) provides spatially distributed information on subsurface hydrologic changes. However, inversion of long monitoring sequences is computationally demanding. Modifying the data misfit, regularization, model parameterization, or petrophysical transformation may also require new gradient derivations and separate implementations. Here, we present AD-TLERT, a unified, GPU-accelerated framework for time-lapse ERT inversion based on automatic differentiation. The framework integrates model parameterization, differentiable petrophysical transformations, forward modeling, data misfit, regularization and auxiliary constraints into a single computational chain. Alternative inversion formulations can therefore reuse the same PDE derivative implementation without re-deriving the complete ERT sensitivity for each case. Comparisons with pyGIMLi showed close agreement in the forward responses, gradients, and recovered resistivity models. Under the tested configuration, AD-TLERT achieved an approximately 51-fold speedup. Synthetic experiments showed that inversion choices affect the amplitude, geometry, and temporal behavior of recovered anomalies. By propagating gradients through the embedded petrophysical relationship, AD-TLERT enabled direct water-content inversion and yielded more accurate estimates than post-inversion conversion for the tested model. A field application further demonstrated how ERT, temperature, and soil-moisture observations can be combined to image snowmelt-driven hillslope wetting. AD-TLERT provides an efficient and flexible framework for time-lapse ERT inversion and hydrologic interpretation.

In recent years, Deep learning-based inversion methods for Ground Penetrating Radar (GPR) data have garnered increasing attention. Such approaches often rely on simulated data for training. However, most existing studies are based on time-domain waveform data, which suffer from issues such as dimensional imbalance, high feature coupling, and computational complexity. Targeting the advanced geological prediction scenario in tunnel engineering, this paper proposes a dual-parameter inversion network based on frequency-domain multi-channel input. The network incorporates the Convolutional Block Attention Module (CBAM) attention mechanism and residual learning paradigm, and applies a parameter scaling balance strategy to mitigate the magnitude difference between permittivity and conductivity, significantly improving training convergence speed and achieving end-to-end dual-parameter inversion of GPR data in tunnel environments. Furthermore, the time-domain data after direct wave removal are transformed into frequency-domain data via Fourier transform to construct multichannel frequency-domain features (real part, imaginary part, and magnitude). This approach substantially reduces training time while preserving data integrity. Experimental results demonstrate that, compared to timedomain and single-channel frequency-domain inputs, the multi-channel frequency-domain method exhibits superior inversion performance, stronger anti-interference capability, and favorable generalization in both simulated and measured data. The multi-channel frequency-domain feature fusion mechanism enriches the feature representation of the data, providing an effective new approach for GPR data inversion.

To address the challenges of low recognition accuracy and high rates of missed and false detections of small targets in ground-penetrating radar images of road internal defects, this paper proposes a lightweight detection algorithm named YOLOv11 (You Only Look Once)-PME, based on an improved YOLOv11 architecture. The method introduces innovations at both the network structure and loss function levels: a lightweight CPU convolutional neural network (PP-LCNet) is adopted as the backbone to enhance feature extraction capability while reducing parameter count; a multi-scale cross-reference attention module (MSCRSimAM) is designed to improve perception and fusion of multi-scale defect features; and the enhanced MPDIoU (EnMPDIoU) loss function is proposed, which incorporates bounding box diagonal constraints and optimizes centre distance weighting to increase sensitivity to the location and shape of defects. Experimental results demonstrate that YOLOv11-PME achieves a mean average precision (mAP@0.5) of 96.8% on a self-established road defect dataset, outperforming the original YOLOv11 by 5.3%, while reducing both parameter count and computational cost by 11.5% and 4.8%, respectively. Field detection results show strong agreement with core validation, indicating that the proposed algorithm exhibits high reliability, generalization capability and strong potential for engineering applications.

Ground penetrating radar (GPR) is a geophysical technique that investigates subsurface media by transmitting and recording high-frequency electromagnetic waves. Among various imaging methods, full waveform inversion (FWI) is widely used for high-resolution reconstruction of subsurface structures. In FWI, the forward and backward wavefields are correlated to compute the gradient for model updating. However, this process requires temporal alignment of the two wavefields in the time domain, which in turn necessitates storing the entire forward wavefield at all time steps. Such full wavefield storage results in extremely high memory demands, posing significant challenges for commonly available computing resources. To address this issue, the boundary saving method is introduced, which stores only the wavefield values on the computational domain boundaries and at the final time step. During gradient computation, the full forward wavefield is accurately reconstructed by backward time propagation using the stored boundary information. Experiments on both synthetic data and field data demonstrate that boundary saving enables high-quality reconstruction of the wavefield and yields FWI results that are nearly identical to those obtained using full wavefield storage, while dramatically reducing memory consumption. Moreover, the method exhibits strong potential for facilitating other high-resolution inversion techniques that require wavefield storage, as well as for enabling large-scale 3D GPR applications.

To address the challenges in GPR-based urban road defect detection-namely, the la-bor-intensive data interpretation, strong subjectivity in manual analysis, and low computational efficiency of FWI-this paper proposes a novel two-stage 'extraction-inversion' framework for efficient and accurate detection of concealed road defects. In the first stage, a YOLO11-based deep learning network is employed to automatically identify defect regions in GPR profiles, significantly reducing the volume of data to be processed. This enables rapid localization of defects such as cracks and voids, while improving both the accuracy and efficiency of defect positioning. In the second stage, a regularized full waveform inversion algorithm is applied to the previously identified anomalous regions for localized reconstruction, achieving high-resolution imaging of typical road defects. This stepwise strategy not only greatly reduces computational costs and processing time, but also retains the strong physical interpretability of full wave-form inversion. Experimental results demonstrate that the proposed method can reduce computational load, while enabling precise reconstruction of the geometry and physical properties of subgrade cracks, voids, and subsidence. This framework offers a new paradigm for intelligent detection and accurate assessment of concealed urban road defects.

Ground‐penetrating radar (GPR) is a widely used technique for near‐surface exploration, providing subsurface imaging of underground targets. However, in practical surveys, random noise severely degrades image quality and compromises interpretational reliability. Conventional GPR denoising approaches often rely on manual parameter tuning and struggle to achieve an effective balance between noise suppression and feature preservation. To address this challenge, this study proposes a hybrid denoising model (HybridDenoiser) that integrates dictionary learning with deep convolutional networks. The model employs an encoder to extract multi‐level features, incorporates a learnable dictionary to achieve sparse representation of these features and uses a decoder for high‐fidelity image reconstruction. Experimental results on both synthetic and field data demonstrate that the proposed method effectively suppresses noise, significantly enhances signal‐to‐noise ratio and structural similarity and better preserves the reflection characteristics of subsurface targets. These findings confirm the model's strong practicality and generalization capability, offering a promising solution for improving GPR image quality in complex environments.

Ground penetrating radar (GPR) is an important shallow geophysical exploration method and can be widely applied in near surface applications. Thereby, the GPR full-waveform inversion (FWI) utilizes all information contained in the data including dynamics and kinematics and therefore has theoretically the highest imaging possibilities. One of the bottlenecks of FWI is its high computational cost and inability to meet the real-time needs for experimental applications. To improve the efficiency of GPR FWI, we provide two methods that can reduce the calculation time. The first is source encoding, which can reduce the number of forward simulations by simultaneously exciting multiple sources in one simulation and mitigating crosstalk noise by encoding the sources. The second is source subsampling, which selects a subset of sources to participate in the inversion, gradually uses more sources during the inversion process, and in the final stage uses all the sources. Numerical experiments show that compared with traditional FWI, both methods effectively reduce the calculation time by providing a similar reconstruction of the medium properties.

Three-dimensional ground penetrating radar (GPR) has gained widespread usage in shallow surface exploration due to its ease of acquisition and ability to capture diverse polarization information Meanwhile, the quantitative interpretation of 3-D GPR data through full waveform inversion (FWI), particularly when incorporating various polarization methods, holds substantial practical significance. Nonetheless, challenges in 3-D GPR FWI, including multiple solutions and high memory demands, limit its theoretical potential. In this study, we propose an efficient 3-D frequency-domain FWI approach utilizing dual-parameter attributes applied to 3-D GPR synthetic polarization data. First, we develop the algorithm, frequency weighting, and gradient preconditioning strategies that are adopted to reduce the nonlinearity and enhance deep illumination of inversion, and the random source strategy is used to improve the efficiency. Subsequently, we apply the algorithm to investigate different polarization data. Then, we use the algorithm to realize 3-D multiparameter quantitative imaging of GPR polarization data and discuss the reconstruction characteristics of different polarization data, which makes 3-D GPR FWI feasible. Our findings not only enhance the understanding of GPR data but also pave the way for more accurate and efficient subsurface exploration using GPR multipolarization data.

Civil engineering structures with damage, defects, or subsurface utilities create a high-contrast exploration environment. These anomalies of interest exhibit different electromagnetic properties from the surrounding medium, and ground-penetrating radar (GPR) has the potential to accurately locate and map their three-dimensional (3D) distributions. However, full-waveform inversion (FWI) for GPR data struggles to simultaneously reconstruct high-resolution 3D images of both permittivity and conductivity models. Considering the magnitude and sensitivity disparities of the model parameters in the inversion of GPR data, this study proposes a 3D dual-parameter FWI algorithm for GPR with a composite model constraint strategy. It balances the gradient updates of permittivity and conductivity models through performing total variation (TV) regularization and minimum support gradient (MSG) regularization on different parameters in the inversion process. Numerical experiments show that TV regularization can optimize permittivity reconstruction, while MSG regularization is more suitable for conductivity inversion. The TV+MSG composite model constraint strategy improves the accuracy and stability of dual-parameter inversion, providing a robust solution for the 3D imaging of subsurface anomalies with high-contrast features. These outcomes offer researchers theoretical insights and a valuable reference when investigating scenarios with high-contrast environments.

Tunnel seismic advanced prediction is a widely used technique in geotechnical engineering due to its non-destructive characteristics and deep detection capability. However, limitations in acquisition space and complex on-site conditions often result in missing traces, damaged channels, and low-resolution data, thereby hindering accurate geological interpretation. Although deep learning models such as U-Net have shown promise in seismic data reconstruction, their emphasis on local features and fixed parameter configurations limits their capacity to capture global and long-range dependencies, thereby constraining reconstruction accuracy. To address these challenges, this study proposes a novel deep unrolling network, TSISTA-Net (Tunnel Seismic Iterative Shrinkage–Thresholding Algorithm Network), specifically designed to improve seismic data quality. Built upon the ISTA-Net architecture, TSISTA-Net incorporates three distinct innovations. First, reflection padding is utilized to minimize boundary artifacts and effectively recover edge information. Second, multi-scale dilated convolutions are employed to extend the receptive field, thereby facilitating the extraction of long-range and multi-scale features from seismic signals. Third, a lightweight and patch-based processing strategy is adopted, guaranteeing high computational efficiency while maintaining reconstruction quality. The effectiveness of the proposed method was validated on both synthetic and real tunnel seismic datasets. On synthetic data, TSISTA-Net achieved a PSNR of 37.28 dB, an SSIM of 0.9667, and an LCCC of 0.9357, outperforming U-Net (35.93 dB, 0.9480, 0.9087) and conventional ISTA-Net (34.04 dB, 0.9167, 0.8878). These results demonstrate superior signal fidelity, structural similarity, and local correlation relative to established baselines. Consistent improvements were also observed on real tunnel datasets, indicating that TSISTA-Net provides an efficient, data-driven solution for tunnel seismic data processing with strong potential for practical engineering applications.

Numerical simulation is a useful tool in ground penetrating radar (GPR) applications, facilitating data interpretation and serving as a foundational component of inversion workflows. However, conventional simulation algorithms suffer from prohibitive computational costs when calculating full wavefields in high-resolution or iterative inversion scenarios. To address this limitation, we propose a novel forward modelling framework that leverages the nonlinear mapping capabilities of convolutional neural networks (CNNs) to generate common-offset GPR data rapidly. Instead of relying on intensive numerical simulations, the framework requires only sparse multi-offset acquisitions or a single supershot configuration as input. Numerical experiments demonstrate good agreement between CNN predicted and fully simulated data and the framework achieves considerate computational acceleration, with speedup ratios reaching up to $32.79 \times$ compared to traditional modelling. Furthermore, multi-target datasets are utilized to test generalization performance. This work establishes a promising method for fast three-dimensional forward modelling and GPR inversion.

Seismic multi-parameter full-waveform inversion (FWI) integrating velocity and density parameters can fully use the kinematic and dynamic information of observed data to reconstruct underground models. However, seismic multi-parameter FWI is a highly ill-posed problem due to the strong dependence on the initial model. An inaccurate initial model often leads to cycle skipping and convergence to local minima, resulting in poor inversion results. The introduction of prior information can regularize the inversion problem, not only improving the crosstalk phenomenon between parameters, but also effectively constraining the inversion parameters, enhancing the inversion efficiency. Multi-parameter FWI based on rock physical constraints can introduce prior information of underground media into the objective function of FWI. Taking a simple layered model as an example, the results show that the inversion strategy based on rock physical constraints can enhance the stability of inversion and obtain high-precision inversion results. Application to the international standard 1994BP model further confirms that the proposed inversion strategy has good applicability to complex geological models.

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 a practical obstacle mainly due to the limited illumination in the common-offset gathering mode. Moreover, the narrow width of the 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-shaped symmetric deep learning network (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 electromagnetic (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 multitask 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, including GPRNet, permittivity inversion network (PINet), and total variation (TV)-regularized FWI. For field validation, four quantitative metrics (i.e., mean squared error (mse), mean absolute error (MAE), structural similarity (SSIM), and multiscale SSIM (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.

Ground penetrating radar (GPR) has emerged as a critical tool for subsurface characterization due to its three-dimensional imaging capabilities in complex geological environments. Nevertheless, existing numerical methods for modeling electromagnetic wave propagation in dispersive media face persistent challenges in balancing modeling accuracy, computational efficiency, and multi-scale adaptability. Conventional approaches often struggle to simultaneously address broadband dispersion characterization, unstructured mesh compatibility for intricate geometries, and optimal boundary reflection suppression. This study proposes a three-dimensional discontinuous Galerkin time-domain (DGTD) algorithm integrated with a complex frequency-shifted perfectly matched layer (CFS-PML) to overcome these limitations. Through the development of an auxiliary differential equation framework for Debye media, the computational complexity of 3D DGTD simulations is effectively reduced. Combined with unstructured mesh discretization, the method enables adaptive modeling of geometrically complex geological structures. Furthermore, the CFS-PML boundary condition is extended to handle broadband wave absorption in lossy media, demonstrating superior performance over conventional uniaxial PML under wide-frequency and oblique incidence conditions. Numerical experiments on a 3D dispersive goaf model reveal electromagnetic energy attenuation patterns, particularly highlighting the amplified dispersion effects on deep anomalous reflectors. The proposed framework synergistically addresses multi-scale modeling precision, dispersion response, and boundary reflection control, establishing a high-fidelity simulation platform for 3D GPR investigations of subsurface targets in heterogeneous dispersive environments.

We present a vector finite element method for 3D ground-penetrating radar forward modeling in the frequency domain using exact perfectly matched layer (EPML) absorbing boundary conditions. The corresponding edge-based finite element solution, for both hexahedral and tetrahedral meshes, is derived in detail, and the attenuation characteristics of the EPMLs are compared to their standard uniaxial counterparts. In doing so, we demonstrate the superiority of EPMLs in eliminating the non-physical reflection at the boundaries of the computational domain. Further, we demonstrate that the use of EPML absorbing boundaries effectively improves the efficiency of 3D ground-penetrating frequency-domain simulations, as they require significantly fewer layers and are less parameter-dependent than conventional uniaxial perfectly matched layers. The practical viability of the proposed simulation approach is demonstrated through its application to complex 3D models, involving pronounced topography along the air–soil interface and strong heterogeneity in the probed surficial region.

Ground penetrating radar (GPR) is a widely applied shallow geophysical exploration method. However, the huge amounts of collected data from high efficiency and sampling rate are extremely time-consuming and high-cost to interpret. As the basis of full waveform inversion (FWI) and reverse time migration (RTM), the numerical simulation of GPR directly affects the accuracy and speed of the data interpretation. Besides, calculating 3D large-scale models on the personal computer (PC) is still difficult with limited memory. Therefore, an efficient and low-cost forward algorithm is required urgently. Inspired by the footprint of the airborne electromagnetic method (AEM), we propose a GPR moving finite domain (MFD) forward algorithm based on the attenuation characteristic of GPR high frequency electromagnetic waves to avoid excessive computation by limiting the calculation to the finite domain. We explore the relation between speedup and precision, summarize the optimal range of the parameter and constrain the MFD to further ensure the acceleration according to the time window. The error source and factors affecting the algorithm's speedup are explored and discussed to demonstrate its performance fully. The extensive numerical experiments emphasize that the algorithm could improve speed efficiently with ignorable loss of accuracy. Finally, the forward modeling of a large 3D model is carried out with the memory decreased by 78 % and the speed increased by 33.88 times on the PC, which is impossible through the conventional FDTD. The reduction of costs lessens the requirements for computer equipment, which is expected to promote the practical process of FWI and RTM.

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) 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.