Neural networks, especially deep learning, have achieved revolutionary advances in several domains, including image and speech recognition, with excellent results. However, their reliance on labeled data, lack of interpretability, and inconsistency with physical principles limit their applicability in groundwater seepage prediction and other scientific disciplines. Physics-Informed Neural Networks (PINNs) significantly improve these issues by integrating physical knowledge with neural networks. This study focuses on modeling the groundwater flow field and proposes a physics-informed river-canal groundwater seepage model (PI-RGSM). This model enables self-supervised learning by incorporating hard constraints of boundary and initial conditions, utilizing hydrogeological parameters and boundary conditions as direct inputs, thus diminishing dependence on observable data. Compared to the baseline PINNs, the PI-RGSM adapts to and accurately predicts diverse seepage situations with just one training session, achieving a mean coefficient of determination of 0.978. To further enhance applicability in complex dynamic groundwater seepage situations, we propose PI-RGSM-K, which builds upon PI-RGSM. This model simulates heterogeneous groundwater seepage fields and improves performance in complex seepage environments through parameterized hydraulic conductivity field K(x, y) and fine-adjusted model architecture, attaining a mean coefficient of determination of 0.982. The PINN models proposed in this study demonstrate exceptional efficacy in precisely forecasting groundwater seepage behavior.

The passive surface wave dispersion imaging is extensively utilized for shallow surface velocity inversion. However, the presence of strong directional noise sources often leads to deviations from the truth dispersion. Conventional beamforming technique can correct dispersion spectrum, but with limited resolution. Additionally, actual records contain random noise, which further compromises imaging quality. To address these challenges concerning dispersion imaging resolution and noise resistance, we propose a high-resolution dispersion imaging method that integrates the multiple signal classification (MUSIC) algorithm with subarray spatial smoothing processing. Initially, velocity is incorporated into the MUSIC algorithm to discern the direction of ambient noise, thereby extracting a sparse f–v spectrum free from random noise interference. To further mitigate the impact of random noise, a subarray spatial-smoothing MUSIC approach is devised, effectively reducing such interferences. Synthetic and field experiments demonstrate its capability to achieve high-resolution dispersion spectrum even in the presence of noise.

The parabolic Radon transform (PRT) is one of the commonly used demultiple methods and can be efficiently realized in the frequency domain. To avoid aliasing, its curvature range (CR) and curvature sampling interval (CSI) are usually set according to the highest frequency sampling standard. Thus, the CR and CSI are identical for all frequencies. However, the CR and CSI are indeed dependent on frequency. The frequency-independent sampling will lead to amplitude loss, resulting in inaccurate estimation of multiples. For this problem, in this article, the sampling theories of CR and CSI are rederived based on the${f}$–${k}$spectrum. The result shows that the maximum CR and CSI are inversely proportional to frequency. This frequency-dependent sampling will lead to nonuniform CSI for each frequency, which causes inconvenient multiple attenuation. Therefore, a variable CSI is further designed to attenuate multiples flexibly. In the overlap region of multiples and primaries, the CSI is identical for all frequencies and follows the maximum CSI of the highest frequency. For other regions, the CSI still depends on frequency. Finally, an amplitude-preserving PRT with frequency-dependent CR and CSI is developed. Compared with the conventional PRT, this method can estimate amplitude more accurately due to the extended CR. Compared with the amplitude-preserving high-order PRT, this method has a lower computational cost due to fewer Radon coefficients to be inverted. Multiple attenuation experiments demonstrate the amplitude-preserving performance and efficiency of the proposed PRT.

As an important elastic parameter, seismic acoustic impedance is usually obtained through poststack inversion. However, there are usually two problems that limit the quality of the inversion results. First, conventional inversion methods typically use regularization terms to enhance the stability of the inversion results, and effective regularization terms are particularly important for accurately inverting seismic impedance. Second, most inversion methods adopt a trace-by-trace inversion strategy, resulting in poor lateral continuity when connecting the inversion results of all traces into a 2-D profile, especially for processing noisy data. To address these two problems, we propose a structure-oriented minimum entropy stabilizer for acoustic impedance inversion that enhances the lateral continuity of the inversion results while restoring the blocky structures of the strata and improving the resolution of the inversion results. The stabilizer consists of a structure-oriented regularization (SOR) operator and the minimum entropy norm. The SOR operator is constructed using the local dip estimated from the seismic data by the plane-wave destruction (PWD) algorithm and constrains the inverted impedance along the structural trend, making it more consistent with geological features. The minimum entropy norm restores the blocky structures and enhances resolution by imposing sparse constraints on the temporal and spatial derivatives of the impedance. Based on synthetic and field seismic data, we compare the inversion results of the proposed method with those of conventional Tikhonov regularization and total variation (TV) regularization methods. The results show that the proposed method exhibits superior performance, especially in processing noisy data.

Based on the Bayesian framework, pre-stack inversion aims to find the solution with the maximum posterior probability under the prior constraint. The prior constraint is usually a mathematical expression of the inverted parameters, and guides the updating of the inversion results. To obtain a stable, high-resolution and high-fidelity inversion result, we introduce a new prior constraint named ‘amplitude entropy’ to help perform the pre-stack inversion. The amplitude entropy can make the chaos of the parameters to be inverted close to those of the known well-logging data. Compared with the traditional L2 prior constraint, amplitude entropy can improve the resolution of the inversion results, and compared with the conventional L1 prior constraint, it can obtain a solution that is more consistent with the geological characteristics. In addition, multi-component seismic data contains richer lithology and fluid information than single-component data. Therefore, in this paper, we directly develop the pre-stack inversion method based on the multi-component seismic data. Furthermore, due to the high nonlinearity of the objective function under the amplitude entropy constraint, the quantum annealing (QA) algorithm is employed to solve the objective function of the joint inversion and find the final solution. Synthetic and field data examples demonstrate that the pre-stack inversion method with the amplitude entropy constraint is effective and stable, especially for processing seismic data with a low signal-to-noise ratio.

The hyperbolic Radon transform (RT) is a widely used demultiple method in the seismic data processing. But this transformation faces two major defects. The limited aperture of acquisition leads to the scissor-like diffusion in the Radon domain, which introduces separation difficulties between primaries and multiples. In addition, the computation of large matrices inversion involved in hyperbolic RT reduces the processing efficiency. In this letter, a specific Convolutional Neural Network (CNN) is designed to conduct a Fast Sparse Hyperbolic Radon Transform (FSHRT). Two techniques are incorporated into CNN to find the sparse solution. One is the coding-decoding structure, which captures the sparse feature of Radon parameters. The other is the soft threshold activation function followed by the end of neural networks, which suppresses the small parameters and further improves the sparsity. Thus, the network realizes the direct mapping between the adjoint solution and the sparse solution. Furthermore, synthetic and field demultiple experiments are carried out to demonstrate the rapidity and effectiveness of the proposed method.

Simultaneous-source exploration improves efficiency and reduces the cost when acquiring seismic data. However, the adjacent shot records interfere with each other, and an efficient deblending way is needed. The traditional truncated singular spectrum analysis (SSA) algorithm is employed in the local window to predict coherent events. After all the local events are predicted, the whole dither noise could be estimated completely. Traditional processing in the time domain complicates deblending. In this letter, a global-frequency SSA is proposed to predict dither noise with a simple iteration scheme. This method will lead to an increase in the rank in the Hankel matrix. Thus, a trigonometric function is introduced to adaptively determine the rank instead of the rank-truncated method. The experiments on actual seismic data show that the proposed method not only improves the deblending performance but also enjoys high efficiency.

Simultaneous sources acquisition attracts intensive attention from both academia and industry due to its greatly improved efficiency in acquiring high-density seismic data. Unfortunately, its merits are compromised by the strong interference noise between adjacent shots. In this letter, we propose a stepwise rank-increasing (RI) method to estimate the crosstalk noise in simultaneous sources acquisition. The proposed algorithm assumes that an ideal common offset gather (COG) can be represented via a low-rank matrix in the time-space domain. The coherent signals are estimated from low-rank decomposition and transformed to the crosstalk noise by employing a priori information about random dithering code, and then the blending noise is subtracted from the blended data. By increasing the rank of coherent signals step-by-step, the crosstalk noise can be gradually estimated with high accuracy. In this letter, singular value decomposition is utilized to increase the rank of COG data. Applications on synthetic and field data sets demonstrate the better performance of the proposed RI method not only by more effectively suppressing noise but also by accelerating the convergence rate.