First break picking is crucial for estimating and simulating surface and shallow medium velocities, particularly in complex mountainous regions. Here, the significant variations in near-surface elevation, the thickness of low-velocity zones, and lateral changes in near-surface velocity result in noticeable differences in trace-to-trace arrival times. The manual picking method is inefficient and unrealistic on massive seismic data. Accordingly, various automatic picking methods have been developed over time, including approaches utilizing seismic record attributes and deep learning techniques, among others. In this paper, we proposed a feature template based nonlinear trace time difference (FT-NltD) correction method to correct nonlinear time difference, turning the nonlinear time difference to linear. Then, we proposed geometric structure constraint multi-attribute Markov decision process (GCMDP) for robust and high-precision automatic first break picking. In the GCMDP, we use linear geometry structure as constraint, dynamically optimize in the picking process, and apply multi-step prediction to the first break position and multi-attribute constraint at the same time, so as to realize the first break picking stably. Finally, we use field data demonstrate the effectiveness of the proposed first break picking method.

Time-frequency representation is essential for analyzing the non-stationary characteristics of seismic signals, providing insights into transient features such as amplitude modulations and phase shifts. Although time-reassigned methods like the Time-Reassigned Synchrosqueezing Transform (TSST), Second-order Transient extracting Transform (STET), and Time-Reassigned multi Synchrosqueezing Transform (TMSST) improve temporal resolution, they struggle to achieve optimal time-frequency localization and energy concentration, limiting their effectiveness in applications such as noise attenuation and subsurface characterization. To address these limitations, we propose the Time-Reassigned Modular High-Resolution Time-Frequency Representation (TMHTFR), which enhances the reassignment process by accurately mapping time-frequency coefficients to the precise group delay (GD). Unlike previous methods that reassign coefficients to the vicinity of the GD, TMHTFR directly maps them to the precise GD, achieving sharper and more accurate TFRs. Additionally, the proposed method is highly flexible and can be easily integrated with alternative GD estimation techniques. A key advantage of TMHTFR is its ability to enhance time-frequency concentration while effectively reducing computational costs. Moreover, TMHTFR inherently produces a TFR with a lower-rank structure, which improves its capability for noise separation and sparsity enforcement. To quantitatively assess time-frequency concentration and energy compaction, we utilize Rényi entropy and the concentration measure (CM), confirming that TMHTFR generates a more structured and well-localized representation compared to conventional methods. Experimental validation on synthetic and real seismic data confirms that TMHTFR effectively attenuates random noise while preserving essential signal features, underscoring its potential as a powerful tool for seismic data processing.

Accurate time–frequency representation (TFR) is essential for resolving spectral components in seismic signal analysis and enhancing geological interpretation. In this study, we present an enhanced (a new) Generalized S-Transform (GST) that integrates a chirp-modulated window, improving time–frequency localization, reducing spectral smearing, and increasing resolution. Furthermore, a multi-objective optimization strategy is employed to tune the GST parameters, effectively distinguishing transient and harmonic components within the signal. These advancements enhance the adaptive characteristics of GST, optimizing the frequency-dependent windowing function for more effective feature extraction. To validate its effectiveness, the proposed method is applied to both synthetic and real seismic data, employing a frequency-weighted RGB mapping approach based on raised cosine basis functions for visualization. Comparative analysis with conventional TFR methods—standard S-Transform (ST), General Linear Chirplet Transform (GLCT), and Adaptive Generalized S-Transform (AGST)—demonstrates that our approach achieves higher resolution and clearer geological feature delineation.

In seismic exploration, the technique of multiple coverage significantly enhances the quality of migration imaging. Migration imaging results are obtained by stacking the common-image gathers (CIGs) from different shot-receiver pairs. However, due to the irregular observation system and the propagation of seismic waves through complex subsurface media, the illumination intensity of CIGs from different shot-receiver pairs is uneven. Conventional stacking methods often overlook the impact of uneven illumination, resulting in inaccurate amplitudes in the imaging results and poorer imaging quality. In this article, we propose an amplitude-preserving stacking imaging method based on illumination weighting. First, we distinguish the illumination areas by constructing a self-organizing mapping network based on feature attributes. Only regions with high and consistently similar imaging wavelets are considered effective illumination and are included in the stacking imaging process. Then, we implement optimal stacking with an illumination-weighted operator designed based on the energy variation relationship in the effective areas. The proposed method can obtain amplitude-preserving and high-resolution stacking results and enhance imaging quality. Finally, the effectiveness of the proposed method is tested using synthetic and field data.

Water-layer-related multiple (WLRM) is a critical type of surface-related multiple. The model-based multiple prediction method has proven effective for predicting WLRMs while requiring less data acquisition compared to data-driven method. The model-based WLRMs prediction process is described as the convolution of recorded data and the seabed primary response. According to the ray theory, the primary response is typically approximated using the first-arrival traveltimes of seabed primary reflection. However, in rugged seabed case, this ray-theory-based method may reduce the accuracy of WLRMs prediction. This paper proposes a WLRMs prediction method based on Born simulation. The proposed method can characterize the multiple diffractions and multi-arrival reflections generated by rugged seabed, resulting in a more accurate WLRMs prediction result. The prediction process consists of two main steps, namely downward extrapolating the sea surface recorded data to the seabed, and upward extrapolating the multiple scattered wavefield generated by the seabed back to the surface. We efficiently implement the wavefield extrapolation in the water-layer using phase shift operators. The synthetic data validate the accuracy of the proposed method in predicting WLRMs from rugged seabed. Then we successfully applied this method to attenuate WLRMs in 3D field data. The demultiple results demonstrate that the WLRMs in the synthetic and field data are effectively suppressed, thus verifying the effectiveness of the proposed method.

Geophysical exploration is developing from qualitative seismic imaging to quantitative imaging, and broadband acoustic impedance is the core. Directly estimating broadband impedance using full-waveform inversion is a strong nonlinear problem. It is difficult to obtain a reliable result in practice. We proposed an alternative way: estimate background velocity, density, and broadband reflectivity first and then fuse them to be the broadband impedance by information fusion. This article studies the method of fusing band-limited reflectivity and background impedance. Due to the observation with band-limited seismic wavelet, only band-limited reflectivity can be obtained even after a lot of processing. The band-limited reflectivity can lead to oscillation error in impedance. Different from the conventional poststack impedance inversion, this article introduces an iterative process without the need of wavelet extraction. Start from the broadband reflectivity that has been subjected to fidelity imaging, least-squares migration, and magnitude calibration. In order to reduce the oscillation error, reflectivity is sparsely promoted such that the reflection coefficients from large to small are gradually fused with background impedance. Reflectivity and impedance are mutually constrained and iteratively updated, and lateral continuity is incorporated. Numerical experiment and 3-D field data application demonstrate the effectiveness of the method. Impedance shows higher interpretability than reflectivity.

The improvement of parameter estimation accuracy depends on the increase of information. The purpose of structure-constrained scattered data fitting is to build a more accurate field by incorporating structure into a few scattered data. This is important for exploration geophysics because only a few well data can be obtained, while a wide range of subsurface parameters need to be estimated. This article introduces a structure-constrained method named direction-orthogonalizing constraint (DOC), which makes directions parallel to the structure orthogonal to parameter gradients. The structure tensor is utilized to extract directions parallel to the structure from seismic images. Then, a DOC radial basis function (RBF) fitting method is developed. Scattered data are approximated by anisotropic RBFs, and DOC is used to bring in structure. Applications on Marmousi density model, 3-D overthrust model, and 3-D field data demonstrate the efficiency and effectiveness of DOC-RBF fitting.

The curvature of the residual moveout (RMO) on common-image gathers (CIGs), which indicates the error in a migration velocity model, is often used as input data in reflection tomography to produce reliable velocity updates. The conventional semblance-based method is widely used for automatic RMO picking. However, moveout picks are often inaccurate and unreliable in areas where the quality of CIGs is poor and the type of RMO in different traces is complex and variable. In this article, we propose an effective and robust scheme for RMO picking with higher accuracy by utilizing a Markov decision process (MDP). RMO picking on a single CIG is modeled as an MDP in high-dimensional attribute space. The desired RMO can be obtained by maximizing the value function with an optimal policy. Then, an effective implementation scheme of RMO picking on multiple CIGs is designed. First, we extract the reflection horizons on the seismic image stacked by CIGs as seed points. Then, the energy spectrum and similarity coefficient are used to determine the size of the state space and update the position of the initial state. Median filtering and smoothing along the horizons are used to remove abnormal parameters and outliers. Finally, the MDP model is implemented and the optimal decision is realized. Geologically plausible moveouts with high accuracy and robustness are extracted. Numerical examples of synthetic and field data demonstrate the effectiveness and validity of the proposed scheme. Furthermore, this scheme can guarantee accurate and robust input moveout data for subsequent tomography.

A physical system produces output due to impulse, which corresponds to a convolution process. Convolution has a very wide tolerance, therefore deconvolution is widespread. When seismic waves propagate in the underground medium, the stable wavelet is affected by several factors: complex factors at source, propagation factors from the source to reflection interface, the reflection interface, propagation factors from the reflection interface to receiver, and complex factors at the receiver. The purpose of surface-consistent correction is to eliminate the influence of complex factors at source and receiver on residual statics, phase, and amplitude of wavelets from the same stable reflector, which is typical deconvolution. Surface-consistent deconvolution can be referred to as a Bayesian estimation problem. However, it requires a great deal of computation for seismic data, and the statistical method should be more efficient. Based on statistics and physical understanding, maximizing the common midpoint (CMP) stack has been proven to eliminate residual statics and phase changes; particle swarm optimization (PSO) algorithm is used to explore the nonconvex parameter space. Then, under the physical assumption that the energy of wavelets from the same reflection interface changes steadily, the prediction-energy-change equation is introduced; the spatial mutations of amplitudes are corrected by solving a nonlinear equation system. Numerical experiments show that the statistical way is effective.

Seismic horizon extraction is important for subsurface structure interpretation and reservoir modeling. Recently developed learning-based seismic interpretation methods show great success in the case of sufficient labeled data but may fail when the labels are limited. Thus, we propose a simple but effective network for seismic horizon identification using only a limited number of labels. To avoid overfitting in the training, we introduce the mechanism of semi-supervised learning (SSL) with virtual adversarial training (VAT). With several seed points, the method can provide a good prediction and suggest regions lacking control points. By adding several seed points in these suggested regions, the performance of the network can be further improved, which can be regarded as an interactive way. In addition, iteratively retraining the network by using the previous high-confidence prediction can further refine the horizon identification. We, finally, compute a full horizon surface without holes and outliers by optimally fitting the horizon points identified by our SSL and reflection slopes estimated from the seismic amplitude image. Applications to two field datasets show our method is superior to conventional methods in picking a seismic horizon with significant waveform variations or across complex discontinuities, such as faults.