Porosity estimation from seismic data is crucial for understanding subsurface rock properties and enhancing reservoir characterization across Earth and Energy sciences. Although deep learning has emerged as a promising solution for porosity prediction, conventional supervised approaches face inherent limitations in seismic applications due to restricted seismic bandwidth constraints and insufficient labeled training data. To address these challenges, we propose a semi-supervised strategy that integrates a low-frequency porosity model (LowF) and a domain-specific closed-loop (CL) network structure. The LowF component, constructed through geostatistical modeling, incorporates essential geological prior knowledge to compensate for bandwidth limitations of seismic data. Concurrently, the CL structure (seismic-to-porosity-to-seismic) fully utilizes the abundant unlabeled seismic data while enforcing direct constraints on porosity predictions. We also perform a supervised porosity-to-seismic mapping to optimize the CL process. Comparative analyses through cross-well blind tests demonstrate the proposed method’s superior performance over conventional supervised learning approach. Furthermore, the incorporation of LowF and CL remarkably enhances the geological continuity and stability of the seismic porosity predictions. Purely supervised model yields geologically implausible predictions, CL-only implementation fails to capture vertical porosity trends, and LowF-only model may introduce bias. The proposed strategy offers insights into various geophysical inversion problems, particularly valuable for reservoir characterization with limited well constraints.

Deep neural networks (DNNs) can automatically fetch specific features from seismic data, which can be used in the process of multiple elimination. An extended single-sided autofocusing guided by an inverse-scattering theory is introduced to remove internal multiples in a data-driven manner, which can be used as labels in DNNs. In this research, we have developed a novel workflow to explore the potential of neural networks in identifying the internal multiples with the guidance of inverse-scattering theory. In particular, we use the U-net with a self-attention (SA) block during the training process, which could extract features from seismic data effectively. The neural network is fed with training data pairs, consisting of the shot records with internal multiples, and the primary-only datasets as labels, which are generated by an extended single-sided autofocusing method. The testing pairs show that internal multiple elimination via the neural network takes the advantage of the extended single-sided autofocusing method and is cheaper when the neural network is well-trained. The numerical results demonstrate the promising performances of the SA U-net method in terms of noise resistance, internal multiples elimination, and the reverse time migration (RTM) images, in comparison with the extended single-sided autofocusing method.

In adjacent sources scenarios, the low angular separation between active sources may degrade the performance of direction-of-arrival (DOA) estimation. In this work, we propose a slide-save based framework to address the problem of extracting multi-source DOAs for closely spaced sources. The basic idea is to identify the DOA estimates corresponding to the locally most dominant source within a sliding time-frequency (TF) window. Three different schemes are introduced to determine the critical DOA estimates in each TF window. The final DOAs are extracted using the retained DOA estimates by extending the histogram-based, clustering-based and Gaussian Mixture Model (GMM)-based multi-source DOA extraction methods. In addition, other intensity-based algorithms can also be incorporated into the proposed framework. Simulation results show that the proposed framework is effective to estimate multi-source DOAs in adjacent sources scenarios.

Wave equation reflection traveltime inversion (RTI) takes advantage of the convexity of traveltime objective function to robustly build the background velocity structure for seismic migration and waveform inversion. However, the current wave-equation-based RTI suffers from slow convergence and low resolution because the widely used gradient-based optimization can not account for the blurring effects caused by the finite observation. To accelerate the convergence and improve the accuracy, we propose a Gauss–Newton RTI (GN-RTI) method by incorporating the Hessian information. We derive the reflection traveltime Fréchet derivative and Hessian matrix based on the Born scattering theory. The explicitly constructed Hessian matrix and point spread functions show that the parameter coupling effects of different spatial locations in RTI vary significantly in the model space. Based on the understandings of these coupling effects, a matrix-free approach is applied to solve the Gauss–Newton equation of RTI using the conjugate-gradient method in a nested inner loop. Synthetic and real data examples show that the proposed GN-RTI method can effectively retrieve the background velocity structures for seismic imaging and subsequent waveform inversion.

In the context of multi-source direction of arrival (DOA) estimation in an enclosed environment, the challenges include reverberation and overlapping of multiple simultaneous active sources. To address these interferences, the identification of time-frequency (TF) bins dominated by the sources signals is essential. In this work, we propose an intensity vector (IV) based TF bins selection technique for DOA estimation using a single acoustic vector sensor (AVS). The proposed technique involves multi-level inliers selection and outliers removal (MLISOR), which is implemented in three steps. In the first step, we derive the distribution of IVs and then select IVs using a norm metric. In the second step, the regions with the highest local IV density in each time frame are identified. In the third step, we cluster the IVs according to their directions and remove the outliers based on the member-to-centroid angle metric. Simulation results show that both the accuracy and the robustness of the proposed technique outperform the existing techniques. The indoor experimental results also verify that the proposed technique is effective and robust in practical situations.

Seismic data processing requires careful interpolation or reconstruction to restore the regularly or irregularly missing traces. In practice, seismic data with consecutively missing traces are quite common, which will lead to a great challenge for conventional interpolation or reconstruction methods. To effectively reconstruct the successively blank traces in seismic data, we proposed a self-supervised deep learning approach, with which the convolutional neural network is trained in a supervised manner with pseudolabels obtained from unlabeled observed data. The pseudolabels are automatically generated by randomly masking the observed data to simulate the consecutively missing scenario. We train a nested U-Net structure (UNet++) with a hybrid loss function so that the local and global structural information can be captured to ensure the quality of reconstruction. A two-step reconstruction workflow is designed to recover the missing recordings with respect to both the receivers and sources. Synthetic and field data examples demonstrate that the proposed self-supervised learning can effectively reconstruct the corrupted seismic data.

The ocean bottom nodes (OBNs) acquire seismic data at a challenging depth to explore the subsurface structures. The recorded body wave and Scholte wave are highly mixed and are difficult to be separated. The strong body wave would influence the high-order modes extraction using the Scholte wave, while the Scholte wave would degrade the imaging of sedimentary structures using body wave. The lacking of effective methods for separating both waves prevents their application. We developed a migration-based method to accurately separate the Scholte wave and body wave in the OBN data. First, we use high-pass filtering to divide the original OBN data into three parts: background noise, high-frequency body wave, and the mixture of Scholte wave and low-frequency body wave. Then, we separate the Scholte wave and low-frequency body wave using migration and demigration based on the fact that they have different limits of reversible-migration velocity. Finally, we generate the separated body wave by subtracting the Scholte wave from the denoised OBN data. For the off-line data, the local orthogonalization method is required to retrieve the weak leakage of Scholte wave around the apices. Theoretical analyses and numerical experiments show that the proposed method can accurately separate Scholte wave and body wave without any visible artifacts while retaining most of their inherent properties. The separated body wave provides a high-quality input for imaging sedimentary structures, and the separated Scholte wave enables the extraction of high-order modes of dispersion curve that are crucial for high-resolution surface-wave inversion.

Blended acquisition improves the efficiency of seismic data acquisition sharply and deblending algorithms are still open to prepare separated data. Most deblending methods are suitable for on-the-grid blended data. However, blended data in field cases is always at off-the-grid samples which poses great challenges in providing accurate deblended results. A binning strategy can assign an off-the-grid sample at its nearest on-the-grid sample approximately with the amplitude and phase bias caused by the existing distance between them. However, the subsequent deblending accuracy is low, especially when the amplitude and phase biases are large. With true off-the-grid data constraints, we introduce a Kaiser window tapered sinc interpolator to link off-the-grid samples and on-the-grid samples during the procedure of compressive sensing-based functional construction. Full expressions of the interpolator and its adjoint operator are provided to generate an iterative thresholding algorithm for off-the-grid blended data deblending. Separated on-the-grid data can be obtained accurately in an iterative manner. The deblending performance of artificially off-the-grid blended data demonstrates the validity of the proposed method quantitatively no matter the amplitude and phase biases are large or small. Field examples of off-the-grid blended data further prove the effectiveness of the proposed method to provide accurate on-the-grid separated data.

The blended acquisition allows multiple sources to be simulated simultaneously in a narrow time interval, which can improve the acquisition efficiency and reduce the acquisition cost tremendously. However, the overlapped information from multiple sources poses challenges for traditional seismic data migration or inversion algorithms. Thus, accurate and efficient deblending should be implemented as a pre-requisite. Traditional inversion-based deblending algorithms can provide deblended data with a high computational burden, especially for a large volume of seismic data. As a deep learning strategy can match seismic data accurately in a nonlinear way through supervised learning, we propose a U-net-based accurate deblending algorithm, which incorporates transfer learning and an iterative strategy. A set of labeled synthetic data with a blending fold of 2 are classified into the training and validation data for U-net training and validation. Field data are regarded as the test data to assess the performance of the trained U-net. To guarantee the deblending performance of the field data to some extent, parts of field data with labels are used to fine-tune the trained U-net based on transfer learning. The fine-tuning procedure is relatively fast within several minutes. To further improve the deblending performance, we incorporate an iterative strategy with the fine-tuned U-net. The deblending performance is promising in the quality and computational efficiency compared with the curvelet-thresholding-based deblending method, which demonstrates the validity of the proposed intelligent deblending method.

The blended acquisition can help improve the seismic data quality or enhance the acquisition efficiency. However, the blended seismic data should first be separated for subsequent traditional seismic data processing steps. The signal is coherent in the common receiver domain, and the blending noise shows randomness when the blending operator is constructed using a random time delay series. The seismic data can be characterized sparsely by the curvelet transform which can be used for deblending. However, it has a high computational cost, especially for large-volume seismic data. The spectrum of the seismic data is band-limited with the conjugate symmetry property, and thus the principal frequency components can characterize the signal accurately. The size of the principal frequency components is at least halved. Thus, we propose to implement the curvelet transform on the principal frequency wavenumber (PFK) domain data instead of the time-space (TX) domain data. The size of the PFK domain data is at least halved compared with the TX domain data, which can improve the deblending efficiency reasonably. The related formulae are fully derived and the efficiency enhancement analysis is provided in detail. One synthetic and two field artificially blended data are provided to demonstrate the validity and flexibility of the proposed method in the efficiency improvement and the deblending performance. The separated gathers can be beneficial for subsequent traditional seismic data processing procedures.

The trace interval in the common shot and receiver gathers is always inconsistent. The inconsistency affects the final performance of seismic data processing, and the reconstruction methods can enhance the consistency. Unfortunately, most interpolation algorithms are suitable in randomly missing cases, and the difficulty increases sharply in regularly missing cases, especially with big gaps. As deep learning (DL) has a strong self-learning ability in nonlinear characterizations to avoid linear events, sparsity, and low rank assumptions, we introduce DL into missing shots' reconstruction. The spatial reciprocity of Green's function is used to provide reasonable training data sets. First, the residual learning networks (ResNets) and the interpolation issue are briefly illustrated. Then, the spatial reciprocity is reviewed and illustrated qualitatively using the common shot and receiver gathers. The similar features in the common shot and receiver gathers guarantee the reasonability to regard the common shot gathers as the training sets and to regard the common receiver gathers as the test sets. The common shot gathers are divided into the training sets to train ResNets and the validation sets to verify the performance of the trained ResNets. Finally, the trained ResNets are used to reconstruct missing shots intelligently in the common receiver gather. Three different data sets are used to prove the validity of the proposed strategy. After reconstruction, the events are more continuous with less serrations and serious frequency wavenumber (FK) aliasing is attenuated effectively. The reconstructed data with a better consistency can improve the accuracy of migration and the final reservoir characterization.

The Radon transform (RT) has been widely used as a powerful tool, especially in exploration geophysics fields, such as multiple removal, interpolation, and velocity analysis. However, the existing strong outlier effects can seriously decrease the accuracy of the traditional RT. Therefore, a robust time-invariant RT (TIRT) is proposed in the mixed time-frequency domain to attenuate the outlier effects by using double L1-norm sparse constraints performed on the data misfit and the Radon model in the time domain. For the TIRT, the forward RT and its adjoint can be implemented in the frequency domain efficiently. Only one matrix inversion for each frequency component is involved in all iterations to speed up the iterations. Then, the 1-D alternating split Bregman (ASB) algorithm is introduced and improved for 2-D Radon model updating efficiently. It involves matrix-vector multiplication operators and two proximity operators. These two proximity operators can guarantee the robustness and sparseness of the proposed method. Numerical examples of synthetic and field data demonstrate the effectiveness and validity of the proposed method. The proposed method is also used for interpolation to decrease the trace interval. After interpolation, seismic data are more continuous with less serrations along the spatial direction and the frequency-wavenumber spectrum is more focused. The interpolated data have wider potential applications in improving the accuracy of the following seismic processing. It should be noted that the proposed robust and efficient RT can also be used in remote sensing and computerized tomography fields instead of the traditional RT.