Distributed acoustic sensing (DAS) has emerged as a transformative technology for high-resolution seismic exploration. However, compared to conventional geophysics, the vertical seismic profile (VSP) data obtained by DAS has a relatively low signal-to-noise ratio (SNR). This limitation stems primarily from the transient fiber deployment in casing operations, which leads to suboptimal fiber-ground coupling and creates characteristic zigzag noise patterns that degrade signal fidelity. This study presents a feature picking principal component analysis (FPPCA) framework for adaptive zigzag noise suppression. The method includes four stages: power spectral density estimation with multilevel spectral smoothing to preserve critical mid-low frequency components, design of frequency-adaptive hanning windows targeting harmonic sidelobe suppression, bandwidth parameter optimization guided by dominant frequency localization to prevent spectral aliasing during feature extraction, and PCA based noise separation using cumulative variance thresholds derived from localized zigzag features. Validation dataset comprising one synthetic and one field DAS-VSP datasets demonstrates the framework’s ability to maintain broadband signal integrity while achieving spectrally consistent noise attenuation.

High-resolution and amplitude-preserved imaging is crucial for mapping impedance interfaces and identifying hydrocarbon reservoirs in the subsurface. Although elastic reverse-time migration (RTM) is capable of imaging complicated structures, it actually is the adjoint of seismic forward modeling and produces unsatisfactory images with irregular acquisition systems and uneven illumination. To address this issue, we develop an elastic image-domain least-squares migration (LSM) method based on the point-spread function (PSF) deconvolution. Instead of choosing P- and S-wave velocities as the reflectivities in conventional elastic LSM, we define the density perturbation as the reflectivity model. Full-wavefield elastic modeling and PS-separation-based RTM are then applied to compute PSFs. This framework does not involve the crosstalk issue because only two types of PSFs, which correspond to the diagonal blocks of the Hessian matrix, are generated. Then, the two kinds of PSFs are, respectively, used for local image deconvolution for PP and PS images to correct the Hessian blurring effect, in which the unit partitioning with multidimensional Gaussian functions is adopted to generate optimal local windows. Numerical experiments demonstrate the feasibility of the proposed method and the potential to enhance image resolution and amplitude fidelity.

Due to finite acquisition aperture, limited frequency bands, and unbalanced illumination, conventional migration often fails to generate high-quality reflectivity images. In contrast, least-squares migration (LSM) can produce high-resolution and amplitude-preserved images by solving a linear inverse problem. Although LSM has been implemented by ray-based and wave-equation propagators, its application has primarily been limited to isotropic media, thereby restricting its ability to handle anisotropy. To mitigate this issue, we propose a least-squares Gaussian beam migration (LSGBM) method for vertical transverse isotropic (VTI) media. Based on an efficient VTI ray tracing, we first derive the Born modeling and adjoint migration operators, and then iteratively update the reflectivity model. To suppress data overfitting artifacts, a multiplicative Cauchy constraint is introduced in the LSGBM to promote a sparse inversion result. Additionally, an approximate diagonal Hessian is employed as a preconditioner to accelerate convergence. Numerical experiments demonstrate that the proposed VTI LSGBM can correct anisotropic effects, enhance spatial resolution, and improve amplitude fidelity, producing high-quality images.

By using multicomponent and multiwave seismic data, elastic reverse time migration (ERTM) can produce accurate PP and PS images for complex structures. One key of ERTM is to decompose the source- and receiver-side wavefields into pure P- and S-waves with correct amplitudes and phases. Conventional wavefield decomposition methods require to solve either a Poisson’s equation or an additional P-wave equation, increasing the computational cost. To mitigate this issue, we present a novel framework of physical constrained neural network (PCNN) to efficiently implement P- and S-wave separation. The new network includes both fully connected and convolutional blocks for data fitting and takes into account the properties of curl-free P-wave and divergence-free S-wave as a physical constraint. After the training, the proposed PCNN can accurately decompose elastic wavefield and produce pure P- and S-waves with correct phases, amplitudes and physical unit. We then apply the PCNN-based method to multicomponent reverse-time migration, in which a modified dot-product imaging condition is used to calculate PP and PS images. Numerical experiments demonstrate that the proposed PCNN-based workflow can produce accurate PP and PS images while improving the computational efficiency by three orders of magnitude compared to traditional Helmholtz-based decomposition methods.

Least-squares migration (LSM) aims to seek the best-fit solution for subsurface reflectivity with high image resolution and balanced amplitudes by minimizing the mismatching between synthetic and observed seismic data. It can be implemented either in data domain or in image domain. Data-domain LSM iteratively updates reflectivity using the gradient-based algorithms. However, it requires expensive computation cost to converge to a good solution, which is still challenging for large-scale datasets under current computational capacity. Point spread function (PSF) deconvolution is an efficient and accurate image-domain LSM approach to reduce migration artifacts caused by the limited aperture and the finite frequency wavelet and improve image resolution. But seismic velocity models have millions of grid points, which makes it prohibitively expensive to directly compute the PSF and its deconvolution operator. To obtain high-resolution images and reduce computing cost, we develop a deep-learning-based method to directly approximate the deconvolution operator of each separated PSF. First, we calculate migrated image and PSFs using one pass of seismic modeling and traditional adjoint migration. Next, we train a conditional generative adversarial networks (cGANs) by using the migrated images, PSFs and migration velocity as the input and the true reflectivity as the labeled data. At last, the trained network is applied to the migrated images, PSFs and migration velocity of test datasets to predict the reflectivity model. With the well-trained cGANs, we can predict high-quality LSM images efficiently and save considerable computational cost. Numerical examples for synthetic models and field data demonstrate that the proposed method can accurately predict PSF deconvolution operators and provide high-quality deblurred LSM images with significantly reduced computational and memory costs.

The subsurface steeply-dipping structures, such as buried hills, fault zones, and salt flanks, are difficult to accurately image in seismic exploration due to weak illumination from large incident angles. To mitigate this issue, we propose an angle-related imaging condition for acoustic and elastic reverse-time migration (ERTM) to improve the image quality of steeply-dipping structures. We first use the wavefield decomposition method based on the Hilbert transform to decompose the extrapolated wavefield into up–down-left–right going components. We observed that the left- and right-going wavefields can accurately image steeply-dipping structures, while the up- and down-going wavefields mainly contribute to the layers with small dipping angles. Then, an angle-related imaging condition is developed to use the decomposed directional wavefields to enhance the image quality of both flat layers and steeply-dipping structures. In ERTM, after the directional wavefield decomposition, the vector Helmholtz decomposition is used to decouple PS waves to produce PP and PS images. Numerical examples demonstrate that the proposed method produces more accurate images than conventional RTM for steeply-dipping structures.

Land seismic data are often obscured by noise, severely affecting the accuracy of subsequent seismic imaging and interpretation. Dictionary learning (DL) is an effective method for noise suppression. However, finding a fast DL method that is suitable for weak signals and can suppress multi-scale strong noise is still a hot topic. In this paper, we introduce a noise suppression method that combines DL with fast adaptive empirical mode decomposition (FABEMD). We leverage the advantages of FABEMD in multi-scale signal decomposition, along with the efficient sparse representation capabilities of DL, to achieve noise suppression for low signal-to-noise ratio seismic signals. We group bi-dimensional intrinsic mode functions based on their cross-correlation coefficients and train dictionaries for components using the sequential generalization K-means method, enhancing computational efficiency and adaptability. Numerical examples using both synthetic and field data validate the practicality and versatility of the proposed method, indicating its improved performance in denoising compared tof-xEMD, BEMD, and traditional DL methods.

As seismic exploration focuses on deep and ultra-deep hydrocarbon targets, seismic data are characterized by weak reflection signals and extremely low signal-to-noise ratio (SNR). Although weak reflections help delineate deep geological structures, the low SNR presents challenges for traditional denoising methods. We propose a high-dimensional adaptive progressive seismic denoising (APSD) method to enhance the SNR of deep weak reflection signals. Instead of using a global noise variance, we estimate local noise variances using a 3-D Laplacian mask based on the local characteristics of seismic data at different locations for nonstationary seismic signals. It employs local noise variance to calculate a Gaussian bilateral kernel function to estimate high-amplitude noise in the time domain and low-amplitude noise in the frequency domain. We further extend this algorithm to three dimensions by adjusting the parameters of the 3-D kernel function during the iterative process. Numerical examples of synthetic and field data demonstrate the feasibility and adaptability of the proposed method. Its comparison with the dictionary learning method and optimal damped rank reduction methods shows that the proposed method can significantly improve the SNR of deep reflection signals and is a good tool for processing deep and ultra-deep seismic data.

The presence of source-related noise, characterized by exceptionally large amplitudes, poses a significant challenge in seismic data processing, impeding the accurate recovery of the effective signal within overlapping regions. In response, we introduce an adaptive time-frequency denoising method tailored to mitigate this issue. First, the seismic data is horizontally sorted, and exponential function fittings are applied to exploit amplitude difference information embedded in the dataset. Then, the curvatures of the exponential functions are computed, and their maximal values are chosen to establish a dynamic threshold curve, offering an estimate for the range of abnormal traces from shallow to deep regions. Next, further refinement of the dynamic threshold curve involves iterative adjustments based on the standard deviation of the curvature functions, resulting in a more precise separation between signal and noise traces. Finally, leveraging the optimized dynamic threshold curve, adaptive threshold value computations are performed at each frequency slice and subsequently applied through soft thresholding to effectively reduce the impact of strong amplitude noise. Numerical examples involving synthetic and field data demonstrate the effectiveness of the proposed method in attenuating strong source-related noise, surpassing the performance of traditional f-k filter, non-convex (NC) threshold and static threshold methods.

Least-squares migration (LSM) produces an accurate solution for subsurface reflectivity by solving a linear inverse problem, which can effectively mitigate the unbalanced subsurface illumination, suppress acquisition footprint and improve image resolution. It can be implemented in the data or image domain. Data-domain LSM requires intensive computations for many times of Born modeling and adjoint migration. By contrast, image-domain LSM requires a large memory storage for calculating and saving the Hessian matrix. Due to the ability of describing sophisticated nonlinear relations, the neural network can be used to approximate Hessian inverse by using the reverse time migration (RTM) image as the input and the true reflectivity model as the output. However, previous neural network-based LSMs mainly focused on the enhancement of image resolution and amplitude fidelity, but few on error and uncertainty analysis of network predicted images. We present a novel multi-task deep learning method for the image-domain LSM to simultaneously estimate Hessian inverse and evaluate kinematic and dynamic errors of network predicted results. We first use the RTM images along with migration velocity and source illumination as the network input and regard both the true reflectivity model and kinematic or dynamic error between predicted and labeled images as the output to train the network weights. Then, the L2-norm misfits of two terms are incorporated in the loss function to calculate the gradient to optimize the network trainable weights for producing an accurate LSM image. Numerical examples demonstrate that as the epoch of network training increases, the imaging accuracy of subsurface reflectors is gradually enhanced and the kinematic and dynamic errors of network predicted results are reduced, suggesting that the proposed multi-task deep learning method is effective in simultaneously predicting high-quality LSM image and conducting quantitative error analysis.

Compared with traditional adjoint migration, the least-squares migration (LSM) can effectively mitigate the unbalanced illumination and limited resolution associated with finite acquisition apertures, complex overburden structures and band-limited records. Data-domain LSM needs many times of Born modeling and adjoint migration to converge to a good solution, which is still challenging for large-scale 3D model under current computational capacity. To reduce computational cost and produce high-quality images, we directly approximate the Hessian inverse in the image-domain LSM using a new framework of generative adversarial networks (GANs). The migrated images, source illumination and migration velocity model are used as input data for the GANs, and the ground-truth reflectivity is utilized as the label data to train the network. Directly applying conventional GAN framework to implement the image-domain LSM leads to dislocated reflection events and incorrect images. To overcome this issue, we develop a new GAN framework that is more suitable for the Hessian approximation of image-domain LSM, which is named as LsmGANs. In the new framework, we use a max-pooling instead of convolution to downsample the feature maps to capture horizontal and vertical variations of reflectors. This enables us to map reflection events to correct location in downsampling. To address the lateral discontinuity of events in the predicted image from conventional GANs, we further apply multiple transform layers to strengthen feature transformation to guide Hessian approximation. Finally, we add the skip connection in the transform layer to enhance the information exchange of the feature channels and avoid the gradient vanishing problem to improve image resolution. Assembling predicted patches to construct a whole reflectivity image is a key step in the neural-network-based LSM. We investigate four strategies using different overlapping ratio and window functions to assemble the LSM patches and observe that less overlapping produces more patch-edge artifacts and the partition of unit with a Gaussian window has the best performance. Numerical experiments for synthetic and field data show that the proposed LsmGAN method can produce high-quality images with balanced amplitudes, reduced artifacts and improved resolution.

Cycle-skipping problem is one of the major impediments for full-waveform inversion (FWI) to accurately recover subsurface velocity models. The multi-scale inversion scheme is a practical and robust strategy to mitigate the cycle-skipping issue. The success of this strategy depends on the existence of low effective frequency components in prestack seismograms. Due to the limited frequency band of the source and receiver, as well as the effects of noises, the low-frequency signals in seismic records are usually either too noisy or totally absent. We explore the possibility of compensating certain low-frequency components for observed band-limited records, and apply compensated data to FWI for accurately building subsurface velocity models. We first assume the convolution model holds true for the prestack seismograms, and validate this assumption using a numerical experiment for the Marmousi model. We find that when there are effective low-frequency signals in the records, high-frequency waveforms can be converted to low-frequency waveforms using a deconvolution and convolution filter. But this strategy fails when the low-frequency signals are missing. Considering the sparsity of seismic wave arrivals, we propose first to estimate the Green’s function by solving anL1-norm regularized linear inverse problem, and then construct a new dataset by convolving the estimated Green’s function with a new source function with low-frequency components. Numerical examples for 2D Amoco and Marmousi models show that the low-frequency compensated data are consistent with the reference data that are computed by using a source wavelet with low-frequency components. By incorporating this low-frequency compensation strategy into traditional multi-scale FWI scheme, we design a modified workflow for recovering the subsurface velocity model hierarchically. Numerical experiments demonstrate that the compensated low-frequency information enables us to resolve large-scale velocity perturbations and mitigate the cycle-skipping problem.

Conventional full-waveform seismic inversion (FWI) tries to estimate a subsurface model that can accurately predict surface records by minimizing an${L} _{\mathbf {2}}$-norm misfit between observed and synthetic data. If the initial model is far away from the true model, the cycle-skipping issue might occur and the${L} _{\mathbf {2}}$-norm-based FWI produces a spurious model. To mitigate this problem, we present a novel FWI scheme using a high-dimensional local coherence misfit function. A 2-D/3-D window is first used to extract local seismic waveform from the common-shot gathers. Then, we apply a normalized cross-correlation to measure the coherence of local synthetic and observed records, which is used as the misfit to iteratively update the subsurface velocity model. The new misfit function enhances the contribution of phase fitting while reducing the amplitude contribution, which helps to increase the tolerance of FWI to an inaccurate initial velocity model. In addition, the computation of local waveform coherence along the temporal and spatial axes can adaptively balance the adjoint source amplitudes for strong near-offset reflections and weak far-offset refractions, which improves the low- wavenumber updates. Numerical experiments for synthetic and field data demonstrate that the proposed FWI scheme has a better tolerance to inaccurate starting models and is less sensitive to cycle-skipping issues compared with the conventional FWI method.

In this paper, we present a portable labware on Google CoLab for Scalable Machine Learning (SML) with PySpark for facilitating research in Science and Engineering (SML4SE) applications. This will allow researchers to access, share, collaborate, and practice hands-on labs anywhere and anytime without time tedious installation and configuration which will help students more focus on learning concepts and getting more experience in hands-on problem-solving skills for big data analytics.

The acquisition footprint, finite-frequency source, and unbalanced subsurface illumination make it difficult for traditional adjoint-based migration to produce a high-quality image for complex structures. By fitting reflection events with linearized simulation data, least-squares migration (LSM) can iteratively incorporate the effects of the Gauss–Newton Hessian (GNH) to produce high-quality depth profiles. However, high computational costs of forward and adjoint simulations limit the LSM applications in production. In this study, we present an efficient approximation approach for the GNH and utilize it as a preconditioner for the misfit gradient of the LSM to accelerate its convergence. The analytic solution of the GNH in homogeneous media reveals that the columns of the GNH are local spatial functions. Based on this observation, we design a space-wavenumber filter to approximate the GNH for heterogeneous media, which can be efficiently computed with the S-transform and spectral division. The mixed-domain property of this filter allows it to automatically take the wavenumber dependence of the GNH into account and, therefore, helps to improve spatial resolution. Numerical examples demonstrate that the approximated GNH can considerably improve the image quality and speed up the convergence of the LSM.

As oil and gas exploration moves towards complicated geological environments, high-resolution and true-amplitude seismic imaging becomes increasingly important for detecting and evaluating hydrocarbon reservoirs. Traditional ray-based and wave-equation imaging methods can be considered as the adjoint operator of seismic forward modeling, which are difficult to produce high-quality images in complicated structures because of limited frequency band, unbalanced illumination and irregular acquisition. Least-squares migration (LSM) generates an inverse solution for subsurface reflectivity model with high image resolution and balanced amplitudes. Previous studies on LSM mainly focused on the developments of theoretical and practical strategies, but few on error and uncertainty analysis. We present a quantitative analysis method to evaluate the errors of LSM results. The ϕdataand ψdatafunctions are first computed based on the local similarity andL2-norm misfit between observed and synthetic data. They are used as data-domain kinematic and dynamic errors, respectively. Then, these local functions are mapped to the subsurface using a Kirchhoff-integral relation to calculate image-domain errors. Numerical examples for synthetic and field data demonstrate that as the iteration of LSM increases, the total kinematic and dynamic errors are reduced, and they vary in different locations. For low signal-to-noise-ratio field data, LSM might enlarge image errors at large iterations because of the overfitting issue, and proper regularization is very important to facilitate the convergence of LSM to a good solution.