The popularity of blended acquisition is surging in the field of seismic exploration because of its higher efficiency and lower cost. As a compromise, a sophisticated deblending framework should be applied to remove interference noise. However, blended sources are usually fired at off-the-grid (OTG) samples, and the recorded data are incomplete because of some inevitable barriers and instrument errors, increasing the challenges to apply classic deblending methods to OTG data. Typically, the binning process and data reconstruction will be introduced for OTG incomplete data before subsequent deblending. Nevertheless, the binning process may cause amplitude and phase distortion, degrading the deblending accuracy. To overcome this problem, we propose a deep learning (DL)-based method without a binning process for OTG deblending and reconstruction, namely, OTGDR, avoiding the errors related to preprocessing routines. The proposed OTGDR framework contains two components: deep image prior (DIP)-inspired coherency-enhancing network and bilinear operator-guided projection onto convex set (POCS) iteration. The DIP incorporates several fully connected (FC) layers, attention mechanism, and skip connection to extract useful features selectively for superior performance, and the following POCS aims to remove the blending and ambient noise iteratively for enhanced signal-to-noise ratio (SNR). Moreover, the proposed OTGDR is completely data-driven and does not require labels for training, which increases its generality and enables it to adapt to different datasets. In our experiments, we compare the proposed OTGDR with classic deblending methods, and the results demonstrate that OTGDR shows superior performance on OTG denoising and reconstruction in terms of fidelity and SNR.

Seismic data is commonly contaminated by different types of noise with varying amplitudes, increasing the challenges of retrieving effective signals from strong background noise. Such issues become even worse when attenuation effects are considered because the amplitude of seismic waves will dissipate after propagation, making seismic signals easier to be inundated by noise, especially at deeper positions. To implement data enhancement and attenuation compensation without noise amplification, we propose a robust framework in a blind manner to reconstruct attenuation-compensated seismic data with a higher signal-to-noise ratio (SNR), namely, structural-oriented blind Q-compensated denoising (SBQD) method. Unlike classic Q-compensated denoising methods, the proposed SBQD does not require wavelet as a prior and can iteratively estimate wavelet and reflectivity series simultaneously, and the final stationary seismic data can be obtained by convolving the estimated wavelet with the reflectivity series. Moreover, guided by local adaptive structural regularization, the proposed SBQD can provide superior results with higher accuracy and fidelity and remove those noise-related artifacts during denoising and compensation. Compared with conventional two-step methods (e.g., denoising and attenuation compensation), the proposed SBQD can implement denoising and compensation simultaneously, which avoids introducing compensation-related errors (e.g., noise amplification) and effectively preserves useful signals. Synthetic and field examples are used to validate the robustness of the proposed SBQD method on noise removal and attenuation compensation for seismic data.

Seismic data reconstruction is a crucial step in seismic data processing, which faces numerous challenges in accurately capturing the complex patterns and structures within the data. Deep learning is revolutionizing the processing of seismic exploration data, enabling more precise imaging of subsurface structures and improving the detection of potential oil and gas reservoirs. We propose a modified least-squares generative adversarial network incorporating the inverse interpolation (LSGAN-II) method for seismic data reconstruction. Our approach integrates inverse interpolation algorithms into a generative adversarial network (GAN) framework to enhance both the accuracy and efficiency of seismic data reconstruction. Initially, a GAN is employed to predict local event slopes in seismic data, where a least-squares loss function is utilized to improve the learning capacity and convergence speed of the deep learning network. Subsequently, the predicted local event slopes are used as regularization operators in inverse interpolation, effectively enhancing the precision of the reconstructed seismic data. A dual-discriminator-based LSGAN-II is developed to implement the seismic data reconstruction process. This network combines the benefits of both GAN and inverse interpolation techniques, utilizing dual discriminator loss functions and a least-squares error loss function to optimize the prediction of local event slopes and the reconstruction of seismic data. The testing of the LSGAN-II method is conducted using two synthetic datasets and one actual dataset, demonstrating its effectiveness and practicality in seismic data reconstruction.

Estimation of porosity and saturation is crucial for shallow gas hydrate exploration in deepwater areas. Owing to the inherent nonlinearity of rock-physics models, many inversion algorithms adopt probabilistic and statistical approaches involving extensive forward simulations, which results in low computational efficiency. The conventional two-step rock-physics inversion process introduces uncertainties that may accumulate as errors. Moreover, traditional pre-stack inversion methods typically neglect absorption and attenuation effects during seismic wave propagation, thereby degrading the quality of the inversion results. To address these limitations and directly estimate porosity and saturation from nonstationary seismic records, we propose a Q-compensated multidimensional rock-physics inversion method. We derive the Jacobian matrix from the rock-physics model to employ first-order Taylor series approximations in the forward modeling. By integrating the linearized rock-physics model with the Aki-Richards equation, we establish a quantitative relationship between petrophysical parameters and seismic records within gas hydrate reservoirs, while accounting for the differential effects of propagation paths on absorption and attenuation across seismic channels. During the inversion process, we utilize shaping regularization in seislet-domain to enhance both accuracy and stability, particularly under noisy conditions. This method not only improves the lateral continuity of seismic inversion results but also mitigates inversion errors caused by noise, thereby enhancing the reliability of the estimates. Results from synthetic and field datasets demonstrate that the proposed method significantly improves both the accuracy and robustness of the inversion.

Multiple attenuation plays an important role in marine seismic data processing, and a slew of methods have been developed for multiple attenuation. However, due to acquisition limitation, the performance of such methods will degrade when it comes to incomplete seismic data. Here, we proposed a novel method to implement data reconstruction and multiple suppression simultaneously. Compared with the two-step methods (e.g., interpolation and multiple attenuation), the proposed method can restore and highlight primary reflections directly without data reconstruction in advance, which avoids introducing interpolation-related errors and simplifies the data processing routines. Based on the incomplete data, we first sort seismic data into common midpoint (CMP) gathers and use normal moveout (NMO) to flatten the primary reflections, and the multiples still retain parabolas. Then, we reassigned the seismic traces randomly to decrease the coherency of the multiples from near-offset to far-offset and applied the damped rank reduction (DRR) method to the disordered traces to reconstruct seismic data and remove the unexpected multiples simultaneously. Compared with conventional two-step methods, the proposed one-step method can suppress multiples and benefit useful signal preservation more effectively. Moreover, in addition to multiples, the proposed method can remove random ambient noise and provide superior results with an improved signal-to-noise ratio (SNR). Synthetic and field examples are used to validate the validity of the proposed method on data reconstruction and multiple attenuation for incomplete seismic data.

Quality factor Q is an important parameter that accounts for the amplitude dissipation and phase distortion of seismic waves propagating in the Earth’s interior. Q estimation with improved accuracy benefits nonstationary seismic inversion, seismic imaging, fluid identification, and so on. Usually, logarithmic spectral ratio (LSR) is widely used to estimate Q based on vertical seismic profile (VSP) and poststack data. However, LSR is very sensitive to noise, and the effect of normal moveout (NMO) distorts the spectrum of the stacked seismic data, leading to an inferior Q estimation result. To weaken the effect of NMO and enhance the accuracy of Q estimation, we expand an improved LSR method in the zero-offset traveltime-local slope (e.g.,$t_{0}-p$) domain and propose a robust prestack Q estimation method based on common midpoint (CMP) gathers. The proposed method incorporates warped mapping (WM) and shaping regularization to stabilize it during Q estimation in the case of low signal-to-noise ratio (SNR). Additionally, we incorporate nonzero-offset information for Q estimation, which weakens the strong dependence on zero-offset information during prestack Q estimation. Compared with the single-gather prestack Q estimation methods (SPQEM), we make the most of the spatial coherence between the adjacent CMP to eliminate the unexpected noise-related outliers during spectral division for improved robustness and accuracy. Numerical examples are used to validate the superior performance of the proposed method, even in the presence of strong ambient noise.

Deep learning methods have gained widespread popularity for effectively suppressing random noise in seismic data. The recent progress in techniques based on supervised learning for attenuating seismic random noise underscores their potential, particularly when an abundant set of training examples is accessible. Unfortunately, collecting an adequate amount of representative training samples is not always feasible. DIP aims to capture a lot of low-level statistical information by using rich implicit prior knowledge inherent in the structure of the generation network itself. Therefore, it is not essential to provide a training database or uncontaminated data as a truth label, whereas only requires a noisy seismic image. In order to boost the performance, we add an explicit prior, weighted total variation, to the standard DIP, which leverages sparsity-promoting priors and restricts the solutions of DIP to satisfy a prior inherent in the seismic data. The proposed method is tested on synthetic seismic data with random noise that follows different distributions, then is applied to field pre- and post-stack seismic data. Furthermore, a comparison is drawn between the new method and the traditional DIP-based denoising method in terms of signal to noise ratio and local similarity. Our method shows more promising results because prior information from both the structure of the network and the seismic data is considered in the denoising processing.

Full waveform inversion (FWI) has been proven as an effective method for subsurface parameter estimation by iteratively reducing the residual between the predictions and the observations. In recent years, FWI has been widely used due to the increasing computing power. However, seismic waves usually suffer from energy dissipation and phase distortion during their propagation in the anelastic medium, which will decelerate the convergence rate of FWI and make the inversion processing even more time-consuming. In this letter, we propose a structure guided FWI method with attenuation compensation to estimate velocity model and$Q$model simultaneously. We refer to the proposed method as structure guided$Q$-compensated FWI (SGQFWI). With the help of a fractional decoupled viscoacoustic equation, we introduce the attenuation compensation mechanism into FWI iterative algorithm, which can effectively compensate the deep weak amplitude, so as to obtain a more accurate inversion gradient and improve the accuracy and efficiency of inversion. Additionally, the structure regularization is added to model update, which helps to retrieve local detailed information more efficiently. Benefit from the incorporation of the priori structure constraint and attenuation compensation, this method has the ability to invert velocity and$Q$model with improved efficiency and resolution. Synthetic and field data examples are adopted to further verify the effectiveness of the proposed method.

The geostatistics stimulation method, as an important tool in subsurface modeling, is crucial for hydrocarbon reservoir characterization. Using geostatistical methods to reproduce complex heterogeneous structures is still challenging because of nonstationarity and computational consumption. We develop a stabilized stochastic simulation method by introducing the generative adversarial network based on a single image (SinGAN). It can preserve multiscale features contained in an individual training image by using a multistage training framework. In order to stabilize the training of the discriminator, the spectral normalization is integrated. We also introduce spatial attention and channel attention mechanism into the network to focus on the most significant features in each training stage, so that these features can be reproduced in the realizations. An adaptive strategy is adopted to automatically choose training stages, which balances the diversity and quality of simulation results and decreases the man-made factor on SinGAN. Several experiments are tested on synthetic and actual training images, respectively. We evaluate the simulation results from many perspectives, including variability, connectivity, probability density distribution, and time-consuming. The successful application of the new method on both categorical and continuous variables indicates that it has a strong ability to reproduce complex subsurface models, even for nonstationary geologic phenomena.

During the secondary seismic exploration in the maturing oil-field, due to the complex ground conditions, well-pump noise strongly reduced the signal-to-noise ratio (SNR) and affected the subsequent application of seismic data. At present, deep learning is mainly used in suppress random noise and ground-roll noise. Due to the obvious difference between the features of well-pump noise with random noise and ground-roll, the existing deep learning seismic denoising method which only extracts the features on one scale is not suitable for the suppression of well-pump noise. Therefore, we adopted the coarse-to-fine denoise strategy and presented a new method using multi-layer generator network (MLGnet) to suppress well-pump coherent noise. In proposed method, the network mainly consists of multi-layer encoder-decoder architecture, which could combine different layer feature information to obtain accurate denoised results. Meanwhile, we split the noisy seismic data into multiple patches in each layer, which could effectively expand the receiving range of denoising network and extract more useful features from well-pump noise. In this way, the proposed network can effectively utilize the multi-scale semantic information to suppress well-pump noise from seismic data. Experimental results on synthetic data and field data illustrated that our approach could obtain high-quality denoised results and retain the valid data to the greatest extent, compared with DnCNN and GAN.

Seismic data interpolation and denoising play vital roles in obtaining complete and clean data in seismic data processing. Seismic data usually misses along various spatial axes and always mix with random noise. In order to obtain complete and clean seismic data, reconstruction technology can interpolate missing data and attenuate random noise. Nonsubsampled contourlet transform is an effective transform to obtain multi-scale and multi-direction sparse domain data for compression sensing interpolation and denoising. However, conventional iterative shrinkage/thresholding cannot handle ill-posed and ill-conditioned equations for solving linear inverse problem. We present a two-step iterative log thresholding method to overcome ill-posed and ill-conditioned problems and improve the convergence rate and solution accuracy, which can interpolate and denoise seismic data simultaneously in the nonsubsampled contourlet transform framework. First, we use nonsubsampled contourlet transform to convert the seismic missing data with random noise to sparse domain. Then, we apply two-step iterative log thresholding algorithm to interpolate and denoise data in sparse domain. The result of each iteration is based on the results of the previous two iterations, which can accelerate convergence rate. In addition, log thresholding can further improve convergence rate and solution accuracy. Finally, we use inverse nonsubsampled contourlet transform to obtain the interpolated and denoised seismic data. The new method can reconstruct the irregularly missing data and attenuate random noise to obtain complete and clean seismic data with high accuracy, which is crucial for seismic imaging and inversion. We demonstrate the applicability and effectiveness of this simultaneous interpolation and denoising technique with successful applications to both synthetic and field data examples.

Low frequency information in seismic data can improve seismic resolution and imaging accuracy, enhance the quality of inversion, and play an essential role in imaging algorithms such as full-waveform inversion. Sufficiently low frequency data can avoid the cycle skipping phenomenon during full-waveform inversion. During seismic data processing, the protection and reconstruction for low frequency information are therefore of great importance. In this paper, we systematically investigate the extrapolation of pre-stack viscoacoustic seismic low frequency data using a dense convolutional network to effectively establish the nonlinear relationship between high and low frequency data, and realize the extrapolation and reconstruction of viscoacoustic 0-5 Hz low frequency data using 5-30 Hz high-frequency component. And the generalizability of the method for different influencing factors such as wavelets, noise, and models is analyzed using Marmousi2 velocity model forward data. It is demonstrated that the method has high robustness and can be applied to different situations, and the accuracy is higher than that of the traditional convolutional neural networks method. The feasibility of the low frequency extrapolation method based on dense convolutional network is also verified by synthetic data, physical experiment simulation data, and field data testing, and superior to the traditional convolutional neural networks method.

The interpolation based on prediction-error filter (PEF) is one of the most effective approaches recently proposed for seismic data reconstruction. However, the number of effective regression equations for estimating the filter coefficients will be much less when missing many seismic traces, which makes the estimated filter coefficients inaccurate or even impossible to be estimated. To improve the accuracy of filter coefficients, in this paper, we design a multiscale and multidirectional PEF, in which the number of effective regression equations can be increased much more, and use it to seismic data reconstruction. First, we estimate the adaptive different directional PEFs using the known data in different scales. The known data can be regularly sampled with randomly or regularly missing, or even both of them. Then, we interpolate missing seismic traces using estimated PEF and the sparse known traces. The regularization in least-squares inversion controls the adaptivity of multiscale multidirectional PEF. The use of more effective regression equations in inversion makes the filter coefficients more accurate. In addition, the multiscale filter can conveniently deal with the case of the simultaneous existence of randomly and regularly missing, while the conventional methods have to be treated separately for randomly and regularly missing. The applicability and effectiveness of the proposed method are examined by synthetic and field data examples.

We devised a new filtering technique for random noise attenuation by weighted multistep adaptive autoregression (WMAAR). We first obtain a series of denoised results by means of different steps adaptive AR, and then we sum these results with different weights. The adaptive AR coefficients are obtained by solving a global regularized least squares problem, in which regularization is used to control the smoothness of these coefficients. The adaptive AR can estimate seismic events with varying slopes since AR coefficients have temporal and spatial variabilities. We derive the weights from the normalized power of local similarity by comparing the result of the nearest step with the ones of other steps. The application of these weights makes the proposed algorithm more effective in fault information conservation. The proposed WMAAR can be implemented both in the frequency-space and in time-space domains. Multidimensional synthetic and field seismic data examples demonstrate that, compared with conventional methods in frequency-space or time-space domain, multistep adaptive AR is more effective in suppressing random noise and preserving effective signals, especially for complex geological structure (e.g., faults).

Seismic data interpolation and reconstruction play an important role in seismic data processing. Seismic data are often inadequately sampled along various spatial axes. We have developed a new approach to interpolate aliased multidimensional seismic data based on the multidimensional adaptive prediction-error filter in frequency domain. First, we estimate the adaptive prediction-error filter coefficients, then interpolate missing traces using the estimated coefficients. Shaping regularization is used to control the smoothness of frequency-domain multidimensional adaptive prediction-error filter coefficients. Instead of estimating prediction-error filter coefficients only along one direction space, we estimate the prediction-error filter coefficients using more information along different direction spaces. So, multidimensional adaptive prediction-error filter using regularized nonstationary autoregression can adaptively estimate seismic events whose slopes vary in multidimensional space. The frequency-domain multidimensional interpolation method can input data at temporal frequency, which can save computer memory and time. For multidimensional seismic data, which miss different number of traces regularly in different axes, the proposed method can be used to interpolate missing traces to obtain more accurate results. The proposed method improves the calculation efficiency by applying shaping regularization and implementation in the frequency domain. The applicability and effectiveness of the proposed method are examined by synthetic and field data examples.