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 acoustic impedance (AI) inversion is essential for reservoir prediction and characterization. In recent years, deep learning has shown immense potential as a data-driven approach in seismic data processing, inversion, and interpretation. As a data-driven method, deep learning-based seismic inversion results better when sufficient labeled data are provided. Overfitting and poor generalization often occur when labels are insufficient. Due to the lack of labeled data in seismic inversion problems, the difficulty of inversion increases, leading to unstable and poor generalization of prediction results. To partially address this issue, we propose a constrained seismic inversion strategy. Since seismic records are time series, we exploit the convolutional neural network (CNN) and bidirectional LSTM (Bi-LSTM) network structures that are more applicable to time series. We combine the physical model and the initial model as constraints to improve the network stability and generalization ability, and impose sparse constraints on the reflection coefficient to further improve the prediction accuracy. The network structure transformation improves the efficiency and stability of the training process. Through numerical experiments and real data tests, it is proved that the proposed method improves the vertical resolution and geological reliability, providing a more stable and efficient method for seismic inversion under conditions of limited labeled data. The overall performance improved by 2% through comparative analysis.

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.

Prestack seismic inversion is one of the most commonly used methods to describe reservoirs. Deep learning (DL) has received wide attention because of its ability to handle complex nonlinear problems. The existing DL-based seismic inversion method adopts a single training dataset, which is prone to poor generalizability and geological artifact. In addition, field data are often difficult to transfer learning due to the lack of a training dataset. To partially overcome these problems, we improve the training dataset and network parameters, thus developing a new DL-based prestacked inversion framework. First, we generate a training dataset using a forward model and pretrain the network by adding labels to a portion of it as the training dataset. We use multitrace information for training and prediction to reduce the lateral geological artifact problem. For unlabeled or less-labeled datasets, we construct data residual loss terms and initial model constraints to achieve weakly supervised or even unsupervised learning, which solves the poor generalizability problem due to insufficient training datasets. Compared with previous data-driven approaches, the inverse framework in this article compensates for the lack of the training dataset, diminishes geological artifacts, and improves generalization and robustness. The effectiveness of the framework is verified by synthetic data from two different models and field data from S-fields, and good inversion results are obtained even with a low signal-to-noise ratio or lack of well data.

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.

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.