Predictive filtering is one of the most widely used denoising algorithms in the seismic data processing community because of its high efficiency and stability in different situations. The traditional predictive filtering, however, is not able to deal with structurally complex data set unless applied in local windows. We develop a novel noncausal predictive filtering method that is free of the windowing step but is able to denoise complicated data set. We extend the stationary predictive filtering method to its nonstationary version, where the predictive filter coefficients vary across the frequency-space domain. The nonstationary predictive filtering (NPF) model requires solving a highly underdetermined inverse problem using an iterative shaping regularization method. The traditional shaping regularization method solves an inverse problem by applying a constant smoothing operator and thus does not consider the heterogeneity of the filter coefficients in the frequency–space domain. We propose to apply a nonstationary smoothing operator to constrain the model in the shaping regularization framework. The smoothing radius in the nonstationary smoothing operator is chosen based ona prioriinformation of the model, e.g., the nonstationarity of the data in the frequency–space domain. The proposed NPF method offers the flexibility in controlling the smoothness and sharpness of the calculated filter coefficients in both frequency and space dimensions. Several synthetic data sets and complicated real data examples are used to demonstrate the advantages of the new method.

Prestack seismic inversion has emerged as a powerful technique for reconstructing parameters attribute to the subsurface properties and building the geophysical parameter models. However, the inversion algorithms always suffer from spatial blur and low resolution. Total variation (TV) regularization preserves the spatial variation boundary of data by highlighting the sparsity of the first-order difference, which is regarded as an important technical means for image restoration. However, when the data do not change along the spatial grid direction, TV regularization is prone to a staircase effect. In this article, a directional TV (DTV) method is proposed to conduct the prestack amplitude variation with offset/angle (AVO/AVA) inversion. The method consists of three essential steps: estimating the seismic slope attribute from the seismic data, introducing seismic slope attribute to the TV regularization to establish the objective function, and optimizing the objective function by the split-Bregman algorithm. Finally, the conventional and proposed methods are applied to the synthetic and the real seismic data. The comparison of different methods demonstrates that the proposed method is applicable to reveal the detailed subsurface models, alleviate the staircase effect or artifact substantially, and further upgrade the quality of prestack inversion results.

The local signal-to-noise orthogonalization algorithm has been widely used in the community of seismic processing and imaging. It helps orthogonalize the signal-and-noise components in an elegant way so that the noise does not contain the signal leakage in seismic denoising. The traditional local signal-to-noise orthogonalization is based on solving a highly underdetermined, ill-posed inverse problem with local smoothness constraint. Due to the inversion nature, the local orthogonalization method requires a large number of iterations and thus is computationally demanding in large-scale applications. Here, we proposed a much accelerated signal-and-noise orthogonalization method, where we design an efficient way for calculating the orthogonalization weight. When new samples are involved in the calculation, we calculate the orthogonalization weight of the new samples by connecting them with the calculated weights of the previous samples. The orthogonalization weight needs to be smoothed and scaled after all samples have been processed to make the resulted orthogonalization weight smooth across the seismic data and match the amplitude level of the initially suppressed noise. In this way, we avoid iterations when calculating the orthogonalization weight. We apply the proposed method to several synthetic and field data examples, have a benchmark comparison with state-of-the-art algorithms, and demonstrate its much accelerated efficiency compared with the traditional local signal-and-noise orthogonalization.

Estimation of subsurface properties by using the scattering integral equation is a method that finds increasing use in near-surface and shallow oil/gas exploration, based on seismic, low-frequency electromagnetic, and surface-radar surveys. The method can accurately simulate physical realizations induced by small-scale perturbations, but its accuracy depends on a suitable low-frequency property model. We propose a 3-D geological-structure-guided model building to provide a reliable low-frequency model and combine it with the Born–Wentzel–Kramers–Brillouin–Jeffreys (WKBJ)-approximation-based inversion algorithm. Instead of the traditional approach based on artificially interpreted horizons, we use 3-D seismic-slope attributes as lateral constraints, which contain more geological information. Plane-wave destruction (PWD) in 3-D is exploited to extract the 2-D slopes along the inline and crossline directions, which are the key factors in computing 3-D slopes. Then, by introducing the shaping regularization, we build low-frequency models by solving the inverse problem. Numerical analysis indicates that an appropriate background model is essential for seismic modeling with the Born–WKBJ approximation. The methodology is applied to synthetic and 3-D field data, and the examples show that it provides reliable background models and improves the inversion performance.

Seismic multicomponent, here refers to P-P wave (PP) and P- shear wave (SV), joint inversion is an important approach to improve the accuracy of S-wave velocity and density prediction. Compared with P-P wave data, converted wave data are more sensitive to these parameters. Thus, introducing these data to the seismic inversion could improve the inversion accuracy of S-wave velocity and density. Due to the travel-time gap between the multicomponent data, multicomponent inversion usually needs to be prepared for registration processing in advance. However, registration methods often suffer from matching errors, which ultimately affect the quality of the inversion results. Based on the optimal transmission idea, a registration-free multicomponent joint amplitude variation with offset/angle (AVO/AVA) inversion algorithm is developed in this article. The proposed method adopts the Earth mover’s distance between the synthetic P-SV wave and the observed P-P wave by calculating the optimal transport path. Besides${\ell _{1-2}}$norm is exploited as the penalty norm, where the regularized misfit function is minimized by the alternating direction method of multipliers (ADMM) algorithm. The synthetic data test and real seismic data application show that the proposed method can retrieve the S-wave velocity and density information better than the conventional method. The proposed method can not only effectively avoid the cumbersome registration steps, but also minimize the registration error and avoid the subsequent error accumulation.

Coherent seismic noise is usually difficult to attenuate due to the similar morphological patterns between noise and useful signals. To attenuate coherent noise, special preknowledge should be utilized in a state-of-the-art approach, which causes significant inconvenience. Here, we develop an automatic method to attenuate coherent noise based on the adaptive dictionary learning algorithm. The adaptive dictionary algorithm can learn the features of both signals and coherent noise and leave obvious morphological differences in the dictionary atoms. These differences in the dictionary atoms can be transformed into statistical differences, which can be measured and then used to distinguish between signal and noise atoms. We evaluate several statistical metrics in characterizing the dictionary atoms and their feasibilities in distinguishing between signal and noise atoms. We find that the kurtosis metric can best represent the differences between signal and noise atoms, and then we design a kurtosis-based filter to reject those high-kurtosis atoms and their corresponding coefficient vectors for suppressing the coherent noise. Synthetic and real data examples demonstrate the performance of the proposed algorithm.

S-wave velocity and mass density, which are two essential parameters in distinguishing lithology and hydrocarbon detection, are very difficult to retrieve even when long-offset gather data are used. P-P and P-SV waves joint inversion has been verified as an effective tool to accurately extract such fluid related parameters. However, registering the travel-time of P-P and P-SV waves on the identical coordinate is a significant but knotty problem for the joint inversion. Therefore, an improved strategy of prestack seismic joint inversion is proposed for accurately transforming the recorded data to elastic-parameter-based interpretive information. First, to overcome the weaknesses of artificial strenching and the local cross correlation-based method, a nonstrenching and globally optimal registration algorithm, i.e., dynamic time warping (DTW), is exploited to match the P-P and P-SV waves. Then, a new method has been developed for the joint inversion method by combining the logarithmic absolute-criterion-based misfit function withl1-2norm-based penalty, which can significantly improve the vertical resolution and stability of inversion results. The numerical examples demonstrate that the DTW algorithm can obtain better registered results than the conventional method. Moreover, the proposed joint inversion method performs better than the conventional prestack inversion in both resolution and accuracy, especially for the S-wave velocity.

Time-lapse (4-D) seismic exploration is one of the essential means for accurately reconstructing the underground geological model, enhancing oil/gas recovery (EOR), and predicting remaining oil distribution. Under the assumption that the rock skeleton is almost unchanged in the process of development, inversion of time-lapse seismic difference data can be used to characterize the dynamic reservoir parameter. However, the inaccuracy of the forward operator, lack of constraints, and inappropriate regularization weight may lead to ill-posedness. Thus, the ill-posedness is still a key factor affecting the accuracy and stability of time-lapse seismic inversion. In this article, an improved difference-and-joint inversion strategy is proposed using the modified linear approximation as the forward operator. First, based on the modified approximation as the forward operator, time-lapse seismic difference inversion is exploited to obtain the variations of elastic parameter reflectance caused by the production-induced model perturbation. Then, we innovatively proposed to take the production-induced model perturbation as constraints, thereby achieving more accurate geological models for multiperiod seismic data joint inversion. Moreover, the L-curve method is exploited in this article to acquire the optimal regularization weight adaptively in each iteration step. Finally, the difference inversion results are used as constraints to precisely invert the geological model by combining multiperiod seismic data.

Reconstructing an accurate and high-resolution subsurface model is attractive in the fields of both geology and seismology. However, due to the band-limited characteristics of seismic data, the inversion greatly depends on the reliability of the initial model. A fairly acceptable initial model could lay a good foundation for seismic inversion. In this article, we first introduce a well-log interpolation method with the local slope as a constraint for building a high-fidelity starting model in prestack amplitude versus offset/angle (AVO/AVA) inversion. First, we briefly review the basic theory of general seismic inversion. Then, instead of using the conventional preconditioned least-squares method, we introduce shaping regularization theory into the geological structure-guided well-log interpolation to accelerate the convergence. We use the plane-wave destruction (PWD) algorithm to extract the slope attribute from seismic data, images, or velocity models. The slope is used as the constraint to solve the inverse problem based on the shaping regularization method. Numerical examples demonstrate that the proposed initial model building method performs better than the conventional ones. It greatly improves the accuracy of inversion results. Furthermore, we apply the proposed model building method to the inverse problems of AVO/AVA inversion and reservoir parameter estimation of several field data sets for the first time, which demonstrate encouraging performance.

Dynamic changes of reservoir parameters within a reservoir are usually estimated by a history matching process based on the production data. However, it is difficult to accurately acquire the spatial distribution using production data as the constraints. We formulate a nonlinear inversion method to dynamically characterize the reservoir parameter variations from time-lapse prestack seismic data. Besides, we introduce the modified Hertz-Mindlin (H-M) model to simulate the changes in the elastic behavior of a turbidite sandstone during production by establishing a link between reservoir parameters and elastic parameters. Then, the exact Zoeppritz equation is exploited as a forward engine to convert these parameters into synthetic time-lapse seismic data. Numerical examples verify that the porosity parameter has a higher reflection sensitivity than the other two parameters, which is followed by the effective pressure. The water saturation parameter, however, is the least sensitive. Following a Bayesian approach, the baseline and monitor seismic data are used in the seismic inversion to establish the regularized augmented function. Combining the modified H-M rock physics model with the exact Zoeppritz equation as a forward operator, a regularized function is minimized with the Gauss-Newton optimization method to determine a model update. We further apply the proposed inversion algorithm to a real seismic data set, including baseline and monitor seismic data. The results demonstrate that the proposed inversion method can not only yield an accurate description of subsurface static reservoir properties but also improve the accuracy of dynamic reservoir parameter characterization.

Patchy saturation of gas and brine within the porous rock can induce significant attenuation and velocity dispersion effects, which in turn have a profound impact on seismic data. Thus, there should be a close relationship between dispersion and reservoir parameters, such as saturation, porosity, and permeability. Hence, using seismic data to determine dispersion information has been the subject of intensive research in recent years. It can help quantitatively predicting gas saturation and monitoring CO2sequestration, a key strategy for mitigation of global warming. Here, a frequency-dependent prestack waveform inversion workflow was proposed to extract the wave-induced fluid flow (WIFF) effect from seismic data (WIFF prestack waveform inversion strategy). The proposed approach consists of three essential parts, comprising spectral decomposition,$Q$-compensated prestack waveform inversion, and frequency-dependent prestack waveform inversion. First,$\ell _{1}$norm constrained inverse spectral decomposition is exploited to provide time-frequency amplitude and phase spectra with high resolution and reliable accuracy. Then, constant-$Q$compensated prestack waveform inversion is used to generate relatively precise$P$- and$S$-wave velocities, density, and Fréchet derivative for the subsequent dispersion inversion. Finally, frequency-divided seismic data and the estimated parameters and Fréchet derivative are used to invert the$P$-wave velocity dispersion. A comparison between the inversion results and band-limited rock physics analysis results shows that the proposed method can provide a quantitative inversion of the velocity dispersion to some extent. The proposed strategy provides a possibility for quantifying dispersion and further estimating gas saturation.

It is widely known that strong noise can decrease the quality of seismic data. However, the anelastic attenuation could be more important to account for the weak amplitude and low quality of seismic data. Here, we develop an inversion framework to simultaneously compensate for the attenuation of seismic data and remove noise, thereby enhancing the quality of seismic data. Instead of directly applying a compensation operator to the input seismic data, we formulate an inverse problem that connects the sparse reflectivity model and the raw seismic data via the convolution and attenuation functions. The random noise is assumed to be the unpredicted part of the forward modeling process. We use the L2-norm regularization for the data misfit and impose a sparsity constraint onto the reflectivity series, e.g., using the L1-norm constraint. We use an iterative preconditioned conjugate gradient method to solve the L1-norm constrained least-squares optimization problem and obtain the reflectivity series. The denoised and compensated data are obtained by applying the convolution operator to the reflectivity. We use several synthetic and field seismic data to illustrate the effectiveness of the presented method.

The plane-wave destruction (PWD) method has been a widely used local slope estimation method in the seismic community. It is based on the discretization of the plane-wave partial differential equation (PDE) and the linearization of the PDE with respect to the local slope. Solving the linearized inverse problem for the slope perturbation is equivalent to solving a smoothness constrained optimization based on a shaping regularization method. The smoothness constraint in the shaping regularization is important in that it not only controls the stability and smoothness of the solution, i.e., slope perturbation, but also affects the accuracy and resolution of the solution. The traditional PWD algorithm is not easy to compromise between the smoothness and resolution of the estimated local slope because it uses a stationary triangle smoothing operator as the shaping operator. Here, we propose to improve the robustness of the PWD algorithm by introducing a nonstationary triangle smoothing operator into the shaping regularization framework in order to adaptively constrain the solution according to the local signal reliability. The smoothing is weak in areas with a higher probability of signals and is strong in areas with a higher likelihood of noise. The smoothing radius can be adaptively estimated based on an optimization model, which is solved by a line-search method. The proposed new slope estimation method is referred to as a nonstationary method compared with the traditional stationary one. The effectiveness and benefits of the new slope estimation method are validated via several synthetic and field data examples.

The quality factor Q is an indispensable parameter for studying wave propagation in viscoelastic media. Q can not only be implemented for improving the quality of wave records but can also be used for directly indicating frequency-dependent anomalies induced by fluids, so it is widely used in seismic exploration and clinical medicine. Q estimation here refers to the extraction of Q information from seismic data; it has aroused lots of attention but is still somewhat controversial due to the limitations of existing methods. In this letter, combined with a logarithmic spectral ratio (LSR) algorithm, we have introduced a sparse-constrained inversion spectral decomposition (ISD) method for average-Q estimation (LSR-ISD), and have used shaping regularization to solve for the spectrum ratio. Then, through regularized linear inversion, average-Q was converted to an interval-Q value. Finally, we have applied this method to synthetic data and field data. Numerical examples and field data application demonstrate that the proposed method produces a series of results with high resolution and good stability.

Seismic waveform inversion has been one of the most studied topics in recent years, which can be implemented both in common shot gather and prestack common midpoint gather. However, there are still several intractable issues to be addressed urgently, such as high-computational complexity, nonuniqueness, and robustness. In this paper, we have developed a model-based prestack waveform inversion (PWI) with a generalized propagation matrix scheme as forward operator, where a regularized function is minimized with the limited memory-Broyden-Fletcher-Goldfarb-Shanno technique to determine a model update corresponding to an adaptively determined regularization weight in each iterative step. To avoid falling into local extrema in the process of solving the objective function, we introduce an optimal transport method into the objective function to improve its convexity and use L-curve method to acquire the optimal regularization weight adaptively. The model tests show that the proposed scheme performs better than the conventional method significantly both on convergence and on accuracy. Furthermore, we apply the PWI with the proposed inversion scheme to the well-logging data and real seismic data. The results demonstrate that the proposed inversion scheme is not only capable of obtaining an accurate description of subsurface properties but also has a good convergence and robustness.

Since most information on S-wave velocity and density exists in the middle to large angle range of seismic data, traditional inversion methods based on the Zoeppritz approximation have difficulty in obtaining satisfactory results. Therefore, as a high-accuracy amplitude varied with angle (AVA) inversion, exact Zoeppritz (EZ) equation inversion has aroused a lot of attention in recent years. As for any other nonlinear inversion, iterative convergence and error are the important problems. In this letter, based on a Bayesian framework, we introduce optimal transport into EZ equation AVA inversion. Then, the limited-memory Broyden-Fletcher-Goldfarb-Shanno method is adopted to solve the regularization-constrained least-square argument function to obtain the inversion results, including P-wave velocity, S-wave velocity, and density. We compare this method with a conventional method, which is based on an L2 norm or weighted L2 norm as a residual method in the model test. The results show that the proposed method not only reduces the error of the results to be smaller than L2 norm, but it also improves the convergence rate.