One of the leading challenges in hydrocarbon recovery is predicting fluid distribution throughout the reservoir, using dispersion of seismic elastic parameters to solve this problem is a method with great potential. Previous studies reveal that predicting frequency-dependent seismic elastic parameters is difficult because of their sensitivity to seismic wave amplitude. The frequency-dependent AVO inversion schemes are widely used to estimate the dispersion gradient attributes for fluid prediction. However, these methods strongly depend on the advanced spectral decomposition and the wavelet overprint effect in time-frequency information. For this reason, this study presents an innovative technique that combines prestack AVO inversion and linear Bayesian inversion algorithm to predict directly frequency-dependent P-wave velocity of multilayered medium from seismic reflection data, which can quantitatively describe the change of P-wave velocity in seismic frequency band. Furthermore, frequency-dependent elastic parameters were used to define a dispersion factor for fluid prediction in thin sandstone reservoirs. The novelty of the study is that the proposed approach introduces prestack AVO inversion to provide reliable initial model and constructs dispersive P-wave velocity inversion framework of layered medium for the first time. Additionally, the dispersive elastic parameters have more potential applications than the dispersion gradient attributes. Tests on the synthetic and real data demonstrate that the frequency-dependent P-wave velocity of multilayered medium can be estimated reasonably and stably. In this application, we use a test well to assess locally the performance of the technique.

A training set with sufficient quantity and reliable quality is crucial for achieving satisfactory results in data-driven acoustic impedance inversion. However, effective data augmentation still faces significant challenges when labeled well data are sparse. In this study, it is proposed a novel impedance sequence augmentation strategy based on the SinGAN multiscale generative adversarial networks under few well conditions. SinGAN requires only a single impedance sequence for training and supports two augmentation modes: Random Impedance Generation Mode (RIGM) and Controllable Impedance Generation Mode (CIGM). RIGM controls diversity between synthetic and true impedance by adjusting the Start Generation Scale (SGS), while CIGM synthesizes impedance by fusing a known low-frequency reference model with high-frequency details derived from well data, the SGS determines the proportion of their integration. Three training sets were established through data augmentation using broadcasting, RIGM, and CIGM on the Marmousi2 model, and were subsequently fed into a CNN-GRU fusion network with identical hyperparameters. Experimental results show that the correlation coefficients (R²) between the estimated and true impedance values reach 0.9111, 0.9282, and 0.9423 for the broadcasting, RIGM, and CIGM methods, respectively. Meanwhile, the CIGM-based model achieves the best overall performance, with an MSE of 0.006 and an SSIM of 0.966, and it accurately characterizes impedance variations across stratigraphic layers and clearly delineates the water–strata interface and associated sand bodies. These findings verify that the proposed augmentation strategy effectively expands the training sample space and enhance impedance prediction accuracy, offering a new promising approach for seismic inversion tasks with sparse labeled data.

As a significant step to characterize reservoir, reservoir properties estimation play an essential role to link elastic parameter with physical property parameter. Most conventional-used estimation methods are implemented in sequential tactics. However, to predict the rock and fluid properties from inverted seismic elastic attributes doesn’t only add cumulative error but also increase uncertainty and computational cost of inversion. We have developed a direct seismic petrophysical inversion method intended for disadvantages of sequential rock inversion methods. The method incorporates the Keys-Xu approximate model into the seismic forward operator, to built a direct correlation between reservoir properties and observed seismic data. Reservoir parameters want to retrieve can be obtained from prestack seismic data based on rock-physics model and exact Zoeppritz equation. The inversion process combines Bayesian theory and Gaussian prior distribution, by which the estimation of petrophysical properties, such as porosity, clay volume, and fluid saturation, can be expressed as a posterior probability density function. The optimal solution is the random value corresponding to the maximum posterior probability density. Theoretical model test and real data sets application show that this method can obtain accurate results. The main advantage of this method is the cumulative error of the two-step method is decreased and the uncertainty in the inversion process is reduced. The use of exact Zoeppritz equation aviod approximation error of other approximations, like Aki-Richards, Shuey, etc, and makes the method applicable to far offset seismic data.

Internal multiple attenuation is a kind of significant coherent noise for imaging and comprehending subsurface structures from primaries in exploration seismic data. Traditional prediction-subtraction strategy heavily relies on predicting the traveltimes and matching the amplitudes for internal multiples, which poses a risk of primary distortions. Neural network methods face challenges about missing primary labels, limited applications on prestack field data, and high demand for prior information and manual intervention. To alleviate these problems, this article develops a physics-informed self-supervised neural network (SSN) to attenuate internal multiples by reducing requirements for prior information and employing the phase resemblance (PR) as the physics loss to adaptively prevent primary distortions. First, the initial internal multiples (IIMs) predicted by the virtual event (VE) method are taken as inputs for SSN to provide prior information, where no authentic primaries are required for training labels. Then, a U-shaped SSN equipped with attention mechanisms and a pyramid dilated convolution (PDC) unit is constructed to map IIMs to the estimated true internal multiples (EIMs) under a physics-informed hybrid loss. We introduce the PR constraint as the physics loss by cross-coherence of traces and kurtosis calculation to adaptively prevent primary distortions and constrain the network training. The result without internal multiples is finally obtained by subtracting EIMs from the recorded data. Synthetic and field data examples demonstrate the superior performance of our method in internal multiple suppression and primary retention ability compared with traditional workflow and the purely data-driven neural network.

Elastic full waveform inversion (FWI) is one of the most popular tools in recovering the subsurface P- and S-velocity models with high resolution. However, it requires either a good starting model or low-frequency data to avoid the cycle-skipping issue. Elastic reflection waveform inversion (ERWI) uses the migration/demigration process to compute the low-wavenumber gradient. One drawback of conventional ERWI is that it mainly relies on the first-order Born scattering and only utilizes primary reflection wave paths, providing limited wavenumber illumination in the update. In this letter, a nonlinear Born scattering operator is incorporated with ERWI for multiparameter reconstruction to mitigate the drawback of the conventional linear Born approximation. Finally, we use numerical examples to show that the nonlinear Born scattering operator allows us to take advantage of the multiples and enlarge the wavenumber illumination in ERWI results.

In seismic data processing, the suppression of internal multiple is a challenging direction. To suppress internal multiples, we propose an unsupervised deep neural network (DNN) method based on adaptive virtual events (AVEs) and joint constraints of multi-DNNs (JCMDNNs). First, we use an AVE method to obtain predicted internal multiples by convolution and cross correlation. The predicted internal multiples can well calibrate true internal multiples and provide good prior information. Second, we use the unsupervised DNN (UDNN) to map the predicted internal multiples to the estimated true internal multiples. Finally, the demultiple results can be obtained by subtracting the estimated true internal multiples from the data containing internal multiples. Three DNNs, one input data, six output data, and six pseudo-labels (PLs), are combined into the base learners and auxiliary learners of UDNN. UDNN uses the nonlinear optimization ability of DNNs to map predicted internal multiples to true internal multiples through the JCMDNNs. Three auxiliary learners correct the outputs of the base learners to reduce the nonlinear mapping deviation of UDNN. Using JCMDNNs by combining all base learners and auxiliary learners is called ensemble learning. Our proposed JCMDNN method does not need true internal multiples and true primaries as the input and output data, which solves the problem of missing training datasets and has wide use ranges. The effectiveness and superiority of our proposed method to suppress internal multiples are demonstrated through two synthetic and one field data examples.

Random noise suppression can greatly improve the signal-to-noise ratio (SNR) of seismic signals. To suppress random seismic noise, we propose an unsupervised deep neural network (UDNN) method based on the local cross-correlation (LCC) loss function and ensemble learning. UDNN with two base learners mainly consists of one input data, two deep neural networks (DNNs), and two output data. The proposed UDNN based on the LCC loss function and ensemble learning (UDNN-LCCEL) method takes full advantage of the nonlinear mapping capabilities of DNNs and maps noisy data into effective noise-free signals by minimizing the total loss function. The total loss function includes the LCC and mean-absolute-error (MAE) loss functions. LCC calculates the local correlation or orthogonalization between output data and the removed noise. By reducing the value of the LCC loss function, we automatically reduce the residual noise and leakage of effective signals in the output data, thus avoiding the overfitting of UDNN. UDNN-LCCEL combines the advantages of two DNNs to obtain ensemble denoised results by ensemble learning. The biggest advantage of our proposed UDNN-LCCEL method is that it does not need to use noise-free data as label data, which can well solve the problem of missing training datasets. The synthetic and field data examples are used to demonstrate that UDNN-LCCEL can achieve good random noise suppression effectiveness.

By increasing the source density, the blended data can significantly improve the seismic data quality. However, the blended data cannot be directly used in the subsequent seismic processing process, and it is necessary to separate the useful signals from the crosstalk noise. For a high-density acquisition with the denser shot coverage survey (DSCS), we propose an unsupervised deep learning (UDL) method to directly deblend the blended data in the common shot gather (CSG). Both the useful signal and the crosstalk noise in the pseudo-deblended data (PDD) are continuously coherent in CSG. By minimizing the final total loss function, the similar coherent signals from the PDD of the main and second sources are extracted using the proposed UDL method. The UDL consists of two U-nets, which extract similar features from the PDD of the main and second sources in the training stage, and directly obtain the deblended results in the test stage. The original unblended data, which may be needed for supervised learning, are not available from the actual collected blended data. However, the proposed UDL method does not require the original unblended data as training data, which solves the lack of training data. The proposed UDL method can be applied to the CSG without providing the delay time and the blending operator, so it has more flexibility. Synthetic data and field data examples show that the proposed UDL method can effectively and directly deblend the blended data in CSG under DSCS.

One of the main objectives in the hydrocarbon reservoir characterization is determining rock and fluid properties that rely extensively on inference from seismic observations. In this letter, we present a novel Bayesian prestack inversion method using frequency-dependent amplitude versus offset (AVO) analysis with the goal to directly estimate gas saturation and porosity of a target thin reservoir zone. The proposed methodology is based on an improved Markov chain Monte Carlo (MCMC) sampling algorithm, which is computationally very coefficient due to its satisfactory acceptance probability and the convergence speed of Markov chains. Using a nonlinear rock physics model (RPM), properly calibrated for the investigating area, and a seismic forward operator based on the frequency-domain propagator matrix approach in the Bayesian inversion framework, we then evaluate the full posterior probability distribution of petrophysical parameters conditioned to seismic data and available prior information, using the MCMC algorithm in which we iteratively sample within the petrophysical property space. The proposed inversion approach is validated through applications to a synthetic reservoir model and the real seismic data from gas-bearing reservoirs with strong velocity dispersion.

Seismic spectral decomposition applications are often restricted to the magnitude component of time–frequency spectra because it has been very challenging to make a meaningful interpretation of the phase information. In seismically thin layers, nevertheless, phase decomposition can be useful for the enhanced delineation of subsurface lateral variations, as seismic phase singularities are believed to tightly relate to the geologic features and geofluid effects. In this letter, we introduce an improved phase decomposition approach based on a high-resolution complex-spectra decomposition technique for better thin reservoir characterizations. The proposed method is applied to decompose seismic responses into the various phase components that sum to reconstruct the original traces. Via assuming the 0° phase seismic data, results from the synthetic and physical modeling examples imply that reflection anomalies associated with reservoir hydrocarbons can be magnified on the specific phase components. This magnification thus allows the reservoir geofluid variations to be better discriminated from certain lithologic influences that also substantially affect the total seismic reflection amplitudes, which are otherwise buried in the broadband responses.

Studies of frequency dependence of seismic data anomalies on partially gas-saturated reservoir have been performed for many years. Essentially, the frequency-dependent seismic signature represents a potential and largely untapped source of information for the detections of subsurface target properties. Through analyzing the anomalous feathers of amplitude variations with the angle of incidence and frequency (AVAF), both theoretically and algorithmically, it is possible to discriminate hydrocarbon from variations in other reservoir properties. For a layered structure model, however, it can be challenging to employ the conventional Zoeppritz equation-based method that may not accurately describe complex reflections considering the effects of both the layered structure of a reservoir and the attenuative and dispersive property of rocks. We introduce a novel hydrocarbon detection approach based on Bayesian inversion of frequency- and angle-dependent reflection signatures from a tight gas sandstone reservoir having strong attenuation and velocity dispersion. The proposed inversion scheme employs the propagator matrix method as a description of seismic responses for the stratified model and spectral decomposition technique to obtain multifrequency amplitude information. The synthetic test and real application show the proposed inversion approach has the potential to be useful in detections of hydrocarbon accumulation.

Adaptive surface-related multiple subtraction is an important step of surface-related multiple elimination (SRME) method. Generally, the traditional methods match the predicted multiples with the original data using obtained filter. In this letter, we propose a matching algorithm based on convolutional neural network (CNN) to strike a balance between the attenuation of multiples and the protection of primaries. Taking the predicted surface-related multiples as input, CNN’s output can better match with the original data. From the processing results of synthetic data, compared with the traditional$L_{1}$-norm or$L_{2}$-norm method, CNN method has lower calculation cost and the signal-to-noise ratio (SNR) of the primaries obtained after matching and subtraction is increased by 3 dB. The test of Pluto data and physical simulation data show that the proposed method can effectively remove surface-related multiples in seismic data.

Internal multiple suppression remains a key challenge in seismic processing due to the tiny velocity and periodicity difference between primary reflections and internal multiples. Existing methods suppress internal multiples with poor adaptivity and efficiency. Internal multiple suppression based on artificial intelligence (AI) faces challenges about highly demanded computing resources and the lack of sufficient labels. This letter redesigns a convolutional neural network (CNN) scheme for internal multiple suppression in terms of training set construction and input strategy to alleviate these problems. We adopt the virtual event (VE) method to generate a few primary labels and develop an internal multiple augmentation strategy to expand the training set and improve the network performance based on small data set. The U-shaped CNN is trained based on augmented datasets and then applied to new seismic data. During the training and prediction process, the entire seismic data are split into vertical patches as network inputs for less computing resources and better demultipling performance. Tests on synthetic and field data demonstrate that our method effectively suppresses internal multiples and exhibits a competitive performance in comparison with existing methods and original demultipling CNN in efficiency, memory cost, and primary retention ability.

Predicting gas-bearing reservoirs in tight sandstone is significant but challenging. Although machine learning (ML), especially deep learning (DL) methods provide a potential for solving the issue, the major challenge of their application to gas-bearing prediction is how to generate accurate intelligent models with limited training sets. To relieve the notorious small-sample problem and the overfitting problem caused by limited well-log data, we propose the semi-supervised learning and transfer learning (SSL-TL) method for qualitative gas-bearing prediction. In the SSL-TL method, we first train the k nearest neighbor (kNN) classifier. And we choose the outputs with high confidence as the pseudo-training samples to extend the training sets of the convolutional neural networks (CNNs). Then, we pre-train the CNNs model with the pseudo-training samples, and subsequently introduce the transfer learning (TL) strategy to fine-tune the pre-trained CNNs model using the real training samples. Finally, we obtain a strong CNNs-based gas-bearing classifier. The TL strategy can make full use of the extended training sets while reducing the negative influence of the pseudo-training samples. We apply the SSL-TL method to a field data set with the limited wells. The test results show that the SSL-TL method has higher lateral continuity in gas prediction and agrees more with the known geological understanding in the studied field compared with the results of the CNNs models trained by other strategies.

Full waveform inversion (FWI) plays a central role in the field of exploration geophysics due to its potential in recovering the properties of the subsurface at a high resolution. A starting model with ample long wavelength components is essential for the success of most FWI algorithms. Reflection waveform inversion (RWI) is one popular way to invert for the long wavelength velocity components from the short offset seismic data by decomposing the gradient of FWI into migration and tomographic terms. However, the transmitted part of Born scattering in conventional RWI still produces high-wavenumber artifacts, which would hinder its convergence. Thus, in this letter, an efficient nontransmission energy norm Born scattering is used in RWI to overcome the drawbacks of conventional RWI. Finally, we use numerical examples to show that the energy norm Born scattering can provide clean reflection energy from the reflector and enhance the low-wavenumber information in the RWI gradient.

Phase reversal is an important feather that can often be observed in seismic amplitude variation versus offset (AVO) analysis. A proper description of phase shift behaviors from a reservoir with multiple pore-fluids, nevertheless, should consider influences of attenuation and velocity dispersion. We propose a novel method here for estimating phase reversals in cases where frequency-dependent attenuation and dispersion are present. Numerical results from the proposed method illustrate that there exist significant variations in terms of magnitude and phase of seismic reflections, between the elastic and anelastic cases. In particular, we observe a gradually continuous phase shift with the angle in place of a phase jump in the elastic model. Numerical results analysis of a frequency-dependent rock physics model indicates a change in gas saturation and fluid patch scale causes apparent impacts on the phase variations from waveform data using the Hilbert transform. The recognition of such phenomena from seismic AVO responses thus offers an obvious potential to strengthen our abilities of detecting hydrocarbon reservoirs. In addition, the proposed method may be of great importance to unconventional reservoir exploration and CO2changes monitoring in brine-filled reservoirs.

Seismic internal multiples are the key factors affecting the accuracy and reliability of velocity analysis and migration. The removal of internal multiples is a challenging direction. To effectively remove the internal multiples from the seismic data, we propose the unsupervised deep neural network (DNN) combined with the adaptive virtual events (AVEs) method. First, we use the AVE method to get the predicted internal multiples, which can calibrate the true internal multiples in the original data, also called the full wavefield data. Second, the unsupervised learning with the DNN is used as a nonlinear operator to minimize the difference between the estimated internal multiples and original data. The trained DNN can obtain the estimated internal multiples through the predicted internal multiples, thereby completing the suppression of the internal multiples. Since our proposed unsupervised learning is essentially an optimization process, it does not require true primaries as the label data to participate in the training process for the DNN. Therefore, our proposed method can deal with the problem of lack of training set and would have some good practical application value with low computational cost. The effectiveness and efficiency of our proposed method are verified through two sets of synthetic data and one land field data examples.

Reliable estimate of the anelastic attenuation factor- Q from seismic records is highly desirable for improving seismic resolution. However, the conventional equivalent- Q or horizontal interval- Q estimation ignores that Q-distribution should hold the same ability for the subsurface structure characterization as seismic data. To pursue an accurate Q-model, we propose a technique for joint reflectivity and structural interval- Q estimation by using nonstationary sparse inversion. We designed a structural interval- Q model by dividing the seismic data into several structural layers with the interpreted horizon(s). Attenuations in each layer are close to each other and can be described by an equivalent- Q or gradient- Q. Based on the attenuation theory, the nonstationary sparse inversion is solved iteratively, where, at each iteration, the equivalent- Q of only one layer is optimized by searching for the corresponding optimum inverted reflectivity, leading to a structural interval- Q model. The main advantages of our method are its objectivity and accuracy because of the integration of the prior structural information from interpreted horizons into joint reflectivity-estimation and Q-estimation. The test of synthetic and field data clearly illustrates that the proposed method enables high-precision structural interval- Q estimation and sufficiently compensates for Q-related attenuation.

Noise attenuation has been a long-standing but still active topic in seismic data processing. The deep convolutional neural networks (CNNs) have been recently adopted to remove the learned random noise from noisy seismic data, but it is still difficult to improve the generalization ability of learned denoisers due to the limited diversity of training data sets. In this letter, we investigate an end-to-end deep denoising CNNs (DCNNs) with a novel data generation method involving multidimensional geological structure features for seismic denoising. To learn an optimized network denoiser, seismic amplitude data are extracted from 3-D synthetic seismic data along three directions (i.e., two spatial directions and one temporal direction) to prepare a training data set. Compared with using seismic data from only a certain single direction to generate all training samples, this strategy enables DCNNs to learn abundant geological structural information from three directions, and helps DCNNs have a better performance on noise reduction. Another 3-D synthetic seismic data and 3-D real land data examples with plentiful faults and fluvial channels are used to illustrate that the optimized network denoiser can be directly extended to attenuate random noise. The denoising results demonstrate that DCNNs learned from the multidimensional geological structures can accomplish the self-adaptive random noise attenuation, and meanwhile preserve spatial geological structures.

Physical and/or economic constraints cause acquired seismic data to be incomplete; however, complete data are required for many subsequent seismic processing procedures. Data reconstruction is a crucial and long-standing topic in the exploration seismology field. We extended our previous works on deep learning (DL)-based irregularly and regularly missing 2-D data reconstruction to 3-D data. A key motivation is that the 3-D convolutional neural network (CNN) can take full advantage of the 3-D nature of the data, and the additional dimension allows more information to contribute to the data reconstruction. DL also avoids many assumptions (e.g., linearity, sparsity, and low-rank) limiting conventional nonintelligent reconstruction methods. We built an artificial neural network (ANN) based on an end-to-end U-Net encoder-decoder-style 3-D CNN. The ANN was trained on large quantities of various synthetic and field 3-D seismic data using a mean-squared-error (MSE) loss function and an Adam optimizer. We demonstrated that the developed 3-D CNN reconstruction method appears to outperform the 2-D CNN for 3-D restoration. We benchmarked the ANN's generalization capacity for recovery of irregularly and regularly sampled 3-D data on several typical seismic data sets, particularly those with high missing percentages or large gaps. An ANN trained with irregularly sampled data can be partly applied to regularly sampled cases. We investigated how a key parameter, i.e., the learning rate, can be experimentally determined. In the context of the presented examples, our methodology provided a substantial improvement over an open-source state-of-the-art rank-reduction-based approach in terms of data fidelity and efficiency.

Instantaneous seismic attributes are commonly used in assisting seismic interpretation and stratigraphy analysis. We compute the instantaneous seismic attributes using 1-D seismic traces and the corresponding quadrature (Hilbert transformed) traces. However, the 1-D seismic trace and the corresponding quadrature trace are sensitive to noise and seismic processing artifacts. To improve the lateral continuity of instantaneous seismic attributes, we propose to compute instantaneous attributes using multichannel seismic traces. Dynamic time warping (DTW) is used to align the seismic traces centered at the analysis point which mitigates the effect of structure dip on the multichannel complex seismic trace analysis (MCSTA). We fine interpolate the 1-D seismic traces to minimize the possible error in the computation of the error matrix of DTW. We also define a constraint in the backtracking of DTW to avoid severe strain (stretch or squeeze) between seismic traces. We obtain the “robust” 1-D complex seismic trace by applying Gaussian smoothing to the aligned complex seismic traces. We finally obtain instantaneous seismic attributes from the smoothed 1-D seismic trace and the corresponding quadrature trace. We show the superiority of new instantaneous attributes by applying our method to real seismic data.

It is an effective way in seismic imaging to make full use of lateral seismic response to break through the limitation of vertical resolution and to improve the accuracy of interpretation. On zero-crossing-time (ZCT) amplitude slices, there is a clearer imprint of underground beds than on non-ZCT slices, providing an important foundation for characterizing interbedded thin beds. However, picking ZCTs is time-consuming with significant manual efforts. In the assumption of horizontally layered media with lateral invariance, we deduce the variation of the cluster number on ZCT and non-ZCT slices with the number of thin beds. Furthermore, based on the statistical analysis on all cluster numbers of a 3-D seismic data set, ZCT, and non-ZCT slices are distinguished according to the difference of the cluster number. As a result, all ZCTs are picked automatically. Considering the influence of noise, the method provides the estimated values and the estimated intervals for all ZCTs to improve reliability. No label is required with this unsupervised learning method. The feasibility and practicability of the proposed method have been verified with numerical and real data experiments.

Normal moveout (NMO) correction is a routine step in seismic data processing, which has an important impact on other seismic processing procedures, seismic inversion, and interpretation. We propose a goal-oriented inversion-based NMO correction method using a convex l2,1-norm. The proposed method corrects the superresolution multichannel offset-dependent reflectivity rather than the bandlimited data itself sample by sample, block by block, or wavelet by wavelet. Therefore, the proposed method can essentially reduce the amplitude and even phase distortion introduced by data-based NMO correction methods in the presence of strong wavelet interference. We impose two goal-oriented constraints including both the temporal sparsity and the horizontal continuity of reflectivity, which are approximately represented by a convex l2,1-norm, on the geometric moveout relationship from offset-dependent trajectories to zero offsets to build a new objective function for NMO correction. The goal-desired temporal sparsity of reflectivity can induce the superresolution solution; meanwhile, the goal-desired horizontal continuity introduces a reasonable intrinsic structure to further limit the solution space and is particularly suitable to processing interfering reflections. Attributing to these two additional constraints, the new NMO correction method can flatten the interfering events and the intersecting events with favorable offset-dependent amplitude and phase variations even in the presence of noise. Synthetic and real data examples are adopted to verify the performance of our method. The results show that goal-oriented inversion-based NMO correction using the l2,1-norm is a potentially effective, stable, and high-quality NMO correction tool, especially for strong wavelet interference and at far offsets.

Inspired by image-to-image translation, we applied deep learning (DL) to regularly missing data reconstruction, aimed at translating incomplete data into their corresponding complete data. With this purpose in mind, we first construct a network architecture based on an end-to-end U-Net convolutional network, which is a generic DL solution for various tasks. We then meticulously prepare the training data with both synthetic and field seismic data. This article is implemented in Python based on Keras (a high-level DL library). We described the network architecture, the training data, and the training settings in detail. For training the network, we employed a mean-squared-error loss function and an Adam optimization algorithm. Next, we tested the trained network with several typical data sets, achieving good performances (even in the presence of big gaps) and validating the feasibility, effectiveness, and generalization capability of the assessed framework. The feature maps for a sample going through the well-trained network are uncovered. Compared with the f-x prediction interpolation method, DL performs better and is capable of avoiding several assumptions (e.g., linearity, sparsity, etc.) associated with conventional interpolation methods. We demonstrated the influences of the network depth, the kernel size of the convolution window, and the pooling function on the DL results. We applied the trained network to dense data reconstruction successfully. The proposed method can overcome noise to some extent. We finally discussed some practical aspects and extensions of the evaluated framework.

The deep exploration has become the focus of attention in the field of earth sciences. Coherence is a routine measure to identify structural and stratigraphic anomalies, such as faults, channels, and fractures in subsurface. However, deep seismic data typically suffer from a low signal-to-noise ratio and a weak reflection amplitude, thus it may not provide a better insight for seismic attribute analysis. The phase information has the ability to detect subtle changes in subsurface but it is sensitive to noise, thereby masking some stratigraphic features in the full-bandwidth data. To address these two issues, we propose a multispectral phase-based geosteering coherence method by combining coherence and spectral decomposition for deep stratigraphic feature characterization. The proposed method can effectively select and utilize the phase components of favorable spectral bands, which can detect different scale geologic discontinuities and reduce or avoid the effect of random noise in deep seismic data. Furthermore, corendering the coherence images of three different frequency components using red-green-blue blending can detect more geologic details in subsurface. The examples including 3-D physical modeling data and real seismic data set of carbonate reservoir from western deep formation are employed to demonstrate the effectiveness of the proposed method. The coherence attributes obtained from the proposed method can detect the weak or hidden geologic details clearer than the geosteering coherence calculated from the broadband seismic data, and it may serve as a future tool for detecting the distribution of geologic abnormalities in deep exploration.

Full waveform inversion (FWI) plays a central role in the field of seismic processing due to the advantage in recovering the properties of the subsurface from seismograms. However, it suffers from more local minima convergence and more serious nonlinearity than the conventional seismic inversion method mainly caused by the lack of low-frequency information in the seismic data or the low-wavenumber components in the starting model. In this letter, we present a novel technique for seismic FWI based the angle difference identity for cosine, which builds an internal connection between high- and low-frequency signals. Thus, we can use the high-frequency information to get a plausible recovery of the low-wavenumber velocity. In addition, we choose the amplitude-independent objective function, which is given by maximizing the cross correlation between the modeled and observed data, to deal with the imperfect amplitude matching in the real case. Finally, a synthetic example of SEG/EAGE salt model is employed to demonstrate the validity of the proposed method, when low-frequency signals are absent.

Time-frequency (TF) analysis is a useful tool for seismic data processing and interpretation. We introduce sparse Bayesian learning (SBL) to TF analysis and propose a new SBL-based high-resolution TF method. The method decomposes the seismic trace into a series of Ricker wavelets using SBL-based sparse representations and subsequently implements Wigner-Ville distribution (WVD) on the decomposed wavelets to produce TF spectra. By iteratively solving a Bayesian maximum posterior and a type-II maximum likelihood, SBL-based decomposition can sequentially obtain an optimal number of Ricker wavelets with different peak frequencies or phases from a preset wavelet dictionary, and can simultaneously invert for the associated sparse TF pseudoreflectivity with the prediction uncertainty. The WVD of SBL-based decomposed wavelets can assemble TF distribution of the reconstructed signals to approximately characterize WVD of the original data. Therefore, the linear stack of WVD of all decomposed independent wavelets is immune from both the notorious cross-term interferences of the traditional WVD and random noise. Synthetic data example involving thin beds and laboratorial physical modeling data example involving several known multicave combinations are used to demonstrate the effectiveness of the proposed SBL-based TF analysis method and illustrate its advantages over WVD and the orthogonal matching pursuit-based TF analysis method. The 3-D real seismic data example is adopted to test its application potential for interpreting deep channels and the karst slope fracture zone. The results show that the proposed SBL-based TF method is a potentially effective, stable and high-resolution seismic TF analysis tool even in the presence of thin beds.

Previous studies have demonstrated that P-wave velocity dispersion at seismic frequencies is often related to hydrocarbons, which results in frequency-dependent P-wave reflection coefficients. This effect is neglected in the conventional amplitude-versus-angle (AVA) inversion, or reduced in most AVA inversion involving seismic dispersion due to the linearization of either the forward modeling or the inversion objective function. As a consequence, there are times when nonnegligible error exists in the inverted dispersion-associated result, which is probably nonnegligible in some cases. In this letter, we adopt the propagator matrix forward modeling derived from the wave equation and the particle swarm optimization (PSO)-based inversion to solve the uncollapsed objective function to avoid any linearization operator at the cost of probably more computational complexity and inversion ill-posedness. To address the ill-posedness, in both the forward modeling and inversion, we introduce rock-physics constraints of frequency-independent S-wave velocity and limited variations of P-wave velocity with frequency. Furthermore, we statistically derive the average frequency-dependent P-wave velocity attribute, the P-wave velocity dispersion intensity attribute, and the characteristic frequency attribute corresponding to the maximum velocity dispersion gradient from multiple experimental inverted dispersive P-wave velocity results. These attributes can be directly applied to detect hydrocarbons. A synthetic data example and a real data example through a drilling well are used to demonstrate that PSO-based prestack stochastic inversion method with rock-physics constraints is effective, and that the statistical attributes derived from the multiple inverted dispersive P-wave velocities can be utilized to favorably indicate gas reservoirs.

Traditional 1-D instantaneous phase (IP) is a routine attribute for detecting structural discontinuities of seismic images. The phase attribute has the ability to detect subtle changes, but it is meanwhile sensitive to noise. Furthermore, the traditional IP attribute is calculated trace by trace and thus cannot effectively utilize geological constraints. The sensitivity of noise and unavailability of geological constraints limit the practical applications of IP attributes. To address these two issues, this letter proposes a 3-D geosteering phase attribute derived from IP. At first, we implement the local stack on IP traces along both the time direction and the trajectory direction of the events to construct new stacked phase traces. Then, we compute the covariance of neighboring stacked phase traces along different spatial directions and extract the directional phase information from the resulting complex-valued covariance. Finally, we derive the so-called geosteering phase attributes by taking the maximal value among the extracted directional phases to approximately characterize the discontinuity measurement perpendicular to the structural trend in a 3-D curved plane. The examples including 3-D synthetic, physical modeling, and real seismic images are adopted to demonstrate the effectiveness of the proposed geosteering phase attributes. The results illustrate that the new geosteering phase attributes can be used as an effective and robust tool for the automatic detection of faults, channels, and even large-scale fracture groups.

At seismic and sonic frequencies, the major cause of wave attenuation and dispersion in fluid-saturated rocks might be the wave-induced fluid flow on microscopic and mesoscopic scales. However, it is challenging to assess these effects as the attenuation mechanisms related to both heterogeneities that cannot be expected to be independent. This is due to the fact that, fluid flow taking placing at the mesoscopic scale may be impacted by squirt flow mechanism in the presence of microscopic heterogeneities via modifying the dry rock to be frequency-dependent complex moduli. Understanding the integrated effects, related to microscopic squirt flow and wave-induced fluid flow of mesoscopic heterogeneities, would be important for quantifying the relative contribution of the interdependent energy loss mechanisms. We introduce a procedure in this letter to estimate the frequency-dependent seismic attenuation and dispersion by considering the combined presence of microscopic and mesoscopic heterogeneities. The corresponding seismic reflections of a finely stratified model with a dispersive reservoir are calculated using a propagator matrix method in the frequency domain to study the sensitivity of seismic signatures to pore-fluid mobility and rock heterogeneities.

Regardless of successful applications of the convolutional neural networks (CNNs) in different fields, its application to seismic waveform classification and first-break (FB) picking has not been explored yet. This letter investigates the application of CNNs for classifying time-space waveforms from seismic shot gathers and picking FBs of both direct wave and refracted wave. We use representative subimage samples with two types of labeled waveform classification to supervise CNNs training. The goal is to obtain the optimal weights and biases in CNNs, which are solved by minimizing the error between predicted and target label classification. The trained CNNs can be utilized to automatically extract a set of time-space attributes or features from any subimage in shot gathers. These attributes are subsequently inputted to the trained fully connected layer of CNNs to output two values between 0 and 1. Based on the two-element outputs, a discriminant score function is defined to provide a single indication for classifying input waveforms. The FB is then located from the calculated score maps by sequentially using a threshold, the first local minimum rule of every trace and a median filter. Finally, we adopt synthetic and real shot data examples to demonstrate the effectiveness of CNNs-based waveform classification and FB picking. The results illustrate that CNN is an efficient automatic data-driven classifier and picker.

Seismic data are increasingly required to be high quality for the continuous improvement of the degree of exploration. From the viewpoint of inversion, the utilization of more information is an effective way to improve the signal-to-noise ratio of seismic data. In this letter, we adopt simultaneous sparsity constraints of the first-order differences of signals along the time direction and two spatial directions, described by minimizing the Cauchy function, as a combined constraint (or regularization) term imposed on the time-domain data misfit to propose an inversion-based 3-D seismic denoising method. In this way, the redundancies among time slices and seismic sections along two spatial directions are simultaneously considered, and the edges along the spatial directions can be preserved. Through analyzing the first-order derivative of the sum of the data misfit term and the designed combined regularization term (or the objective function), we derive that the relationship between data and desired signal samples in the range of the first-order neighborhood can be expressed as a linear system with seven data-dependent coefficients. Furthermore, it can be inferred that the sparsity constraints of signal differences along different dimensional directions of 3-D data have some complementary functions of noise reduction and signal preservation. We use a 3-D synthetic data set, a 3-D real poststack data set, and a 3-D real prestack data set to determine that the proposed method is an effective amplitude-preservation denoising tool with an acceptable computational cost.

Attenuating random noise is a fundamental yet necessary step for subsequent seismic image processing and interpretation. We introduce a sparse Bayesian learning (SBL)-based seismic denoise method by using the physical wavelet as the basis function. The physical wavelet estimated from seismic and well logging data can appropriately describe the characteristics of the seismic data. Thus, it is an appropriate choice of basis function. Moreover, the tradeoff regularization parameter for determining denoise quality can be adaptively estimated according to the updated data misfit and sparseness degree during the iterative process of the SBL algorithm. The motivation behind the denoise method using sparse representations is that seismic signals can be sparsely represented by using several physical wavelets, whereas noise cannot. Both synthetic and real seismic data examples are adopted to demonstrate the effectiveness of the method.

In seismic exploration, the wavelet-filtering effect and Q-filtering (amplitude attenuation and velocity dispersion) effect blur the reflection image of subsurface layers. Therefore, both wavelet- and Q-filtering effects should be reduced to retrieve a high-quality subsurface image, which is significant for fine reservoir interpretation. We derive a nonlinear time-variant convolution model to sparsely represent nonstationary seismograms in time domain involving these two effects and present a time-variant deconvolution (TVD) method based on sparse Bayesian learning (SBL) to solve the model to obtain a high-quality reflectivity image. The SBL-based TVD essentially obtains an optimum posterior mean of the reflectivity image, which is regarded as the inverted reflectivity result, by iteratively solving a Bayesian maximum posterior and a type-II maximum likelihood. Because a hierarchical Gaussian prior for reflectivity controlled by model-dependent hyper-parameters is adopted to approximately represent the fact that reflectivity is sparse, SBL-based TVD can retrieve a sparse reflectivity image through the principled sequential addition and deletion of Q-dependent time-variant wavelets. In general, strong reflectors are acquired relatively earlier, whereas weak reflectors and deep reflectors are imaged later. The method has the capacity to avoid false artifacts represented by sequential positive or negative reflectivity spikes with short two-way travel time, which typically occur within stationary deconvolution outcomes. Synthetic, laboratorial, and field data examples are used to demonstrate the effectiveness of the method and illustrate its advantages over SBL-based stationary deconvolution and TVD using an l2-norm or an l1-norm regularization. The results show that SBL-based TVD is a potentially effective, stable, and high-quality imaging tool.