The attenuation of seismic field noise using self-supervised deep learning has gained attention due to its label-free training process. However, common self-supervised methods are limited by the pixelwise independence assumption, which does not align with field seismic noise characteristics, and suffer from signal leakage due to receptive fields containing inherent blind spots or traces. In this paper, we propose a self-supervised random noise attenuation method based on the non-pixelwise independence assumption. By considering the spatial correlation map of field noise, we extend the blind spot to a generalized blind neighborhood, ensuring that the prediction pixel is not influenced by neighboring pixels with noise correlation greater than zero. The blind neighborhood size controls how much spatial correlation is disrupted, allowing our method to handle random noise with varying spatial correlation. Since larger blind neighborhoods may lead to signal loss, we introduce an automatic trade-off between noise correlation disruption and signal preservation during training. Experiments on real seismic noise attenuation (including random and tracewise coherent noise) demonstrate the superiority of our method in destroying the spatial coherence of noise and preventing useful signal leakage.

Sedimentary cycles are the fundamental building blocks of sedimentary sequences, resulting from the superposition of periodic sedimentary events at different scales. Seismic reflection data contain multiscale sedimentary cycle information in the subsurface. Accurate extraction multiscale sedimentary cycle information from seismic data is key to realizing multiscale sequence stratigraphy analysis. This article proposes a workflow for multiscale sedimentary cycle characterization by combining variational mode decomposition (VMD) and synchrosqueezing optimal basic wavelet transform (SOBWT) methods. The workflow first derives the relationship between different-scale sedimentary cycles and their reflectivity amplitude spectrum and proposes a method for determining the number of intrinsic mode functions (IMFs) and center frequencies parameters of VMD. Subsequently, VMD is employed to decompose the different-scale seismic reflection from seismic data. Further, SOBWT and ridge extraction methods are introduced to extract instantaneous dominant frequency attributes from IMF profiles to characterize different-scale sedimentary cycles and to divide sedimentary cycle units. Applications on synthetic and field data demonstrate that the proposed workflow can effectively separate seismic reflection characteristics of different-scale sedimentary cycles from seismic data. The instantaneous dominant frequency attributes proposed based on SOBWT and ridge extraction methods can effectively characterize the thin bed thickness variation of different-scale sedimentary cycle and can assist in sedimentary cycle unit identification. This provides an important tool for subsequent sequence stratigraphy research.

Usually, inverse problems are ill-posed. The solution to the inverse problem is indeterminate, meaning that for given observational data, there may be multiple possible solutions. It is not sufficient to give a definite solution to common seismic inverse problems. In this study, we provide stochastic solutions for seismic inverse problems (denoising and reconstruction). We sample a range of possible and high-quality solutions for a given observation with various degradations from the posterior distribution through Langevin dynamics with conditional score function, all shown to be reasonable results; for example, the stochastic solutions we sampled may contain as many geological structures of interest to the expert as possible. Experimental results on synthetic and field data verify the superiority of posterior sampling. In particular, our method has obvious advantages over other methods, such as traditional and (supervised, self-supervised, and unsupervised) deep learning (DL) methods, especially in denoising under extremely low signal-to-noise ratio (SNR) and reconstruction for data with consecutively missing traces and noise. We also analyze the advantages of our approach and concluded that successful generative modeling of seismic data by the score-based generative models (SGMs) is the key to posterior sampling for the inverse problems, which all benefit from the seismic data prior implicit in the trained score network in the SGM.

High-dimensional time-frequency (TF) transforms are essential tools in seismic data processing. However, commonly used transforms such as Ridgelet, Curvelet, and Contourlet exhibit limitations in time-shifting invariance and basis function selection, which impacts on their effectiveness in seismic data analysis. To address these limitations, this study introduces optimal basic wavelet (OBW)-Ridgelet, a novel approach integrating the OBW with the Ridgelet transform. By combining OBW with Ridgelet, this method aims to enhance the TF localization for seismic structural analysis and time-shifting invariance property. We also present a workflow for seismic discontinuity detection, employing the C3 algorithm to the decomposed seismic data to get multiscale coherence and introduce the similarity coefficient for scale selection of the multiscale coherence. Synthetic and field data examples demonstrate the effectiveness and robustness of the proposed method, yielding promising results for seismic signal interpretation. The integration of OBW-Ridgelet enriches the toolkit for seismic signal analysis and holds the potential for refining seismic feature detection and interpretation in practical applications.

Improving the resolution of nonstationary reflection seismic data without well data is challenging, as it requires prior estimation of the$Q$-value. The coupling of reflectivity sequence and wavelet introduces spectral fluctuations, rendering the extraction of$Q$highly unstable. While some statistical wavelet amplitude estimation methods, such as spectral shaping (SS) and contraction operator mapping (COM), can yield smooth wavelet amplitude spectra, they do not contribute to$Q$analysis as they lack a physical mechanism for absorption attenuation. Therefore, we propose an absorption-constrained wavelet power spectrum inversion (AWPSI) method based on the segmented stationary convolution model (SSCM). The absorption constraint (AC) term incorporates prior knowledge of the medium’s$Q$-effect and enables simultaneous inversion of wavelet amplitude spectra for all windows. Incorporating AWPSI into COM and SS methods leads to AWPSI-COM and AWPSI-SS methods, which yield higher precision wavelet power spectra and remove the spectral fluctuations caused by reflectivity sequences. We demonstrate that AWPSI enables COM to extract wavelet amplitude spectra more accurately while preserving the attenuation characteristics caused by$Q$-effect. Using the equivalent$Q$field obtained by the AWPSI-COM method, an inverse$Q$-filter can be performed to generate accurate high-resolution seismic profiles. Synthetic and actual stacked seismic data verify the effectiveness of the proposed method.

Recovering the useful signal from seismic field data is critical in seismic data processing. Seismic field data are usually coupled by a useful signal and field noise (random noise with unknown distribution), making them difficult to decouple. Unfortunately, subject to the assumption biases of data prior and noise prior, different random noise attenuation methods may have different performance biases. Suppose data-driven supervised deep learning methods have plenty of labeled [real noisy(field), clean(useful)] data pairs. In that case, they will learn useful information from the labeled dataset and relax the biases of the data-prior and noise-prior assumptions. To this end, we first use the invertible Neural Network (INN) to disentangle the field data in observational space into the latent variable in latent space. Then, by manipulating the latent variable’s partitions encoding high- and low-frequency information, INN can generate quality-controlled fake field data and decouple useful signal and field noise parts from field data in its backward pass. To gain decoupling and generative capabilities, the training of our INN only requires a relatively small labeled dataset containing field-useful data pairs. Sampling in latent space, the trained INN can generate an infinite number of paired [fake-field, useful] samples. Experiments show that our method can effectively decouple useful signal and field noise, and the noise of the fake field data is close to field noise. The generated paired dataset can benefit downstream tasks such as field noise attenuation.

Random noise attenuation is a critical step in seismic data processing. Since the distribution of field noise is complex and unknown, this poses a challenge to noise attenuation methods where the default noise distribution is known, such as a Gaussian distribution. To address this issue, we propose a method called Seismic Random Noise Gaussianization Framework (SRNGF) to attenuate random noise with unknown distribution. Specifically, SRNGF couples the Gaussianization subproblem and Gaussian denoising subproblem based on the Plug-and-Play (PaP) framework. The Gaussianization submodule with learnable parameters maps seismic data with the noise of unknown distribution to the one corrupted by Gaussian noise. The learnable parameters can be updated through unsupervised online training according to the noise of the unknown distribution on a single field data. The gaussian denoising submodule, which can be replaced by seismic denoiser, aims only for Gaussian noise removal, making SRNGF incorporate the denoiser prior for seismic data. Thus, we incorporate different kinds of seismic (non-deep/deep learning (DL)) denoisers into SRNGF and give their corresponding implementations of SRNGF. Experiments on noise with unknown distribution qualitatively and quantitatively validate the superiority of SRNGF. SRNGF improves the results of non-DL/DL seismic denoiser by a large margin.

The frequency-dependent amplitude-versus-offset (FAVO) method has great potential for reservoir parameters estimation. However, it is hard work to establish the FAVO inversion model. It is also difficult to solve the inverse problem for FAVO by traditional methods. In this paper, we propose a new workflow to extract the reservoir fluid parameters from the FAVO gathers based on a deep neural network (DNN). The proposed method is applied to predict the tight sandstone gas reservoir properties. Within the framework of this workflow, we generate the synthetic FAVO gathers. First, we establish the petrophysical model using the logging interpretation results. Then, the Backus average, Biot-Gassmann fluid substitution, velocity dispersion equations of the binary medium, and Rüger equation are applied to generate the FAVO reflectivity series. By introducing the DNN-based seismic wavelet estimation method and the optimal basis wavelet transform (OBWT), we can generate different frequency components of the seismic wavelet. These different frequency components are used to convolve the FAVO reflectivity series to obtain FAVO gathers that are used to generate the sample pairs for DNN training. At the same time, the OBWT is used to decompose the real AVO gathers to get the FAVO gathers. Finally, to testify its validity and effectiveness, the proposed workflow is applied to synthetic and field data.

The time-frequency (TF) analysis (TFA) tools are usually used to analyze the seismic reflection signals to assist the sedimentary cycle division. The high-resolution TFA results are beneficial to characterize the dominant frequency changes caused by the variations of the stratum thickness. The multisynchrosqueezing transform (MSST) is an iterative version of the synchrosqueezing transform (SST), which provides a more concentrated TF representation than the SST. So, the MSST is suitable for the sedimentary cycle characterization. However, it is a hard task to construct an appropriate basic wavelet. In this study, by combining the MSST and optimal basic wavelet (OBW), we proposed a multisynchrosqueezing OBW transform (MSOBWT) to help the sedimentary cycle division. The proposed method first defines the dominant frequency location condition (DFLC) that ensures the MSST to reassign the TF spectrum to the dominant frequencies position. Further, the OBW is introduced to construct the basic wavelet that satisfies the DFLC. Finally, the synthetic traces and field data are used to testify its effectiveness for the sedimentary cycle division.

Random noise attenuation is a key step in seismic field data processing. With the rise of artificial intelligence, deep learning (DL) algorithms are gradually introduced into seismic random noise suppression. The most commonly used DL paradigm takes mean squared error (MSE) as loss function, the default assumption is that its error term obeys independently identically distribution (IID) Gaussian, and its noise level involved preset-hyperparameters in the local area of data cannot be adjusted adaptively in the training phase. This leads to the poor generalization of deep denoiser on Non-IID noises. In this study, we propose a deep learning framework based on Non-IID pixel-wise Gaussian noise modeling, which integrates noise attenuation and noise level estimation into a unique Bayesian framework. The framework can adaptively characterize the noise and data distribution in the local area of noisy data through the variational inference (VI) technique, which allows the network to see more noises of varying degrees and learn effective information from them. Thus, our proposed framework called VI-Non-IID inclines to have better noise characterization and generalization capabilities, which brings better performance on seismic field noise attenuation. Furthermore, we conduct a series of experiments on seismic synthetic and field data to test the performance of two implementations of VI-Non-IID: VI-Non-IID(Unet) and VI-Non-IID(DnCNN). A lot of results validate the superiority of our proposed VI-Non-IID framework. Specifically, VI-Non-IID can explicitly predict the denoised data and its corresponding noise level map simultaneously, and succeed in attenuating unknown field noises while preserving the useful seismic signals.

Sedimentary cycle division is an important step for sequence stratigraphy analysis. For the division of sedimentary cycle using seismic data, a key issue is characterizing the changes of dominant frequencies caused by the changes of stratum thickness with high accuracy and high resolution. The synchrosqueezing transform (SST) can provide a time–frequency (TF) representation with high resolution by synchrosqueezing the TF spectrum, which helps the sedimentary cycle identification. Unfortunately, it is a hard task to choose an appropriate basic wavelet, which influences the accuracy of the SST to characterize the sedimentary cycle. To solve this issue, we construct a synchrosqueezing optimal basic wavelet transform (SOBWT) to optimally characterize the sedimentary cycle. We first propose a criterion to construct the basic wavelet of SST by deriving the dominant frequency location condition and defining the similarity coefficient condition of the basic wavelet. Then, we introduce the optimal basic wavelet (OBW) to construct the basic wavelet that satisfies the dominant frequency location condition and the similarity coefficient condition. Note that we term the SST with a basic wavelet that satisfies the dominant frequency location condition and the similarity coefficient condition as the SOBWT. Finally, we apply the proposed SOBWT to synthetic and field data to testify its validity and effectiveness and compare it with conventional SST-based methods. The application results illustrate that it is much more convenient and easier for the sedimentary cycle division based on the SOBWT results.

Continuous wavelet transform (CWT) is often used to extract the peak frequency attribute for characterizing the thin-bed thickness. Good joint time-frequency (TF) resolution is beneficial for the extraction of peak frequency. However, due to the Heisenberg’s uncertain principle, the time and frequency resolution of CWT cannot be obtained simultaneously. In this paper, combining the adaptive superlet transform and the optimal basic wavelet, a super-resolution optimal basic wavelet transform (SROBWT) is proposed to obtain the best joint TF resolution. The optimal basic wavelet matching the seismic wavelet is constructed as a basic wavelet of the adaptive superlet transform. Herein, taking the best joint TF resolution of the seismic wavelet as the target, a parameter selection method is proposed for the adaptive superlet transform. Furthermore, based on the proposed SROBWT and wedge model, a workflow is proposed to characterize the thin-bed thickness. The synthetic and field seismic data are employed to demonstrate the validity of the proposed methods. All the corresponding results show that the SROBWT has a better joint TF resolution than the conventional methods and the proposed workflow can correctly characterize the spatial variation of the thin-bed thickness, which is beneficial for further sediment sources analysis and reservoir prediction.

Wavelet and reflectivity inversion (WRI) is an important issue in seismic data processing. To overcome the ill-posedness of WRI inversion with more efficient parameter selection and better lateral continuity of reflectivities, we propose a new WRI algorithm named compact smoothness and relative sparsity (CSRS) algorithm, where a normalized compact constraint and a normalized smooth regularization is proposed for the wavelet inversion, and a relative sparsity constraint is proposed for the reflectivity inversion. The proposed constraints and regularization make the parameters of WRI easy to be selected. The proposed relative sparsity constraint can lead to a reflectivity profile with good lateral continuity as it can be suitable for various seismic data with a fixed sparsity parameter. We also propose an efficient algorithm for solving corresponding WRI optimization problem. The whole WRI problem is divided into reflectivity inversion subproblem and wavelet inversion subproblem by using alternating iterative method, where the initial wavelet is estimated by smoothing the absolute amplitude spectrum of averaged seismic data. The proximal algorithm is applied to solve both reflectivity inversion subproblem and wavelet inversion subproblem. By replacing Toeplitz matrix multiplication with fast Fourier transform (FFT) and using compact wavelet, our algorithm can be efficient for 3D seismic data. The numerical examples on 2D synthetic data, 2D offshore field data and 3D onshore field data demonstrate that, compared to Toeplitz-sparse matrix factorization (TSMF) algorithm, the CSRS algorithm with fixed default parameters can get high-resolution reflectivities with better lateral continuity, and requires much less computational time.

Continuous wavelet transform (CWT) is an effective tool for seismic time-frequency (TF) analysis. Selecting a matched wavelet to the analyzed seismic wavelet is a key issue for accurately characterizing TF features of seismic data. The three-parameter wavelet (TPW) can match different seismic wavelets by adjusting the three parameters. However, it is difficult to select appropriate parameters for matching TPW to seismic wavelets in real applications. In this letter, we propose a basic wavelet construction method by using the TPW and the deep learning network. The proposed workflow first builds a mapping relationship between seismic wavelet and seismic data by using the alternating iterative deep neural network (AIDNN). Based on this relationship, we then estimate a seismic wavelet. Using the estimated seismic wavelet, we can finally construct an analytical basic wavelet by matching the TPW to the extracted wavelet. Note that we named the TPW with optimal parameters as the optimal basic wavelet (OBW), and its wavelet transform is OBWT. To demonstrate the validity and effectiveness of the proposed approach, we apply it to synthetic traces and field data for characterizing their TF features. The results show that OBWT preserves the amplitude better and has a higher resolution than the CWT with mismatched basic wavelets to the seismic wavelet, which is helpful for seismic data analysis in the future.