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.

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.

Seismic inversion can be used to invert the subsurface acoustic impedance leveraging migrated seismic section, which can help lithology interpretation. It is not easy to predict impedance directly from post-stack seismic data. In the field data, the interference of random noise aggravates the difficulty of impedance inversion. Previous work mainly focused on trace-by-trace strategy leading to poor lateral continuity. We propose a two-dimensional (2D) temporal convolutional network (TCN)-based post-stack seismic low-frequency extrapolation and a TCN-based impedance prediction method. We use a two-step workflow for acoustic impedance prediction from post-stack seismic data. First, we use a neural network (LE-Net) for the low-frequency extrapolation of seismic data, and then we use another neural network (AI-Net) to predict acoustic impedance. The input to LE-Net is high-frequency band-limited seismic and low-frequency impedance data. Seismic data after low-frequency extrapolation and low-frequency impedance are used to predict impedance. 2D TCN and multi-trace input data can introduce spatial information from surrounding traces. The output of the network is single-trace data. The proposed network can ensure the single-trace prediction accuracy and improve lateral continuity. Numerical experimental results show that our proposed two-step workflow, named AI-LE, performs well on Marmousi II and has a certain generalization on the SEAM model. The results on field data show that AI-Net can predict relatively accurate impedance. The low-frequency extrapolation of seismic data can help improve the performance of impedance prediction.

The well-known cycle-skipping problem in full-waveform inversion (FWI) can make the iterative solution fall into local minima and produce an undesired inverted result when reliable low-frequency components in seismic data and a good initial model are not available. The recovery of low-frequency data can effectively solve the cycle-skipping problem. However, hardware limitations have made it difficult to obtain reliable low-frequency components in seismic data. Thus, we adopt a multiscale and cross-scale convolutional neural network (MCCNN) to build the nonlinear mapping between high-frequency and low-frequency data from synthetic training datasets. The major benefit of MCCNN is that it can fully use the multiscale and cross-scale information in the high-frequency data to predict the low-frequency data. Several numerical experiments show the effectiveness and benefits of the low-frequency recovery of MCCNN. On one hand, introducing the in-stage multiscale and across-stage cross-scale information can accelerate the convergence rate in the training process and improve the low-frequency prediction accuracy. On the other hand, MCCNN has good generalization abilities in predicting the low-frequency data from the Marmousi and overthrust models, different model sizes, and wavelet types and frequencies. The acoustic FWI results show that the predicted low-frequency data can effectively prevent the inversion from falling into a local minimum and help FWI obtain an accurate velocity model even if we start from a poor initial model.

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.

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.