Seismic instantaneous frequency (IF), as one of the instantaneous attributes, is widely used for seismic interpretation and stratigraphy analysis. The Hilbert transform (HT)-based complex analysis approaches are commonly used to extract seismic IF, which are sensitive to kinds of noise contained in field data. Although the normalized HT (NHT) improves the antinoise property of HT by normalizing the original trace, the HT-based methods are a global operator that is not suitable for the local analysis. For example, IF calculated by using the HT-based method is unstable when meeting strong seismic events. In this letter, we propose a workflow to extract local IF (LIF) and then apply it to describe superposed sands. Note that the proposed workflow extracts a stable IF result even when processing a seismic trace with strong events. To demonstrate the effectiveness of the proposed workflow, we apply it to both synthetic and field data. Compared with results from HT and NHT, the proposed workflow provides a stable IF extraction and offers potentials in precisely highlighting superposed sands.

The convolutional model, which describes the relation among poststack seismic data, wavelet, and reflectivity, is the foundation of seismic deconvolution (SD). However, this model is only an approximation of the seismic wave equation, and it may not work in complex cases especially when the medium is anelastic, heterogeneous, and anisotropic. In this article, we propose a generalized convolutional model for poststack seismic data. A deep-learning-based data correction term is added to characterize the data ingredients that cannot be characterized by the convolutional model. The data correction term of the new model is realized using the long-short term memory (LSTM)-based deep learning architecture, of which parameters are learned based on the dataset from several well logs. Based on the new model, we propose an SD method and investigate its performance in building reflectivity models using complex numerical examples. The results verified that the new model can accurately characterize complex seismic data, which cannot be characterized by a convolutional model. In addition, the proposed SD method has significant advantages over traditional methods in building high-fidelity reflectivity models in complex cases.

Time-frequency analysis (TFA) is a powerful tool for describing time-frequency (TF) features of seismic data, such as short-time Fourier transform and S-transform. Recently, sparse time-frequency analysis (STFA) is proposed for enhancing TF readability of commonly used TFA tools. However, STFA is often solved via an optimal inverse problem with a prior regularization term, which is difficult to set in practice, where the key regularization parameters are sensitive to noise. Moreover, it often takes expensive calculation time, especially for 3D field data application. We build a deep learning based workflow for implementing STFA to obtain sparse time-frequency (STF) spectra, termed the sparse time-frequency network with transfer learning (STFNTL). We first adopt a Marmousi II reflectivity model and Ricker wavelets with different dominant frequencies to generate synthetic training data set. Then, we adopt a simplified STFA method with optimized parameters to generate synthetic training labels, i.e., sparse TF spectra. Afterward, we propose the sparse time-frequency network (STFN) based on a simplified Unet model, which is trained using synthetic training data and corresponding STF labels. Moreover, to enhance the generalization of STFN, we introduce an adaptive transfer learning strategy based on small samples of field data and their corresponding STF labels. Finally, synthetic and field data are utilized to illustrate the effectiveness and generalization ability of our proposed model.

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.

The data-consistency item is a necessary condition for a reliable solution to the inverse problem. However, the current supervised-based deep-learning reconstruction approaches generally lack the data-consistency item, which directly leads to unreliable subsurface images for field data. To resolve this problem, we have developed a consistent least-squares reverse time migration (CLSRTM) approach using convolutional neural networks (CNNs), which is referred to as CNN-CLSRTM. The key point is that we have enforced that the predicted recording via the inverted image from the CNN model is consistent with the observed recording in the least-squares sense. We utilize the standard reverse time migration (RTM) image of single-shot recording as the input of the constructed CNN model. As a result, the optimal reflection image can be obtained by iteratively updating the parameters of CNN by minimizing the data residuals. Benefiting from the similarity of RTM images of adjacent recordings and the representation ability of the well-trained CNN model, we can directly predict the optimal reflection image for the testing datasets in a very fast way, which can greatly improve computational efficiency. Through synthetic and field data sets, we have determined that the proposed CNN-CLSRTM approach can retrieve high-resolution images with balanced amplitudes and continuous events. At the same time, our approach has better antinoise ability inherited from the benefit of CNN model compared to the standard LSRTM approach. In addition, we analyze the generalization ability of the CNN model for synthetic and field datasets.

Noise attenuation is a very important step in seismic data processing, which facilitates accurate geologic interpretation. Random noise is one of the main factors that lead to reductions in the signal-to-noise ratio (SNR) of seismic data. It is necessary for seismic data, including complex geological structures, to develop a number of new noise attenuation technologies. In this article, we concern with a new variational regularization method for random noise attenuation of seismic data. Considering that seismic reflection events often have spatially varying directions, we first employ the gradient structure tensor (GST) to estimate the spatially varying dips point by point and propose the structure-oriented directional total generalized variation (DTGV) (SODTGV) functional. Then, we employ the SODTGV as a regularizer to establish an ℓ2-SODTGV model and develop the primal-dual algorithm for solving this model. Next, the choice of the model parameters is discussed. Finally, the proposed model is applied to restore noisy synthetic and field data to verify the effectiveness of the proposed workflow. For contrastive methods, we select the structure adaptive median filtering (SAMF), anisotropic total variation (ATV), total generalized variation (TGV), DTGV, median filtering, KL transform, SVD transform, and curvelet transform. The synthetic and real seismic data examples indicate that our proposed method can preferably improve the vertical resolution of seismic profiles, enhance the lateral continuity of reflection events, and preserve local geologic features while improving the SNR. Moreover, the proposed regularization method can also be applied to other inverse problems, such as image processing, medical imaging, and remote sensing.

Coherence algorithm is widely used to describe geological discontinuity and subtle features of seismic data. Traditional coherence algorithms often use the linear correlation measurement to measure the relationship between two seismic traces. It does not work well because seismic data do not obey the normal distribution. To describe the coherence measurement of seismic data, we propose an improved coherence algorithm by combining the mutual information (MI) and third-generation coherence (C3) algorithm. The MI is a measurement of the general dependence and used to describe nonlinear relationships between two variables. Note that, the MI does not require that variables obey specific distribution (e.g., the normal distribution). Note that, we calculate precise MI values using the copula function. In addition, we introduce the information divergence to save calculation time by replacing the eigenvalue decomposition of the C3 algorithm. To demonstrate the effectiveness of the proposed algorithm, we apply it to field data. Field data experiments demonstrate the effectiveness of the proposed algorithm to describe geological discontinuity and heterogeneity, such as channels with different thicknesses.

Achieving a proper time-frequency (TF) resolution is the key to extract information from seismic data using TF algorithms and characterize reservoir properties using decomposed frequency components. The generalized S-transform (GST) is one of the most widely used TF algorithms. However, it is difficult to choose an optimized parameter set for the whole seismic data set. In this paper, we propose to set the parameters of the GST adaptively using the instantaneous frequency (IF) of seismic traces. Our workflow begins with building a relationship between the parameter set of the GST and IF using a synthetic wedge model. We use the IF as an indicator for the time thickness of each trace in the wedge model. We then compute the TF spectrum of each trace using the GST with different parameter sets and compare the similarity between the computed TF spectrum and theory TF spectrum. The parameter set with the largest similarity is regarded as the best parameter set for each trace in the wedge model. In this manner, we build a relationship between the parameter set and IF value. We can finally choose the optimum parameter set for the GST according to the IF values of seismic traces. We name the proposed workflow as the self-adaptive GST (SAGST). To demonstrate the validity and effectiveness of the proposed SAGST, we apply it to synthetic seismic traces and field data. Both synthetic and real data examples illustrate that the SAGST can obtain a TF representation with a high TF resolution.

In this letter, a new method is introduced for a seismic time-frequency (TF) analysis. The proposed method is called synchrosqueezing generalized S-transform (SSGST), which belongs to a postprocessing procedure of the GST. The frequency-dependent Gaussian window used in the standard S-transform may be not suitable for real applications. In order to overcome this limitation, the frequency-dependent Gaussian window is replaced by a parameterized function containing three parameters. These three parameters result in flexibility in the variation of TF resolution. Then, the synchrosqueezing transform is employed to squeeze the TF coefficients of the GST to achieve an energy-concentrated TF representation. Synthetic examples and field data show that the SSGST achieves a high resolution and has the potential in highlighting geological structures with high precision.

Time-frequency (TF) analysis can reveal local variations in seismic data processing and interpretation, where seismic signals are nonstationary and time varying. High-quality TF representation (TFR) is important for revealing the local information about these nonstationary seismic signals and describing geological structures. Due to the Heisenberg uncertainty principle, traditional TF methods (e.g., short time Fourier transform and continuous wavelet transform) cannot get the finest time resolution and the best frequency resolution at the same time, which leads to ambiguous TFR with a negative effect on the seismic signal analysis. Concentration in frequency and time is proposed to distinguish the different TF contents of time-dependent signals with time-varying amplitude and instantaneous frequencies. We introduce this promising TF analysis tool to seismic data processing. Experiments on synthetic signals and seismic data show its validity and effectiveness, which is helpful for seismic data interpretation in the future.

An approach is proposed to improve the resolution of nonstationary seismic data by adaptive molecular decomposition. For each seismic trace, a set of nonuniform molecular windows is constructed according to the attenuation trend described by smoothed weighted and damped instantaneous frequencies (WDIF) located at the trace's envelope peaks. Such that in each window, the seismic trace is approximately stationary. These nonuniform molecular windows are used to produce a couple of Molecular-Gabor frames. For the trace segment in each window, the spectrum-broadening and energy compensation are performed in Molecular-Gabor domain. Subsequently, a high-resolution version of the nonstationary seismic data can be obtained after inverse Molecular-Gabor transform. Applications of this method to both synthetic and real data show that the proposed method works well for a general earth Q-model that varies with travel time, and can expand the frequency band and recover the absorbed energy of the nonstationary seismic trace effectively.