The angle gathers are the data basis of prestack seismic inversion, and their resolution directly determines the resolution of the inverted elastic parameters. Seismic reflectivity inversion (SRI) is a technique that is able to estimate reflectivity from seismic data, and consequently improve the resolution of seismic data. However, the existing SRI method for angle gathers faces two problems: (1) The assumption that the wavelet is known does not align with reality; (2) Compared with the exact Zoeppritz equation, approximation equations will introduce errors in large angles. To overcome these shortcomings, in this paper, we propose a new blind SRI method for enhancing the resolution of angle gathers. This method can simultaneously build the wavelet and reflectivity of angle gathers without the need for a predefined wavelet, and an angle-based regularization term is constructed to ensure the continuity in angle especially in noisy cases. We use both synthetic experiments on a modified Marmousi model and also a field data experiment using a dataset from the Hampson-Russell software to assess the performance of the proposed method and compare its performance with an existing method. The results clearly validate the effectiveness of the proposed method and its superiority over the existing method in producing high-quality reflectivity models for angle gathers.

Low-rank approximation (LRA) is a powerful technique for seismic diffraction separation and imaging, providing higher-resolution images of subsurface discontinuities compared to traditional reflection imaging. However, in complex wavefields where reflections lack distinct low-rank characteristics, diffractions and reflections can overlap within the same eigenimages, making traditional LRA less effective for separation. To address this limitation, we propose a diffraction separation and imaging method based on multi-directional wavefield low-rank approximation (MDWLRA). The MDWLRA method employs multi-directional wavefield decomposition (MDWD) to divide complex wavefields into angular slices with similar dip angles. These slices are classified as either diffraction slices or reflection slices, with the latter containing mostly reflections and some residual diffractions. LRA is then applied to the reflection slices to separate the remaining diffractions from reflections. By reducing wavefield complexity using MDWD, reflections in the reflection slices exhibit clearer low-rank characteristics than those in the full wavefields, allowing for more effective separation using LRA. Numerical tests on synthetic data from the modified Sigsbee2A model and field data demonstrate that the MDWLRA method outperforms traditional methods, achieving more accurate separation with fewer leakages than traditional LRA, while also improving diffraction fidelity compared to the Curvelet-transform-based method.

Blind seismic acoustic-impedance (AI) inversion is a technique for obtaining the AI of the subsurface medium without given a wavelet. An effective way to solve the blind inversion problem is to split the multi-parameter problem into two single-parameter subproblems and solve them in an alternative iteration way. However, this method becomes time-consuming when dealing with large-scale 3D problems and faces challenges in selecting suitable regularization parameters. To overcome these shortcomings, we propose a deep learning accelerated blind seismic AI inversion (DLA-BSAII) method. It mainly has three steps: (1) Only a few 2D profiles are selected from the whole 3D data, and their corresponding AI models and wavelets are inverted using conventional blind seismic AI inversion method. (2) The results of the first step are used to train deep networks to realize the nonlinear mapping from a 2D seismic profile to AI and wavelet. In addition, the trained deep networks are used to generate predictions of AI models and wavelets for the remaining 2D profiles. (3) Benefiting from the predicted AI models and wavelets, a new alternative iteration method with fewer but more effective regularization terms is proposed to obtain the final inverted AI models and wavelets of the remaining 2D profiles. It has the advantages of easier selection of regularization parameters and faster convergence speed. Synthetic and field data examples verify that DLA-BSAII outperforms conventional methods in terms of both efficiency and inversion accuracy.

Extracting a reliable model of quality factor$Q$from the spectral information of seismic signals is a significantly important step for seismic imaging and reservoir characterization. However, the conventional$Q$estimation approach based on the frequency domain is susceptible to the high oscillative spectrum created by the unavoidable random and coherent noise in the observed signal. To address this issue, we introduce an absorption-constrained wavelet power spectrum inversion (AWPSI) method. The inversion involves absorption constraint (AC) and spectrum constraint (SC), where the AC term is a novel constraint for estimating the wavelet’s amplitude spectrum or power spectrum. By treating medium absorption as a physical prior and utilizing information from all waveforms rather than individual ones, AWPSI can yield high-quality wavelet power spectra and ensure stable$Q$estimation results. In addition, the proposed method has no limitations on the type of wavelet. Since its inversion target is wavelet power spectra, AWPSI is broadly applicable to various frequency-based$Q$estimation approaches. We validate the effectiveness of the proposed method using both synthetic and actual vertical seismic profile (VSP) data.

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.

The bilinear based method is one of the commonly used tools in time-frequency analysis (TFA) fields. However, it suffers from the trade-off of high resolution and cross-term interference. We propose WVDNet, a semi-supervised learning model for time-frequency analysis based on the Wigner-Ville distribution (WVD), to reduce the cross-term existing in WVD and relax the requirements of the training data set. The proposed WVDNet is based on the Mean-Teacher model to enable the task model to exploit the unlabeled training data. We first build a synthetic data set for model training, that contains different kinds of amplitude-modulated and frequency-modulated (AM-FM) signals. Next, a task model of WVDNet is designed and the consistency regularization based method is utilized to promote model training. Finally, experiments are conducted on both synthetic and real-world data, showing the effectiveness of suppressing cross-term and strong generalization ability.

Diffraction separation and imaging are important for subsurface discontinuities characterization. However, conventional diffraction separation methods may loss validity when the diffractions and reflections do not have discernible differences in data domain. Moreover, due to limited acquisition geometry and narrow frequency band of seismic data, the diffraction imaging methods that use conventional ray-based or wave-equation-based migration operators may produce images with low resolution. We propose a diffraction separation and least-squares imaging method based on multi-scale and multi-directional wave-field and image decomposition. First, by using the multi-scale and multi-directional properties of the generalized curvelet transform, we reproduce the diffractions from the plane-wave sections according to the differences between the diffractions and reflections in terms of scale and angle. When the diffractions and reflections do not have discernible differences in data domain, their migrated images generally have different dip angles. Therefore, we propose a plane-wave least-squares diffraction imaging method with a curvelet-domain regularization which suppresses the images of residual reflections with small dip angles. Finally, we obtain high-resolution images of the subsurface discontinuities by using a regularized conjugate gradient method. Synthetic and field data examples verify the superiority of the proposed diffraction separation method over the plane-wave destruction filter in terms of better suppression of the reflections and better recovery of the diffractions. Compared with plane-wave reverse time migration, the proposed diffraction imaging method effectively suppresses the residual reflectors and produces images with higher resolution and signal-to-noise ratio.

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.

Time–frequency analysis (TFA) technology plays a significant role in seismic signal processing. The time–frequency representation (TFR) calculated using the TFA method is helpful for the localization of time-varying frequencies within the signal. Nevertheless, limited by the Heisenberg uncertainty principle, traditional linear TFA methods always provide blurred TFRs, which makes them difficult to distinguish details of time–frequency structures. Recently, the synchrosqueezing transform (SST) was designed to improve the concentration of the TFR. The SST can provide a much concentrated TFR for the weakly frequency-modulated (FM) signal, but it is not effective for the interpretation of strongly FM signals, such as the thin interbed in seismic exploration. In this work, we propose a new tool by introducing the multi-synchrosqueezing operator to the frame of wavelet transform (WT). Employing an iterative operator to correct the frequency estimation of the original SST step-by-step, it thus can calculate a TFR with better concentration and robustness. Synthetic signals and a field seismic data are employed to verify the performance of the proposed method for characterizing the time-varying frequency features.

Least-squares reverse time migration (LSRTM) can estimate high-quality reflectivity of subsurface medium from seismic data. However, the subsurface reflectivity depends on reflection angles, and its variations over reflection angles are extremely important because they can be used to estimate sub-surface physical properties for seismic interpretation. We present a new formulation of the LSRTM method that can estimate reflection-angle-dependent reflectivity from seismic data. We derive a forward modeling operator which predicts the reflection data without calculating the reflection angles, and verify that it approximately equals to the reflection-angle-dependent wave-equation-based Kirchhoff modeling operator under the assumption that the velocity perturbation is small and the reflection angle is smaller than the critical angle. Based on the proposed modeling operator associated with the adjoint of the angle-dependent wave-equation-based Kirchhoff modeling operator, we reformulate LSRTM as an inverse problem to invert for reflection-angle-dependent reflectivity using a preconditioned conjugate gradient algorithm. The algorithm uses a low-rank filter as the preconditioner to attenuate migration artifacts. Imaging tests on synthetic and field seismic data are used to verify validity and superiority of the proposed method. The tests illustrate that the proposed method can produce the reflection-angle-dependent reflectivity with much higher signal-to-noise ratio, resolution and amplitude fidelity than reverse time migration. Compared with conventional LSRTM, it can produce more focused stacked image when the migration velocity contains errors. Moreover, conventional LSRTM only produces the angle-independent reflectivity, whereas the proposed method has the feasibility to produce the reflection-angle-dependent reflectivity.

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.

Time-frequency (TF) analysis is an available tool to estimate seismic absorption qualitatively. The high TF concentration is a key factor for the seismic attenuation qualitative estimation. To obtain a more concentrated TF representation, we propose a sparse TF method based on sparse representation (SR) and sparse Group-Lasso (GL) penalty function. Based on the SR theory, TF representation can be regarded as an inverse problem, and thus, sparse GL penalty function can be added in this inverse problem to enhance the TF concentration. Sparse GL penalty function, includingl1penalty andl2,1penalty, can provide group-wise and within-group sparsity for TF coefficients. Using the proposed sparse GL-based TF (GLTF) method, we develop a workflow to characterize seismic attenuation qualitatively. Finally, a synthetic data of viscoacoustic model and a 2-D field data are applied to test the validity and effectiveness of the proposed workflow for indicating the gas and oil reservoirs.

Lithology classification in well logging plays a significant role in evaluating the quality of oil and gas reservoirs. Conventionally, the manual interpretation method is of much more limited use, partly because it is time-consuming, but mainly because it is subjective. This is due primarily to the massive volume of logging data and the dependence of the experience of geophysical practitioners. By considering the features that logging data are typically sequential and long short-term memory (LSTM) network is well-suited to process a sequential signal, an LSTM-based architecture is proposed to identify rock facies based on borehole data automatically in the study area. The tests based on data from one well of the tight gas sandstone reservoir demonstrate that, when the sample size and the number of hidden layer neurons are appropriately set, the trained LSTM-based Adam optimizer can precisely recognize the rock facies boundaries than that based on Sgdm and Rmsprop optimizers. Additionally, results on another eight wells in the same study area statistically show a good generalization of the trained LSTM. Moreover, another complex reservoir with similar lithology interbedding also demonstrates the usefulness of the LSTM-based network.

One important application of time-frequency analysis (TFA) is seismic spectral decomposition for reservoir characterization. However, traditional seismic TFA techniques are usually limited by diffused TF distribution, which can result in unreliable seismic interpretations. Synchrosqueezing transform (SST) is an effective TFA method that improves the concentration of the TF representation (TFR) of nonstationary signals. However, for the signal with a rapidly varying instantaneous frequency, the SST method suffers from a blurred TFR. In this letter, we propose a novel TFA method called time-synchroextracting transform (TSET) that provides highly concentrated TFR for transient signals where the TF curve is nearly parallel to the frequency axis. We applied the proposed TSET to synthetic signals and field seismic data to verify its validity of time localization and effective delineation of subsurface geological information.

In[1], the grant number in the first footnote for the National Postdoctoral Program for Innovative Talents should be BX20190279.

Synchrosqueezing transform (SST) is an effective time-frequency analysis (TFA) approach for the processing of nonstationary signals. The SST shows a satisfactory ability of the TF localization of the nonlinear signal with a slowly time-varying instantaneous frequency (IF). However, for the signal of which ridge curves in the TF domain are fast varying, or even almost parallel to the frequency axis, the SST will provide a blurred TF representation (TFR). To solve this issue, the transient-extracting transform (TET) was recently put forward. The TET can effectively characterize and extract transient features in the much concentrated TFR for the strongly frequency-modulated (FM) signal, especially the impulse-like signal. However, contrary to the SST, it is not suitable for weak FM modes. In this study, we propose a TFA method called the time-synchroextracting general chirplet transform (TEGCT). The TEGCT can achieve a highly concentrated TFR for strong FM signals as well as weak FM ones. Quantized indicators, the concentration measurement and the peak signal-to-noise ratio, are used to analyze the performances of the proposed method compared with those of other methods. The comparisons show that the TEGCT can provide a result with better TF localization. Then, the proposed method was applied to the spectrum analysis of the seismic data for oil reservoir characteristics. The horizontal slices of the offshore 3-D seismic data show that the TEGCT delineates more distinct and continuous subsurface channels in a fluvial-delta deposition system. All the results illustrate that our proposed method is a good potential tool for seismic processing and interpretation in the geoscience.

By building an adaptive filter bank, the empirical wavelet transform (EWT) decomposes an analyzed signal into several intrinsic mode functions (IMFs). Although some applications have certified the effectiveness of the EWT, the effectiveness of the EWT is affected obviously when analyzing nonstationary signals (e.g., seismic data). In this letter, we propose an improved EWT (IEWT) to decompose a nonstationary seismic signal into several IMFs and describe its frequency features. After computing the Fourier spectrum of the seismic signal, the scale-space representation (SSR) is used to extract the slowly varying component of the Fourier spectrum. Then, the frequency components contained in the seismic signal and the boundaries can be obtained using the central frequency information. Finally, we obtain an adaptive spectrum segmentation using detected boundaries based on the SSR. Afterward, the proposed algorithm obtains accurate and stable IMFs in decomposing the nonstationary seismic signal. To demonstrate the effectiveness of the proposed IEWT, we apply it to synthetic seismic signal and field data.