Deep carbonate sedimentary cycle division is a core geological theory for analyzing sedimentary environments and provides important guidance for predicting the distribution of high-quality reservoirs. As a key technique, time-frequency (TF) analysis primarily focuses on the high-resolution characterization of dominant frequency variations caused by changes in stratum thickness. To enhance TF resolution, this study proposes a matching extracting transform (MET) to better characterize sedimentary cycles. Initially, the method constructs a matching chirp rate estimator (MC), leveraging the relationship between the instantaneous frequency (IF) estimator and the group delay estimator within the short-time Fourier transform domain, to capture the slope of the IF trajectory. Subsequently, based on the properties of the MC, a chirp rate valid domain (CVD) for the MC is defined to constrain its computational interval. Within this CVD, a maximum criterion under the chirp transform is then employed to extract the signal’s IF trajectory accurately. Finally, the TF coefficients are reassigned along the retrieved IF trajectory, enhancing TF energy concentration while maintaining signal reconstruction fidelity, as validated numerically. Applications to both simulated sedimentary cycle models and field deep carbonate seismic data demonstrate that the proposed MET is a potential tool for sedimentary cycle division.

Accurate segmentation of rock mass discontinuities from 3D remote sensing point clouds is a critical task for automated geological structure characterization and rock mass stability analysis. To enhance the robustness and accuracy of discontinuity detection and segmentation in complex rock outcrops, this paper proposes a robust normal vector estimation method based on 3D point clouds. This method first defines a Voxel Geodesic Distance (VGD) to replace the traditional Euclidean distance for constructing structure-sensitive neighborhoods, which effectively avoids cross-structure interference and enhances the robustness of neighborhood selection. Then, an adaptive parameter combining local curvature and normal residuals is introduced to dynamically adjust the M-estimation weights, enhancing the robustness of normal estimation under noise and structural variation. Finally, by integrating VGD-based path weighting and adaptive M-estimation weighting, normal vectors are iteratively estimated to improve stability and continuity, particularly around boundaries and holes. Experiments on multiple real-world outcrop datasets demonstrate that the proposed method achieves superior consistency, robustness, and accuracy in detecting discontinuities, holes, fractures, and structural boundaries in complex rock surfaces. This approach provides a reliable foundation for automated discontinuity detection, orientation analysis, and subsequent 3D structural modeling in remote sensing applications.

The time–frequency (TF) characteristics of seismic signals make it possible to accurately identify the boundaries of natural gas. In particular, the transient-extracting transform (TET) improves the time resolution of the unstable signal TF representation (TFR) by extracting only the points on the group delay (GD) trajectory. However, the GD estimator of TET lacks certain accuracy for frequency-varying signals. To overcome this problem, this article proposes an improved GD (IGD) estimator. First, in the short-time Fourier transform (STFT) domain, based on the GD estimator of the frequency-varying signal, the GD estimator problem is transformed into a fixed-point problem, and the IGD estimator is constructed. Then, combining the advantages of TET, an improved TET was proposed. Finally, through the simulated geological model test of ITET, the root mean square error of the model’s reflectivity structure is only 0.001. Combined with the analysis of seismic data, the effectiveness of this method in the positioning of reflectivity structure is verified, which can provide strong support for subsequent seismic interpretation.

Time-frequency analysis (TFA) is widely used to describe the time-frequency (TF) features of seismic data, thanks to its superior capability in analyzing nonstationary signals. Among the commonly used TFA techniques, the time-reassigned synchrosqueezing transform (TSST) and transient-extracting transform (TET) provide a TF spectrum with high-time resolution for seismic signals. However, both TSST and TET cannot simultaneously emphasize both sharpening and reconstruction performance. This article proposes a transient matching squeezing transform (TMST) that integrates these two performances. First, drawing on the idea of TET, define the group delay (GD) band center to trace the GD trajectory of the signal. Then, explore the properties of the GD estimator and theoretically construct a matching GD (MGD) estimator based on these properties. Finally, incorporating the idea of TSST employs the MGD estimator to squeeze the dispersed TF coefficients to the GD band center, thereby sharpening the original TF spectrum while preserving the reconstruction of the original signal, as validated by numerical simulations. Furthermore, the application of the simulated geological model and field seismic data shows that the proposed TMST can effectively reveal geological features, making it a powerful tool for seismic signal analysis.

Time-frequency (TF) analysis (TFA) can reveal geological information hidden in seismic reflection data, but most methods focus on trace-by-trace analysis of seismic data with a lack of lateral constraints. In this letter, a novel multichannel TF transform (MCTFT) is proposed and applied for describing tight sandstone channel reservoirs. First, a formation dip parameter is introduced to capture the lateral variation of seismic data. Then, the MCTFT is constructed with the windowing idea of short-time Fourier transform (STFT), where the dip parameter is determined by solving a plane wave equation. Moreover, the coherence is taken as a trade-off between single- and multichannel processing to avoid the latter over-smoothing the edges of geological features. Compared to the single-channel TFA method, the MCTFT can provide a more laterally continuous spectral decomposition that clearly describes tight sandstone channel reservoirs. A synthetic wedge model and two field seismic data are employed to verify the effectiveness of the proposed method.

Time-frequency (TF) analysis (TFA) is a vital spectral decomposition tool for reservoir characterization due to its superiority in analyzing nonstationary signals. Two newly developed TFA methods, the synchroextracting transform (SET) and transient-extracting transform (TET), provide a concentrated TF representation for seismic signals. However, the SET and TET are respectively only valid for harmonic signals with slow-varying instantaneous frequencies and transient signals of which the TF ridge almost parallels the frequency axis. This article proposes a centroid-oriented extracting transform (COET) to analyze mixed signals containing harmonic and transient features. First, we construct an objective function in the short-time Fourier transform (STFT) domain to link the most relevant signal features via the TF centroid. Then, the main direction of energy diffusion is defined by the TF centroid to separate the signal into harmonic and transient modes. Finally, a divide-and-conquer strategy is utilized to locally minimize the objective function in the frequency and time directions, respectively, thereby extracting the STFT coefficients at all optimal TF points while keeping the lossless reconstruction of the original signal. Such a COET provides both high time and frequency concentrations with strong noise immunity, as numerical signals elaborate. The application of field seismic data further indicates that the proposed COET clearly highlights the detailed information of different reservoir distributions, which is a promising tool for seismic spectral decomposition.

A time–frequency (TF) analysis (TFA) method plays a significant role in seismic signal processing. However, traditional seismic TFA techniques always provide blurred TF representations (TFRs) with low temporal resolution. The transient-extracting transform (TET) is an effective TFA tool that improves the temporal resolution of TFR of nonstationary signals. However, the TET suffers from nonreassigned point (NRP) problem, which can result in unreliable seismic interpretations. In this article, a novel TF transform is proposed to address this problem, named the time-reassigning transform (TRT). In the short-time Fourier transform (STFT) domain, this TRT searches for local maximum points of the spectral energy along the time direction instead of searching for group delay (GD) fixed points such as the TET. At these points, the STFT coefficients are reassigned into a sparser TFR while eliminating the NRP problem, as verified by two synthetic signals and a simulated seismic trace. Finally, application analysis on a geological model and field seismic data shows that the proposed TRT is a potential seismic data analysis tool.

Sedimentary cycle division is a critical task within sequence stratigraphy and provides significant guidance value in the exploration of gas resources. For the division of sedimentary cycles by analyzing the time-frequency (TF) curves of seismic data, the key lies in high-resolution highlighting of changes in dominant frequency induced by variations in layer thickness. To improve the energy concentration of TF analysis (TFA) methods, this article proposes an adaptive peak extracting transform (APET) for characterizing sedimentary cycle patterns. In this APET, we first establish a local peak criterion within the short-time Fourier transform (STFT) framework to obtain instantaneous frequency (IF) trajectories. Subsequently, a time-varying window function is constructed by Rényi entropy to determine the optimal window length at each moment. Finally, the TF coefficients are reallocated to the retrieved IF within the optimal window. The local peak criterion and the time-varying window function effectively enhance the TF resolution. The synthesized signals verify that the proposed APET exhibits highly focused TF representation (TFR). In addition, we apply APET to several typical sedimentary cycle models and field seismic data, indicating that the proposed method is a potential tool for sedimentary cycle analysis.

Thin interbed analysis has guiding significance for oil and gas exploration, and it is feasible to precisely predict their thickness variation through the time-frequency (TF) features of seismic signals. In this article, an auto-reassigning transform (ART) is proposed to analyze seismic thin interbeds. This ART retrieves the instantaneous frequency (IF) trajectory by local maxima, then determines the TF coefficients within the effective window by the 3σ criterion, and finally reassigns these coefficients automatically to the retrieved IF trajectory. Therefore, such ARTs provide a more concentrated TF representation with reconstruction capability. Synthetic signals and seismic data are employed to demonstrate the effectiveness of the proposed ART by comparing it with state-of-the-art TF analysis methods.

Synchrosqueezing transform (SST) benefits from an instantaneous frequency (IF) estimator in the time-frequency domain, providing an energy-concentrated time-frequency representation to describe the time-varying frequency of seismic signals. To enhance the concentration performance of SST, this paper theoretically proposes a statistical SST (SSST) by constructing a spectrum-weighted IF estimator in the short-time Fourier transform (STFT) domain. In this SSST, a linear chirp signal is introduced to better capture its chirp rate, and then the quadratic STFT spectra are weighted by a window-related weighting function. On this basis, two equations related to the IF and chirp rate are constructed to derive the spectrum-weighted IF estimator. Finally, the STFT coefficients are squeezed to the estimated IF trajectories by a frequency fixed-point iterative algorithm, thereby providing a more concentrated time-frequency representation for multi-component signals than existing advanced methods, while enabling to retrieve each component. Two synthetic examples and one field seismic data on thin interbeds are utilized to demonstrate the effectiveness of the proposed SSST and show its ability to highlight the time-varying frequency features of seismic signals, which is a promising seismic data analysis tool, such as characterizing thin interbed thickness variations.

Synchrosqueezing transform (SST) is a high-resolution time-frequency (TF) analysis (TFA) approach for seismic spectral anomaly detection. Here, a novel method called multisynchrosqueezing generalized S-transform (GST) is proposed and applied for the identification of tight sandstone gas reservoirs. In this method, a signal model named the Gaussian-Modulated Signal Model (GMSM) is introduced to estimate the instantaneous frequency (IF) of the signal in the GST’s spectrum. Then, an iterative algorithm constantly approximating IF is constructed to provide a highly energy-concentrated TF representation while allowing for signal reconstruction. Compared to some advanced TFA methods, the proposed method has better energy-concentrated performance due to an accurate estimate of the IF. A simulated signal and field data are employed to verify the effectiveness of the proposed method. It is concluded that the proposed method has great potential as a TFA technique for identifying tight sandstone gas reservoirs.

Time-frequency (TF) analysis has received considerable attention in seismic spectral anomaly detection for its superiority in significantly revealing the frequency content of seismic signals changing with time variation. In this letter, a novel method termed second-order horizontal multi-synchrosqueezing transform (SHMSST) is proposed for hydrocarbon reservoir identification. First, a Gaussian-modulated linear chirp model is constructed in the frequency domain for describing the signals with slowly or rapidly linear-varying group delay. Then, the second-order local group delay estimation of the model is deduced in the TF domain through an approach similar to the instantaneous frequency estimation in the synchrosqueezing transform (SST). Finally, the rearrangement procedure is executed iteratively to concentrate the blurry TF energy into the estimated group delay, which provides an energy-concentrated TF representation for the signals with distinct nonlinear and nonstationary features. Synthetic signal and field seismic data illustrate the effectiveness of the proposed SHMSST in time localization and direct hydrocarbon detection.

Polynomial chirplet transform (PCT) can effectively characterize the instantaneous frequency (IF) of mono-mode frequency-modulated (FM) signal, but it is unsuitable to analyze multimode signals. Here, we propose synchrosqueezing PCT (SPCT) for amplitude-modulated (AM) and FM signals with multimode, and apply it to tight sandstone gas reservoirs. First, a multikernel operator is constructed to concentrate the energy near the IF of each mode, and then an IF estimator is derived to further reassign the energy to the corresponding IF ridge. This not only achieves a highly energy-concentrated time-frequency representation, but also retains its invertibility. The synthetic signal is employed to validate the effectiveness of the SPCT. The application on field seismic data also demonstrates that the SPCT can effectively identify tight sandstone gas reservoirs.

The W transform (WT), employing a Gaussian window with non-stationary dominant frequency weight, is suitable for reservoir description with high time resolution at low-frequency band. In this letter, we generalize the WT through designing a novel frequency-varying Gaussian standard deviation with a two-parameter multivariate composite exponential form of the dominant frequency, namely generalized WT (GWT), which can avoid the singularity of WT caused by the non-differentiability of its standard deviation at the dominant frequency, thus obtaining a smoother and more flexible window. Compared with the S-transform (ST) and WT, the proposed method provides a better time-frequency (TF) representation performance. The analysis results of simulated seismic trace and field seismic data illustrate that the GWT can effectively characterize gas-bearing reservoirs.

Time–frequency (TF) analysis (TFA) plays an important role in seismic hydrocarbon reservoir identification, which is attributed to its ability to effectively identify the oil and gas seismic response characteristics of geological bodies in different frequency bands. In this letter, we introduce a novel TFA method termed high-order synchroextracting transform (SET) and apply it to the high-precision identification of gas-bearing reservoirs. Under the premise of short-time Fourier transform (STFT), this method defines a new synchroextracting operator (SEO) based on high-order approximations of signal amplitude and phase. Furthermore, only the TF information highly correlated with the TF characteristics of the signal is extracted from the STFT spectrum by using the SEO. Therefore, for a wider variety of the nonstationary signal, a highly energy-concentrated TF representation can be effectively obtained. The application of STFT and different-order SET on 1-D synthetic signal and field seismic data verifies the effectiveness of the proposed method.

In order to remove random noise in seismic data, this letter proposes a seismic data denoising method based on tensor decomposition and total variation (TDTV). Based on the self-similarity of seismic data, this method first groups similar patches into a stack, then utilizes the low-rank tensor approximation strategy to restore the structural effective information of the seismic section. Considering that the approximate seismic section obtained after CANDECOMP/PARAFAC (CP) decomposition and patch aggregation is unsmooth, this letter introduces the total variation (TV) constraint to perform anisotropic diffusion, and protects edge information while smoothing. Finally, the gradient descent method is used to solve the whole model. The TDTV method proposed in this letter can not only effectively denoise synthetic and field seismic section but also restore structural and edge information. Experimental results show that the proposed method outperforms many state-of-the-art denoising methods.

The maximum vertical seismic resolution is a critical parameter in seismic data processing and interpretation. In general, conventional methods such as spectral whitening and zero-phase deconvolution assume randomness in the reflectivity spectrum that may not always be valid. The method proposed herein, extrapolated multiresolution singular value decomposition (EMRSVD), avoids some of these assumptions. We reasonably assume that original seismic data constitute a low-frequency component of high-resolution data, of which high-frequency component is attenuated. To recover this high-resolution component, EMRSVD adaptively extrapolates attenuated high-frequency information based on multiresolution singular value decomposition (MRSVD) and polynomial fitting to broaden the valid frequency bandwidth and improve the resolution of original seismic data. In our work, we first decompose a signal into a series of approximate and detailed subsignals exhibiting different resolutions using MRSVD. Then, we apply a polynomial fitting algorithm to the singular values corresponding to the detailed subsignals and obtain an expression of the singular values. Next, based on this expression, we extrapolate new singular values to construct new detailed subsignals. We repeat this process iteratively, where the number of iterations is determined by a modified variance model with an exponential transformation. Finally, we add these extrapolated detailed subsignals back into the original signal to obtain a high-resolution result. Examples with two synthetic signals and one field seismic data demonstrate that the proposed method significantly improves the resolution of seismic data without introducing noise and efficiently broadens the frequency bandwidth of reflection signals without sacrificing low-frequency information, which facilitates the resolution of thin layers.

Seismic reflectivity inversion is widely applied to improve the seismic resolution to obtain detailed underground understandings. Based on the convolution model, seismic inversion removes the wavelet effect by solving an optimization problem. Taking advantage of the sparsity property, the ℓ1-norm is commonly adopted in the regularization terms to overcome the noise/interference vulnerability observed in the lp-losses minimization. However, no one has provided a deterministic conclusion that ℓ1-norm regularization is the best choice for seismic reflectivity inversion. Instead of using an unproved fixed regularization norm, we propose an optimal seismic reflectivity inversion approach. Our method adaptively adopts an ℓp-loss-ℓq-regularization (i.e., ℓp,q-regularization) for p = 2, 0q-norm regularization. Then, the majorization-minimization and CV algorithms are briefly described. The performance of the proposed seismic inversion approach is evaluated through synthetic examples and a field example from the Bohai Bay Basin, China.

In this letter, we combine anisotropic and isotropic diffusion models and establish a combined energy variational model for seismic denoising. We propose a dynamic threshold to separate seismic sections into different feature areas and to choose different diffusion methods more precisely according to the characteristics of the seismic sections. Multilevel noise and multilevel edges can be treated automatically. Denoised results from a synthetic model and from field seismic sections demonstrate that our proposed model can suppress random noise and preserve the features of seismic sections efficiently.