Seismic Time-frequency Analysis Research Articles

Application of sparse S transform network with knowledge distillation in seismic attenuation delineation

Time-frequency analysis is a successfully used tool for analyzing the local features of seismic data. However, it suffers from several inevitable limitations, such as the restricted time-frequency resolution, the difficulty in selecting parameters, and the low computational efficiency. Inspired by deep learning, we suggest a deep learning-based workflow for seismic time-frequency analysis. The sparse S transform network (SSTNet) is first built to map the relationship between synthetic traces and sparse S transform spectra, which can be easily pre-trained by using synthetic traces and training labels. Next, we introduce knowledge distillation (KD) based transfer learning to re-train SSTNet by using a field data set without training labels, which is named the sparse S transform network with knowledge distillation (KD-SSTNet). In this way, we can effectively calculate the sparse time-frequency spectra of field data and avoid the use of field training labels. To test the availability of the suggested KD-SSTNet, we apply it to field data to estimate seismic attenuation for reservoir characterization and make detailed comparisons with the traditional time-frequency analysis methods.

Cycle-consistent Generalized S-transform Network for Seismic Time-frequency Analysis

Cycle-consistent Generalized S-transform Network for Seismic Time-frequency Analysis

Time-reassigned multisynchrosqueezing of the S-transform for seismic time-frequency analysis

Time-reassigned multisynchrosqueezing of the S-transform for seismic time-frequency analysis

Synchrosqueezing Transform Based on Frequency-Domain Gaussian-Modulated Linear Chirp Model for Seismic Time–Frequency Analysis

The synchrosqueezing transform (SST) has attracted much attention as a post-processing technique since it was proposed. In recent years, improvements to SST have been made. However, the existing methods are mainly based on the time-domain signal model, and the weak frequency modulation assumption for the components composing the signal is always taken into account. Thus, the signals characterized by a rapidly changing instantaneous frequency (IF) may fail to be adequately tackled. To address this problem, the paper presents a novel seismic time–frequency analysis method via synchrosqueezing transform where a frequency-domain Gaussian modulated linear chirp model is utilized to deduce the SST. The group delay (GD) rather than the IF estimator is implemented to compute an estimation of the ridge. Furthermore, a new synchrosqueezing operator is constructed to rearrange the energy around the ridge. A synthetic example verifies the efficiency and robustness of the proposed SST method, which generates better results than some classic time–frequency analysis (TFA) approaches, e.g., short-time Fourier transform (STFT) and STFT-based SST (FSST). A field dataset further demonstrates this method’s potential in the delineation of subsurface geological structures.

Seismic time-frequency analysis via time-varying filtering based empirical mode decomposition method

We proposed a seismic time-frequency analysis method using time- varying filtering based empirical mode decomposition (TVF-EMD). TVF-EMD is a recently-developed signal decomposition method in the field of nonstationary signal processing. The method is suitable for chirp signals, which address the mode mixing problem. TVF-EMD decomposes the non-stationary signal into IMFs with fixed bandwidth and then applies the instantaneous amplitude, frequency, and phase to build the time-frequency spectrum based on the Hilbert transform. Different from empirical mode decomposition (EMD), TVF-EMD uses the time-varying B-spline filter and adaptively calculates the cut-off frequency at each moment for mode decomposition, which is suitable for non-stationary signal processing. Synthetic and field data examples demonstrate comparing with the conventional methods, TVF-EMD has better time-frequency concentration and is more suitable for processing.

Application of adaptive parameterized S‐transform to delta sandstone reservoir identification

ABSTRACTTime–frequency analysis plays an important role in seismic interpretation and reservoir identification because it reveals the variation of seismic frequency contents over time. The S‐transform is recognized as an efficient method for seismic time–frequency analysis, but its frequency distribution biases the actual Fourier spectrum due to the linear frequency‐dependent term in the analytical window. In this paper, an improved S‐transform, named adaptive parameterized S‐transform, is proposed for identifying delta sandstone reservoirs. In the proposed method, three parameters are introduced into the S‐transform to better adjust the time–frequency resolution in different frequency bands. Then these parameters are selected adaptively by using the concentration measure to provide a highly energy‐concentrated time–frequency representation for seismic signals. Two synthetic examples validate the effectiveness of the proposed method. Analysis of field seismic data illustrates that it can provide a better reservoir interpretation with a high resolution. Comparisons between the wavelet transform, S‐transform, and modified S‐transform prove the superiority of the proposed method in describing reservoir distribution and decreasing the uncertainty of reservoir detection. This paper presents a complementary approach to current methods for reservoir detection and identification.

Matching Demodulation Synchrosqueezing S Transform and its Application in Seismic Time–Frequency Analysis

Time–frequency (TF) analysis is a powerful tool to describe the frequency response of subsurface rocks and hydrocarbon reservoirs. In this letter, the matching demodulation synchrosqueezing S transform (MDSST) that achieves a highly concentrated TF representation was introduced to seismic TF analysis. The MDSST includes two steps: the matching demodulation technique is preprocessing that provides a rough estimation of instantaneous frequency (IF) of the analyzed signal, and the synchrosqueezing transform (SST) is postprocessing that produces an accurate IF. Numerical experiments on synthetic and real signals demonstrate the superiority of the MDSST in seismic TF analysis.

Seismic Time-Frequency Analysis Based on Time-Reassigned Synchrosqueezing Transform

In this paper, we propose a novel seismic time-frequency analysis method via the time-reassigned synchrosqueezing transform (TSST), in which the time-frequency coefficients are reassigned in the time direction rather than in the frequency direction as the short-time Fourier-based synchrosqueezing transform (FSST) does. Such a technique can not only produce a highly concentrated time-frequency representation (TFR) for a wide variety of strongly frequency modulated signal, but also allow for the reconstruction of the modes with a high accuracy. Numerical experiments on synthetic signal and field data demonstrate the effectiveness of this new method, and show that the proposed method is more suitable for extracting seismic time-frequency feature and identifying the thin layers compared with the traditional FSST, which offers the potential in highlighting subtle geological structures.

Seismic time–frequency analysis as a robust method to estimate the fluid saturation: A case study of carbonates reservoir, Iran

ABSTRACTThe propagation of seismic waves through a saturated reservoir compresses the fluid in the pore spaces. During this transition, parts of seismic energy would be attenuated because of intrinsic absorption. Rock physics models make the bridge between the seismic properties and petrophysical reality in the earth. Attenuation is one of the significant seismic attributes used to describe the fluid behaviour in the reservoirs. We examined the core samples using ultrasonic experiments at the reservoir conditions. Given the rock properties of the carbonate reservoir and experiment results, the patchy saturation mechanism was solved for substituted fluid using the theory of modulus frequency. The extracted relationship between the seismic attenuation and water saturation was used in time–frequency analysis. We performed the peak frequency method to estimate the Q factor in the Gabor domain and determined the water saturation based on the computed rock physics model. The results showed how the probable fault in the reservoir has stopped the fluid movement in the reservoir and caused touching the water‐bearing zone through drilling.

Construction of Optimal Basic Wavelet via AIDNN and Its Application in Seismic Data Analysis

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.

Time-Synchroextracting General Chirplet Transform for Seismic Time–Frequency Analysis

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.

Self-Adaptive Generalized S-Transform and Its Application in Seismic Time–Frequency Analysis

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.

Seismic Time–Frequency Analysis via Adaptive Mode Separation-Based Wavelet Transform

To better reveal time-varying spectral components of nonstationary seismic signals, time–frequency analysis (TFA) has been widely applied in seismic processing and analysis. In this letter, we propose an advanced seismic TFA method based on an optimal spectral mode separation and an adaptive wavelet bank design. The proposed adaptive mode separation-based wavelet transform (AMSWT) generates a superior time–frequency resolution. In addition, because the wavelet bank is adaptively built on the intrinsic spectral modes, the ability to accurately characterize geophysical structures has been significantly improved. To demonstrate the effectiveness of the proposed AMSWT method, we apply it on both synthetic and field data. Compared with the results from continuous wavelet transform (CWT), empirical mode decomposition (EMD), variational mode decomposition (VMD), and empirical wavelet transform (EWT), AMSWT provides a higher resolution and offers potentials in precisely highlighting stratigraphy boundaries.

A Novel Approach for Seismic Time-Frequency Analysis Based on High-Order Synchrosqueezing Transform

Time-frequency analysis always plays a central role in the field of seismic processing due to the advantage in characterizing nonstationary signals. In this letter, we present a novel technique for seismic time-frequency analysis based on the high-order synchrosqueezing transform, which obtains more accurate instantaneous frequencies by using the higher order approximations for both amplitude and phase in order to achieve a highly energy-concentrated time-frequency representation. A synthetic example is employed to demonstrate the validity of the proposed method in sharpening time-frequency representation. Application on field data example further proves its potential in enhancing time-frequency resolution and delineating stratigraphic characteristics with higher precision and renders that this technique is promising for seismic data analysis.

High-Resolution Seismic Time–Frequency Analysis Using the Synchrosqueezing Generalized S-Transform

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.

Weighted $\boldsymbol{l_1}$-norm constrained sparse regularization and alternating directions method of multipliers for seismic time-frequency analysis

Seismic time-frequency analysis is of great importance in seismic signal processing.We study a sparse inversion-based algorithm for computing the time-frequency analysis of reflection seismograms.We first formulate the forward problem using the windowed inverse Fourier transform,and then we establish a weighted $l_1$-norm constrained minimization model for solving the unknown model parameter vector (the Fourier frequency coefficients).To realize the minimization problem, an alternating directions method of multipliers (ADMM) is applied. Numerical experiments based on the well-known short time Fourier transform (STFT), the continuous wavelet transform (CWT) and the proposed algorithm are analyzed. It indicates from the comparison results that the proposed model and the related algorithm can produce a spectral decomposition of the seismic data with high resolution thanthat of the STFT and CWT.

The Synchrosqueezing Algorithm Based on Generalized S-transform for High-Precision Time-Frequency Analysis

In this paper, a new time-frequency analysis method—Synchrosqueezing Generalized S-transform (SSGST)—is proposed to meet the needs of high-resolution seismic signal processing and interpretation. The basic wavelet of the generalized S-transform (GST) in the paper is a modulated harmonic wave with four undetermined parameters that can be constructed by adjusting the four parameters to make the GST more suitable for seismic signals processing. The SSGST method squeezes and reconstructs the complex coefficient spectra of GST results along the frequency direction so that the energy distributions on the time-frequency spectra are concentrated around the real instantaneous frequency of the signal; thus, the time-frequency resolution can be improved. Based on mathematical theory, the basic principle of the new transformation method is given, and the mathematical expressions of the positive transformation and lossless inverse transformation of the method are strictly deduced. The experimental results of numerical signals illustrate that the proposed method can correctly decompose signals with different spectral characteristics into a high time-frequency resolution spectrum and can recovery the original signal from the time-frequency spectrum with satisfying reconstructing accuracy. Application on field seismic data shows the superiority of the new method in seismic time-frequency analysis for hydrocarbon detection.

High-Precision Spectral Decomposition Method Based on VMD/CWT/FWEO for Hydrocarbon Detection in Tight Sandstone Gas Reservoirs

Seismic time-frequency analysis methods can be used for hydrocarbon detection because of the phenomena of energy and abnormal attenuation of frequency when the seismic waves travel across reservoirs. A high-resolution method based on variational mode decomposition (VMD), continuous-wavelet transform (CWT) and frequency-weighted energy operator (FWEO) is proposed for hydrocarbon detection in tight sandstone gas reservoirs. VMD can decompose seismic signals into a set of intrinsic mode functions (IMF) in the frequency domain. In order to avoid meaningful frequency loss, the CWT method is used to obtain the time-frequency spectra of the selected IMFs. The energy separation algorithm based on FWEO can improve the resolution of time-frequency spectra and highlight abnormal energy, which is applied to track the instantaneous energy in the time-frequency spectra. The difference between the high-frequency section and low-frequency section acquired by applying the proposed method is utilized to detect hydrocarbons. Applications using the model and field data further demonstrate that the proposed method can effectively detect hydrocarbons in tight sandstone reservoirs, with good anti-noise performance. The newly-proposed method can be used as an analysis tool to detect hydrocarbons.

Wavelet transform with generalized beta wavelets for seismic time-frequency analysis

Using the continuous wavelet transform (CWT), the time-frequency analysis of reflection seismic data can provide significant information to delineate subsurface reservoirs. However, CWT is limited by the Heisenberg uncertainty principle, with a trade-off between time and frequency localizations. Meanwhile, the mother wavelet should be adapted to the real seismic waveform. Therefore, for a reflection seismic signal, we have developed a progressive wavelet family that is referred to as generalized beta wavelets (GBWs). By varying two parameters controlling the wavelet shapes, the time-frequency representation of GBWs can be given sufficient flexibility while remaining exactly analytic. To achieve an adaptive trade-off between time-frequency localizations, an optimization workflow is designed to estimate suitable parameters of GBWs in the time-frequency analysis of seismic data. For noise-free and noisy synthetic signals from a depositional cycle model, the results of spectral component using CWT with GBWs display its flexibility and robustness in the adaptive time-frequency representation. Finally, we have applied CWT with GBWs on 3D seismic data to show its potential to discriminate stacked fluvial channels in the vertical sections and to delineate more distinct fluvial channels in the horizontal slices. CWT with GBWs provides a potential technique to improve the resolution of exploration seismic interpretation.

Introduction to special section: Seismic time-frequency analysis

Analyzing the time-frequency features of seismic traces plays an important role in seismic stratigraphy analysis and hydrocarbon detection. The spectral decomposition algorithms can be categorized into (1) simple projection methods and (2) computationally intensive least-squares approaches. This