Conventional Time-frequency Peak Filtering Research Articles

Random Noise Suppression Method of Micro-Seismic Data Based on CEEMDAN-FE-TFPF

As rock fractures caused by micro-seismic events has potential safety hazards to underground workers, it is often necessary to accurately locate the micro-seismic source for hidden danger investigation. Micro-seismic data are generated in complex underground environments which are significantly affected by random noise. These data greatly influence subsequent micro-seismic source location, energy estimation, and disaster monitoring. In this paper, a new denoising method based on Time-Frequency Peak Filtering (TFPF) and Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) is proposed for micro-seismic data. Micro-seismic data are decomposed into several Intrinsic Mode Functions (IMFs) by CEEMDAN. Then, discriminant factors are used to determine which IMF needs to be denoised by TFPF. Finally, the denoised result is reconstructed by inverse CEEMDAN. By comparing and analyzing different entropies, Fuzzy Entropy (FE) is selected as the best discriminant factor. The CEEMDAN-FE-TFPF denoising method can effectively avoid the influence of fixed window length of the conventional TFPF method. The effectiveness and superiority of this method are verified by experiments of synthetic and actual data.

A Hybrid De-Noising Algorithm for the Gear Transmission System Based on CEEMDAN-PE-TFPF

In order to remove noise and preserve the important features of a signal, a hybrid de-noising algorithm based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), Permutation Entropy (PE), and Time-Frequency Peak Filtering (TFPF) is proposed. In view of the limitations of the conventional TFPF method regarding the fixed window length problem, CEEMDAN and PE are applied to compensate for this, so that the signal is balanced with respect to both noise suppression and signal fidelity. First, the Intrinsic Mode Functions (IMFs) of the original spectra are obtained using the CEEMDAN algorithm, and the PE value of each IMF is calculated to classify whether the IMF requires filtering, then, for different IMFs, we select different window lengths to filter them using TFPF; finally, the signal is reconstructed as the sum of the filtered and residual IMFs. The filtering results of a simulated and an actual gearbox vibration signal verify that the de-noising results of CEEMDAN-PE-TFPF outperforms other signal de-noising methods, and the proposed method can reveal fault characteristic information effectively.

2-D TFPF based on Contourlet transform for seismic random noise attenuation

The time–frequency peak filtering (TFPF) algorithm is useful for attenuating seismic random noise. Conventional TFPF processes each channel of the seismic record independently with a fixed window length (WL), which is a one-dimensional algorithm due to filtering along the channel direction. However, the fixed WL is not appropriate for all frequency components at the same time, so using this technique cannot preserve the reflected signals effectively. Also, Conventional TFPF ignores the spatial characteristics of reflection events, resulting in poor continuity of seismic events and serious loss of the correlation among channels. Here we introduce a new spatiotemporal method, called two-dimensional (2-D) TFPF based on Contourlet transform, which considers spatial correlation and improves the performance of the TFPF. Regarding the event as the contour in an image and using Contourlet transform (CT) to the record, we can find the optimal radial filtering trace which best matches the event, and then sample the record to extract signals along the trace. In this way, frequencies of sampled signals are low and similar. After applying the TFPF along the trace instead of along each channel, the estimation bias is decreased due to the low frequency. Moreover, using the same WL is suitable as a result of similar frequencies. Experiments on synthetic models and the field data illustrate that the new method performs well in random noise attenuation and reflection event preservation.

Simultaneous denoising and preserving of seismic signals by multiscale time-frequency peak filtering

Time frequency peak filtering has been successfully applied to eliminate pervasive random noise in the time-frequency domain. The linearity of the signal is crucial for denoising in the time frequency peak filtering method. We usually apply pseudo Wigner–Ville distribution to make the signal locally linear in time. However, there is a pair of contradiction in window length selection for pseudo Wigner–Ville distribution. If we choose a short window length for pseudo Wigner–Ville distribution in the time frequency peak filtering, it leads to good preservation for signals, but the denoising performance is relatively poor. So the contradiction between the signal preservation and noise attenuation cannot be solved by a fixed window length. In this paper, we present a multiscale time frequency peak filtering to solve this problem. In the novel method, we adopt a Laplacian pyramid to decompose the seismic data into multiple scale components. These components have different frequencies. Then a short window length can be chosen for signal-dominant scale to preserve the signal and a long window length is applied to noise-dominant scale by the time frequency peak filtering to suppress more noise. We test the performance of our proposed method on both synthetic and real seismic data. Tests demonstrate that the multiscale time frequency peak filtering based on Laplacian pyramid can eliminate the random noise more effectively and preserve events of interest better than the conventional time frequency peak filtering.

Noise Attenuation for Seismic Data by Hyperbolic-Trace Time-Frequency Peak Filtering

Time-frequency peak filtering (TFPF) is a method commonly used for seismic random noise attenuation due to its excellent practical application. However, a conventional TFPF often produces significant deviations at the peak or valley of the signal where the linearity is poor. Here, we propose a novel hyperbolic-trace TFPF (HT-TFPF) approach to reduce these deviations and recover the effective signal more completely. In this method, a hyperbolic trace with a certain curvature is ascertained by fitting the reflection event to scan the seismic record. Data sequences are extracted from the seismic record along these hyperbolic traces, and their linearity is greatly improved. Then, they are taken as a new input for TFPF. HT-TFPF can preserve the signal amplitude while achieving an excellent performance of noise suppression with a long unbias window length. Tests on both synthetic records and common shot point data indicate that the HT-TFPF method can attenuate more random noise and recover events more clearly and continuously than the conventional TFPF.

Varying-Window-Length TFPF in High-Resolution Radon Domain for Seismic Random Noise Attenuation

The time–frequency peak filtering (TFPF) algorithm is an effective method for seismic random noise attenuation. The conventional TFPF filters seismic data only along the channel direction, ignoring the spatial characteristics of the reflection events, which results in the loss of directional information. In order to improve the filtering performance of TFPF, we adopt a Radon transform to implement spatiotemporal 2-D TFPF, which is doing TFPF in the Radon domain. Since this method takes the spatial correlation of the reflection events into account, it could extract the reflection events better than the conventional TFPF. As the conventional Radon transform may produce a smearing phenomenon, we apply an improved least squares high-resolution Radon transform to assist TFPF in this letter. Thus, the events can be highly focused to energy points in different positions of the Radon domain. Then we identify the signal parts and process them by TFPF with short window length (WL). The other parts are considered as noise, and we process them by TFPF with long WL. By virtue of this new method, we can preserve the valid signal better and suppress the random noise more effectively. Through experiments on the synthetic seismic records and the field seismic data, the new method possesses a superior performance in random noise attenuation and seismic event preservation compared with the conventional TFPF and Radon TFPF methods.

Matching-Pursuit-Based Spatial-Trace Time-Frequency Peak Filtering for Seismic Random Noise Attenuation

Time-frequency peak filtering (TFPF) is an effective seismic random noise attenuation method at low signal-to-noise ratio (SNR). However, the conventional TFPF is biased for seismic signals with high frequency. We propose a spatial-trace TFPF (ST-TFPF) algorithm for reducing random noise in seismic data and simultaneously the bias of TFPF. The proposed method takes into consideration the lateral coherence between the neighboring traces as constraint of TFPF. To reduce bias, this algorithm takes TFPF along seismic events. The first stage of the proposed method preliminarily identifies the position of seismic reflection events using matching pursuit. The second stage consists of analyzing time delay of neighboring traces to construct spatial traces along seismic events. The last stage of algorithm consists of encoding seismic data along the constructed spatial traces and detecting the pseudo-Wigner-Ville distribution peaks of the encoded signals to reduce random noise. We assess our method on the synthetic and field data. The results illustrate that the ST-TFPF extends the signal preserving ability of TFPF in a wider range of window length at low SNR. Furthermore, comparison with conventional TFPF and wavelet denoising method shows that our method outperforms the two methods in random noise attenuation and seismic signal enhancement.

Seismic random noise attenuation and signal-preserving by multiple directional time-frequency peak filtering

Time-frequency peak filtering (TFPF) is an effective method for seismic random noise attenuation. The linearity of the signal has a significant influence on the accuracy of the TFPF method. The higher the linearity of the signal to be filtered is, the better the denoising result is. With this in mind, and taking the lateral coherence of reflected events into account, we do TFPF along the reflected events to improve the degree of linearity and enhance the continuity of these events. The key factor to realize this idea is to find the traces of the reflected events. However, the traces of the events are too hard to obtain in the complicated field seismic data. In this paper, we propose a Multiple Directional TFPF (MD–TFPF), in which the filtering is performed in certain direction components of the seismic data. These components are obtained by a directional filter bank. In each direction component, we do TFPF along these decomposed reflected events (the local direction of the events) instead of the channel direction. The final result is achieved by adding up the filtering results of all decomposition directions of seismic data. In this way, filtering along the reflected events is implemented without accurately finding the directions. The effectiveness of the proposed method is tested on synthetic and field seismic data. The experimental results demonstrate that MD–TFPF can more effectively eliminate random noise and enhance the continuity of the reflected events with better preservation than the conventional TFPF, curvelet denoising method and F–X deconvolution method.

Local spatiotemporal time–frequency peak filtering method for seismic random noise reduction

To achieve a higher level of seismic random noise suppression, the Radon transform has been adopted to implement spatiotemporal time–frequency peak filtering (TFPF) in our previous studies. Those studies involved performing TFPF in full-aperture Radon domain, including linear Radon and parabolic Radon. Although the superiority of this method to the conventional TFPF has been tested through processing on synthetic seismic models and field seismic data, there are still some limitations in the method. Both full-aperture linear Radon and parabolic Radon are applicable and effective for some relatively simple situations (e.g., curve reflection events with regular geometry) but inapplicable for complicated situations such as reflection events with irregular shapes, or interlaced events with quite different slope or curvature parameters. Therefore, a localized approach to the application of the Radon transform must be applied. It would serve the filter method better by adapting the transform to the local character of the data variations. In this article, we propose an idea that adopts the local Radon transform referred to as piecewise full-aperture Radon to realize spatiotemporal TFPF, called local spatiotemporal TFPF. Through experiments on synthetic seismic models and field seismic data, this study demonstrates the advantage of our method in seismic random noise reduction and reflection event recovery for relatively complicated situations of seismic data.

Variable-Eccentricity Hyperbolic-Trace TFPF for Seismic Random Noise Attenuation

Seismic noise attenuation to improve signal-to-noise ratio plays an important role in seismic data processing. In recent years, time-frequency peak filtering (TFPF) has been introduced and applied to seismic random noise attenuation successfully. However, in the conventional TFPF, the window length (WL) is fixed and used for all frequency components. As a consequence, serious loss of the effective components is unavoidable due to the inappropriate WL. The recently proposed radial-trace TFPF adapts radial-trace transform to reduce the dominant frequencies of the effective signals. Nevertheless, the radial traces with a fixed inclination angle have some limitations for bent reflection events. To resolve these shortcomings, this paper presents a novel variable-eccentricity hyperbolic-trace TFPF. In this novel method, the noisy record is first resampled along a family of spatial–temporal hyperbolic filtering traces of different bending degrees. In this way, the spatial correlation between the adjacent channels is taken into account, the linearity of the input signals is enhanced, and the estimation bias of the instantaneous frequency is reduced. Moreover, there is little difference between the reduced dominant frequencies. A fixed WL is suitable for all reduced dominant frequencies without distortion of the effective components. Finally, we evaluate the performance of our method on some synthetic records and field data. The experimental results illustrate that our proposed method attenuates random noise effectively and recovers the effective reflection events smoothly and more continuously compared with the other methods.

Radial-Trace Time–Frequency Peak Filtering Based on Correlation Integral

Time-frequency peak filtering (TFPF) has been widely applied to suppress the random noise in seismic data in recent years. Conventional TFPF adopts a pseudo-Wigner-Ville distribution to ensure the approximate linearity of the signal. However, a short window length (WL) cannot effectively attenuate the random noise and a long WL can hardly recover the subtle structures of seismic events. In this letter, we discuss the different correlation integral values of signal and noise in the radial-trace domain for identifying the noise and signal segments. Then, a longer WL according to the noise intensity is used to remove the random noise and a shorter WL according to the frequency characteristics of the signal is used to preserve the details of the signal. The experiment results on both the synthetic model and the field seismic data show that this method can effectively remove noise from seismic record and maintain the amplitude of the valid signal.

Intermediate-Frequency Seismic Record Discrimination by Radial Trace Time–Frequency Filtering

In this letter, we research a spatiotemporal-domain-based time-frequency peak filtering (TFPF) method in order to remove the large error (bias) of the conventional TFPF in intermediate-frequency seismic record discrimination. An intermediate-frequency seismic signal is one whose dominant frequency is about 40 Hz or higher. To find a balance between noise attenuation and reflected signal preservation, the radial-trace TPFT (RT-TFPF) takes both the unbiased condition and the adjacent seismic traces' correlation into consideration, and uses the RT transform to obtain a reduced-frequency input to decrease the TFPF error. Therefore, this method can discriminate some reflection events weakened by the conventional TFPF algorithm. First, we decrease the intermediate frequencies along RTs nearly aligned with the reflection event. Then, we obtain a less biased TFPF estimation with suitable window length τ. Finally, we recover the original intermediate frequency with the inverse RT transform. With the RT-TFPF, we can enhance reflection events without sacrificing frequency components while attenuating as much random noise as possible. Experiments on both synthetic model and field data demonstrate that the RT-TFPF performs well both in random noise attenuation and intermediate-frequency preservation, in addition to presenting advantages over the conventional TFPF.

Random-Noise Attenuation for Seismic Data by Local Parallel Radial-Trace TFPF

Time-frequency peak filtering (TFPF) is a new and effective tool for random-noise attenuation in the time-frequency domain. The conventional TFPF processes each channel of the seismic record independently with a fixed window length (WL). However, different frequency signals have different optimal WLs. Obviously, a fixed WL cannot effectively attenuate random noise for all frequency components at the same time. Depending on the geometry of the reflection, we can assume that the moveout of the reflected event is locally linear. With this in mind and taking the spatial correlation of the reflection events between adjacent channels in different layers into account, we propose a novel approach which is to do the TFPF along the local direction of the reflection event instead of along the channel. This method is called the local parallel radial-trace TFPF. It not only has the advantage of TFPF in denoising but also reduces the sensitivity of WL, making the filtering more flexible and effective. Both the synthetic model and seismic data have proved its better performance in noise attenuation and effective component preservation.

An Amplitude-Preserved Time–Frequency Peak Filtering Based on Empirical Mode Decomposition for Seismic Random Noise Reduction

Time-frequency peak filtering (TFPF) is a classical filtering method in time-frequency domain. It applies Wigner-Ville distribution to estimate the instantaneous frequency of an analytical signal. There is a pair of contradiction in this method, i.e., selecting a short window length may lead to good preservation for signal amplitude but bad random noise reduction whereas selecting a long window length may lead to serious attenuation for signal amplitude but effective random noise reduction. In order to make a good tradeoff between valid signal amplitude preservation and random noise reduction, we adopt empirical mode decomposition (EMD) to improve the TFPF results. The new idea is to utilize the decomposition characteristic of EMD which decomposes a signal to several modes from high to low frequency and to take advantage of the time-frequency filtering characteristic of TFPF which can recognize the valid signal component in the time-frequency plane in order to achieve effective random noise reduction together with good amplitude preservation. Through some experiments on synthetic seismic models and field seismic records, we show the better performance of the new method compared with the conventional TFPF.

Parabolic-Trace Time-Frequency Peak Filtering for Seismic Random Noise Attenuation

Time-frequency peak filtering (TFPF) has been applied to seismic random noise attenuation in recent years. In the conventional TFPF, a fixed window length (WL) is used for all frequencies signals. Different frequencies signals have different optimal WLs. A fixed WL cannot effectively attenuate random noise for all frequencies signals. In this letter, we present a nonlinear parabolic-trace TFPF (PT-TFPF) to resolve this problem. In the novel approach, a new data matrix is extracted by resampling seismic record along some parabolic traces. It contains both temporal and spatial information of the seismic record and is taken as the new input of TFPF. In each data sequence, the linearity of the effective signals is improved and the degree of improvement is associated with the similarity of the filtering trace to the event. In addition, the dominant frequencies of the effective signals are concentrated to be similar. Thus, a fixed WL can effectively attenuate the random noise with less distortion. The optimal filtering traces are selected based upon the Canny edge detection algorithm. Finally, the effectiveness of the proposed approach is tested on the synthetic record and field data. The experimental results show that the proposed PT-TFPF has better performance than the conventional TFPF.

Seismic Random Noise Elimination by Adaptive Time-Frequency Peak Filtering

Time-frequency peak filtering (TFPF) with fixed window length effectively attenuates random noise in seismic data, but performs well only for slow-varying seismic signals. To surmount the limitation, we propose the adaptive time-frequency peak filtering with the signal-dependent window length related to the belongings of seismic data to the signal, the signal nonlinearity and the local noise variance. The fuzzy c-means clustering algorithm is used to obtain the belongings in feature space, which incorporates spatial information including local similarity feature, local mean and local median in immediate neighborhood. As a result, the window length is set different for signal and noise and relatively small for the signal with high nonlinearity. We test the proposed method on both synthetic and field seismic data, and our experimental results illustrate that the adaptive method achieves better performance over the conventional TFPF both in random noise attenuation and the effective components preservation.

Spatiotemporal Time–Frequency Peak Filtering Method for Seismic Random Noise Reduction

The time-frequency peak filtering (TFPF) is an effective method for seismic random noise reduction. To achieve a higher level of noise suppression in seismic records, we propose a novel approach in which we apply the TFPF method in Radon domain. This method, called spatiotemporal TFPF, can be applied with different types of Radon transforms (linear, parabolic, etc.) depending on the geometry of the reflection. The new method is similar to the principle of ridgelet, which is doing 1-D wavelet in linear Radon domain so that there is a parameter representing direction brought in the filtering process. Although the ridgelet has the wonderful ability to process reflection events with linearly changing characteristics, for curving events, it shows lack of effectiveness. With this in mind, and taking the superiority of TFPF into consideration, the new method as mentioned previously is proposed. Thus, it breaks the limitation of doing filtering in linear Radon domain to make the filtering more flexible and plays the advantage of TFPF in denoising. Using both synthetic and real seismic data, we show the better performance of the new method in random noise reduction and higher continuity and clarity of reflection events compared to the conventional TFPF.

Noise Attenuation for 2-D Seismic Data by Radial-Trace Time-Frequency Peak Filtering

The time-frequency peak filtering (TFPF) is an effective tool in random-noise attenuation and has been applied to seismic record denoising in recent years. The window length (WL) of the time-frequency distribution (TFD) is the key to the conventional TFPF technology. A fixed WL is not optimal for both the low- and high-frequency components at the same time; an adaptive WL results in serious distortion of the reflected waveform. In this letter, we discuss a modified TFPF along the radial-trace direction and prove its advantage in TFD window selection. Experiments on both synthetic models and field data show that the radial-trace TFPF result is no longer much influenced by the WL as the conventional TFPF. Furthermore, it can provide better performance in both random-noise attenuation and reflected signal preservation with a fixed WL.