Time-frequency Peak Filtering Research Articles

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.

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.

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.

Random denoising and signal nonlinearity approach by time-frequency peak filtering using weighted frequency reassignment

Time-frequency peak filtering (TFPF) may efficiently suppress random noise and hence improve the signal-to-noise ratio. However, the errors are not always satisfactory when applying the TFPF to fast-varying seismic signals. We begin with an error analysis for the TFPF by using the spread factor of the phase and cumulants of noise. This analysis shows that the nonlinear signal component and non-Gaussian random noise lead to the deviation of the pseudo-Wigner-Ville distribution (PWVD) peaks from the instantaneous frequency. The deviation introduces the signal distortion and random oscillations in the result of the TFPF. We propose a weighted reassigned smoothed PWVD with less deviation than PWVD. The proposed method adopts a frequency window to smooth away the residual oscillations in the PWVD, and incorporates a weight function in the reassignment which sharpens the time-frequency distribution for reducing the deviation. Because the weight function is determined by the lateral coherence of seismic data, the smoothed PWVD is assigned to the accurate instantaneous frequency for desired signal components by weighted frequency reassignment. As a result, the TFPF based on the weighted reassigned PWVD (TFPF_WR) can be more effective in suppressing random noise and preserving signal as compared with the TFPF using the PWVD. We test the proposed method on synthetic and field seismic data, and compare it with a wavelet-transform method and [Formula: see text] prediction filter. The results show that the proposed method provides better performance over the other methods in signal preserving under low signal-to-noise ratio.

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.

A Sparse NMF-SU for Seismic Random Noise Attenuation

A novel method based on nonnegative matrix factorization (NMF) spectral unmixing is proposed for land seismic additive random noise attenuation. In the method, the noisy seismic signal is first decomposed into a collection of intrinsic mode functions (IMFs) instead of being directly processed. These IMFs can be considered as a new set of observations. In the short-time Fourier transform (STFT) spectrum of each IMF, the degree of mixing from the effective signal and the random noise is considerably reduced. Then, a sparse NMF is used to unmix the STFT spectrum of each IMF. We get the subsignals out of the separated subspectrums by the inverse STFT. Finally, the desired signal is reconstructed from the subsignals by K-means clustering algorithm. Experimental results of both synthetic and real seismic records show that the proposed method can significantly suppress random noise and preserve the effective signal components. Comparisons with time-frequency peak filtering and f-x filtering further verify its better performance.

Suppression of strong random noise in seismic data by using time-frequency peak filtering

Time-frequency peak filtering (TFPF) is highly efficient in suppressing random noise in seismic data. Although the hypothesis of stationary Gaussian white noise cannot be fulfilled in practical seismic data, TFPF can effectively suppress white and colored random noise with different intensities, as can be theoretically demonstrated by detecting such noise in synthetic seismic data. However, a “zero-drift” effect is observed in the filtered signal and is independent of the average power and variance of the random noise, but related to its mean value. Furthermore, we consider the situation where the local linearization of the seismic data cannot be satisfied absolutely and study the “distortion” characteristics of the filtered signal using TFPF on a triangular wave. We found that over-compensation is possible in the frequency band for the triangular wave. In addition, it is nonsymmetrical and has a relationship to the time-varying curvature of the seismic wavelet. The results also present an improved approach for TFPF.

Parameter Estimation of the Projectile In-Bore Based on Time-Frequency Analysis

Combined time-frequency peak filtering with wavelet modulus maxima, the millimeter wave interferometer echo signal process is presented, extracting the instantaneous frequency(IF) of the projectile in-bore. Based on that, the projectile’s velocity and acceleration curves are estimated and the length of the cannon is also calculated that’s consistent with the actual, which provides a strong basis for designing and improving weapons. And this approach ,with some commonality, can also be used to extract the IF of other signals.

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.

Signal Enhancement by Time-Frequency Peak Filtering

Time-frequency peak filtering (TFPF) allows the reconstruction of signals from observations corrupted by additive noise by encoding the noisy signal as the instantaneous frequency (IF) of a frequency modulated (FM) analytic signal. IF estimation is then performed on the analytic signal using the peak of a time-frequency distribution (TFD) to recover the filtered signal. This method is biased when the peak of the Wigner-Ville distribution (WVD) is used to estimate the encoded signal's instantaneous frequency. We characterize a class of signals for which the method implemented using the pseudo WVD is approximately unbiased. This class contains deterministic bandlimited nonstationary multicomponent signals in additive white Gaussian noise (WGN). We then derive the pseudo WVD window length that gives a reduced bias when TFPF is used for signals from this class. Testing of the method on both synthetic and real life newborn electroencephalogram (EEG) signals shows clean recovery of the signals in noise level down to a signal-to-noise ratio (SNR) of -9 dB.