This article utilizes Savitzky-Golay (SG) filter to eliminate seismic random noise. This is a novel method for seismic random noise reduction in which SG filter adopts piecewise weighted polynomial via leastsquares estimation. Therefore, effective smoothing is achieved in extracting the original signal from noise environment while retaining the shape of the signal as close as possible to the original one. Although there are lots of classical methods such as Wiener filtering and wavelet denoising applied to eliminate seismic random noise, the SG filter outperforms them in approximating the true signal. SG filter will obtain a good tradeoff in waveform smoothing and valid signal preservation under suitable conditions. These are the appropriate window size and the polynomial degree. Through examples from synthetic seismic signals and field seismic data, we demonstrate the good performance of SG filter by comparing it with the Wiener filtering and wavelet denoising methods.

The deep convolutional neural networks (CNNs) have been shown excellent performances for image denoising. However, the denoising CNN model trained with a specific noise level cannot deal with the images which have spatiotemporally variant random noise and low signal-to-noise ratio (SNR), such as seismic images. To this end, we propose a patch-based denoising CNN method, namely PDCNN. Specifically, we cluster the overlapping patches of noisy image into K classes where the image patches have close noise levels in each class, and then choose a suitable model for denoising the corresponding class from a series of well-trained CNN models. By embodying the structural statistics, we propose a CNN model selection criterion with a structural-dependent parameter. In contrast to the manual model selection process, the more accurate CNN model is chosen automatically and effectively. The capability of the PDCNN is demonstrated on synthetic and field seismic images. Experimental results show that the proposed method largely benefits from using multiple CNN models to jointly denoise, and leads to the satisfactory denoising performance in spatiotemporally variant seismic random noise reduction and structural signal preservation. INDEX TERMS Convolutional neural networks (CNNs), clustering, patch, seismic image denoising, signal preservation, spatiotemporally variant random noise.

S U M M A R YWhen the signal-to-noise (S/N) ratio is less than −3 dB or even 0 dB, seismic events are generally difficult to identify from a common shot record. To overcome this type of problem we present a method to detect weak seismic signals based on the oscillations described by a chaotic dynamic system in phase space. The basic idea is that a non-linear chaotic oscillator is strongly immune to noise. Such a dynamic system is less influenced by noise, but it is more sensitive to periodic signals, changing from a chaotic state to a large-scale periodic phase state when excited by a weak signal. With the purpose of checking the possible contamination of the signal by noise, we have performed a numerical experiment with an oscillator controlled by the Duffing-Holmes equation, taking a distorted Ricker wavelet sequence as input signal. In doing so, we prove that the oscillator system is able to reach a large-scale periodic phase state in a strong noise environment. In the case of a common shot record with low S/N ratio, the onsets reflected from a same interface are similar to one other and can be put on a single trace with a common reference time and the periodicity of the so-generated signal follows as a consequence of moveout at a particular scanning velocity. This operation, which is called 'horizontal dynamic correction' and leads to a nearly periodic signal, is implemented on synthetic wavelet sequences taking various sampling arrival times and scanning velocities. Thereafter, two tests, both in a noisy ambient of −3.7 dB, are done using a chaotic oscillator: the first demonstrates the capability of the method to really detect a weak seismic signal; the second takes care of the fundamental weakness of the dynamic correction coming from the use of a particular scanning velocity, which is investigated from the effect caused by near-surface lateral velocity variation on the periodicity of the reconstructed seismic signal. Finally, we have developed an application of the method to real data acquired in seismic prospecting and then converted into pseudo-periodic signals, which has allowed us to discriminate fuzzy waveforms as multiples, thus illustrating in practice the performance of our working scheme.

Taking the advantage of CVS (Chaotic Vibrator System) sensitivity of large-scale periodic phase-state response to quasi-periodic or periodic signals, a series of numerical experiments were made to understand the ability of CVS to detect weak effective seismic signals in the common-shot seismic record distorted by strong stochastic noise. The results demonstrate that the large-scale periodic phase-states of CVS are correlated with the signal composition of the quasi-periodic wavelet sequence constructing from horizontal moveout of seismic events, noise strength and the noise distortion degree to signal. For the same kind of events, the higher the noise distortion degree is, the lower the detectable SNR can be reached by CVS. For seismic data with the same noise distortion degree, the closer the scanning seismic velocity (the trial moveout velocity) approaches to the accurate velocity, the higher the detectable SNR can be reached by CVS. Moreover, the truncating scanning velocities form an asymmetric belt, which indirectly makes CVS achieve a large-scale periodic phase-state and then the ratio of wavelet distortion coefficients in events can be a biggish variable scope.Keywords: seismic prospecting event, phase-state of chaotic vibrator system, signal-to-noise ratio (SNR), truncating scanning velocity, distortion coefficient vector D.Seismic method is a major tool in the oil and gas exploration. The SNR enhancement of seismic data is significant for the fine exploration of oil and gas. Therefore, many filtering techniques were developed and successfully applied to improving the SNR of seismic data [1][2][3] . However, for seismic data with strong stochastic noise (e.g., SNR is less than 1), the developed and widely used filtering methods are still hard to effectively suppress the stochastic noise. Especially, more attention is paid to carrying out seismic prospecting in the areas such as deserts, hills and forests, with very complicated surface geologic conditions of much stronger stochastic noise in seismic data acquired in such kinds of difficult conditions. The suppression of stochastic noise will be also remarkably beneficial to converted shear wave processing with multi-component seismic data, deep sounding seismic data processing and reliable extraction and identification of weakly reflected characteristics of oil/gas reservoirs. In order to solve the problem, taking the advantage of specific characteristics of CVS, namely the strong sensitiveness of large-scale periodic phase-state response to the quasi-periodic or periodic signals coupled with strong stochastic noise [4,5] , we have successfully processed seismic data with SNR less than 1 and even to -8 dB [4] .In order to use the chaotic vibrator method to extract weak seismic signals, seismic trace wavelet along the same event in the common-shot seismic record should be moved to the specific position along a time axis with equal time interval to form a quasi-periodic signal series. For convenience, we call the process the horizontal moveout, and the word ...

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