Random noise suppression of marine seismic data based on improved generalized S transform
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摘要: 常规广义S变换采用固定的高斯窗参数，在时频分析时不能够兼顾高低频端的信号，同时标准S逆变换在时频域滤波时会产生滤波噪音。本文提出了基于变频率高斯窗的广义S变换，同时改进了S逆变换公式。该方法不仅提升了信号时频谱的聚焦度，而且还消除了滤波噪音。通过计算包含随机噪声干扰信号的瞬时信噪比阈值，然后根据不同阈值有针对性的选择压制随机噪音的处理策略。合成数据和实际地震数据处理结果表明，该方法能够有效的压制随机噪音，提高地震数据信噪比。Abstract: Conventional generalized S transform (GST) uses fixed parameters for Gaussian window, which makes it impossible to take into account the high and low frequency signals in the time-frequency analysis. At the same time, the standard S inverse transform produces filtering noise when filtering in the time-frequency domain. In this paper, a generalized S transform based on variable frequency Gaussian window is proposed, and the inverse S transform formula is revised. This method not only improves the focus of the frequency spectrum of the signal, but also eliminates the filtering noise. By calculating the instantaneous signal-to-noise ratio threshold value of the signal containing random interference noise, and according to different threshold values, the processing strategy of suppressing the random noise is selected in a targeted manner. The processing results of synthetic data and actual seismic data show that the method can effectively suppress random noise and improve the signal-to-noise ratio of seismic data.
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图 1 理想时频谱与不同控制参数的广义S变换的时频谱
a. 理想时频；b. p=0.7，λ=1对应的时频谱；c. p=0.9, λ=1对应的时频谱；d. p=1，λ=1标准S变换时频谱；e. p=1.2，λ=1对应的时频谱；f. p=1，λ=1.2对应的时频谱；g. p=1，λ=0.9对应的时频谱；h. p=1，λ=0.6对应的时频谱。
Figure 1. Ideal time-frequency spectrum and time-frequency spectrum of S transform using different control factors
a. ideal time-frequency spectrum, b. p=0.7, λ=1 corresponding to time-frequency spectrum, c. p=0.9, λ=1 corresponding to time-frequency spectrum, d. p=1, λ=1 corresponding to time-frequency spectrum, e. p=1.2, λ=1 corresponding to time-frequency spectrum, f. p=1, λ=1.2 corresponding to time-frequency spectrum, g. p=1, λ=0.9 corresponding to time-frequency spectrum, h. p=1, λ=0.6 corresponding to time-frequency spectrum.
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图 2 合成信号时频谱图
a. 标准S变换，b. 广义S变换（p=0.8，λ=1），c. 改进的广义S变换（p=0→1，λ=1）。
Figure 2. Synthetic signal time-frequency spectrum
a. the standard S transform, b. conventional generalized S transform (p=0.8, λ=1), c. improved generalized S transform (p=0→1, λ=1).
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图 3 含随机噪声的地震信号时频谱图
a. 标准S变换，b. 广义S变换（p=0.8, λ=1），c. 改进的广义S变换（p=0→1, λ=1）。
Figure 3. Time-frequency spectrum of seismic signal with random noise
a. the standard S transform, b. conventional generalized S transform (p=0.8, λ=1), c. improved generalized S transform (p=0→1, λ=1) .
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图 4 标准S逆变换时频滤波效果图
a. 合成信号，b. 合成信号时频域滤波，c. 时间域滤波效果。
Figure 4. Effect of time and frequency filtering of standard S inverse transform
a. synthetic signal, b. time and frequency filtering of synthetic signal, c. filtering effect of time field.
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图 5 准确滤波结果和不同滤波方法计算的差值
a. 准确滤波结果，b. 标准逆变换计算差值（红色）和改进逆变换（蓝色）计算差值。
Figure 5. Accurate filtering result and difference calculated by different filtering methods
a. accurate filtering result, b. difference calculated by standard S inverse transform (red) and difference calculated by improved S inverse transform (blue).
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图 6 含噪地震记录去噪效果图
a. 48道模拟地震记录， b. 含白噪声的模拟地震记录， c. 去除噪声的模拟地震记录。
Figure 6. Denoising effect for seismic records with noise
a. 48 channels simulated seismic record, b. simulated seismic record with white noise, c. simulated seismic record after denoising.
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图 7 单道信号对比图
a. 加白噪声后与未加噪声单道信号对比， b. 去噪后与未加噪声单道信号对比。
Figure 7. Comparison of single channel signals
a. comparison of single channel signals with noise and those without noise, b. comparison of single channel signals without noise and those after noise reduction.
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图 8 时频域滤波效果对比
a. 不含白噪声模拟地震道的时频谱，b. 含白噪声模拟地震道的时频谱，c. 去除噪声模拟地震道的时频谱。
Figure 8. Comparison of filtering effects in time-frequency domain
a. time and frequency spectrum of simulated seismic channel without noise, b. time and frequency spectrum of simulated seismic channel with white noise, c. time and frequency spectrum of simulated seismic channel after noise reduction.
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图 10 两种方法压制噪声效果对比
a. 改进广义S变换压噪后剖面，b. 传统广义S变换压噪后剖面，c. 改进广义S变换去除的噪声，d. 传统广义S变换去除的噪声。
Figure 10. Comparison of noise suppression effects between two methods
a. denoised profile by improved generalized S transform, b. denoised profile by traditional generalized S transform, c. noise removal by improved generalized S transform, d. noise removal by generalized S transform.
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