Random noise attenuation method of seismic signal based on the fractional order wavelet domain GSM model
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摘要:
地震信号中的随机噪声是一种干扰波，严重降低了地震信号的信噪比，并影响着资料的后续处理和分析.本文根据地震信号中有效信号和随机噪声的差异，结合分数阶B样条小波变换与高斯尺度混合模型提出了一种地震信号随机噪声压制方法.首先利用分数阶B样条小波变换将含噪地震信号映射到最优分数阶小波时频域内，然后对各小波子带系数分别建立高斯尺度混合模型，由贝叶斯方法估计出源地震信号小波系数，最后使用分数阶B样条小波逆变换重构得到降噪后的地震信号.利用本文方法对合成地震记录和实际地震信号进行降噪处理，实验结果表明本文方法能够有效地压制地震信号中的随机噪声，并且较好地保留了有效信号.
Abstract:Random noise is a kind of interference wave, which reduces the signal-to-noise ratio of the seismic signal. It also affects the subsequent data processing and analysis of the seismic signal. According to the differences of the effective signal and the random noise, this paper puts forward a new method combining the fractional order B spline wavelet transform with Gaussian Scale Mixture model to attenuate the random noise of the seismic signal. Firstly, the seismic signal is transformed into the optimal factional wavelet time-frequency domain using the fractional order B spline wavelet. Gaussian Scale Mixture model is set up for each sub-band coefficients. Bayesian method is used to estimate the wavelet coefficients of the original seismic signal. Finally, the denoised seismic signal can be reconstructed using the fractional order B spline wavelet inverse transform. Through experiments on synthetic records and the field seismic signal, the results demonstrate that the proposed method can attenuate random noise of the seismic signal effectively.
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图 1
分数阶B样条小波分解和合成示意图
Figure 1.
Schematic diagram of fractional order B spline wavelet decomposition and synthesis
图 2
含噪合成地震信号以及它的一层分数阶B样条小波分解系数
Figure 2.
The noisy synthetic seismic signal and the one layer fractional B spline wavelet transform coefficients
图 5
单道地震信号降噪结果及对应的振幅谱
Figure 5.
The denoised results of single channel seismic signal and corresponding amplitude spectrum
表 1
降噪后的SNR和MSE
Table 1.
SNR and MSE values after denoising
σ 降噪前 小波域GSM模型 小波软阈值 小波硬阈值 本文方法 SNR SNR MSE SNR MSE SNR MSE SNR MSE 50 -0.39 10.92 185.12 9.02 286.16 10.51 203.34 11.09 177.84 60 -1.97 9.40 263.50 8.24 342.61 9.33 266.68 9.88 234.95 70 -3.31 8.11 353.37 7.60 397.01 8.68 310.00 8.82 299.76 
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