基于分数阶小波域GSM模型的地震信号随机噪声压制方法
|
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.
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.
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.
引文
Andrews D F,Mallows C L.1974.Scale mixtures of normal distributions.Journal of the Royal Statistical Society Series B-Methodological,36(1):99-102.
Cao S,Chen X.2005.The second-generation wavelet transform and its application in denoising of seismic data.Applied Geophysics,2(2):70-74.
Donoho D L,Johnstone J M.1994.Ideal spatial adaptation by wavelet shrinkage.Biometricka,81(3):425-455.
Gao G R,Xu L P,Feng D Z.2013.Image denoising based on the NSST domain GSM model.Geomatics and Information Science of Wuhan University(in Chinese),38(7):778-782.
Li X Y,Zhang J,Kong X Q,et al.2013.High frequency seismic nosie adaptive suppression based on discrete wavelet transform.Geophysical and Geochemical Exploration(in Chinese),37(1):165-170.
Lin H B,Ma H T,Li Y,et al.2015.Elimination of seismic random noise based on the SW statistic adaptive TFPF.Chinese Journal of Geophysics(in Chinese),58(12):4559-4567.
Lin H B,Li Y,Ma H,Xu L.2016.Simultaneous seismic random noise attenuation and signal preservation by optimal spatiotemporal TFPF.Journal of Applied Geophysics,128:123-130.
Liu H Y,Wei Z H,Zhang Z R.2009.Total variation image denoising based on fractional B-spline wavelet.Computer Engineering Applications(in Chinese),45(11):19-21.
Parkan M S,Siahkoohi H R,Parkan M S,et al.2014.The multidimensional complete ensemble empirical mode decomposition and its application in seismic denoising.Journal of the History of the Behavioral Sciences,32:297-301.
Portilla J,Strela V,Wainwright M J,et al.2003.Image denoising using scale mixtures of gaussians in the wavelet domain.IEEETransactionsonImageProcessing,12(11):1338-1351.
Shuai S,Han L G,Lv Q T,et al.2013.Seismic random noise suppression using an adaptive nonlocal means algorithm.Applied Geophysics,10(1):33-40.
Tang R,Zhang J D,Zhang Q.2013.Hybrid Fourier-wavelet image denoising using local Gaussian scale mixtures model.Laser Infrared(in Chinese),43(5):592-595.
Unser M,Blu T.2000.Fractional splines and wavelets.Siam Review,42(1):43-67.
Wu Z C,Liu T Y.2008.Wavelet transform methods in seismic data noise attenuation.Progress in Geophysics,23(2):493-499.
Zhang H,Liu T,Zhang Y.2009.Denoising of seismic data via multiscale ridgelet transform.Earthquake Science,22(5):493-498.
Zhang Z,Cui C,Liu K.2011.Iterative hard-threshold algorithm with momentum.Electronics Letters,47(4):257-259.
高国荣,许录平,冯冬竹.2013.利用非抽样Shearlet域GSM模型进行图像去噪.武汉大学学报(信息科学版),38(7):778-782.
李雪英,张晶,孔祥琦等.2013.基于离散小波变换的地震资料自适应高频噪声压制.物探与化探,37(1):165-170.
林红波,马海涛,李月等.2015.基于SW统计量的自适应时频峰值滤波压制地震勘探随机噪声研究.地球物理学报,58(12):4559-4567.
刘红毅,韦志辉,张峥嵘.2009.分数阶B样条小波域的图像变分去噪.计算机工程与应用,45(11):19-21.
彭才,朱仕军,孙建库等.2007.小波变换域K-L变换及其去噪效果分析.石油物探,46(2):112-114.
唐锐,张敬东,张祺.2013.局部高斯尺度混合模型的傅里叶-小波图像降噪.激光与红外,43(5):592-595.
Cao S,Chen X.2005.The second-generation wavelet transform and its application in denoising of seismic data.Applied Geophysics,2(2):70-74.
Donoho D L,Johnstone J M.1994.Ideal spatial adaptation by wavelet shrinkage.Biometricka,81(3):425-455.
Gao G R,Xu L P,Feng D Z.2013.Image denoising based on the NSST domain GSM model.Geomatics and Information Science of Wuhan University(in Chinese),38(7):778-782.
Li X Y,Zhang J,Kong X Q,et al.2013.High frequency seismic nosie adaptive suppression based on discrete wavelet transform.Geophysical and Geochemical Exploration(in Chinese),37(1):165-170.
Lin H B,Ma H T,Li Y,et al.2015.Elimination of seismic random noise based on the SW statistic adaptive TFPF.Chinese Journal of Geophysics(in Chinese),58(12):4559-4567.
Lin H B,Li Y,Ma H,Xu L.2016.Simultaneous seismic random noise attenuation and signal preservation by optimal spatiotemporal TFPF.Journal of Applied Geophysics,128:123-130.
Liu H Y,Wei Z H,Zhang Z R.2009.Total variation image denoising based on fractional B-spline wavelet.Computer Engineering Applications(in Chinese),45(11):19-21.
Parkan M S,Siahkoohi H R,Parkan M S,et al.2014.The multidimensional complete ensemble empirical mode decomposition and its application in seismic denoising.Journal of the History of the Behavioral Sciences,32:297-301.
Portilla J,Strela V,Wainwright M J,et al.2003.Image denoising using scale mixtures of gaussians in the wavelet domain.IEEETransactionsonImageProcessing,12(11):1338-1351.
Shuai S,Han L G,Lv Q T,et al.2013.Seismic random noise suppression using an adaptive nonlocal means algorithm.Applied Geophysics,10(1):33-40.
Tang R,Zhang J D,Zhang Q.2013.Hybrid Fourier-wavelet image denoising using local Gaussian scale mixtures model.Laser Infrared(in Chinese),43(5):592-595.
Unser M,Blu T.2000.Fractional splines and wavelets.Siam Review,42(1):43-67.
Wu Z C,Liu T Y.2008.Wavelet transform methods in seismic data noise attenuation.Progress in Geophysics,23(2):493-499.
Zhang H,Liu T,Zhang Y.2009.Denoising of seismic data via multiscale ridgelet transform.Earthquake Science,22(5):493-498.
Zhang Z,Cui C,Liu K.2011.Iterative hard-threshold algorithm with momentum.Electronics Letters,47(4):257-259.
高国荣,许录平,冯冬竹.2013.利用非抽样Shearlet域GSM模型进行图像去噪.武汉大学学报(信息科学版),38(7):778-782.
李雪英,张晶,孔祥琦等.2013.基于离散小波变换的地震资料自适应高频噪声压制.物探与化探,37(1):165-170.
林红波,马海涛,李月等.2015.基于SW统计量的自适应时频峰值滤波压制地震勘探随机噪声研究.地球物理学报,58(12):4559-4567.
刘红毅,韦志辉,张峥嵘.2009.分数阶B样条小波域的图像变分去噪.计算机工程与应用,45(11):19-21.
彭才,朱仕军,孙建库等.2007.小波变换域K-L变换及其去噪效果分析.石油物探,46(2):112-114.
唐锐,张敬东,张祺.2013.局部高斯尺度混合模型的傅里叶-小波图像降噪.激光与红外,43(5):592-595.