基于压缩感知的小波阈值和CEEMD联合去噪方法
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摘要
中深层地质条件复杂,地震资料品质差,主要表现为:地震资料信噪比低、有效信号弱.如何在去噪的同时有效保留弱有效信号,获取高信噪比的地震数据成为地震数据处理的关键问题.传统小波阈值与互补集合经验模态分解(CEEMD)联合去噪方法相比单一方法可以获取更高品质的地震数据.基于压缩感知理论的去噪方法利用地震数据在变换域中的稀疏特性,通过设定稀疏基矩阵和测量矩阵,可以将地震数据去噪问题转化成求解最优化问题,通过最优解重构原始信号,实现对地震资料的去噪处理.该方法能够在有效衰减随机噪声的同时最大限度的保留有效信号.本文基于压缩感知理论开展小波阈值去噪方法研究,并在此基础上结合CEEMD方法对含噪较多的固有模态分量进行有针对性的随机噪声压制.通过对含噪数据开展不同方法的去噪结果对比可见,本文方法可以在保证高信噪比的基础上更为有效的保留弱有效信号,数值试算验证了该方法对弱有效信号地震数据去噪具有显著优势.
The mid-deep even super-deep layer seismic exploration has gradually turns to the focus of current seismic exploration. The geological conditions of the mid-deep layers are usually complex and the quality of the seismic data is poor, the main performance is that the signal to noise ratio is low and the useful signal is weak. Therefore, the key problem of seismic data processing is that how to effectively save the weak signal during the denoising process and how to get seismic data with high signal to noise ratio. The traditional wavelet threshold and Complete Ensemble Empirical Mode Decomposition(CEEMD)jointed denoising method can obtain seismic data with higher quality compared to both single method. The denoising method based on compressed sensing theory utilizes the sparse characteristics of seismic data in the transform domain. By setting the sparse basis matrix and the measurement matrix, the seismic data denoising problem can be transformed into solving the optimal problem. The original signal is reconstructed by the optimal solution to realize the denoising of the seismic data. This method can effectively attenuate random noise while maximally retaining the effective signal. In this paper, we do research on the wavelet threshold denoising based on the compressed sensing theory, on the basis of this concept, we suppress the noise of the IMF components with abundant random noise combining the CEEMD method. Through the denoising results of the noise data using different methods, it can be concluded that this approach can better preserve the weak signal while ensuring the high signal to noise ratio. The numerical examples verify the distinct advantages of our approach on denoising of the mid-deep layer seismic data with weak signal.
The mid-deep even super-deep layer seismic exploration has gradually turns to the focus of current seismic exploration. The geological conditions of the mid-deep layers are usually complex and the quality of the seismic data is poor, the main performance is that the signal to noise ratio is low and the useful signal is weak. Therefore, the key problem of seismic data processing is that how to effectively save the weak signal during the denoising process and how to get seismic data with high signal to noise ratio. The traditional wavelet threshold and Complete Ensemble Empirical Mode Decomposition(CEEMD)jointed denoising method can obtain seismic data with higher quality compared to both single method. The denoising method based on compressed sensing theory utilizes the sparse characteristics of seismic data in the transform domain. By setting the sparse basis matrix and the measurement matrix, the seismic data denoising problem can be transformed into solving the optimal problem. The original signal is reconstructed by the optimal solution to realize the denoising of the seismic data. This method can effectively attenuate random noise while maximally retaining the effective signal. In this paper, we do research on the wavelet threshold denoising based on the compressed sensing theory, on the basis of this concept, we suppress the noise of the IMF components with abundant random noise combining the CEEMD method. Through the denoising results of the noise data using different methods, it can be concluded that this approach can better preserve the weak signal while ensuring the high signal to noise ratio. The numerical examples verify the distinct advantages of our approach on denoising of the mid-deep layer seismic data with weak signal.
引文
Du X L, He L Z, Hou W. 2007. A study of wavelet threshold denoising based on empirical mode decomposition(EMD) [J]. Journal of Beijing university of technology (in Chinese), 33(3): 265-272.
Liu J X, Han S L, MA J. 2006. Application of wavelet analysis in seismic data denoising [J]. Progress in Geophysics (in Chinese), 21(2): 541-545.
Liu W, Cao S Y, Cui Z. 2015. Random noise attenuation based on compressive sensing and TV rule [J]. Geophysical Prospecting for Petroleum (in Chinese), 54(2): 180-187.
Miao X G, Moon W M. 1999. Application of wavelet transform in reflection seismic data analysis [J]. Geosciences Journal, 3(3): 171-179.
Sifuzzaman M, Islam M R, Ali M Z. 2009. Application of wavelet transform and its advantages compared to Fourier transform [J]. Journal of Physical Sciences, 13: 121-134.
Song W Q, Zhang Y, Wu C D, et al. 2017. The method of weak seismic reflection signal processing and extracting based on multitrace joint compressed sensing [J]. Chinese Journal Of Geophysics (in Chinese), 60(8): 3238-3245, doi: 10.6038/cjg20170828.
Tian Y N, Li Y, Lin H B, et al. 2015. Application of GNMF wavelet spectral unmixing in seismic noise suppresion [J]. Chinese J. Geophys.(in Chinese),58(12):4568- 4575,doi: 10.6038/cjg20151219.
To A C, Moore J R, Glaser S D. 2009. Wavelet denoising techniques with applications to experimental geophysical data [J]. Signal Processing, 89(2): 144-160.
Wang J, Li Z C, Wang D Y. 2014. Research on wavelet threshold denoising method of seismic data based on CEEMD [J]. Geophysical Prospecting for Petroleum (in Chinese), 53(2): 164-172.
Wang X W, Wang H Z. 2014. A research of high-resolution plane-wave decomposition based on compressed sensing [J]. Chinese Journal Of Geophysics (in Chinese), 57(9): 2946-2960, doi: 10.6038/cjg20140920.
Wu Z C, Liu T Y. 2008. Wavelet transform methods in seismic data noise attenuation [J]. Progress in Geophysics (in Chinese), 23(2): 493- 499.
Wu Z H, Huang N E. 2004. A study of the characteristics of white noise using the empirical mode decomposition method [J]. Proc. Roy. Soc. London, 460(2046): 1597-1611.
Wu Z H, Huang N E. 2009. Ensemble Empirical Mode Decomposition: A Noise Assisted Date Analysis Method [J]. Advances in Adaptive Data Analysis, 1(1): 1- 41.
Yang Z M, Huang D Y. 1994. Application of wavelet transform in improving both signal/noise ratio and resolution of seismic data [J]. OGP. (in Chinese), 29(5): 623- 629.
Yeh J R, Shieh J S, Huang N E. 2010. Complementary Ensemble Empirical Mode Decomposition: A Novel Noise Enhanced Data Analysis Method [J]. Advances in Adaptive Data Analysis, 2(2): 135-156.
Zhao Y, Yue Y X, Huang J L, et al. 2015. CEEMD and wavelet transform jointed de-noising method [J]. Progress in Geophysics (in Chinese), 30(6): 2870-2877, doi: 10.6038/pg20150655.
杜修力, 何立志, 侯伟. 2007. 基于经验模态分解(EMD)的小波阈值除噪方法[J]. 北京工业大学学报, 33(3): 265-272.
柳建新, 韩世礼, 马捷. 2006. 小波分析在地震资料去噪中的应用[J]. 地球物理学进展, 21(2): 541-545.
刘伟, 曹思远, 崔震. 2015. 基于压缩感知和TV准则约束的地震资料去噪[J]. 石油物探, 54(2): 180-187.
宋维琪, 张宇, 吴彩端, 等. 2017. 多道联合压缩感知弱小反射地震信号提取处理方法[J]. 地球物理学报, 60(8): 3238-3245, doi: 10.6038/cjg20170828.
田雅男, 李月, 林红波, 等. 2015. GNMF小波谱分离在地震勘探噪声压制中的应用[J]. 地球物理学报, 58(12): 4568- 4575, doi: 10.6038/cjg20151219.
王姣, 李振春, 王德营. 2014. 基于CEEMD的地震数据小波阈值去噪方法研究[J]. 石油物探, 53(2): 164-172.
王雄文, 王华忠. 2014. 基于压缩感知的高分辨率平面波分解方法研究[J]. 地球物理学报, 57(9): 2946-2960, doi: 10.6038/cjg20140920.
吴招才, 刘天佑. 2008. 地震数据去噪中的小波方法[J]. 地球物理学进展, 23(2): 493- 499.
杨忠民, 黄大云. 1994. 小波变换在提高资料的信噪比和分辨率中的应用[J]. 石油地球物理勘探, 29(5): 623- 629.
赵迎, 乐友喜, 黄健良, 等. 2015. CEEMD与小波变换联合去噪方法研究[J]. 地球物理学进展, 30(6): 2870-2877, doi: 10.6038/pg20150655.
Liu J X, Han S L, MA J. 2006. Application of wavelet analysis in seismic data denoising [J]. Progress in Geophysics (in Chinese), 21(2): 541-545.
Liu W, Cao S Y, Cui Z. 2015. Random noise attenuation based on compressive sensing and TV rule [J]. Geophysical Prospecting for Petroleum (in Chinese), 54(2): 180-187.
Miao X G, Moon W M. 1999. Application of wavelet transform in reflection seismic data analysis [J]. Geosciences Journal, 3(3): 171-179.
Sifuzzaman M, Islam M R, Ali M Z. 2009. Application of wavelet transform and its advantages compared to Fourier transform [J]. Journal of Physical Sciences, 13: 121-134.
Song W Q, Zhang Y, Wu C D, et al. 2017. The method of weak seismic reflection signal processing and extracting based on multitrace joint compressed sensing [J]. Chinese Journal Of Geophysics (in Chinese), 60(8): 3238-3245, doi: 10.6038/cjg20170828.
Tian Y N, Li Y, Lin H B, et al. 2015. Application of GNMF wavelet spectral unmixing in seismic noise suppresion [J]. Chinese J. Geophys.(in Chinese),58(12):4568- 4575,doi: 10.6038/cjg20151219.
To A C, Moore J R, Glaser S D. 2009. Wavelet denoising techniques with applications to experimental geophysical data [J]. Signal Processing, 89(2): 144-160.
Wang J, Li Z C, Wang D Y. 2014. Research on wavelet threshold denoising method of seismic data based on CEEMD [J]. Geophysical Prospecting for Petroleum (in Chinese), 53(2): 164-172.
Wang X W, Wang H Z. 2014. A research of high-resolution plane-wave decomposition based on compressed sensing [J]. Chinese Journal Of Geophysics (in Chinese), 57(9): 2946-2960, doi: 10.6038/cjg20140920.
Wu Z C, Liu T Y. 2008. Wavelet transform methods in seismic data noise attenuation [J]. Progress in Geophysics (in Chinese), 23(2): 493- 499.
Wu Z H, Huang N E. 2004. A study of the characteristics of white noise using the empirical mode decomposition method [J]. Proc. Roy. Soc. London, 460(2046): 1597-1611.
Wu Z H, Huang N E. 2009. Ensemble Empirical Mode Decomposition: A Noise Assisted Date Analysis Method [J]. Advances in Adaptive Data Analysis, 1(1): 1- 41.
Yang Z M, Huang D Y. 1994. Application of wavelet transform in improving both signal/noise ratio and resolution of seismic data [J]. OGP. (in Chinese), 29(5): 623- 629.
Yeh J R, Shieh J S, Huang N E. 2010. Complementary Ensemble Empirical Mode Decomposition: A Novel Noise Enhanced Data Analysis Method [J]. Advances in Adaptive Data Analysis, 2(2): 135-156.
Zhao Y, Yue Y X, Huang J L, et al. 2015. CEEMD and wavelet transform jointed de-noising method [J]. Progress in Geophysics (in Chinese), 30(6): 2870-2877, doi: 10.6038/pg20150655.
杜修力, 何立志, 侯伟. 2007. 基于经验模态分解(EMD)的小波阈值除噪方法[J]. 北京工业大学学报, 33(3): 265-272.
柳建新, 韩世礼, 马捷. 2006. 小波分析在地震资料去噪中的应用[J]. 地球物理学进展, 21(2): 541-545.
刘伟, 曹思远, 崔震. 2015. 基于压缩感知和TV准则约束的地震资料去噪[J]. 石油物探, 54(2): 180-187.
宋维琪, 张宇, 吴彩端, 等. 2017. 多道联合压缩感知弱小反射地震信号提取处理方法[J]. 地球物理学报, 60(8): 3238-3245, doi: 10.6038/cjg20170828.
田雅男, 李月, 林红波, 等. 2015. GNMF小波谱分离在地震勘探噪声压制中的应用[J]. 地球物理学报, 58(12): 4568- 4575, doi: 10.6038/cjg20151219.
王姣, 李振春, 王德营. 2014. 基于CEEMD的地震数据小波阈值去噪方法研究[J]. 石油物探, 53(2): 164-172.
王雄文, 王华忠. 2014. 基于压缩感知的高分辨率平面波分解方法研究[J]. 地球物理学报, 57(9): 2946-2960, doi: 10.6038/cjg20140920.
吴招才, 刘天佑. 2008. 地震数据去噪中的小波方法[J]. 地球物理学进展, 23(2): 493- 499.
杨忠民, 黄大云. 1994. 小波变换在提高资料的信噪比和分辨率中的应用[J]. 石油地球物理勘探, 29(5): 623- 629.
赵迎, 乐友喜, 黄健良, 等. 2015. CEEMD与小波变换联合去噪方法研究[J]. 地球物理学进展, 30(6): 2870-2877, doi: 10.6038/pg20150655.