MP算法在地震信号去噪中的应用研究
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摘要
提高地震资料的分辨率是地震资料数字处理过程中所需要解决的一项主要任务,而提高地震记录的信噪比是提高分辨率的先决条件。本文主要是研究匹配追踪(MP)算法在地震资料去噪中的初步应用。
本文首先介绍了地震资料中的噪声特点及其形成原因,进而对常用的相干噪声及非相干噪声的去噪方法分别进行了简要的介绍及分析。
然后,介绍了稀疏分解的基本理论,并对匹配追踪(MP)算法的原理及具体实现作了详细的说明。针对MP算法在地震信号分解中的应用,本文通过对地震信号特性的分析,选取了非零相位的Ricker子波来构建过完备原子库,并取得了很好的效果。
本文通过对面波干扰特性的研究,采用了基于频率滤波的MP算法实现了对叠前地震资料中面波干扰的去除。该方法主要利用了面波干扰的频率特性,通过经验值选取一个阈值频率,将MP分解过程中小于该阂值频率的时频原子进行去除,从而达到去除面波干扰的目的。根据MP算法的特性,MP算法的速度随着待分解信号长度的增加呈指数级下降。因此,为了进一步提高算法的速度,文中通过对两种加窗方法的讨论,采用了自适应加窗处理方法来减小每一步分解中的信号长度,进而提高了算法的整体速度。
最后,本文采用了基于倾角扫描的MP方法对叠前地震资料中的线性干扰进行去除。该方法充分利用了线性干扰的特性,首先利用线性干扰的线性相干特性,通过倾角扫描和小窗口技术,将地震资料截取到小区域内进行处理。然后通过对该数据体进行相关性分析来判定该数据体内是否包含线性干扰,若该数据体的平均相关系数大于某一阈值则说明该数据体内包含线性干扰,需要对其进行去噪处理。基于线性干扰的频率特性及其线性分布特性,文中进一步提出了频率去除方法和位移去除方法,即分别利用MP分解所提取出的时频原子的频率参数和位移参数来判定该原子是否满足线性干扰特性,实现了对线性干扰的有效去除。由于该算法也需应用到小窗口技术,因此对于时窗的选取文中也进行了具体的分析。
对于以上提出的每一种方法,文中都进行了针对实际地震信号的仿真实验,并对结果进行了详细分析,证明了文中所提出方法的有效性。
To improve the resolution of seismic data is a main task in the seismic data processing, and its prerequisite condition is to improve the signal-to-noise ratio. This paper is the preliminary application in denoising of seismic signal with matching pursuit algorithm.
Firstly the paper introduces the characteristic of the noises in seismic data, and then it introduces the denoising methods in coherent noises and non-coherent noises, and analyses the advantages and disadvantages of these methods.
Then, the basic theory of sparse decomposition is introduced, and dose detailed explanation to the theory and implementation of the matching pursuit algorithm. Applying to the application of MP in seismic signals'decomposition, through some analyses of seismic signal's characteristics in the paper, the non-zero phase's Ricker wavelet is selected to establish the over-complete dictionary.
The method of Matching Pursuit algorithm based on frequency filtering is provided in order to wipe out surface wave interferences through the study of this noise's characteristics. This method is based on the frequency property of surface wave interferences, a threshold frequency is selected by experience value, and then the time-frequency atoms whose frequency is less than the threshold will be removed so as to reach the purpose of wiping out the surface wave interferences. According to the characteristic of MP algorithm, the speed of this algorithm is decreased exponentially with the increase of the signal's length. Therefore, in order to further improve the algorithm's speed, two kind of adding window methods is discussed, a self-adapt adding window method is provided through reducing the signal's length in every step to improve the whole speed of the algorithm.
Finally, this paper proposes a MP method based on dip scanning to remove linear interference. This method makes full use of the linear noises'characteristics. Firstly, it through dip scanning and small window techniques to cut out the seismic data into a small area to denoise. Then, through the correlation analysis to determine whether the area's data contain linear interference. If the average correlation coefficient of this data is larger than threshold value, then there is linear noises in the data which need to be denoised. Base on the frequency and linear property of linear interference, frequency method and translation method is provided in the paper. One is based on the frequency parameter of time-frequency atoms to judge whether it meets the characteristics of linear interference, and the other one is based on the translation parameter. Linear noises can be wiped out through these two methods. Since the algorithm is also applied to the small window technology, the detailed analyses have been done about how to select the time window.
There are lots of simulation experiments on every algorithm, and the results are analyzed in detail. These simulation experiments have verified the efficiency of these methods.
本文首先介绍了地震资料中的噪声特点及其形成原因,进而对常用的相干噪声及非相干噪声的去噪方法分别进行了简要的介绍及分析。
然后,介绍了稀疏分解的基本理论,并对匹配追踪(MP)算法的原理及具体实现作了详细的说明。针对MP算法在地震信号分解中的应用,本文通过对地震信号特性的分析,选取了非零相位的Ricker子波来构建过完备原子库,并取得了很好的效果。
本文通过对面波干扰特性的研究,采用了基于频率滤波的MP算法实现了对叠前地震资料中面波干扰的去除。该方法主要利用了面波干扰的频率特性,通过经验值选取一个阈值频率,将MP分解过程中小于该阂值频率的时频原子进行去除,从而达到去除面波干扰的目的。根据MP算法的特性,MP算法的速度随着待分解信号长度的增加呈指数级下降。因此,为了进一步提高算法的速度,文中通过对两种加窗方法的讨论,采用了自适应加窗处理方法来减小每一步分解中的信号长度,进而提高了算法的整体速度。
最后,本文采用了基于倾角扫描的MP方法对叠前地震资料中的线性干扰进行去除。该方法充分利用了线性干扰的特性,首先利用线性干扰的线性相干特性,通过倾角扫描和小窗口技术,将地震资料截取到小区域内进行处理。然后通过对该数据体进行相关性分析来判定该数据体内是否包含线性干扰,若该数据体的平均相关系数大于某一阈值则说明该数据体内包含线性干扰,需要对其进行去噪处理。基于线性干扰的频率特性及其线性分布特性,文中进一步提出了频率去除方法和位移去除方法,即分别利用MP分解所提取出的时频原子的频率参数和位移参数来判定该原子是否满足线性干扰特性,实现了对线性干扰的有效去除。由于该算法也需应用到小窗口技术,因此对于时窗的选取文中也进行了具体的分析。
对于以上提出的每一种方法,文中都进行了针对实际地震信号的仿真实验,并对结果进行了详细分析,证明了文中所提出方法的有效性。
To improve the resolution of seismic data is a main task in the seismic data processing, and its prerequisite condition is to improve the signal-to-noise ratio. This paper is the preliminary application in denoising of seismic signal with matching pursuit algorithm.
Firstly the paper introduces the characteristic of the noises in seismic data, and then it introduces the denoising methods in coherent noises and non-coherent noises, and analyses the advantages and disadvantages of these methods.
Then, the basic theory of sparse decomposition is introduced, and dose detailed explanation to the theory and implementation of the matching pursuit algorithm. Applying to the application of MP in seismic signals'decomposition, through some analyses of seismic signal's characteristics in the paper, the non-zero phase's Ricker wavelet is selected to establish the over-complete dictionary.
The method of Matching Pursuit algorithm based on frequency filtering is provided in order to wipe out surface wave interferences through the study of this noise's characteristics. This method is based on the frequency property of surface wave interferences, a threshold frequency is selected by experience value, and then the time-frequency atoms whose frequency is less than the threshold will be removed so as to reach the purpose of wiping out the surface wave interferences. According to the characteristic of MP algorithm, the speed of this algorithm is decreased exponentially with the increase of the signal's length. Therefore, in order to further improve the algorithm's speed, two kind of adding window methods is discussed, a self-adapt adding window method is provided through reducing the signal's length in every step to improve the whole speed of the algorithm.
Finally, this paper proposes a MP method based on dip scanning to remove linear interference. This method makes full use of the linear noises'characteristics. Firstly, it through dip scanning and small window techniques to cut out the seismic data into a small area to denoise. Then, through the correlation analysis to determine whether the area's data contain linear interference. If the average correlation coefficient of this data is larger than threshold value, then there is linear noises in the data which need to be denoised. Base on the frequency and linear property of linear interference, frequency method and translation method is provided in the paper. One is based on the frequency parameter of time-frequency atoms to judge whether it meets the characteristics of linear interference, and the other one is based on the translation parameter. Linear noises can be wiped out through these two methods. Since the algorithm is also applied to the small window technology, the detailed analyses have been done about how to select the time window.
There are lots of simulation experiments on every algorithm, and the results are analyzed in detail. These simulation experiments have verified the efficiency of these methods.
引文
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[2]姚姚.地震波场与地震勘探[M].北京：地质出版社,2006.
[3]刘财,陈业全,刘洋,等.勘探地震资料处理新方法及新技术[M].北京：科学出版社,2006.
[4]N. Ricker. The form of laws of propagation of seismic wavelets[J]. Geophysics,1953, 18(1):10-40.
[5]P. Embree, J.P. Burg, M.M. Backus. Wide-band velocity filtering——the pie-slice process[J]. Geophysics,1963,28(6):948-974.
[6]E.A. Robinson, S. Treitel. Principles of digital wiener filtering[J]. Geophysical Prospecting,1967,15(3):311-333.
[7]R.B. Ricker. Inverse convolution filters[J]. Geophysics,1962,27(1):4-18.
[8]J.F. Claerbout. Toward a unified theory of reflector mapping[J]. Geophysics,1971,36(3): 467-481.
[9]钱绍瑚.地震勘探[M].武汉：中国地质大学出版社,1988.
[10]A.H. Balch, M.W. Lee, J.J. Miller, R.T. Ryder. The use of vertical seismic profiles in seismic investigations of the earth[J]. Geophysics,1982,47(6):906-918.
[11]夏洪瑞,陈德刚,周开明.地震资料处理中随机干扰消除方法分析[J].石油物探,2004,42(1)：93-96.
[12]Herrmann F J. Curvelet-domain matched filtering[C]. Expanded Abstracts of 78th Annual International SEG Meeting,2008.
[13]Liu X W, Nian J B, Liu H. Generalized S-transform based seismic attenuation analysis[J]. Progress in Geophysics,2006,29(1):20-24.
[14]赵天资,宋炜,王尚旭.基于匹配追踪算法的时频滤波去噪方法[J].石油物探,2008,47(4)：367-371.
[15]Claerbout J F. Slant-stacks and radial traces[R]. Stanford Exploration Project Report, 1975.
[16]Zhu W H, Kelamis P G, Liu Q L. Acquisition/Processing—Linear noise attenuation using local radial trace median filtering[J]. The Leading Edge,2004,23(8):728-729.
[17]余波,黄中玉,谈大龙,等.径向道滤波法去线性干扰[J].石油物探,2005,44(2)：109-112.
[18]夏洪瑞,唐勇.径向道技术在消除相干噪声中的应用[J].勘探地球物理进展,2007,30(6)：448-458.
[19]Cherkassky V, Yunqian M. Practical selection of SVM parameters and noise estimation for SVM regression[J]. Neural Networks,2004(17):113-126.
[20]王润秋,郑桂娟,付洪洲,等.地震资料处理中的形态滤波去噪方法[J].石油地球物理勘探,2005,40(3)：277-282.
[21]詹毅.地震资料叠前去噪方法研究[D].成都：成都理工大学博士毕业论文,2005.
[22]高少武,周兴元,蔡加铭.时间域单频干扰波的压制[J].石油地球物理勘探,2001,36(1)：51-55.
[23]周小伟.地震资料多次波去除研究[D].西安：长安大学硕士毕业论文,2008.
[24]刘法启,张关泉.小波变换与f—k算法在滤波中的应用[J].石油地球物理勘探,1996,31(6)：782-792.
[25]武喜尊.τ—P变换在煤田地震勘探资料处理中的应用[J].中国煤田地质,1994,6(2)：70-76.
[26]宗涛,孟鸿鹰,贾玉兰,等.小波包域前后向预测去噪[J].地球物理学报,1998,41(增刊)：337-346.
[27]Liu X. Ground roll suppression using the Karhunen-Loeve transform[J]. Geophysics. 1999,64(2):564-566.
[28]李亚峻,李月,杨宝俊.SVD与小波变换相结合抑制面波与随机噪声[J].计算机工程与应用,2007,43(31)：182-184.
[29]Canales, L. Random noise reduction[C].54th Annual International Meeting, SEG,1984.
[30]徐伯勋,白旭滨,于常青.信号处理及应用[M].北京：地质出版社,1997.
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