基于分频处理的叠前地震资料中面波压制
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摘要
为了满足日益增长的能源需求,地震勘探已经从东部转移到西北部,从平原转移到沙漠,在这些地区采集到的地震资料中包含着很强的线性干扰和面波,其中面波的存在使得地震数据的信噪比急剧降低,有效性也遭到了极大的破坏。因此,必须对叠前资料中的面波干扰进行压制,而常用的面波处理方法如f-x滤波,f-k滤波,小波变换等,已不能满足这种需要。
论文首先介绍了面波特点及多尺度分析的基本理论和性质,接着利用面波与有效波在频谱上的差异,分别采用多尺度变换中的二维小波变换和Curvelet变换,将地震记录分解到不同的频带内,只在面波的优势频段内进行压制处理,以保证其他频段的有效信号不会受到损伤。主要研究内容如下：
首先,对地震记录做二维小波变换,在频率波数域中确定面波的优势频段；然后,对这些区域的小波系数进行阈值处理,本文将面波压制中的阈值选取与图像处理里的阂值构造方法联系起来,引入了均值及直方图两种图像阈值方法,并将其与常用的两种阈值函数分别应用到理论模型及实际地震数据的面波压制中,对比处理后的结果发现：地震记录经直方图阈值方法处理之后,其信噪比及分辨率都得到了明显提升。最后,将本文提出的基于小波变换及直方图阈值的面波压制算法与常用的面波处理方法分别应用到实际地震资料处理中,实验结果表明：本文提出的算法在压制面波的同时有效信号也得到了增强,处理效果要优于常用处理方法。
接着,采用Curvelet变换对地震数据进行处理,它是在小波分析基础上发展起来的且能够最优表示具有曲线奇异的二维信号。算法具体思路为：首先对地震资料进行Curvelet变换,在Curvelet域中确定面波的优势频带；其次根据面波视速度低的特点,选择其在Curvelet域内对应的方向系数矩阵,利用本文建立的时域角度与Curvelet域方向的对应关系,只需根据面波在地震记录中的角度范围,就可确定其在Curvelet域的系数矩阵；接着,利用本文改进的加权均值阈值方法及其他三种阈值,对已确定存在面波的方向系数矩阵进行迭代阈值处理。理论模型及实际地震记录均证明了改进阈值的有效性。
最后,将本文提出的两种分频算法分别对实际地震资料进行面波压制,通过对处理结果分析发现：两种算法都能很好的压制面波,且Curvelet变换分频算法在有效波的连续性保持上要强于小波分频方法。
To meet the increasing demand of energy, seismic exploration has been shifted from the east to the northwest and from plains to deserts, where the seismic data gathered are always contaminated by severe linear noise and surface wave. With the presence of surface wave, the signal-to-noise ratio of the seismic data decreases rapidly, and the validness of the seismic data has been gravely damaged. Therefore, the surface wave in the pre-stack must be suppressed, while the conventional denoising methods, such as f-x filtering, f-k filtering, wavelet transform and so on, perform ineffectively to suppress surface wave.
In this paper, we first introduce the characteristics of the surface wave, and the basic theory and properties of multi-scale analysis. Then, based on the differences of spectrum between surface wave and the reflection signal, the seismic data has been sorted into different bands using the 2-D wavelet transform and Curvelet transform respectively, both of which are able to achieve multi-scale transform. With regard to the protection of signals in other bands, the processing has been applied to band dominated by surface wave. The main contents of the paper are as follows:
First,2-D wavelet transform was exploited to treat seismic record. The dominant frequency band of the surface wave in the frequency-wave number domain was determined prior to other treatments. Meanwhile, a practical connection was established between the selection of thresholds and methods of constructing thresholds in image processing, which paved the way for the introduction of average threshold and histogram threshold. In the second place, wavelet coefficients of the determined band of surface wave were further segregated with the two proposed image thresholds. These two image thresholds and two other common threshold functions were applied to theoretical analysis and actual seismic data respectively and results showed that the signal-to-noise ratio and the resolution of the seismic data were improved remarkably through the processing of histogram threshold. In the last place, the algorithm posed in this paper based on the wavelet transform and histogram threshold, together with conventional methods, was utilized to suppress surface wave in actual seismic data, which demonstrated that the proposed algorithm effectively suppressed surface wave and enhanced the reflection signal.
Then, Curvelet transform was implemented for the processing of seismic data, which has been proposed as an alternative to wavelet transform on the basis of wavelet analysis and is equipped with the ability to best represent two-dimensional signal with some plane curve singularities. The critical steps of Curvelet transform are specified as follows:Step 1. Seismic data was processed in the utilization of Curvelet transform to determine the leading band of surface wave in the Curvelet domain; Step 2. A corresponding relationship between the time domain and the direction of Curvelet domain was advanced for the purpose of defining Curvelet coefficient matrix in various orientations just according to the angle ranges of surface wave, which takes advantages of low apparent velocity of surface wave; Step 3. The Curvelet coefficient matrix was iterated through the proposed threshold derived from weighted average and other three thresholds. Compared with the other three thresholds, both theoretical model analysis and processing of actual seismic data demonstrated the effectiveness of the improved threshold.
Finally, the two proposed algorithms are applied to actual suppression of surface wave in seismic data respectively, and comparative analysis of results proved that Curvelet transform performed more effectively to maintain the continuity of the reflection signal than wavelets.
论文首先介绍了面波特点及多尺度分析的基本理论和性质,接着利用面波与有效波在频谱上的差异,分别采用多尺度变换中的二维小波变换和Curvelet变换,将地震记录分解到不同的频带内,只在面波的优势频段内进行压制处理,以保证其他频段的有效信号不会受到损伤。主要研究内容如下：
首先,对地震记录做二维小波变换,在频率波数域中确定面波的优势频段；然后,对这些区域的小波系数进行阈值处理,本文将面波压制中的阈值选取与图像处理里的阂值构造方法联系起来,引入了均值及直方图两种图像阈值方法,并将其与常用的两种阈值函数分别应用到理论模型及实际地震数据的面波压制中,对比处理后的结果发现：地震记录经直方图阈值方法处理之后,其信噪比及分辨率都得到了明显提升。最后,将本文提出的基于小波变换及直方图阈值的面波压制算法与常用的面波处理方法分别应用到实际地震资料处理中,实验结果表明：本文提出的算法在压制面波的同时有效信号也得到了增强,处理效果要优于常用处理方法。
接着,采用Curvelet变换对地震数据进行处理,它是在小波分析基础上发展起来的且能够最优表示具有曲线奇异的二维信号。算法具体思路为：首先对地震资料进行Curvelet变换,在Curvelet域中确定面波的优势频带；其次根据面波视速度低的特点,选择其在Curvelet域内对应的方向系数矩阵,利用本文建立的时域角度与Curvelet域方向的对应关系,只需根据面波在地震记录中的角度范围,就可确定其在Curvelet域的系数矩阵；接着,利用本文改进的加权均值阈值方法及其他三种阈值,对已确定存在面波的方向系数矩阵进行迭代阈值处理。理论模型及实际地震记录均证明了改进阈值的有效性。
最后,将本文提出的两种分频算法分别对实际地震资料进行面波压制,通过对处理结果分析发现：两种算法都能很好的压制面波,且Curvelet变换分频算法在有效波的连续性保持上要强于小波分频方法。
To meet the increasing demand of energy, seismic exploration has been shifted from the east to the northwest and from plains to deserts, where the seismic data gathered are always contaminated by severe linear noise and surface wave. With the presence of surface wave, the signal-to-noise ratio of the seismic data decreases rapidly, and the validness of the seismic data has been gravely damaged. Therefore, the surface wave in the pre-stack must be suppressed, while the conventional denoising methods, such as f-x filtering, f-k filtering, wavelet transform and so on, perform ineffectively to suppress surface wave.
In this paper, we first introduce the characteristics of the surface wave, and the basic theory and properties of multi-scale analysis. Then, based on the differences of spectrum between surface wave and the reflection signal, the seismic data has been sorted into different bands using the 2-D wavelet transform and Curvelet transform respectively, both of which are able to achieve multi-scale transform. With regard to the protection of signals in other bands, the processing has been applied to band dominated by surface wave. The main contents of the paper are as follows:
First,2-D wavelet transform was exploited to treat seismic record. The dominant frequency band of the surface wave in the frequency-wave number domain was determined prior to other treatments. Meanwhile, a practical connection was established between the selection of thresholds and methods of constructing thresholds in image processing, which paved the way for the introduction of average threshold and histogram threshold. In the second place, wavelet coefficients of the determined band of surface wave were further segregated with the two proposed image thresholds. These two image thresholds and two other common threshold functions were applied to theoretical analysis and actual seismic data respectively and results showed that the signal-to-noise ratio and the resolution of the seismic data were improved remarkably through the processing of histogram threshold. In the last place, the algorithm posed in this paper based on the wavelet transform and histogram threshold, together with conventional methods, was utilized to suppress surface wave in actual seismic data, which demonstrated that the proposed algorithm effectively suppressed surface wave and enhanced the reflection signal.
Then, Curvelet transform was implemented for the processing of seismic data, which has been proposed as an alternative to wavelet transform on the basis of wavelet analysis and is equipped with the ability to best represent two-dimensional signal with some plane curve singularities. The critical steps of Curvelet transform are specified as follows:Step 1. Seismic data was processed in the utilization of Curvelet transform to determine the leading band of surface wave in the Curvelet domain; Step 2. A corresponding relationship between the time domain and the direction of Curvelet domain was advanced for the purpose of defining Curvelet coefficient matrix in various orientations just according to the angle ranges of surface wave, which takes advantages of low apparent velocity of surface wave; Step 3. The Curvelet coefficient matrix was iterated through the proposed threshold derived from weighted average and other three thresholds. Compared with the other three thresholds, both theoretical model analysis and processing of actual seismic data demonstrated the effectiveness of the improved threshold.
Finally, the two proposed algorithms are applied to actual suppression of surface wave in seismic data respectively, and comparative analysis of results proved that Curvelet transform performed more effectively to maintain the continuity of the reflection signal than wavelets.
引文
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[2]付燕.人工地震信号去噪方法研究[D].西北工业大学博士学位论文.2002：1-17.
[3]熊章强,周竹生,张大洲.地震勘探[M].中南大学出版社,2010：10-85.
[4]王有新.应用地震数据处理方法[M].石油工业出版社,2009：1：148.
[5]姚姚.地震波场与地震勘探[M].地质出版社,2006年：75-142
[6]Rayleigh L. On waves propagated along the plane surface of anelastic solid[J]. Proceedings of the London Mathematic Society,1887,17:4-11.
[7]何樵登,韩立国,朱建伟等.地震波理论[M].吉林大学出版社,2005：70-77.
[8]李媛媛.小波变换去除面波的方法研究[D].长安大学硕士学位论文.2004：4-9.
[9]李卫忠,张明振,王成礼等.压制面波的波场分离方法[J].石油地球物理勘探,1998,33(5)：679-690.
[10]T. S. Durrani, D. Bisset. The Radon Transform and its Properties[J]. Geophysics.1984,49(8):1180-1187.
[11]罗省贤,李录明.几种叠前去噪方法[J].石油地球物理勘探,1997,32(3)：411-417.
[12]胡天跃.地震资料叠前去噪技术的现状与未来[J].地球物理学进展,2002,17(2)：218-223.
[13]张军华,吕宁,田连玉等.地震资料去噪方法技术综合评述[J].地球物理学进展,2006,21(2)：546-553.
[14]刘洋,王典,刘财.数学变换方法在地震勘探中的应用[J].吉林大学学报.2005：1-8.
[15]詹毅.地震资料叠前去噪方法研究[D].成都理工大学博士学位论文.2005：81-96.
[16]张贤达.现代信号处理[M].第二版.清华大学出版社,2007：362-431.
[17]D. Gabor. Theory of communication[J]. J.Inst.Electr.Eng.1946,93:429-457.
[18]Jaideva C.Goswami,Andrew K.Chan小波分析理论、算法及其应用[M].许天周,黄春光译.国防工业出版社,2007：45-84.
[19]J.Morlet. Sampling theory and wave propagation[C]. Proc.51st Annual International Meeting of the Society of Exploration Geophysicists, Los Angeles,1981.
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[21]E J. Candes, D L. Donoho. Curvelets-A Surprisingly Effective Nonadaptive Representation For Objects with Edges[M]. TN:Vanderbilt University Press, 1999.
[22]E J. Candes, D L. Donoho. New Tight Frames of Curvelets and optimal Representations of Objects with C2 Singularities[J]. Commun. Pure Appl. Math.2002,57:219-266.
[23]E J. Candes, L Demanet, D L.Donoho, Lexing Ying. Fast Discrete Curvelet Transforms[R]. Applied and computational mathematics, California Institute of Technology,2005:1-43.
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