用独立分量分析方法实现地震转换波与多次反射波分离
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摘要
独立分量分析(ICA)是新兴的一种统计学方法。其目的是寻求对非高斯分布数据进行有效表示,使得各个基分量在统计学意义上独立,或者尽最大可能独立。这种表示意在获取数据的基本结构,可有效实现特征提取和信号分离。本文概述ICA的基本理论和快速算法,并在分析地震记录特点的基础上,阐明采用ICA方法可以实现对沉积地区远震记录中转换波和多次反射波的分离。研究结果表明,ICA方法可有效地分离地震转换波和多次反射波,并由此获得较为合理的地下间断面初步解释结果,从而有利于扩展接收函数技术的应用。
There arc some strong velocity discontinuities or transitions in the earth's curs! and upper man tie, which can be reconginzed by tracing converted-wavc phases in seismic wave records. However, when seismic stations are set in sedimentary area, the recorded converted-wave information will be masked by the recorded multiple reflected-waves caused by sedimentary formations. In this case, it is hard to identify the velocity discontinuity from receiver function. Now there are not many effective methods to separate the mixed seismic converted wave and multiple reflected-waves. In this paper, a new methods is proposed based on Independent Component Analysis (ICA) to implement the separation of seismic converted-wave and multiple reflected-waves recorded in sedimentary basin.ICA is a novel statisticsal method, which was developed recently for data analysis and signal process ing. The purpose is to find a representation of Non-Gaussian multivariate date, so that each components of the vector are statistically independent, or as independent as possible. In many applications, the aim transformation is to capture the basic structrue in data, including features abstraction and signals separation. Independent Component Analysis usually represents data by linear transformation. Based on higher-order statistics, ICA is not only de-correlation but independent compared with Principal Component Analysis, factor analysis and projection pursuit, which are based on de-correlation. In sedimentary basin, large seismic converted-wave and multiple reflected-waves are mixed, which conforms to the basic ICA Model under some conditions. ICA can be used to separate them. In this paper, we first summarize the principal theory and some fast algorithms, at the same time, numerically implement the fast ICA (FastICA for short) and its updated version by the author. On the base of analyzing the features of seismic signals, we do preliminary studies and try to apply ICA in seismic signals separation. We suppose that the seismic records of each station set in the sedimentary area are some linear mixture of seismic converted-wave and multiple re-flected-waves. The experimental data were acquired in a sedimentary basin of Shandong Province. There were 18 receiver functions obtained from corresponding seismic records. The separation was executed in time and frequency domain respectively and the FastICA algorithm was adopted. Our work shows a good prospect of ICA application in seismic signals separation of transformed-wave and multiples. On the separated convcrted-wave records, the seismic phases can be traced easily and more accurate interpretation of velocity discontinuities can be obtained. The specific operation is : in time domain, we included two close stations' records in one group and used FastICA to separate two signals from them, supposing that separated signals were converted-wave and multiple reflected wave respectively; in frequency domain, we first transformed the two receiver functions into frequency Domain, then applied FastICA to real part and imaginary part respectively, thirdly, combined the ICA results according to the real and imaginary part, finally inversed them from frequency domain to time domain. So we separate the converted and reflected signals. Some details of the separated signals were presented in the paper.In conclusion, the paper proposed a separation method of seismic converted wave and multiple reflected waves in sedimentary area. Moreover, the paper presented a preliminary interpretation of velocity discontinuities in the earth. The reserach results show that the ICA method to separate converted and reflected wave is feasible. For the problem dealt in the paper, the effects processed in time or freqency domain arc similar. The ICA based Method extended the use of receiver function technique.Due to the ambiguity of basic ICA, the separated signal is of sign undetermined. So the Extended ICA should be studied and applied in the subject of the paper to overcome the problem, thus better effects will be obtained.
There arc some strong velocity discontinuities or transitions in the earth's curs! and upper man tie, which can be reconginzed by tracing converted-wavc phases in seismic wave records. However, when seismic stations are set in sedimentary area, the recorded converted-wave information will be masked by the recorded multiple reflected-waves caused by sedimentary formations. In this case, it is hard to identify the velocity discontinuity from receiver function. Now there are not many effective methods to separate the mixed seismic converted wave and multiple reflected-waves. In this paper, a new methods is proposed based on Independent Component Analysis (ICA) to implement the separation of seismic converted-wave and multiple reflected-waves recorded in sedimentary basin.ICA is a novel statisticsal method, which was developed recently for data analysis and signal process ing. The purpose is to find a representation of Non-Gaussian multivariate date, so that each components of the vector are statistically independent, or as independent as possible. In many applications, the aim transformation is to capture the basic structrue in data, including features abstraction and signals separation. Independent Component Analysis usually represents data by linear transformation. Based on higher-order statistics, ICA is not only de-correlation but independent compared with Principal Component Analysis, factor analysis and projection pursuit, which are based on de-correlation. In sedimentary basin, large seismic converted-wave and multiple reflected-waves are mixed, which conforms to the basic ICA Model under some conditions. ICA can be used to separate them. In this paper, we first summarize the principal theory and some fast algorithms, at the same time, numerically implement the fast ICA (FastICA for short) and its updated version by the author. On the base of analyzing the features of seismic signals, we do preliminary studies and try to apply ICA in seismic signals separation. We suppose that the seismic records of each station set in the sedimentary area are some linear mixture of seismic converted-wave and multiple re-flected-waves. The experimental data were acquired in a sedimentary basin of Shandong Province. There were 18 receiver functions obtained from corresponding seismic records. The separation was executed in time and frequency domain respectively and the FastICA algorithm was adopted. Our work shows a good prospect of ICA application in seismic signals separation of transformed-wave and multiples. On the separated convcrted-wave records, the seismic phases can be traced easily and more accurate interpretation of velocity discontinuities can be obtained. The specific operation is : in time domain, we included two close stations' records in one group and used FastICA to separate two signals from them, supposing that separated signals were converted-wave and multiple reflected wave respectively; in frequency domain, we first transformed the two receiver functions into frequency Domain, then applied FastICA to real part and imaginary part respectively, thirdly, combined the ICA results according to the real and imaginary part, finally inversed them from frequency domain to time domain. So we separate the converted and reflected signals. Some details of the separated signals were presented in the paper.In conclusion, the paper proposed a separation method of seismic converted wave and multiple reflected waves in sedimentary area. Moreover, the paper presented a preliminary interpretation of velocity discontinuities in the earth. The reserach results show that the ICA method to separate converted and reflected wave is feasible. For the problem dealt in the paper, the effects processed in time or freqency domain arc similar. The ICA based Method extended the use of receiver function technique.Due to the ambiguity of basic ICA, the separated signal is of sign undetermined. So the Extended ICA should be studied and applied in the subject of the paper to overcome the problem, thus better effects will be obtained.
引文
[1] A. Hyvarinen. Survey on independent component analysis [J]. Neural Computing Surveys, 1999, 2 (1) :94-128．
[2] A. Hyvarinen. E. Oja. Independent component analysis : Algorithm and application[J]. Neural Network, 2000,13(4) :411-430．
[3] C. Jutten, J. Herault, Blind separation of sources. Part I : An adaptive algorithm hased on neuro mimetic architecture [J]. Signal Processing, 1991． 24(1) : 1-10．
[4] Yin-ming Cheng. Lei Xu. Independent component ordering in ICA time series analysis [J]. Neurocomput-ing. 2001 ,41(2) : 145-152．
[5] T-W. Lee. Independent component analysis: Theory and Application [M]. Dordrecht (The Netherlands): Kluwer Academic Publisher, 1998．
[6] A. Hyvarinen, E. Oja. A fast fixed-point algorithm for independent component analysis [J]. Neural Computation. 1997,9(7) :1483-1492．
[7] W. B. Rossow, A.Chedin. Rotation of EOFs by Independent component analysis: Towards solving the mixing problem in the decomposition of Geophysical time series [J]. J. Atmost. Sci. ,2002． 59(1) : 111-123．
[2] A. Hyvarinen. E. Oja. Independent component analysis : Algorithm and application[J]. Neural Network, 2000,13(4) :411-430．
[3] C. Jutten, J. Herault, Blind separation of sources. Part I : An adaptive algorithm hased on neuro mimetic architecture [J]. Signal Processing, 1991． 24(1) : 1-10．
[4] Yin-ming Cheng. Lei Xu. Independent component ordering in ICA time series analysis [J]. Neurocomput-ing. 2001 ,41(2) : 145-152．
[5] T-W. Lee. Independent component analysis: Theory and Application [M]. Dordrecht (The Netherlands): Kluwer Academic Publisher, 1998．
[6] A. Hyvarinen, E. Oja. A fast fixed-point algorithm for independent component analysis [J]. Neural Computation. 1997,9(7) :1483-1492．
[7] W. B. Rossow, A.Chedin. Rotation of EOFs by Independent component analysis: Towards solving the mixing problem in the decomposition of Geophysical time series [J]. J. Atmost. Sci. ,2002． 59(1) : 111-123．
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