近地震波的小波相对能量分布特征分析
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摘要
地震波具有非平稳信号特征,能量分布在一个有限带宽范围内。本文根据小波变换的时频特性和分层分解关系,得到了近地震(震中距小于300km)峰值能量的频率主要集中在3～6Hz频段这一初步结果。统计分析结果证明了这种方法对于近地震波分析的有效性和可靠性,同时也表明基于小波变换的地震相对能量分布特征可以更准确的给出地震信号的细节。结果对于地震震源及地震波传播规律的研究以及工程抗震设计具有一定的参考意义。
Seismic waves have characteristics of non-stationary signals,and their energy distribution is in a finite frequency band.In addition,they contain a significant amount of information about sources and media.Analysis of seismic signals is used to determine the sources and propagation medium and for further study of earthquake mechanisms.Fourier transform is a classic method used for signal processing.Because it is a pure frequency domain analysis method,its shortcoming is lost time information.The Fourier transform method stringently requires that the system is linear and that the signal is stationary.Therefore,high limitations are placed on non-stationary signals.For short-time Fourier transform,constraints of the window function result in difficulties in simultaneously obtaining good resolution in time and frequency domain.Because the wavelet transform has the characteristic of multi-resolution,the time and frequency windows can be dynamically adjusted as the signals changes;thus,the characteristics of local information expression capability is improved in the time and frequency domain.Therefore,the dynamic characteristics of the seismic waves in the frequency and time domain should be determined by the multi-resolution decomposition of seismic signals.In this paper,the multiresolution decomposition of discrete wavelet transform is used to show decomposition of a synthetic waveform that is rebuilt by different level signals of decomposition.The standard square error is 1.554 2e-019,and the root mean square error is 7.351 2e-012 between original and rebuilt signals.The signal is not distorted due to decomposition and reconstruction processing.These results satisfy the requirements of computational analysis.Moreover,nine earthquakes records obtained from the Gansu Seismic Network with a magnitude range of ML3.3-4.2 were processed by using the same methods. Results indicate a relative energy distribution range of 1-15 Hz and an energy peak of 3-6 Hz for the local seismic wave(Δ<300 km).For one earthquake,the relative energy distribution of the earthquake differs among stations,which is caused by the focal radiation pattern and medium differences.The statistical test results show that the error level and results of synthetic waveform testing are consistent.This method can accurately determine near seismic energy distribution in the frequency domain characteristics,which is conducive to the study of seismic wave variation in various frequency bands.Moreover,statistical results show that this method is effective and reliable for obtaining details of seismic wave variation.However,it is difficult to explain the phenomenon such that the frequency of the peak energy changes from low to high with an increase in epicenter distance.Therefore,this topic requires further study.In addition,it should be noted that if such a method is used to process data for wavelet window length,some energy may be lost in the calculation process.The results of this study provide reference value in the research of earthquake sources,radiation patterns and seismic wave propagation in an anisotropic medium,and aseismic design for engineering applications.
Seismic waves have characteristics of non-stationary signals,and their energy distribution is in a finite frequency band.In addition,they contain a significant amount of information about sources and media.Analysis of seismic signals is used to determine the sources and propagation medium and for further study of earthquake mechanisms.Fourier transform is a classic method used for signal processing.Because it is a pure frequency domain analysis method,its shortcoming is lost time information.The Fourier transform method stringently requires that the system is linear and that the signal is stationary.Therefore,high limitations are placed on non-stationary signals.For short-time Fourier transform,constraints of the window function result in difficulties in simultaneously obtaining good resolution in time and frequency domain.Because the wavelet transform has the characteristic of multi-resolution,the time and frequency windows can be dynamically adjusted as the signals changes;thus,the characteristics of local information expression capability is improved in the time and frequency domain.Therefore,the dynamic characteristics of the seismic waves in the frequency and time domain should be determined by the multi-resolution decomposition of seismic signals.In this paper,the multiresolution decomposition of discrete wavelet transform is used to show decomposition of a synthetic waveform that is rebuilt by different level signals of decomposition.The standard square error is 1.554 2e-019,and the root mean square error is 7.351 2e-012 between original and rebuilt signals.The signal is not distorted due to decomposition and reconstruction processing.These results satisfy the requirements of computational analysis.Moreover,nine earthquakes records obtained from the Gansu Seismic Network with a magnitude range of ML3.3-4.2 were processed by using the same methods. Results indicate a relative energy distribution range of 1-15 Hz and an energy peak of 3-6 Hz for the local seismic wave(Δ<300 km).For one earthquake,the relative energy distribution of the earthquake differs among stations,which is caused by the focal radiation pattern and medium differences.The statistical test results show that the error level and results of synthetic waveform testing are consistent.This method can accurately determine near seismic energy distribution in the frequency domain characteristics,which is conducive to the study of seismic wave variation in various frequency bands.Moreover,statistical results show that this method is effective and reliable for obtaining details of seismic wave variation.However,it is difficult to explain the phenomenon such that the frequency of the peak energy changes from low to high with an increase in epicenter distance.Therefore,this topic requires further study.In addition,it should be noted that if such a method is used to process data for wavelet window length,some energy may be lost in the calculation process.The results of this study provide reference value in the research of earthquake sources,radiation patterns and seismic wave propagation in an anisotropic medium,and aseismic design for engineering applications.
引文
[1]李英,张淑贞,许康生.小波降噪方法在地震信号处理中的应用[J].西北地震学报,2006,28(2):159-162.LI Ying,ZHANG Shu-zhen,XU Kang-sheng.Application ofWavelet Transfer in Seismic Signal Denoise[J].NorthwesternSeismological Journal,2006,28(2):159-162.
[2]刘希强,沈萍,山长仑,等.数字化地震波形资料的时频分析方法及应用[J].西北地震学报,2004,26(2):118-124.LIU Xi-qiang,SHEN Ping,SHAN Chang-lun,et al.Time-fre-quency Method and Its Application in Digital Seismic Wave Da-ta Processing[J].Northwestern Seismological Journal,2004,26(2):118-124.
[3]姚家骏,杨立明,冯建刚.常用时频分析方法在数字地震波特征量分析中的应用[J].西北地震学报,2011,33(2):105-109.YAO Jia-jun,YANG Li-ming,FENG Jian-gang.Applicationof Common Time-Frequency Analysis Methods in AnalyzingCharacteristic Quantity of Digital Seismic Wave[J].North-western Seismological Journal,2011,33(2):105-109.
[4]王燕,刘俊民,王晓明,等.地震阈值监测技术中的震级校正[J],西北地震学报,2011,33(4):319-321.WANG Yan,LIU Jun-min,WANG Xiao-ming,et al.Magni-tude Calibration of Seismic Threshold Monitoring[J].North-western Seismological Journal,2011,33(4):319-321.
[5]杨福生.小波变换的工程分析与应用[M].北京:科学出版社,2000:42-68.YANG Fu-sheng.Application and Engineering analysis ofWavelet Transfer[M].BeiJing:Science Press,2000:42-68.
[6]胡昌华,张军波,夏军,等.基于MATLAB的系统分析与统计[M].西安:西安电子科技大学出版社,1999:210-232.HU Chang-hua,ZHANG Jun-bo,XIA Jun,et al.Statisticsand Analysis of System Based on MATLAB[M].Xi′an:Xi′anUniversity of Electronic Science and Technology Press,1999:210-232.
[7]许康生,李秋红,李英.大地震前近台背景噪声的频谱分析[J].西北地震学报,2012,34(2):150-153.XU Kang-sheng,LI Qiu-hong,LI Ying.Analysis on theSpectrum of Background Noise in Stations Near by Epicentersof Two Great Earthquakes[J].Northwestern SeismologicalJournal,2012,34(2):150-153.
[8]刘希强,孙亚强,赵冰,等.地震震中实时动态定位的方法研究[J].西北地震学报,2012,34(4):342-348.LIU Xi-qiang,SUN Ya-qiang,ZHAO Bing,et al.Researchon Real-time Evolutionary Earthquake Epicentral location[J].Northwestern Seismological Journal,2012,34(4):342-348.
[9]Daubechies I.Orthonormal Bases of Compactly SupportedWavelet[J].Communication Pure and Applied Mathematics,1988,41(7):909-996.
[2]刘希强,沈萍,山长仑,等.数字化地震波形资料的时频分析方法及应用[J].西北地震学报,2004,26(2):118-124.LIU Xi-qiang,SHEN Ping,SHAN Chang-lun,et al.Time-fre-quency Method and Its Application in Digital Seismic Wave Da-ta Processing[J].Northwestern Seismological Journal,2004,26(2):118-124.
[3]姚家骏,杨立明,冯建刚.常用时频分析方法在数字地震波特征量分析中的应用[J].西北地震学报,2011,33(2):105-109.YAO Jia-jun,YANG Li-ming,FENG Jian-gang.Applicationof Common Time-Frequency Analysis Methods in AnalyzingCharacteristic Quantity of Digital Seismic Wave[J].North-western Seismological Journal,2011,33(2):105-109.
[4]王燕,刘俊民,王晓明,等.地震阈值监测技术中的震级校正[J],西北地震学报,2011,33(4):319-321.WANG Yan,LIU Jun-min,WANG Xiao-ming,et al.Magni-tude Calibration of Seismic Threshold Monitoring[J].North-western Seismological Journal,2011,33(4):319-321.
[5]杨福生.小波变换的工程分析与应用[M].北京:科学出版社,2000:42-68.YANG Fu-sheng.Application and Engineering analysis ofWavelet Transfer[M].BeiJing:Science Press,2000:42-68.
[6]胡昌华,张军波,夏军,等.基于MATLAB的系统分析与统计[M].西安:西安电子科技大学出版社,1999:210-232.HU Chang-hua,ZHANG Jun-bo,XIA Jun,et al.Statisticsand Analysis of System Based on MATLAB[M].Xi′an:Xi′anUniversity of Electronic Science and Technology Press,1999:210-232.
[7]许康生,李秋红,李英.大地震前近台背景噪声的频谱分析[J].西北地震学报,2012,34(2):150-153.XU Kang-sheng,LI Qiu-hong,LI Ying.Analysis on theSpectrum of Background Noise in Stations Near by Epicentersof Two Great Earthquakes[J].Northwestern SeismologicalJournal,2012,34(2):150-153.
[8]刘希强,孙亚强,赵冰,等.地震震中实时动态定位的方法研究[J].西北地震学报,2012,34(4):342-348.LIU Xi-qiang,SUN Ya-qiang,ZHAO Bing,et al.Researchon Real-time Evolutionary Earthquake Epicentral location[J].Northwestern Seismological Journal,2012,34(4):342-348.
[9]Daubechies I.Orthonormal Bases of Compactly SupportedWavelet[J].Communication Pure and Applied Mathematics,1988,41(7):909-996.
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