冀鲁豫交界地区尾波Q值研究
摘要
为了恰当地描述地球介质的非弹性特征,必须采用一个合适的物理参数对值特性进行描述。地球介质的品质因子(Q值)就可以很好地反映由于地球内部介质应力变化而引起的岩石性质的变化。地震波在介质中传播,其衰减强弱与介质(岩石)的性质密切相关,进而也能很好地反映介质品质因子的变化。
一、研究目的
在无法直接对地球介质进行研究的情况下,通过天然地震研究区域介质的Q值及频率衰减指数,了解某一区域地球内部介质的特性,把握区域应力总体特征。同时,给出不同频率的Q值随时间变化特征,为地震分析预报提供一定的科学依据。
二、研究方法
在总结众多介质品质因子计算方法的基础上,结合研究区域的地震活动特征,采用基于单次散射的S波及其尾波品质因子求解方法,对地震实例进行计算,得出研究结果。
三、研究内容
1、对利用尾波测量品质因子的方法进行了汇总,根据前人研究结果并结合具体实例讨论了品质因子与地震震源距、不同流逝时间的关系。
2、为解决由于地震波在纵向介质中穿透深度的不同而导致不同地震之间的品质因子无法对比的问题,提出了在同一区域内,由散射波波阵面所围成的散射椭球体具有同一深度的技术思路,以此来确定尾波流逝时间。这样求取的品质因子能够有效去除地震波传播路径不同而造成的“假异常”现象。这种方法能较好地反映品质因子的异常变化与地震孕育过程的关系。
3、以冀鲁豫交界地区为研究区域,选取符合条件的21次天然地震为研究对象,利用改进后的尾波测定方法,拟合得到了品质因子与频率之间的统计关系为Qc ? 28 .7f1.15,反映了该地区地震波平均衰减特性和应力总体特征,并与青岛崂山地区介质衰减特性进行了对比。
4、初步分析了研究区域地震活动水平与不同频段尾波值的对应关系,得出区域构造应力随时间变化特征,以期捕捉到品质因子的时间变化与地震孕育过程的关系,进一步提高地震预测的准确率。通过地震实例分析,研究区域地震活动水平增强的过程与地震应力水平增强的过程较为一致。2009年下半年以来冀鲁豫交界地区地震活动增强,对应的高频段尾波Q值有所升高,表明研究区域构造应力随地震活动的增强而增强,应予以密切关注。
Quality factor Q value is the description of the main parameters of earth medium properties. The changes of the properties of rock because of the changes of stress, such as the state of cranny, the transference of liquid, the upsurge of hot substance etc, will bring the changes of Quality factor. Because the attenuation of the seismic wave in the medium has a direct relation with the Quality factor, so to research the Quality factor of natural seismic and then to understand the properties of the medium inside the earth is one of the primary directions of research. Based on the predecessors' research production, in order to reflect the change of the stress in the same area and remove the influence by the difference of ray paths of seismic wave, this paper improves the method to measure the Quality factor, and different earthquake using different passage of time measured methods. The physical model and measured method is scientific and innovative in some extent.
According to previous research results, this paper studied seismic wave attenuation on the 21 earthquake records of Puyang station, and discussed the relationship between the quality factor with versus frequency; Using the determination method of coda wave quality factor , it eliminated effectively the impact on the quality factor measurements caused by the earthquake seismic wave scattering in the vertical penetration depth on the same or different earthquakes .It will help to capture relationship with the abnormal changes characteristics of the quality factor and the earthquake preparation process. Using the improved model, this paper calculated the Coda Wave Q value of Hebei-Shandong-Henan border, then given the relationship of Quality factor with frequency attenuation and the Temporal changes of the Regional media attenuation.
一、研究目的
在无法直接对地球介质进行研究的情况下,通过天然地震研究区域介质的Q值及频率衰减指数,了解某一区域地球内部介质的特性,把握区域应力总体特征。同时,给出不同频率的Q值随时间变化特征,为地震分析预报提供一定的科学依据。
二、研究方法
在总结众多介质品质因子计算方法的基础上,结合研究区域的地震活动特征,采用基于单次散射的S波及其尾波品质因子求解方法,对地震实例进行计算,得出研究结果。
三、研究内容
1、对利用尾波测量品质因子的方法进行了汇总,根据前人研究结果并结合具体实例讨论了品质因子与地震震源距、不同流逝时间的关系。
2、为解决由于地震波在纵向介质中穿透深度的不同而导致不同地震之间的品质因子无法对比的问题,提出了在同一区域内,由散射波波阵面所围成的散射椭球体具有同一深度的技术思路,以此来确定尾波流逝时间。这样求取的品质因子能够有效去除地震波传播路径不同而造成的“假异常”现象。这种方法能较好地反映品质因子的异常变化与地震孕育过程的关系。
3、以冀鲁豫交界地区为研究区域,选取符合条件的21次天然地震为研究对象,利用改进后的尾波测定方法,拟合得到了品质因子与频率之间的统计关系为Qc ? 28 .7f1.15,反映了该地区地震波平均衰减特性和应力总体特征,并与青岛崂山地区介质衰减特性进行了对比。
4、初步分析了研究区域地震活动水平与不同频段尾波值的对应关系,得出区域构造应力随时间变化特征,以期捕捉到品质因子的时间变化与地震孕育过程的关系,进一步提高地震预测的准确率。通过地震实例分析,研究区域地震活动水平增强的过程与地震应力水平增强的过程较为一致。2009年下半年以来冀鲁豫交界地区地震活动增强,对应的高频段尾波Q值有所升高,表明研究区域构造应力随地震活动的增强而增强,应予以密切关注。
Quality factor Q value is the description of the main parameters of earth medium properties. The changes of the properties of rock because of the changes of stress, such as the state of cranny, the transference of liquid, the upsurge of hot substance etc, will bring the changes of Quality factor. Because the attenuation of the seismic wave in the medium has a direct relation with the Quality factor, so to research the Quality factor of natural seismic and then to understand the properties of the medium inside the earth is one of the primary directions of research. Based on the predecessors' research production, in order to reflect the change of the stress in the same area and remove the influence by the difference of ray paths of seismic wave, this paper improves the method to measure the Quality factor, and different earthquake using different passage of time measured methods. The physical model and measured method is scientific and innovative in some extent.
According to previous research results, this paper studied seismic wave attenuation on the 21 earthquake records of Puyang station, and discussed the relationship between the quality factor with versus frequency; Using the determination method of coda wave quality factor , it eliminated effectively the impact on the quality factor measurements caused by the earthquake seismic wave scattering in the vertical penetration depth on the same or different earthquakes .It will help to capture relationship with the abnormal changes characteristics of the quality factor and the earthquake preparation process. Using the improved model, this paper calculated the Coda Wave Q value of Hebei-Shandong-Henan border, then given the relationship of Quality factor with frequency attenuation and the Temporal changes of the Regional media attenuation.
引文
[1]卓玉如,杨玉荣.地球介质品质因子Q值论文集[C].北京:地震出版社,1989.
[2]周蕙兰.地球内部物理[M].北京:地震出版社,1990.
[3]徐彦,苏有锦,秦嘉政.Q值研究动态[J].地震研究,2004,27(4):385-389.
[4] Andesong D L,R. S.Hart.Q of the Earth[J].J Geophys Res,1978,83 (B12):5869-5882.
[5] Anderson D L,Archambeau C B.The Anelasticity of the Earth[J].J Geophys Res,1964,69:2071-2084.
[6] Anderson D L,BENMA,ARCHAMBEAU C B.Attenuation of Seismic Energy in the Upper Mantle[J].J Geophys Res,1965,70:1441-1448.
[7]傅淑芳,徐大方.地幔瑞利面波的频散和衰减[J].地球物理学报,1985,28 (2):198-207.
[8] Hwang H J,Brian J M.Shear velocities Qβand the frequency dependence of Qβin stable and tectonically active regions from surface wave observations[J].J Geophys Res,1987,90:575-613.
[9] Singh D D.Q-structure beneath the north and central Indian Ocean from the inversion of observed Love and Rayleigh wave attenuation data[J].Phys Earth Planet Inter,1990,59:243-258.
[10]吴建平,曾融生.青藏高原Q值结构反演[J].地震学报,1996, 16(2):208-214.
[11]李光品,徐果明,高尔根,等.中国东部地壳、上地幔横波品质因子的三维层析成像[J].地震学报,2000,22(1):73-81.
[12]洪学海,朱介寿,曹家敏,等.中国大陆地壳、上地幔S波品质因子三维层析成像[J].地球物理学报,2003,46(5):642-651.
[13]Solomon.Lateral variation of attenuation of P and S waves beneath the United States[J].Bull Seism Soc Amer,1970,60(3):819-83.
[14]Aki K.Attenuation of shear waves in the lithosphere for frequencies from 0.05 to 25 Hz[J].Phys Earth Planet,1980,21:50-60.
[15]Yoshimoto K , Sato H,Yoshihisa,etal.Frequency-dependent attenuation of P and S waves in the Kanto area,Japan,based on the coda normalization method[J].Geophys J Int,1993,114:165-174.
[16]Yoshimoto K,Sato H,Yoshihisa,etal.Frequency-dependent attenuation of high-frequency and waves in the upper crust in western Nagano,Japan[J].Pure Appl Geophys,1998,153:489-502.
[17] Chung Tae Woong,Sato H.Attenuation of high frequency P and S waves in the crust of south-eastern Korea[J].Bull Seism Soc Amer,2001,91(6): 1867-1874.
[18]王勤彩,刘杰,郑斯华,等.云南地区与频率有关的P波、S波衰减研究[J].地震学报,2005,27(6):588-597.
[19]Atkinson G M,Mereu R F.The shape of ground motion attenuation curves in southeastern Canada[J].Bull Seism Soc Amer,1992, 82(5):2014-2031.
[20]高龙生.我国有关尾波研究的进展[J].地球物理学报,1994,37(增刊):242-250.
[21]Aki K.Analysis of seismic coda of local earthquakes as scatter waves[J].J Geophys Res,1969,74:615-631.
[22]Aki K,Chouet B.Origin of coda waves : sorce,attenuation,and scattering effects[J].J Geophys Res,1975,80:3322-3342.
[23]Sato H.Energy propagation including scattering effects,single isotropic scattering approximation[J].J Geophys Res,1977,25:27-41.
[24]Chouet B,Aki K,Tsujiura M.Regional variation of the scaling law of earthquake source spectra [J].Bull Seism Soc Amer,1978,68:49-79.
[25]Jin A,Aki K.Spatial and temporal correlation between coda Q-1 and seismicity and its physical mechanism[J].J Geophys Res,1989,94: 14041-14059.
[26]Jin A,Aki K.Tempera correlation between coda Q-1 and seismicity-evidence for a structural unit in the brittle-ductile transition zone[J].J Geodynamics,1993,17:95-120.
[27]Sato H.Temporal changes in scattering and attenuation associatedwith the earthquake occurrencea review of recent studies on coda waves[J].Pure Appl Geophys,1988,126:465-497.
[28]Xie J,O W Nuttli.Interpretation of high-frequency coda at large distances:stochastic modeling and method of inversion [J],Geophysical Journal,1988,95:579-595.
[29]Wu R S.Seismic wave scattering and the small scale inhomogeneities in the lithosphere[D].Ph.D.Thesis Massachusetts Institute of Technology,Cambridge,Mass.1984.
[30]Tie A.On scattering of seismic waves by a spherical obstacle[D].Georgia inst.of Technl.,Atlanta.GA.USA Doctoral,1987.
[31]Wu R S.Attenuation of short period seismic waves due to scattering[J].Geophys Res Lett,1982,9:9-12.
[32]Wu R S.Multiple scattering and energy transfer of seismic waves-separation of scattering effect from intrinsic attenuation--Ⅰ.theoretical modelling[J].Geophys J R Astr Soc,1985,82:57-80.
[33]Wu R S,Aki K.scattering characteristics of elastic waves by an elastic heterogeneity[J].Geophysics,1985,50:582-595.
[34]Gao L S,Lee L C,Biswas N N and Aki K.comparison of the effects between single and multiple scattering on coda wave of local earthquake[J].Bull Seism Soc Am,1983,73:377一389.
[35] Gao L S,Biswas N N,Lee L C and Aki K.effects of multiple scattering on coda waves in threedimensional medium[J].Pure and Appl Geophys,1983,121:3-15.
[36] Herrmann R B.Q estimates using the coda of local eart- hquakes[J]. Bull Seism Soc Am,1980,70:447-468.
[37] Chen P S,O W Nuttli,Ye W H et al. Estimates of short-period Q values and seismic moments from coda waves for earthquake of the Beijing-Yunnan regions of China[J].BSSA,1984,74:1189-1207.
[38]秦嘉政,阚荣举.龙陵地震前后区域Q值和平均剪应力的分布特征[J].地震学报,1986,增刊:57一71.
[39]秦嘉政,阚荣举.用近震尾波估算昆明及其周围地区的Q值机地震矩[J].地球物理学报,1986,29(2):145-155.
[40]马宏生,刘杰,张国民,等.云南地区尾波Qc值的分布特征及其初步解释[J].地震,2006,26(3):37-43.
[41]秦嘉政,李宁,胡克坚.1985年云南禄劝地震余震尾波Q值的某些研究[J].地震学报,1987,9:239-252.
[42]程德利,张裕中.尾波观测与Q值分布[J].地震学报,1985,7:398-407.
[43]王伟君,刘杰.1999年岫岩地震序列尾波Qc的变化过程[J].地震,2004,24(4):37-44.
[44]Xie J K , Nuttli O W.Lg coda Q of continental Africa[J].EOS,1987,68:1362.
[45]丛连理,胡家富,吴小平,等.中国大陆及邻近地区Lg尾波的Q值分布[J].中国科学, 2002,32 (8): 617-624.
[46]胡家富,丛连理,吴小平,等.云南及周边地区Lg尾波Q值的分布特征[J].地球物理学报,2003,46(6):809-813.
[47]Lee, W. H. K.,R.E.Bennett and K.L.Meagher. A method of estimating magnitude of local earthquakes from signal duration, open file report, 28 pp., Nat. Center for Earthquake Res., U.S. Geol. Surv., Menlo park, Calif. 1972.
[48]秦嘉政,陈培善.用地震的持续时间测定川滇地区近震震级[J].地震学报,1984,6:56-64.
[49]Jin A,Aki K.Temporal change in coda Q before the Tangshan earthquake of 1976 and the Haicheng earthquake of 1975[J].J Geophys Res,1986,91:665-673.
[50]Jin A,Aki K.Spatial and temporal correlation between coda Q and seismicity in China[J].Bull Seism Soc Am,1988,78:741-769.
[51]向宏发,王学潮,虢顺民等.聊城一兰考隐伏断裂第四纪活动性的综合探测研究[J].地震地质,2000,22(4):351-359.
[52]许华明,周斌,耿师江等.磁县大名断层分段特征及活动性[J].华北地震科学,2010,28(1):1-7.
[53]Dominguez T, Rebollar C J. Attenuation of coda waves at the Cerro Prieto Geothermal Fileld, Baja California, Mexico[J].Bull.Seim.Soc.Am.1997,87:1368-1374.
[54]Cong L J,Mejia Mitchell B J.Attenuation dispersion of P waves in near the New Madrid seismic zone[J].Bull.Seism.Soc.Am.2000 ,90(3):679-689.
[55] Kumar,N,Parvez I A,Virk H S.Estimation of coda wave attenuation for NW Himalayan region using local earthquakes[J].Physics of the Earth and Planetary Interiors,2005,151:243-258.
[56]刘希强,石玉燕,曲均浩,等.品质因子的尾波测定方法讨论[J].中国地震,2009,25(1):11-23.
[57] Pulli J J. Attenuation of coda waves in New England[J].Bull.Seim. Soc.Am.1984,74:1149-1166.
[58]刘明,徐洪波,宁国勤编著.数字信号处理—原理与算法实现[M].北京:清华大学出版社,2006:207-212.
[59]王济,胡尧编著.MATLAB在振动信号处理中的应用[M].北京:中国水利出版社,2005:134-137.
[2]周蕙兰.地球内部物理[M].北京:地震出版社,1990.
[3]徐彦,苏有锦,秦嘉政.Q值研究动态[J].地震研究,2004,27(4):385-389.
[4] Andesong D L,R. S.Hart.Q of the Earth[J].J Geophys Res,1978,83 (B12):5869-5882.
[5] Anderson D L,Archambeau C B.The Anelasticity of the Earth[J].J Geophys Res,1964,69:2071-2084.
[6] Anderson D L,BENMA,ARCHAMBEAU C B.Attenuation of Seismic Energy in the Upper Mantle[J].J Geophys Res,1965,70:1441-1448.
[7]傅淑芳,徐大方.地幔瑞利面波的频散和衰减[J].地球物理学报,1985,28 (2):198-207.
[8] Hwang H J,Brian J M.Shear velocities Qβand the frequency dependence of Qβin stable and tectonically active regions from surface wave observations[J].J Geophys Res,1987,90:575-613.
[9] Singh D D.Q-structure beneath the north and central Indian Ocean from the inversion of observed Love and Rayleigh wave attenuation data[J].Phys Earth Planet Inter,1990,59:243-258.
[10]吴建平,曾融生.青藏高原Q值结构反演[J].地震学报,1996, 16(2):208-214.
[11]李光品,徐果明,高尔根,等.中国东部地壳、上地幔横波品质因子的三维层析成像[J].地震学报,2000,22(1):73-81.
[12]洪学海,朱介寿,曹家敏,等.中国大陆地壳、上地幔S波品质因子三维层析成像[J].地球物理学报,2003,46(5):642-651.
[13]Solomon.Lateral variation of attenuation of P and S waves beneath the United States[J].Bull Seism Soc Amer,1970,60(3):819-83.
[14]Aki K.Attenuation of shear waves in the lithosphere for frequencies from 0.05 to 25 Hz[J].Phys Earth Planet,1980,21:50-60.
[15]Yoshimoto K , Sato H,Yoshihisa,etal.Frequency-dependent attenuation of P and S waves in the Kanto area,Japan,based on the coda normalization method[J].Geophys J Int,1993,114:165-174.
[16]Yoshimoto K,Sato H,Yoshihisa,etal.Frequency-dependent attenuation of high-frequency and waves in the upper crust in western Nagano,Japan[J].Pure Appl Geophys,1998,153:489-502.
[17] Chung Tae Woong,Sato H.Attenuation of high frequency P and S waves in the crust of south-eastern Korea[J].Bull Seism Soc Amer,2001,91(6): 1867-1874.
[18]王勤彩,刘杰,郑斯华,等.云南地区与频率有关的P波、S波衰减研究[J].地震学报,2005,27(6):588-597.
[19]Atkinson G M,Mereu R F.The shape of ground motion attenuation curves in southeastern Canada[J].Bull Seism Soc Amer,1992, 82(5):2014-2031.
[20]高龙生.我国有关尾波研究的进展[J].地球物理学报,1994,37(增刊):242-250.
[21]Aki K.Analysis of seismic coda of local earthquakes as scatter waves[J].J Geophys Res,1969,74:615-631.
[22]Aki K,Chouet B.Origin of coda waves : sorce,attenuation,and scattering effects[J].J Geophys Res,1975,80:3322-3342.
[23]Sato H.Energy propagation including scattering effects,single isotropic scattering approximation[J].J Geophys Res,1977,25:27-41.
[24]Chouet B,Aki K,Tsujiura M.Regional variation of the scaling law of earthquake source spectra [J].Bull Seism Soc Amer,1978,68:49-79.
[25]Jin A,Aki K.Spatial and temporal correlation between coda Q-1 and seismicity and its physical mechanism[J].J Geophys Res,1989,94: 14041-14059.
[26]Jin A,Aki K.Tempera correlation between coda Q-1 and seismicity-evidence for a structural unit in the brittle-ductile transition zone[J].J Geodynamics,1993,17:95-120.
[27]Sato H.Temporal changes in scattering and attenuation associatedwith the earthquake occurrencea review of recent studies on coda waves[J].Pure Appl Geophys,1988,126:465-497.
[28]Xie J,O W Nuttli.Interpretation of high-frequency coda at large distances:stochastic modeling and method of inversion [J],Geophysical Journal,1988,95:579-595.
[29]Wu R S.Seismic wave scattering and the small scale inhomogeneities in the lithosphere[D].Ph.D.Thesis Massachusetts Institute of Technology,Cambridge,Mass.1984.
[30]Tie A.On scattering of seismic waves by a spherical obstacle[D].Georgia inst.of Technl.,Atlanta.GA.USA Doctoral,1987.
[31]Wu R S.Attenuation of short period seismic waves due to scattering[J].Geophys Res Lett,1982,9:9-12.
[32]Wu R S.Multiple scattering and energy transfer of seismic waves-separation of scattering effect from intrinsic attenuation--Ⅰ.theoretical modelling[J].Geophys J R Astr Soc,1985,82:57-80.
[33]Wu R S,Aki K.scattering characteristics of elastic waves by an elastic heterogeneity[J].Geophysics,1985,50:582-595.
[34]Gao L S,Lee L C,Biswas N N and Aki K.comparison of the effects between single and multiple scattering on coda wave of local earthquake[J].Bull Seism Soc Am,1983,73:377一389.
[35] Gao L S,Biswas N N,Lee L C and Aki K.effects of multiple scattering on coda waves in threedimensional medium[J].Pure and Appl Geophys,1983,121:3-15.
[36] Herrmann R B.Q estimates using the coda of local eart- hquakes[J]. Bull Seism Soc Am,1980,70:447-468.
[37] Chen P S,O W Nuttli,Ye W H et al. Estimates of short-period Q values and seismic moments from coda waves for earthquake of the Beijing-Yunnan regions of China[J].BSSA,1984,74:1189-1207.
[38]秦嘉政,阚荣举.龙陵地震前后区域Q值和平均剪应力的分布特征[J].地震学报,1986,增刊:57一71.
[39]秦嘉政,阚荣举.用近震尾波估算昆明及其周围地区的Q值机地震矩[J].地球物理学报,1986,29(2):145-155.
[40]马宏生,刘杰,张国民,等.云南地区尾波Qc值的分布特征及其初步解释[J].地震,2006,26(3):37-43.
[41]秦嘉政,李宁,胡克坚.1985年云南禄劝地震余震尾波Q值的某些研究[J].地震学报,1987,9:239-252.
[42]程德利,张裕中.尾波观测与Q值分布[J].地震学报,1985,7:398-407.
[43]王伟君,刘杰.1999年岫岩地震序列尾波Qc的变化过程[J].地震,2004,24(4):37-44.
[44]Xie J K , Nuttli O W.Lg coda Q of continental Africa[J].EOS,1987,68:1362.
[45]丛连理,胡家富,吴小平,等.中国大陆及邻近地区Lg尾波的Q值分布[J].中国科学, 2002,32 (8): 617-624.
[46]胡家富,丛连理,吴小平,等.云南及周边地区Lg尾波Q值的分布特征[J].地球物理学报,2003,46(6):809-813.
[47]Lee, W. H. K.,R.E.Bennett and K.L.Meagher. A method of estimating magnitude of local earthquakes from signal duration, open file report, 28 pp., Nat. Center for Earthquake Res., U.S. Geol. Surv., Menlo park, Calif. 1972.
[48]秦嘉政,陈培善.用地震的持续时间测定川滇地区近震震级[J].地震学报,1984,6:56-64.
[49]Jin A,Aki K.Temporal change in coda Q before the Tangshan earthquake of 1976 and the Haicheng earthquake of 1975[J].J Geophys Res,1986,91:665-673.
[50]Jin A,Aki K.Spatial and temporal correlation between coda Q and seismicity in China[J].Bull Seism Soc Am,1988,78:741-769.
[51]向宏发,王学潮,虢顺民等.聊城一兰考隐伏断裂第四纪活动性的综合探测研究[J].地震地质,2000,22(4):351-359.
[52]许华明,周斌,耿师江等.磁县大名断层分段特征及活动性[J].华北地震科学,2010,28(1):1-7.
[53]Dominguez T, Rebollar C J. Attenuation of coda waves at the Cerro Prieto Geothermal Fileld, Baja California, Mexico[J].Bull.Seim.Soc.Am.1997,87:1368-1374.
[54]Cong L J,Mejia Mitchell B J.Attenuation dispersion of P waves in near the New Madrid seismic zone[J].Bull.Seism.Soc.Am.2000 ,90(3):679-689.
[55] Kumar,N,Parvez I A,Virk H S.Estimation of coda wave attenuation for NW Himalayan region using local earthquakes[J].Physics of the Earth and Planetary Interiors,2005,151:243-258.
[56]刘希强,石玉燕,曲均浩,等.品质因子的尾波测定方法讨论[J].中国地震,2009,25(1):11-23.
[57] Pulli J J. Attenuation of coda waves in New England[J].Bull.Seim. Soc.Am.1984,74:1149-1166.
[58]刘明,徐洪波,宁国勤编著.数字信号处理—原理与算法实现[M].北京:清华大学出版社,2006:207-212.
[59]王济,胡尧编著.MATLAB在振动信号处理中的应用[M].北京:中国水利出版社,2005:134-137.