最小相位地震仪及其相频特性的确定
MINIMUM-PHASE SEISMOGRAPHS AND THE DETERMINATION OF THEIR PHASE RESPONSES
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摘要: 本文根据最小相位系统判据,对目前我国地震台站普遍使用的几种类型地震仪做了分析指出,这些仪器都是最小相位系统;最小相位系统的相频特性可由其幅频特性计算出来.作者按照地震台站观测规范规定,标定了 DD-1型、DK-1型和基式地震仪的幅频特性.然后,用希尔伯特(Hilbert)变换由实测幅频特性计算了它们的相频特性.并把计算结果与用相位特性测试仪器实测的结果做了比较:对于 DD-1型地震仪,在从0.0125秒到12.5秒的周期范围内,最大误差小于5;对于 DK-1地震仪,在从0.05秒到100秒的周期内,最大误差小于5;对于基式地震仪,在从0.01秒到100秒的周期范围内,最大误差小于1.5.这种方法可以解决台站仪器相频特性的标定问题.标定精度比快速傅里叶变换(FFT)方法和用近似解析表达式计算方法要高.应用这种方法的关键是能对被测系统幅频特性曲线高频段和低频段的斜率做出正确的判断.这种方法的误差取决于幅频特性曲线的标定精度.用插值方法计算,计算的尾差和截断误差可以不必考虑.Abstract: On the basis of minimum-phase criteria analysis has been made for some kinds of seismographs which are now in common use at Chinese seismological stations. The result shows that such seismographs are minimum-phase systems. The phase responses may be calculated from their amplitude responses.According to The Operating Code for eismological Observation promulgated by State Seismological Bureau the amplitude desponse of the type DD-1, DK-1, and SK seismographs have been calibrated and their phase responses were calculated from these amplitude responses by the Hilbert transformation. The calculated phase responses were compared with that measured by a phasometer. The maximum error was found to be less than 5 for type DD-1 and DK-1 seismographs in the period range from 0.0125 s to 12.5 s and 0.05 s to 100 s, respectively. For type SK seismograph in the period range of 0.01s to 100s the maximum error is less than 1.5.This technique may be used to calibrate the seismograph phase response at the permanent stations. It is more accurate than the FFT method and the analytical method by means of approximate expression of a transfer function.The key to the use of this technique lies in the correct judgement of the slopes of the higher and lower frequency parts of the amplitude response curve. The error depends on the calibration accuracy of the amplitude response. By interpolation the tail and the truncation error may be neglected.
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[1] 中国科学院地球物理所,地震仪器概论,科学出版社,1975.
[2] W. D. T.戴维斯,自适应控制系统的识别,(中译本,潘裕焕译)科学出版社,1977,
[3] .A. Plesinger, R. Vich, On the identification of seismometrie systems and correction of recorded signals for identified tranfer functions, Z. GeoPTaysik, 38, 543——554, 1972.
[4] N.K. Sinha, Estimation of transfer function of continuous system from sampled data, Proc.IEE, 119, 1972.
[5] З.И.,Аранович,Э.И.Зеликман,и др.,Вопросы имульсной калибровки сейсмогигескихтов, Veröff. Zentralinst. Phys. Erde, 31, Teil, 2, 1975.
[6] H. Bakun. William, Dratler Jay, Jr., Empirical transfer functions for stations in the central Califonia seismological network, Menlo Park, California, 1976.
[7] Jon Berger, D. C. Agnew, R. L. Parker, Seismic system calibration: 2.cross——spectral calibration using random binary signals, Bull. Seism. Soc.Am., 69, 1, 271——288, 1979.
[8] 燃料化学工业部石油地球物勘探局计算中心站等,地震勘探数字技术,第二册,科学出版社,1974,
[9] 绪方胜彦著,现代控制工程,(中译本,卢伯英译),科学出版社,1976.
[10] 王广福,地震观测系统的标定与检查,地震出版社,(待出版).
[11] N. A.安斯提,地震勘探仪器,(中译本,牛毓荃等译),科学出版社,1976,
[12] P. M. Bolduc, R M.Ellis, and R. D., Russelh Determination of the seismograph phase responae from amplitude response, Bull. Seism. Soc, Am., 62, 6, 1665——1672, 1972.[1] 中国科学院地球物理所,地震仪器概论,科学出版社,1975.
[2] W. D. T.戴维斯,自适应控制系统的识别,(中译本,潘裕焕译)科学出版社,1977,
[3] .A. Plesinger, R. Vich, On the identification of seismometrie systems and correction of recorded signals for identified tranfer functions, Z. GeoPTaysik, 38, 543——554, 1972.
[4] N.K. Sinha, Estimation of transfer function of continuous system from sampled data, Proc.IEE, 119, 1972.
[5] З.И.,Аранович,Э.И.Зеликман,и др.,Вопросы имульсной калибровки сейсмогигескихтов, Veröff. Zentralinst. Phys. Erde, 31, Teil, 2, 1975.
[6] H. Bakun. William, Dratler Jay, Jr., Empirical transfer functions for stations in the central Califonia seismological network, Menlo Park, California, 1976.
[7] Jon Berger, D. C. Agnew, R. L. Parker, Seismic system calibration: 2.cross——spectral calibration using random binary signals, Bull. Seism. Soc.Am., 69, 1, 271——288, 1979.
[8] 燃料化学工业部石油地球物勘探局计算中心站等,地震勘探数字技术,第二册,科学出版社,1974,
[9] 绪方胜彦著,现代控制工程,(中译本,卢伯英译),科学出版社,1976.
[10] 王广福,地震观测系统的标定与检查,地震出版社,(待出版).
[11] N. A.安斯提,地震勘探仪器,(中译本,牛毓荃等译),科学出版社,1976,
[12] P. M. Bolduc, R M.Ellis, and R. D., Russelh Determination of the seismograph phase responae from amplitude response, Bull. Seism. Soc, Am., 62, 6, 1665——1672, 1972.
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