This paper derives a mathematical description of the complex stretch processor’s response to bandlimited Gaussian noise having arbitrary center frequency and bandwidth. The description of the complex stretch processo...This paper derives a mathematical description of the complex stretch processor’s response to bandlimited Gaussian noise having arbitrary center frequency and bandwidth. The description of the complex stretch processor’s random output comprises highly accurate closed-form approximations for the probability density function and the autocorrelation function. The solution supports the complex stretch processor’s usage of any conventional range-sidelobe-reduction window. The paper then identifies two practical applications of the derived description. Digital-simulation results for the two identified applications, assuming the complex stretch processor uses the rectangular, Hamming, Blackman, or Kaiser window, verify the derivation’s correctness through favorable comparison to the theoretically predicted behavior.展开更多
Passive image interferometry （PII） is becoming a powerful tool for detecting the temporal variations in the Earth＇s structure, which applies coda wave interferometry to the waveforrns from the cross-correlation of ...Passive image interferometry （PII） is becoming a powerful tool for detecting the temporal variations in the Earth＇s structure, which applies coda wave interferometry to the waveforrns from the cross-correlation of seismic ambient noise. There are four techniques for estimating temporal change of seismic velocity with PII： moving-window cross-correlation technique （MWCCT）, moving-window cross-spectrum technique （MWCST）, stretching technique （ST） and moving-window stretching technique （MWST）. In this paper, we use the continuous seismic records from a typical station pair near the Wenchuan Ms8.0 earthquake fault zone and generate three sets of waveforms by stacking cross-correlation function of ambient noise with different numbers of days, and then apply four techniques to processing the three sets of waveforms and compare their results. Our results indicate that the techniques based on moving-window （MWCCT, MWCST and MWST） are superior in detecting the change of seismic velocity, and the MWCST can give a better estimate of velocity change than the other moving-window techniques due to measurement error. We also investigate the clock errors and their influences on measuring velocity change. We find that when the clock errors are not very large, they have limited impact on the estimate of the velocity change with the moving-window techniques.展开更多
文摘This paper derives a mathematical description of the complex stretch processor’s response to bandlimited Gaussian noise having arbitrary center frequency and bandwidth. The description of the complex stretch processor’s random output comprises highly accurate closed-form approximations for the probability density function and the autocorrelation function. The solution supports the complex stretch processor’s usage of any conventional range-sidelobe-reduction window. The paper then identifies two practical applications of the derived description. Digital-simulation results for the two identified applications, assuming the complex stretch processor uses the rectangular, Hamming, Blackman, or Kaiser window, verify the derivation’s correctness through favorable comparison to the theoretically predicted behavior.
基金supported by National Natural Science Foundation of China (No. 41074061)Basic Research Plan of the Institute of Earthquake Science, China Earthquake Administration (No. 2007-13)
文摘Passive image interferometry （PII） is becoming a powerful tool for detecting the temporal variations in the Earth＇s structure, which applies coda wave interferometry to the waveforrns from the cross-correlation of seismic ambient noise. There are four techniques for estimating temporal change of seismic velocity with PII： moving-window cross-correlation technique （MWCCT）, moving-window cross-spectrum technique （MWCST）, stretching technique （ST） and moving-window stretching technique （MWST）. In this paper, we use the continuous seismic records from a typical station pair near the Wenchuan Ms8.0 earthquake fault zone and generate three sets of waveforms by stacking cross-correlation function of ambient noise with different numbers of days, and then apply four techniques to processing the three sets of waveforms and compare their results. Our results indicate that the techniques based on moving-window （MWCCT, MWCST and MWST） are superior in detecting the change of seismic velocity, and the MWCST can give a better estimate of velocity change than the other moving-window techniques due to measurement error. We also investigate the clock errors and their influences on measuring velocity change. We find that when the clock errors are not very large, they have limited impact on the estimate of the velocity change with the moving-window techniques.
