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Interstation surface wave analysis by Frequency-domain Wiener deconvolution and modal isolation

DEPARTMENT OF EARTH AND ATMOSPHERIC SCIENCES SAINT LOUIS UNIVERSITY, P.O. BOX 8099, LACLEDE STATION, ST. LOUIS, MISSOURI 63156

Abstract

A new technique which combines frequency-domain Wiener filtering and modal isolation is developed for determining interstation phase velocities, group velocities, and attenuation coefficients for seismic surface waves. Frequency-domain Wiener filtering is more effective than time-domain Wiener filtering for the determination because it uses a smaller window lag which produces a smoother interstation Green's function. This leads to greater accuracy and stability when noise-contaminated data are analyzed. We optimize Wiener filtering in the frequency domain by applying two trapezoidal windows of different lags to the cross-correlation function between two stations and to the autocorrelation function of the first station, respectively. The windowed correlation functions are then transformed to the frequency domain. The interstation Green's function in this technique is the ratio of the smoothed cross-spectrum to the smoothed auto-spectrum of the first station. Frequency-domain Wiener filtering is equivalent to time-domain Wiener filtering when the same rectangular window is applied to both the correlation functions.

Wiener filtering, however, cannot efficiently remove higher mode interference when the higher modes are superimposed on the fundamental mode in the correlation functions. To more thoroughly eliminate the effects of such interference, phase-matched filtering or time-variable filtering can be employed to isolate one particular mode at each of two stations. Frequency-domain Wiener deconvolution is then applied to calculate the Green's function. The interstation group velocites can be obtained by applying the multiple filter technique to the Green's function, and can be refined by phase-matched filtering. The amplitude and phase spectra of the Green's function are used to calculate attenuation coefficients and phase velocities, respectively, for the interstation medium.

This new technique is compared with other methods by applying them to both noise-contaminated synthetic seismograms and real data. The proposed technique is found to be superior, particularly in period ranges where the signal-to-noise is low.

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