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Application of frequency variable filters to surface-wave amplitude analysis

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

Abstract

The problem of spectral biasing due to frequency domain filtering of surface-wave seismograms is investigated, and the method of frequency variable filters (FVF) is developed to compensate for this bias. As a result, the FVF can significantly improve signal to noise in the filtering process, except at points which require increased frequency domain resolution due to biasing. A detailed comparison of some currently accepted surface-wave filters is made in order to clarify the development of the FVF algorithm. Three long-period, surface-wave seismograms are tested with FVF and compared to two other methods, the multiple filter technique and the phase-matched filter (PMF). Emphasis is placed on finding limitations in all the methods, not on routine processing. Results of the tests show that the FVF and PMF are an improvement over multiple filter technique, in that the results of processing can be diagnosed in both the time and frequency domains. In addition, the FVF is more successful than PMF in removing higher mode contamination from fundamental mode Rayleigh waves. Another conclusion is that care must be taken in defining the limits of frequency domain resolution for the FVF. Some bias due to convolutional smoothing must be accepted, or the FVF becomes a simple all-pass filter. Multiple filter technique and PMF have a similar problem, which is due fundamentally to the uncertainty principle between time and frequency.

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