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Numerical experiments in the estimation of frequency-wavenumber spectra of seismic events using linear arrays

TEXAS INSTRUMENTS, INC., DALLAS, TEXAS

Abstract

Studies in the measurement of frequency-wavenumber spectra of transient events have been conducted using theoretical and analog model data recorded along a 21-element, inline array. Straightforward numerical transformation, assuming space stationarity, gives good definition of the dominant (Rayleigh) mode, but little information concerning higher modes. The presence of spatial non-stationarity due primarily to cross correlation between modes complicates the fine structure of the spectral estimate. Averaging over redundant space lags is necessary to remove this. Additional difficulties arise from side lobes due to use of the finite length array. The amplitude of the side lobes can be reduced by using a space lag window. In the present case this gives indications of the higher modes, but these indications are so ill-defined as to be useless for determining dispersion. The effects of amplitude deviations between channels are also studied.

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				A. F. LINVILLE and S. J. LASTER Near-surface dispersion studies at Tonto Forest Seismological Observatory Bulletin of the Seismological Society of America, June 1, 1967; 57(3): 311 - 340. [Abstract] [PDF]