An experimental study of phase angle fluctuation in seismic waves in random heterogeneous media: time-series analysis based on multivariate AR model

Abstract

SUMMARY Effects of small-scale heterogeneities on seismic waveform fluctuations were studied by physical model experiments. Using a laser Doppler vibrometer, we recorded elastic waves propagating through a granite block at 180 observation points that were arranged as an equally spaced circular array. A disc-shaped PZT source was attached on the other side surface of the circular array for realizing equivalent positions with respect to both source radiation pattern and travel distances of waves. Waveform pairs were selected out from the 180 waveforms, and cross spectra of time-windowed partial waveforms were calculated by applying the multivariate AR model. By comparing waveforms of two observation points, the cross-spectral amplitudes and phases are obtained with respect to the lapse time by moving the time window, or to the spatial distance by changing the pairs of observation points. We obtain distributions of cross-spectral phase values for frequency and the lapse time of waveforms. The distributions indicate phase fluctuation of waves in random media with respect to frequency and lapse time. Heterogeneity of the rock sample is expressed as a 1-D exponential autocorrelation functions (ACF); e2 exp(−|r|/a), where r is the distance, and a and e are the correlation length (0.22 mm) and the strength of heterogeneity (8.5 per cent), respectively. The distributions are plotted against ka; the product of wavenumber and correlation length. For small ka, the distributions of phase are close to the Gaussian distributions with small variances, but the variances quickly become large above ka≈ 0.2–0.3. Then the distributions become uniform between −π and π. This suggests that the incoherent scattered waves become dominant above a critical ka value (or a critical frequency for a medium), and phase information in later portions of waveforms will be lost. This may be important for extracting reflection, refraction or converted waves that are assigned as signals from geologic discontinuities because those signals may be strongly distorted by scattered waves produced from the small-scale heterogeneities of earth's media.