In order to study the effect of heterogeneity on the arrival time and energy fluctuations of seismic waves, we made laboratory-scale physical model experiments by observing elastic waves propagating through crystalline rock samples having different scales of heterogeneity. A laser Doppler vibrometer was used to measure the waveforms. About 100 waveforms were obtained over a square grid with a spacing of 1 mm in linear profiles for Westerly and Oshima granite samples, which correspond to small and large scales of heterogeneity, respectively. The same measurement was done for steel block, which is a homogeneous medium. Characteristic scale length of heterogeneity of Westerly and Oshima granites are found to be 0.22 mm and 0.46 mm, respectively; the values were obtained from spatial autocorrelation function of velocity fluctuation based on microstructure photo image. The arrival time of P wave was determined by searching the best-fit point that divides the waveform into two different autoregressive (AR) models based on Akaike information criterion (AIC). This method automatically yields the arrival time of P waves, and the fluctuation of arrival time can be studied as a statistical distribution. We also calculated logarithmic values of the wave energy and studied their fluctuation. The observed fluctuations of the arrival time and the log of wave energy show nonsymmetric distributions. Both the variances of arrival time and log-energy distributions increase with increasing scale length of heterogeneity. This indicates a positive correlation between the variances of the fluctuation and the scale length of heterogeneity. The study also reveals that the correlation coefficient between fluctuations of arrival time and energy of seismic wave increases with increasing length of heterogeneity.

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