A physical-model study of the statistics of seismic waveform fluctuations in random heterogeneous media

Using laboratory-scale physical models, we studied seismic waveform fluctuation in 3-D heterogeneous media, and evaluated the effects of short-wavelength random heterogeneity on seismic waves. We made two series of experiments: (1) waves are excited by the same source signal and propagate through three kinds of granitic rocks with different scales of heterogeneity, and (2) waves are excited by different frequencies but propagating through the same rock. A compression-mode piezoelectric transducer was attached to one side of the block, and the waveforms were measured at a 10 mm radius circular array with a 2 degrees spacing, located on the other side. 180 waveforms are obtained at equal source-receiver distances with an equal wave radiation from the source. The source signals are one- or two-cycle sine-wave pulse with 0.5 MHz for different heterogeneities, and 0.25, 0.5, 1 and 2 MHz for the same heterogeneity. Waveforms were recorded by using a system equipped with a laser Doppler vibrometer as a sensor of elastic waves. The rock heterogeneities were investigated as the 1-D velocity fluctuations obtained from the 2-D microstructure images of the rock. By applying the exponential autocorrelation function, heterogeneities in the three rocks are characterized by similar fluctuation intensities (7.9-9.3 per cent) but different scale lengths ranging from 0.22 to 0.92 mm. We calculated the spatial correlation of waveforms, the correlation between an averaged waveform and observed waveforms, the energy partition with respect to lapse time, and the statistical distributions of the waveform parameters: correlation coefficients, traveltimes of P wave, and the log values of the P-phase energy. Correlation of waveforms, energy partition and statistical parameters of waveforms are investigated as a function of the normalize scale parameter ka : the product of wave number and the characteristic scale length of heterogeneity. We found that waveform parameters change the trends at kasimilar to 0.2-0.3. When ka exceeds 0.2-0.3, scattered waves become strong and waveforms become more complicated. This may indicate a transition from an equivalent homogeneous medium to a scattering medium for seismic waves propagating through random heterogeneous medium.