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SUMMARY 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 ° 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 ka∼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.

SUMMARY The structure of the Earth is represented by a wide spectrum of small‐ and large‐scale structures. However, tomographic imaging techniques based on ray theory are often applied inappropriately in models with a characteristic length of heterogeneity smaller than the wavelength and width of the Fresnel zone. In other words, the conditions for ray theory are not satisfied in such models. It is therefore necessary to apply the diffraction theory of waves in tomographic reconstruction techniques in order to retrieve images of the Earth with a more general theory for wave propagation than ray theory. Physically speaking, scattering theory takes the finite‐frequency effect of waves into account. We performed a test of ray theory and scattering theory in an ultrasonic wave experiment and in a numerical finite‐difference experiment using random media with correlation lengths smaller than the width of the Fresnel zone. We used a stochastic approach to compute the mean squared value of time‐shift variations calculated from ray theory and diffraction theory. The theoretical results were compared with the experimental values obtained in the laboratory experiment using rock samples with different length‐scales of heterogeneity and from numerical experiments on wave propagation in quasi‐random media. We observed that ray theory systematically overestimates the mean squared value of time‐shift variations, while the observed statistical values from the laboratory experiments are well predicted by scattering theory. This means that tomographic imaging techniques based on ray theory suffer from a loss of resolution when the reconstructing models have a characteristic length of heterogeneity smaller than the width of the Fresnel zone.