Subsurface structures contain small-scale random heterogeneities which generate scattered waves. Considerable fluctuations appear in seismic waveform when heterogeneity scales are comparable or a little smaller than the dominant seismic wavelengths. Waveform fluctuation by scattering can be examined in laboratory experiments by using random heterogeneous materials as scale models. A laser Doppler vibrometer is used to accurately record waveforms propagating through a model specimen. By taking advantages of laboratory experiments, one can reveal some quantitative relationships between wave fluctuations and the intensity or the characteristic scale length of random heterogeneity. Variations in travel times, fluctuations of amplitude, phase, and particle-motion, as well as envelope formation are examined with respect to the statistical properties of random heterogeneities. The variations can be characterized in terms of the scale-invariant values, ka and kL, the wavelength-normalized values for the characteristic scale length of heterogeneity and the wave travel distance, respectively. On the basis of experimental results, we obtain the boundary between equivalent homogeneous media approach and scattering random media approach. The two different approaches come from two different properties of the same medium in wave propagation problems, depending on the values of ka and kL. The boundary is critical in seismic imaging techniques, because strong scattered waves degrade the seismic signals used for imaging and deteriorate the image quality.