Laboratory Measurements of Elastic Wave Attenuation by Scattering due to Random Heterogeneities

Abstract

Scattering attenuation and spatial fluctuation of P waves traveling through a scattering medium were examined experimentally by using an ultrasonic technique. 2-D models of random media used in laboratory experiments are characterized by a triangular correlation function and a 2.4% standard deviation in velocity and density. The range of wave length covered in the experiments corresponds to 2<ka<33, where k is the wave number and a is the correlation distance of the heterogeneities, i.e., the heterogeneity size. The results obtained are as follows: (1) When the P waves travel sufficiently long compared with the wave length through the models of random media, the travel-time fluctuation, σ(t), is small, i.e., about 3-4% of the wave period at intermediate frequencies of ka=4-13.5, but at a high frequency of ka=33 σ(t) is large, i.e., about 11% of the wave period. In contrast to the above, the amplitude fluctuation, σ(lnA), is large, i.e., about 22-25% at ka=4-13.5, but at ka=33 it is small, i.e., less than 10%. (2) When the forward-scattering effect such as the travel-time fluctuation is neglected, the scattering attenuation, Q^-1, increases with ka for ka<3, has a peak around ka=3-5, then decreases with ka. This frequency dependence of Q^-1 is in harmony with the observed frequency dependence of Q_β^-1 for shear waves. (3) From results (1) and (2) it is concluded that forward scattered energy should not be counted as lost energy when we calculate the scattering attenuation of seismic waves traveling though a scattering medium. (4) Result (1) suggests that initial motions as well as the subsequent phase of direct P or S wavelets are strongly contaminated by ununiform forward-scattered energy: Fourier amplitudes for entire parts of the wavelets should be used to determine the attenuation of the waves as a function of frequency.