LABORATORY MEASUREMENTS OF SPATIAL FLUCTUATION AND ATTENUATION OF ELASTIC-WAVES BY SCATTERING DUE TO RANDOM HETEROGENEITIES

To study the effects of strong scattering on elastic waves, spatial fluctuation and scattering attenuation of P waves were examined by laboratory experiments for 2-D models of random media approximately characterized by a triangular correlation function in the range of 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) For ka>10, both the intensity and the correlation distance of the amplitude fluctuation are approximate for any phase of the P-wave train. The correlation distance nearly agrees with the heterogeneity size. These fluctuation properties are quite consistent with the theoretical prediction by the forward-scattering approximation. (2) For 3<ka<6, the fluctuation intensity becomes stronger in later phases of the P-wave train. This shows that scattering is approximately isotropic, and therefore, the scattered energy increases with time within the P-wave train. The correlation distance of the amplitude fluctuation disagrees with the heterogeneity size, and it shows a frequency-dependent property decreasing from 7 a to 4 a with the increase of ka from 3 to 6. These properties for 3<ka<6 have not yet been predicted theoretically. (3) For ka<3, though the fluctuation is considerably smaller compared with that of ka>10 and 3<ka<6, the fluctuation property is considered similar to that of 3<ka<6. (4) The observed scattering attenuation, Q-1, increases with ka for ka<3, has a peak around ka=3∼5, and then decreases with ka. (5) When θmin = 15° and σ = 0.075, the theoretical Q-1 curve, predicted by the approximate theory of Wu, roughly matches the observed Q-1 values, where θmin is the minimum scattering angle measured from the propagation direction of the P waves and σ is the rms of fractional velocity fluctuation. This suggests that the energy scattered in the range of θ>15° is lost from the P waves, while the energy scattered in the range of θ<15° is retained; and that the approximate theory overestimates by about three times the σ value of the model media used owing to the neglect of multiple scattering. (6) When the size of velocity heterogeneities responsible for forward scattering at 3<ka<6 is estimated from the θmin value of 15° on the basis of Wu's theory, it nearly agrees with the correlation distance for the initial phase of the P-wave train. © 1990 Birkhäuser Verlag.