Scattering of P Waves by Random Velocity Heterogeneities

Abstract

In order to investigate the variation of spatial amplitude fluctuation with the increases of wave propagation in the medium with randomly distributed velocity heterogeneities, an ultrasonic model experiment was carried out by using perforated duralumin plate. P waves composed of several peaks and troughs was radiated from PZT compressional cylinder and was observed in the profiles transversal to the direction of wave propagation. Average amplitude level A of each phase of P wave in the profile and amplitude fluctuation δA were obtained. From the analysis of the average amplitude level and the amplitude fluctuation, the following results were obtained: when the wavelength approachs the average size of heterogeneities, the average amplitude level attenuates remarkably with the increase of distance of wave propagation and simultaneously the amplitude fluctuation becomes intensive ; variance σ^2(δA/A) of fluctuation rate of amplitude, which is proportional to fluctuation rate (δI/I) of energy flow I, increases nearly in proportion to time measured from P onset, and its growth rate per unit time depends strongly on the distance of wave propagation and the wave frequency, and from the analysis of the growth rate of variance per unit distance, these characteristics can be considered as being due to isotropic scattering; predominant length of the fluctuation, which corresponds to predominant period of oscillatory distributions of amplitudes along the profiles, is six to eight times the average size of heterogeneities, but short-period fluctuation appears in later phases.