Amplitude attenuation of impulsive waves in random media based on travel time corrected mean wave formalism

Abstract

Waves gradually collapse with propagation through media with random velocity fluctuation; however, impulsive waves propagate without large attenuation when the wavelength is shorter than the correlation distance. The Q−1 value predicted from the usual mean wave formalism monotonously increases with frequency even in the high-frequency limit, due to taking a mean over waves with large travel time fluctuations caused by the long scale velocity fluctuation compared with the wavelength studied. We propose a new statistical averaging method appropriate for the amplitude attenuation measurement of impulsive waves, in which the mean wave is defined after the correction of travel time fluctuations. We investigate impulsive scalar waves propagation in three-dimensional media with homogeneous and isotropic random fractional velocity fluctuation, based on the binary interaction approximation in this improved mean wave formalism. We successfully derive the Q−1 value that has a peak of the order of the mean square fractional velocity fluctuation around the frequency corresponding to the correlation distance and decreases with frequency in the high-frequency limit, when the random media is characterized by the von Karman autocorrelation function. The correction of travel time fluctuation is shown to be equivalent to the neglect of energy scattering around the forward direction.