Large fluctuation of wave amplitude produced by small fluctuation of velocity structure

Abstract

Seismic velocity structure of the real Earth is described by a combination of deterministic large scale structure and small scale fluctuation. When waves propagate in media having the small scale fluctuation, the fluctuation makes the rays bend, introduces focussing and defocusing, and produces fluctuations of wave amplitude. To estimate the size of wave amplitude fluctuation that is caused by velocity fluctuation, the variances of wave amplitudes are evaluated as a function of propagation distance from numerical simulations of scalar wave propagation in 3D random media having Gaussian or exponential autocorrelation functions. The simulations are performed using a phase screen method, which is a numerical procedure for solving the parabolic wave equation. The following conclusions are obtained from the simulations that use two types of incident wave: stationary monochromatic sine wave and transient Ricker wavelet. For velocity fluctuation as small as several percent, the variance of wave amplitude is larger than the square of its average in some cases of high frequency waves. These results show the importance of small error and fine spatial resolution of velocity structure model for proper modeling of wave amplitude. When the fluctuation of the velocity structure is large, the wave amplitude variance increases with the propagation distance until it reaches some peak value after which it decreases with the increase of propagation distance. The variance for the Ricker wavelet incidence is smaller than that for a monochromatic sine wave. Because of the stochastic dispersion due to the small fluctuation of velocity structure, the maximum amplitude decreases with the propagation distance even if there is neither an intrinsic absorption nor back-scattering for the Ricker wavelet incidence.