Velocity shift using the Rytov approximation

Abstract

The high-frequency propagation of acoustic plane waves in a weakly heterogeneous random stationary 2-D medium is considered. The apparent velocity of the wave is larger than the velocity corresponding to the background homogeneous medium; the difference is called velocity shift. Both this shift and the variance of the apparent velocity are calculated using the Rytov approximation; explicit formulas are given when the covariance of the medium is Gaussian. This enables one to show several properties of the shift and the variance, which are illustrated by some numerical experiments on the wave equation.