Statistical moments of travel times at second order in isotropic and anisotropic random media

We study the high-frequency propagation of acoustic plane and spherical wav es in random media. With the geometrical optics and the perturbation approa ch, we obtain the travel-time mean and travel-time variance at the second o rder. The main hypotheses are the Gaussian distribution of the acoustic spe ed perturbation and a factorized form for its correlation function. The sec ond-order travel-time variance explains the nonlinear behaviour at large pr opagation distance observed with numerical experiments based on ray tracing . Usually, homogeneity and isotropy of the refractive index are considered. Using the geometrical anisotropy hypothesis we extend the theory to a gene ral class of statistically anisotropic random media.