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 waves in random media. With the geometrical optics and the perturbation approach, we obtain the travel-time mean and travel-time variance at the second order. The main hypotheses are the Gaussian distribution of the acoustic speed perturbation and a factorized form for its correlation function. The second-order travel-time variance explains the nonlinear behaviour at large propagation 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 general class of statistically anisotropic random media.