Born series sums for wave propagation in anisotropic, random media

The Born series for random wave propagation is considered for the physically interesting regime: the radiation wavelength short compared with the correlation lengths of the medium and the range large compared with such lengths. We treat a Gaussian medium with a Gaussian‐form correlation function. These specializations lead to integrals for the moments with integrands which are themselves mainly of Gaussian form and can be performed algebraically using multivariate Gaussian distribution formulas. Specifically, for moments the, say, eighth‐order Born term involves a 24‐fold integration of which 16 can be done algebraically using the formulas. We are able for a two‐scale anisotropic medium to sum the Born series for the first and second moments of the radiation field. The results reduce to familiar ones when we specialize to isotropic media. A novel characteristic is that for certain parameter ranges where the vertical medium scale Lv is very small compared with the horizontal scale LH diffraction effects ca...