Representation of random media in acoustic scattering calculations

Turbulence, internal waves, surface roughness, and other environmental variations in the atmosphere and ocean randomly scatter sound. Realistic representation of these variations is important for numerical wave propagation calculations. In principle, there are two primary approaches to create these representations: (1) physics-based, dynamical models for the atmosphere or ocean and (2) kinematic synthesis of random fields with prescribed statistical properties that do not necessarily capture the medium dynamics. The most common kinematic approach involves synthesizing fields from randomly phased Fourier modes. For statistically inhomogeneous media, the Fourier modes generalize to empirical orthogonal functions. An alternative kinematic approach, called filtered Poisson processes, distribute spatially localized functions with randomized positions and orientations. Quasi-wavelets (QWs) are a filtered Poisson process intended for turbulence and other self-similar media. While both the Fourier and QW approaches can be formulated to reproduce specified second moments of the random field, if the representations are constructed too sparsely, higher-order moments such as the kurtosis will be unrealistic. The kinematic approaches also underlie phase screen methods, which can be quite useful when the Markov approximation is valid.