This paper deals with the problem of the intensity fluctuations arising in a wave when it propagates through a medium that is randomly inhomogeneous in space and time. It is assumed that multiple scattering can occur and that the intensity fluctuations can become large. The parabolic moment equation for the fourth moment of the wave field is solved for a monochromatic point source immersed in the medium. Approximate expressions are obtained for the space–time spectrum of intensity fluctuations at any distance in the medium. The solution of the fourth moment equation is compared with results of the Rytov method of smooth perturbations, and the limitations of the latter are discussed.

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