Abstract: In this paper, by means of the plane wave representation for the radiation of a diretional point source, the general expression of space-time correlation function of the noise field in the ocean is derived. This expression is applied to inhomogenous shallow water and inhomogenous deep water. The organic relation of the space-time correlation function of the noise field with ambient parameters is established.
By means of singularity condition of point （noise） source near the receiver, the calculus of space-time correlation function of the noise field is simplified. Whereas, the space-time correlation function of noise field in homogenous shallow water is calculated with the normal mode method.