A theoretical analysis of the space time correlations of random noise measured at two points separated a distance ξ and heighthabove a reflecting plane is formulated. The random‐incidence correlation function is discussed for noise independent of angle of incidence, omnidirectional receivers, and for a reflection coefficient Γ = ±1. Certain aspects of the resulting anisotropy of the noise field are pointed out, but attention is directed toward predicting the influence of the receiving‐point‐aspect ratio 2h/ξ on the value of the measured correlation function. It is shown that the space‐time correlation function for large‐aspect ratios approaches in the limit a form identical with that resulting for zero reflection Γ = 0. Also, the possibility of reducing the value of the spatial‐correlation function for band‐limited noise by judicious choices of ξ and 2h/ξ is pointed out.