Quantifying the emergence rate of spatio‐temporal correlations of the ambient wave field from finite duration sample realizations.

The spatiotemporal correlations measured between receivers in a diffuse wave field convey information about the point‐to‐point propagation of waves between the receiver locations. An issue of practical experimental importance is how much data must be accumulated to generate a useful estimate of the expectation value of the spatiotemporal correlations. The uncertainty associated with a finite duration realization of the sample cross correlation function for an arbitrary environment is derived. Using this, a method for modeling the emergence rate of the expectation value of the spatiotemporal correlations is discussed. As examples, the cases of free space and the ocean waveguide are considered. Practical experimental implications are discussed.