Using only ocean ambient noise recordings it is possible to approximate the local time domain Green's function (TDGF) and extract the time delays associated with different ray path between the elements of a bottom hydrophone array. Comparing the strength of the noise correlation function taken over increasing time windows with residual fluctuations points to an optimum time window to use in the noise correlation function. Through comparison with computer simulations the resulting time series is shown to accurately approximate noise responses in the environment. Analysis of the TDGF gives accurate environmental detail, specifically the critical angle at the water-sediment interface.