It has been established theoretically and confirmed experimentally that two-point crosscorrelation functions (CFs) of diffuse acoustic noise result in approximations to Green's functions (GFs), which describe deterministic sound propagation between the two measurement points. In this paper we present approximations to GFs in the 20-70 Hz band that were obtained by cross-correlating concurrent records of ambient noise measured on near-bottom instruments at 5 and 10 km range in a 100 m deep coastal ocean environment in the Florida Straits. Interpretation of the measured CFs is challenging inasmuch as neither ray nor modal arrivals are temporally resolved. We employ a modal expansion of the wavefield to perform forward modeling of the CFs. This process requires that differences between CFs and GFs be accounted for. Using several different parameterizations of the seafloor structure, the inverse problem is investigated by performing an exhaustive search over the relevant parameter space to find the set of parameters that minimizes the integrated squared difference between simulated and measured CFs. Results show that simulated CFs yield 96.33% and 70.64% correlation coefficients with measured CFs at 5 and 10 km respectively. Moreover, a best-fitting geoacoustic model is obtained as a secondary result.