Correlation among multipaths for long rang propagation

The multipath arrivals in ocean acoustic tomography are the important observations for the inversion to a sound speed profile and then to temperature. They are also implicit in any matched field processing beamforming. While the covariance of ray path travel times has been examined (Flatte and Stoughton, JGR 91, C6), the correlations among the waveforms of these multipaths has never been determined. There are two conflicting hypotheses: i) the paths radiate from a source, so they must be correlated. ii) Alternatively, the small scale ocean inhomogeneities randomize the paths since they traverse different ocean masses. At short ranges and low frequencies, the paths are correlated, whereas at long ranges and high frequencies, they are uncorrelated. Reality is somewhere in between. We have a power law medium which at large scales correlates paths but decorrelates them at small scales. The key quantity distinguishing the scales is the Fresnel zone extent. We analyze the correlation from two perspectives. A th...