The frequency invariability of the warped modal signal and the warped signal autocorrelation function in shallow water is discussed.A method is proposed for passive source-range estimation based on the frequency invariability and warping transform of signal autocorrelation function received by a single hydrophone in a range-independent or weak range-dependent shallow water environment.In the method,a guided source with a known range is employed to provide the crucial and relative invariant scaled features.The experimental data in shallow water with an iso-speed profile and a fluctuated thermocline are used to verify this approach.The relative errors of the source range estimation are basically less than 10%.
In this paper,a modified warping operator for homogeneous shallow water based on the Beam-Displacement Ray-Mode(BDRM)theory is presented.According to the BDRM theory,the contribution of the beam displacement and the time delay to the group velocity can be easily considered in a shallow water waveguide.A more accurate dispersion formula is derived by using the cycle distance formula to calculate the group velocity of normal modes.The derived dispersion formula can be applied to the homogeneous shallow water waveguide.Theoretically,the formula is related to the phase of the reflection coefficient and suitable for various bottom models.Furthermore,based on the derived dispersion relation,the modified warping operator is developed to obtain linear modal structures.For the Pekeris model,the formulae for the phase of the reflection coefficient are derived in this work.By taking account of the effect of the bottom attenuation on the reflection coefficient,the formula for the phase of the reflection coefficient including the bottom attenuation is obtained for the Pekeris model with a lossy bottom.Performance and accuracy of different formulae are evaluated and compared.The numerical simulations indicate that the derived dispersion formulae and the modified warping operator are more accurate.
A long-range sound propagation experiment was conducted in the West Pacific Ocean in summer 2013.The signals received by a towed array indicate that the travel speed of pulse peak(TSPP)in the convergence zones is stable.Therefore,an equivalent sound speed can be used at all ranges in the convergence zones.A fast calculation method based on the beam-displace-ment ray-mode(BDRM)theory and convergence zone theory is proposed to calculate this equivalent sound speed.The computation speed of this proposed method is over 1000 times faster than that of the conventional calculation method based on the normal mode theory,with the computation error less than 0.4%compared with the experimental result.Also,the effect of frequency and sound speed profile on the TSPP is studied with the conventional and fast calculation methods,showing that the TSPP is almost independent of the frequency and sound speed profile in the ocean surface layer.
