Two coupled-mode methods, namely DGMCM （Direct-Global-Matrix Coupled- Mode Method） and CCMM （Consistent Coupled-Mode Method）, are analyzed and compared. First, both of these two methods provide two-way solutions, and hence they are accurate models. Second, the series of local vertical modes in DGMCM converges as fast as that in CCMM, whereas DGMCM has a more tolerable requirement of the number of segments than CCMM. Third, these two models obtain the field solution by solving the coupled-mode system with different coefficient matrices, in which the computational effort for the required parameters is almost the same. Finally, DGMCM can handle some problems which are difficult for CCMM, such as in a waveguide with a rough bottom, a line source located right on top of a sloping bot- tom, or in the presence of multiple sources. In DGMCM, closed-form expressions for coupling matrices in a two-layer waveguide are given. In addition, the formulation for the line-source problem in plane geometry is derived to update CCMM.
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.
