Methods To Compute Wideband Wavenumbers And Equivalent Coupled-mode Matrix

Normal mode theory is usually used to compute the acoustic field in the real ocean waveguides. It is also the standard tool to analyze the characteristics of the sound propagation in ocean channel such as multiple-path propagation, dispersion, attenuation and sound fluctuation, etc. The normal mode method is widely used in some underwater acoustic technologies including ocean tomography, model-based matched-field processing for target localization, the inversion of acoustic parameters of sea bottom, channel equalization of underwater acoustic communication.With the developing of the underwater acoustic technologies, the normal mode method has to be improved to satisfy the demand of the real-time wideband acoustic field computation and the analysis of the real observed acoustic data. So, in this thesis, we mainly solve two fold problems:rapid computation of the wideband eigen-wavenumbers and the computation of the equivelent coupled-matrix.(1) In real shallow water waveguides, the modal eigen-wavenumbers can be determined by searching the locations in the complex plane of the eigen-wavenumbers at which the complex phase function Φ is a multiple of π [Tindle, J. Acoust. Soc. Am.96,1777-1782 (1994)]. Here, a Hamiltonian method is introduced for tracing the path in the complex plane along which the phase function keeps real. This method reduces the computation of eigen-wavenumbers by transform the 2D (complex wavenumber plane) foots-finding problem into the 1D (Im(Φ)=0) foots-finding problem.(2) The Hamiltonian method can also be extended to compute the broadband modal eigen-wavenumbers or the modal dispersion curves in the underwater waveguide with fluid/elastic bottoms. This method reduces the 3D (frequency× the complex wavenumber plane) foots-finding problem to N×1D (the number of modes× dispersion curve) foots-finding problem. For each trapped or leaky normal mode, a different Hamiltonian is constructed in the complex plane and used to trace automatically the complex dispersion curve with the eigen-wavenumber in a reference frequency as the initial value. In contrast to the usual methods, the dispersion curve for each mode is determined individually (single-mode wideband computation).(3) According to the closure condition of the modal eigenfunctions. the modal eigenfunctions of the computing frequency can be presented as the summation of the modal eigenfunctions of the reference frequency as the orthogonal basis which coefficients composed the transformation matrix. Then the matrix equation of eigenvalues and the transformation matrix is constructed using the orthogonality of the modal eigenfunction, and can be solved by the singular value composition method.(4) In real applications, the equivalent coup led-matrix of the trapped modes is usually observed, which can be used to explain the sound scattering of the fluctutive bottom, the effective attenuation of the bottom and modification of the reverberation models. Following Evans’s forework, two-layer model is firstly used to introduce the decopling of the coupled-matrix equations of the trapped modes and the leaky modes. By decoupling, the equivalent coup led-matrix of the trapped modes, which is modified by considering the influence of the leaky modes, can be extracted. Then the computation of the inversion of some matrices introduced by decoupling could be solved by using the Born approximation. The decouping method can also be extended to the N-layer model on the help of the Born approximation, By this way, the dimension of the coupled-matrix is not changed, but the accuracy of the coupled-mode method is improved.