A Hamiltonian method for finding broadband modal eigenvalues
(a) In traditional methods, the modal phase velocities for every frequency sample are computed along the vertical arrow, and the dispersion curve of each mode is obtained using extrapolation process. (b) For each mode, given the corresponding phase velocity at a reference frequency, the dispersion curve can be traced automatically using the Hamiltonian method.
(a) The curve in the complex k plane (bold line), the open circles are located at eigenvalues using the Hamiltonian method while the stars are the results of kraken. (b) The real part of the phase function Re(Φ) as a function of Re(k) along the line , the dots are located at eigenvalues.
(a) The curve in the complex plane for three-layer elastic waveguide. (b) The real part of the phase function as a function of Re(k) along the curve. The dots are located at the eigenvalues.
The complex dispersion curves of different modes (first mode to eighth mode from left to right) in 3D space [Re(k), Im(k), frequency].
The normalized temporal waveform comparison for the case that the horizontal range between the source and receiver at depths 32 and 30 m, respectively, is 5 km. (a) is obtained by the Hamiltonian-WKB method, (b) is obtained by kraken.
Differences (dB) between the two temporal waveforms as shown in Fig. 3.
Parameters for the Perkeris waveguide (300 Hz).
Eigenvalues comparison between Hamilton resolver and kraken for Perkeris waveguide.
Parameters for the three layer waveguide.
Broadband eigenvalues comparison between Hamilton resolver and KRAKEN.
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