原文传递
Low-frequency wavenumber limits
for P-SV modes
| 题名： | Low-frequency wavenumber limits for P-SV modes |
| 作者： | Sven Ivansson |
| 关键词： | fluid-solid medium, propagator technique, compound matrix, asymptotic analysis, underwater acoustics, seismology, plate acoustics |
| 摘要： | For laterally homogeneous fluid-solid media, it has previously been shown that all low frequency P-SV modes such that the horizontal wavenumber tends to zero with the frequency can be determined explicitly. Interface waves and different types of bending waves are particular examples of such modes. They continue to exist as propagating modes down to arbitrarily low frequencies. Propagating modes in general, however, typically have lower cutoff frequencies, below which the horizontal wavenumber leaves the real axis. In the present paper, it is shown how all low-frequency P-SV modes can be determined for which the horizontal wavenumber does not tend to infinity as the frequency tends to zero. It turns out that a low-frequency wavenumber limit will indeed exist for such a mode. For each fluid-solid medium, the low-frequency modal wavenumber limits can be determined as the zeros of a particular entire analytic function. The evaluation of this analytic function involves solution of ordinary differential equation (ODE) systems. An interesting result is that the analytic function can be factorized. In addition to obvious factors providing the modal wavenumber limits at the origin, there will be one factor from each fluid or solid region. Hence, the modes with nonzero wavenumber limits decouple into region-dependent classes at low frequency. This result is further elucidated by an asymptotic analysis of the mode forms. Even at higher frequencies, the modes can apparently be classified according to their low-frequency connections to particular regions. |
| 报告类型： | 科技报告 |
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