Low-Frequency Wavenumber Limits for P-SV Modes (Modvagtal vid lae Frekvens)

摘要

For laterally homogeneous fluid-solid media, it has previously been shown that211u001eall low-frequency P-SV modes such that the horizontal wavenumber tends to zero 211u001ewith the frequency can be determined explicitly. Interface waves and different 211u001etypes of bending waves are particular examples of such modes. They continue to 211u001eexist as propagating modes down to arbitrarily low frequencies. Propagating modes 211u001ein general, however, typically have lower cutoff frequencies, below which the 211u001ehorizontal wavenumber leaves the real axis. In the present paper, it is shown how 211u001eall low-frequency P-SV modes can be determined for which the horizontal 211u001ewavenumber does not tend to infinity as the frequency tends to zero. It turns out 211u001ethat a low-frequency wavenumber limit will indeed exist for such a mode. For each 211u001efluid-solid medium, the low-frequency modal wavenumber limits can be determined 211u001eas the zeros of a particular entire analytic function. The evaluation of this 211u001eanalytic function involves solution of ordinary differential equation (ODE) 211u001esystems.