Radiation & Trapping of Waves in a Compressible Stratified Fluid

1. Radiation and trapping of acoustic and gravity waves in a compressible stratified fluid from time-varying bottom boundaryShingo WatadaEarthquake Research Institute, University of Tokyo

2. for homogeneous fluid atmosphere Ground

3. Questions The horizontal phase velocity of the bottom boundary faster or slower than the sound velocity can change the transfer function? If the wave frequency is above or below the acoustic cut-off frequency and the buoyancy frequency, how the transfer function expressed?

4. Theory atmosphere Acoustic transfer function between gravitationally stratified fluid and overlying ground. Ground Starting with vertical linear momentum and mass conservation, and adiabatic compression of fluid, we obtain Dispersion relation Buoyancy frequency

5. Transfer function of isothermal gravitationally stratified atmosphere Plane wave solution 3.2km/s 0.5km/s 0.2km/s 0.5km/s 3.2km/s 0.2km/s

6. Ionospheric propagation of long-period acoustic waves 1km/s Where are the Rayleigh waves we have Just as observed at the ground? Why we do not see them in the ionosphere? Heki and Ping 2005 How can we model the waveform?

7. Conclusion Theoretical transfer function for isothermal gravitational stratified Compressible atmosphere is derived. The phase and amplitude of the transfer function is no longer constant, but is a function of wavenumber and frequency. In the modeling of radiation of long-period acoustic waves near the cut-off frequency, gravitaional stratification significantly change the phase and amplitude. Trapped acoustic waves and gravity waves generated by the seismic waves and tsunamis have phases 90 degrees off from that of propagating waves. Trapped acoustic waves and gravity waves have opposite phase polarities.