Seismic resonances of spherical acoustic cavities

We study the interaction of a seismic wavefield with a spherical acoustic gas- or fluid-filled cavity. The intention of this study is to clarify whether seismic resonances can be expected, a characteristic feature that may help in detecting cavities in the subsurface. This is important for many applications, in particular the detection of underground nuclear explosions, which are to be prohibited by the Comprehensive Test Ban Treaty. To calculate the full seismic wavefield from an incident plane wave that interacts with the cavity, we considered an analytic formulation of the problem. The wavefield interaction consists of elastic scattering and the wavefield interaction between the acoustic and elastic media. Acoustic resonant modes caused by internal reflections in the acoustic cavity show up as spectral peaks in the frequency domain. The resonant peaks coincide with the eigenfrequencies of the un-damped system described by the particular acoustic medium bounded in a sphere with stiff walls. The filling of the cavity could thus be determined by the observation of spectral peaks from acoustic resonances. By energy transmission from the internal oscillations back into the elastic domain, the oscillations experience damping, resulting in a frequency shift and a limitation of the resonance amplitudes. In case of a gas-filled cavity, the impedance contrast is still high, which means low damping of the internal oscillations resulting in very narrow resonances of high amplitude. In synthetic seismograms calculated in the surrounding elastic domain, the acoustic resonances of gas-filled cavities show up as persisting oscillations. However, due to the weak acoustic–elastic coupling in this case, the amplitudes of the oscillations are very low. Due to a lower impedance contrast, a fluid-filled cavity has a stronger acoustic–elastic coupling, which results in wide spectral peaks of lower amplitudes. In the synthetic seismograms derived in the surrounding medium of fluid-filled cavities, acoustic resonances show up as strong but fast decaying reverberations.