Backscattering of Sound by Spherical Shells in Water.

Investigated here are generalized Lamb wave excitations in spherical shells submerged in water generated by incident acoustical radiation fields. We restrict our attention to a single observation point in the backscattered far field. The response of the shell is investigated in the time-frequency plane via smoothed Wigner Distributions computed by sampling the partial wave series representation of the frequency response to an incident pulse. The frequency response, or form function, contains the Lamb wave excitation spectrum as well as diffractive excitations and the specular reflection. These distinct contributions can be extracted from the partial wave series representation via Resonant Scattering Theory (RST) or Sommerfeld-Watson Transform (SWT) techniques and thus render interpretations of the features displayed in the time-frequency plane. The advantage of time-frequency methods over single domain methods is that one can see what frequencies are excited by the incident field and also see at what time those contributions will arrive at the observation point relative to the specular return. Time-frequency methods also indicate the relative magnitudes of the contributions as they are associated with the energy density of the signal in the (t, f) plane. Lamb wave excitations of particular interest are those excitations associated with large temporal and spectral signatures, a mid frequency enhancement and a high frequency enhancement. We model these excitations via a ray acoustic approximation which is derivable from SWT. At present, the mid frequency enhancement is the best understood excitation. Though not as well understood, the ray acoustic approximation applied to the high frequency enhancement yields very good qualitative agreement with a partial wave series representation of the form function. This latter high frequency enhancement gives rise to very "prompt" radiation. In the far field, its arrival time at a detector is very close to that of the specular reflection. This high frequency enhancement is associated with a "backward" moving wave as its phase velocity is opposite in direction to its group velocity.