Acoustic scattering by bubbles in naturally occurring mud sediments

Abstract

Naturally occurring sediment mud contains bubbles created by decaying vegetable matter. Work reported by Preston Wilson etal. (ca. 2007) has determined via x-ray tomography systems that mud bubbles are not spherical in shape, but resemble oblate spheroids and are “inhomogeneously distributed.” These features are explained in terms of the card-house structure of mud with an adaptation of the fracture mechanics ideas of Boudreau etal. (ca. 2002). The scattering of sound at low frequencies by such nonspherical bubbles has both monopole and dipole components. The scattered wave associated with the monopole term is proportional to the bubble volume. The dipole term involves an effective entrained mass tensor, which is found by a solution of Laplace's equation. All bubbles, regardless of shape, have a smallest resonance frequency, and the scattered radiation near the resonance frequency is monopole in character. Example solutions for the resonance frequencies and the scattering near resonance are given for oblate spheroidal bubbles, and a suggested interpolation from low frequencies to resonance frequencies is given. A discussion is also given of how one can make use of the range-evolving form of compact-source generated pulses to infer information about the bubbles near the propagation path.