Scattering of Sound by Gas Bubbles in Water and Sediments

ABSTRACT In this paper, a self-consistent multiple scattering approach with suitable pair-correlation function is employed to study acoustic wave propagation through water and sediments containing gas bubbles. The effects of surface tension, shear viscosity of the liquid and thermal conduction in the gas bubbles are considered in the analysis. In the Rayleigh limit, closed form expressions are given as a function of concentration of bubbles. Numerical results are presented for both phase velocity and coherent attenuation as a function of frequency near the fundamental resonance of the bubble for various values of concentration of bubbles. INTRODUCTION Gas bubbles in water and sediments control the long-range, low-frequency underwater sound propagation, especially at or near the fundamental resonance frequency of the bubbles. A bubble in water very effectively absorbs and scatters the sound wave when it propagates at or near the natural pulsation frequency of the bubble. Thus, sound propagating through an extended bubble swarm undergoes dispersion, and one is normally interested in studying the frequency dependent phase velocity and attenuation in such media. During the past several decades, many empirical relationships and experimental approaches have been developed, and excellent review articles were published by Anderson and Hampton.l. Most of the available theoretical results are confined to single scattering approximations 2 which are strictly valid for very low volume fraction (concentration) of bubbles. It has been observed, however, that natural sediments contain gas bubbles as much as 16% by volume. For such media, the effects of multiple scattering on the sound propagation are of great practical importance. In this paper, a self-consistent multiple scattering formalism using the T-matrix3 of a single scatterer in conjunction with a self-consistent pair correlation function is employed to study the phase velocity and coherent attenuation of acoustic waves in an elastic medium containing a random distribution of gas bubbles. This is based on the assumption .that gas bubbles are significantly larger than the individual sediment particles, and bubbles in sediments can be treated as if they were immersed in a continuous homogeneous elastic medium. 1 If the embedding medium cannot support shear waves, the model will then serve us to study bubbles in water. In the analysis of gassy water, the effects of surface tension, shear viscosity of the liquid and thermal conduction in the gas are considered. Numerical results are presented for both phase velocity and coherent attenuation as a function of frequency near the fundamental resonance of the bubble for various values of concentrations of bubbles. FORMULATION OF THE PROBLEM We consider N number of elastic scatterers which are referred to a coordinate system as shown in Figure 1. It is assumed that all scatterers are spherical in shape and have the same elastic properties.