An Inversion of Acoustical Attenuation Measurements to Deduce Bubble Populations

Abstract

Abstract Measurement of natural bubble populations is required for many areas of ocean science. Acoustical methods have considerable potential for achieving this goal because bubbles scatter sound strongly close to their natural frequency, which depends largely on the bubble radius. The principle of using bulk acoustical attenuation caused by a bubble population to infer the number and size of bubbles present is well established, and appropriate methods for measuring broadband acoustical attenuation are also well developed. However, the numerical methods currently used to invert the acoustical attenuation to get the bubble size distribution are complex and time consuming. In this paper, a method for the inversion is presented that uses the physics of bubble resonance to restructure the problem so that it can be accurately carried out using a simple matrix inversion. This inversion method produces results that are correct to within a few percent over two orders of magnitude of bubble size. The most significant remaining issue for acoustical bubble measurement is the potential presence of bubbles that are resonant outside the measurement frequency range. The mathematical structure outlined here considerably simplifies the investigation of this problem, and calculations are presented that show this effect to be minor in many cases.