A Method to Determine Bubble Distribution in Liquid Using Data of Inverse Acoustical Scattering

Abstract

Information on bubble distributions in liquids is required for various applications. Employment of inverse acoustic scattering is the usual path to determine these distributions. This path is based on solving a Fredholm first kind integral equation leading to an ill-posed mathematical problem. The usual regularization methods for such a problem are quite complex and require introduction of some tuning parameters. Meanwhile, as shown in this paper, another method works well for media, where acoustic waves propagate with the small losses. This method is based on extraction of a singular Cauchy integral in the above-mentioned equation and of the further inversion of this integral. Such a regularization via inversion is a simple operation that gives numerically stable solutions. Here, this regularization is described, verified using the method of manufactured solutions, and validated with the well-known already published experimental data.