Abstract

An acoustic field scattered by a single inhomogeneity consists of components of different orders of multipolarity. For symmetric or weak-contrast inhomogeneities of a small wave size, these components are related to multipole components of an initial incident field by a set of scattering coefficients. It is established that the admissible range of each of these coefficients on the complex plane is a circle in the presence of absorption in the inhomogeneity and a circumference in the absence of absorption. The solution of the inverse problem for the purpose of reconstructing the mentioned inhomogeneity may encounter difficulties, since the spatial spectrum of the secondary sources is excessively expanded due to the multiple scattering, and an error is introduced into the reconstruction results. Sets of values of the monopole scattering coefficient are established on the complex plane for which this effect manifests itself to the greatest extent.

中文翻译：

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小波长非均匀性正反散射问题解的特征

摘要

由单个不均匀性散射的声场由不同阶数的多极性组成。对于小波长的对称或弱对比度不均匀性，这些分量通过一组散射系数与初始入射场的多极分量相关。可以确定的是，这些系数在复平面上的允许范围是在不均匀存在吸收的情况下是一个圆，在不存在吸收的情况下是一个圆周。出于重建上述不均匀性的目的，反问题的解决方案可能会遇到困难，因为次级源的空间光谱由于多重散射而过度扩展，并且在重建结果中引入了误差。