Excitation of a layered sphere by 𝑁 acoustic sources: Exact solutions, low-frequency approximations, and inverse problems

Acoustic excitation of a layered sphere by N N external and internal point sources is considered. The direct problem is solved by developing a T-Matrix method leading to the analytical determination of all the involved acoustic fields. Low-frequency far-field approximations are derived for different source distributions and scatterer’s characteristics. The behaviour of the scattering cross sections is investigated. Several inverse problems are formulated and solved analytically; thus the respective unknown quantities are recovered explicitly. These problems include localization of the sources, determination of their number, identification of the core’s type and extraction of the parameters of the scatterer’s layers.