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The interaction of a point-source spherical acoustic wave with a bounded obstacle possesses various attractive and useful properties in direct and inverse scattering theory. More precisely, concerning the direct scattering problem, the far-field interaction of a point source with an obstacle is, under certain conditions, stronger compared to that of a plane wave. On the other hand, in inverse scattering problems the distance of the point-source from the obstacle constitutes a crucial parameter, which is encoded in the far-field pattern and is utilized appropriately for the localization and reconstruction of the obstacle’s physical and geometrical characteristics. The research of point-source scattering initiated in (1), dealing with analytical investigations of the scattering problem by a circular disc. The main results for point-source scattering by simple homogeneous canonical shapes are collected in the classic books (2) and (3). The techniques of the low-frequency theory (4) in the point-source acoustic scattering by soft, hard, impedance surface, and penetrable obstacles were introduced in (5), (6), and (7), where also explicit results for the corresponding particular spherical homogeneous scatterers were obtained. Moreover, in (5), (6), and (7) simple far-field inverse scattering algorithms were developed for the determination of the sphere’s center as well as of its radius. On the other hand, point-source near-field inverse scattering problems for a small soft or hard sphere were studied in (8). For other implementations of near-field inverse problems see (9), and p. 133 of (10); also we point out the point-source inverse scattering methods analyzed in (11). In all the above investigations the incident wave is generated by a point-source located in the exterior of the scatterer. However, a variety of applications suggests the investigation of excitation problems, where a layered obstacle is excited by an acoustic spherical wave generated by a point source located in its interior. Representative applications concern scattering problems for the localization of an object, buried in a layered medium (e.g. inside the earth), (12). This is due to the fact that the Green’s function of the layered medium (corresponding to an interior point-source) is utilized as kernel of efficient integral equation formulations, where the integration domain is usually the support of an inhomogeneity existing inside the layered medium. Besides, the interior point-source excitation of a layered sphere has significant medical applications, such as implantations inside the human head for hyperthermia or biotelemetry purposes (13), as well as excitation of the human brain by the neurons currents (see for example (14) and (15), as well as the references therein). Several 11

Inverse Scattering in the Low-Frequency Region by Using Acoustic Point Sources