Wave field singularity aspects in large-size scatterers and inverse problems

It is known that any scattered wave field carrying energy into infinity must have source singularity centers within a bounded space. Otherwise, the scattered field should be identically equal to zero everywhere (Kupradze 1935). In this paper, attention is paid to localization of these singularities under the assumption that every scattered wave is determined uniquely by its own singularities. Investigations have shown that these singularities are distributed as "bright centers" and the distance between them depends on frequency. To determine the position (localization) of the scattered wave field singularities, the functions describing converging and diverging waves are used. Based on these concepts and the method of auxiliary sources, an efficient numerical method to reconstruct a field up to its singularities is suggested. The localization of singularities is used for partial representation of the scattered fields, which reduces significantly the number of unknowns in describing the scattering process and leading into optimized inverse scattering problem solutions.