A multi-frequency inverse source problem

Abstract

This paper is concerned with an inverse source problem that determines the source from measurements of the radiated fields away at multiple frequencies. Rigorous stability estimates are established when the background medium is homogeneous. It is shown that the ill-posedness of the inverse problem decreases as the frequency increases. Under some regularity assumptions on the source function, it is further proven that by increasing the frequency, the logarithmic stability converts to a linear one for the inverse source problem.