An inverse moving point source problem in inhomogeneous acoustic media: uniqueness, stability and reconstruction

This paper is concerned with the simultaneous recovery of the trajectory and intensity of an unknown moving point source in an inhomogeneous acoustic medium. We prove that the whole-boundary measurements over a finite time interval uniquely determine the moving source. Furthermore, under suitable propagation and rank assumptions, Lipschitz stability of determining both the trajectory and intensity is derived using waveforms measured at four fixed receivers outside the source region. A novel Volterra--Euler reconstruction scheme is developed for solving the inverse problem, and the error estimate is derived for the proposed scheme. Numerical experiments are presented to demonstrate the effectiveness of the proposed numerical method.