| Abstract: |
| This talk is concerned with uniqueness, stability and algorithms for inverse moving point source problems modeled by the acoustic wave equation. The purpose is to recover the orbit of a moving point source from the dynamical data recorded at a finite number of observation points. In the time domain, we derive an ordinary differential equation for the distance function between an observation point and the moving target. Solving such ODEs at four observation points yields the orbit function of the moving source. The frequency-domain method is to Fourier-transform the time-dependent source problem of the wave equation into an equivalent source problem of the Helmholtz equation with multi-frequency near-field data. This turns out to be a special wavenumber-dependent inverse source problem in the time-harmonic regime. We shall discuss the concept of non-observation directions and a non-iterative approach for imaging the orbit function. A comparision of the time-domain and frequency-domain method will be remarked at the end of the talk. |
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