| Abstract: |
| Inverse scattering in layered media has a wide range of applications, including geophysical exploration, submarine detection, and medical imaging. In this talk, we develop a selective focusing method for identifying multiple unknown buried scatterers in a layered medium. The method is derived through asymptotic analysis of the time reversal operator, which is challenging due to the absence of an explicit form for the layered Green`s function and the limited aperture measurements. We demonstrate that each small sound-soft and sound-hard particle gives rise to one and three significant eigenvalues, respectively, and the corresponding eigenfunction generates an incident wave focusing selectively on each unknown particle. Finally, we employ the time reversal method as an initial indicator and propose an effective Bayesian inversion scheme to reconstruct multiple buried extended scatterers for enhanced resolution. Numerical experiments are provided to demonstrate the efficiency. |
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