Abstract
We are concerned with the inverse scatter- ing problem (ISP) in acoustics within the Marchenko inversion scheme. The quantum ISP is first discussed and applied in order to exhibit certain characteris- tics and application prospects of the method which could be useful in extending it to classical systems. We then consider the ISP in acoustics by assuming plane waves propagating in an elastic, isotropic, and linear medium. The wave equation is first transformed into a Schrodinger-like equation which can be brought into the Marchenko integral equation for the associated nonlocal kernel the solution of which provides us the full information of the underlying reflective profile. We apply the method in several model problems where the reflection coefficient of the multi-layer reflective medium is used as input to the ISP and in all cases we obtain excellent reproduction of the original structure of the scatterer. We then applied the inverse scatter- ing scheme to construct profiles with certain predeter- mined reflection and transmission characteristics.
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