A Newton method for simultaneous reconstruction of an interface and a buried obstacle from far-field data

TL;DR

This paper introduces a Newton-based iterative method for reconstructing both an interface and a buried obstacle in acoustic scattering problems using far-field data, without prior knowledge of boundary conditions.

Contribution

The method allows simultaneous reconstruction of the interface and obstacle, and can determine boundary conditions without prior information, advancing inverse scattering techniques.

Findings

Effective reconstruction demonstrated with multi-frequency data

Method does not require prior boundary condition knowledge

Numerical examples confirm robustness and accuracy

Abstract

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves from a penetrable and buried obstacles. By introducing a related transmission scattering problem, a Newton iteration method is proposed to simultaneously reconstruct both the penetrable interface and the buried obstacle inside from far-field data. A main feature of our method is that we do not need to know the type of boundary conditions on the buried obstacle. In particular, the boundary condition on the buried obstacle can also be determined simultaneously by the method. Finally, numerical examples using multi-frequency data are carried out to illustrate the effectiveness of our method.