A Newton method for simultaneous reconstruction of an interface and a buried obstacle from far-field data
This work addresses the challenging inverse scattering problem of reconstructing both an interface and a buried obstacle for applications in non-destructive testing and geophysics, but the results are incremental as they extend existing Newton-type methods to a more complex scenario.
The paper proposes a Newton iteration method to simultaneously reconstruct a penetrable interface and a buried obstacle from far-field acoustic scattering data, without prior knowledge of the obstacle's boundary condition. Numerical examples with multi-frequency data demonstrate the method's effectiveness.
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.