Reverse time migration for inverse acoustic scattering by locally rough surfaces

Consider the inverse scattering of time-harmonic point sources by an infinite rough surface which is supposed to be a local perturbation of a plane. A novel version of reverse time migration is proposed to reconstruct the shape and location of the rough surface. The method is based on a modified Helmholtz-Kirchhoff identity associated with a special rough surface, leading to a modified imaging functional which always reaches a peak on the boundary of the rough surface for sound-soft case and penetrable case, and hits a nadir on the boundary of the rough surface for sound-hard case. Numerical experiments are presented to show the powerful imaging quality, especially for multi-frequency data.Comment: 29 pages,26 figure

Simultaneous recovery of a locally rough interface and the embedded obstacle with the reverse time migration

Consider the inverse acoustic scattering of time-harmonic point sources by an unbounded locally rough interface with bounded obstacles embedded in the lower half-space. A novel version of reverse time migration is proposed to reconstruct both the locally rough interface and the embedded obstacle. By a modified Helmholtz-Kirchhoff identity associated with a planar interface, we obtain a modified imaging functional which has been shown that it always peaks on the local perturbation of the interface and on the embedded obstacle. Numerical examples are presented to demonstrate the effectiveness of the method.Comment: 21 pages, 19 figure

Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems

In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotropic scatterers. The truncated uniaxial PML problem is proved to be well-posed and stable, based on the Laplace transform technique and the energy method. Moreover, the $L^2$-norm and $L^{\infty}$-norm error estimates in time are given between the solutions of the original scattering problem and the truncated PML problem, leading to the exponential convergence of the time-domain uniaxial PML method in terms of the thickness and absorbing parameters of the PML layer. The proof depends on the error analysis between the EtM operators for the original scattering problem and the truncated PML problem, which is different from our previous work (SIAM J. Numer. Anal. 58(3) (2020), 1918-1940).Comment: 23 pages, 1 figure. arXiv admin note: text overlap with arXiv:1907.0890