Reverse time migration for inverse obstacle scattering with a generalized impedance boundary condition

ABSTRACT

We consider the inverse scattering problem of determining the shape of an impenetrable two-dimensional obstacle with a generalized impedance boundary condition from near-field measurements. We propose the reverse time migration method where the imaging functional is defined as the imaginary part of the cross-correlation. Our analysis shows that, on the one hand, the imaging functional has contrast at the boundary of the scatterer and decays outside the scatterer; On the other hand, the imaging functional is always positive thus may have better stability properties. These imply that the approach has powerful imaging quality which is confirmed in our numerical experiments.

Keywords:

• Inverse acoustic scattering
• generalized impedance boundary condition
• reverse time migration method

2010 Mathematics Subject Classifications:

• 35J05
• 65N21
• 65R32
• 78A46

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research of J. Li is supported by the National Natural Science Foundation of China [grant number 11601042] and Education Department of Hunan Province [grant number 16C0035].