A simple method of reconstructing a point-like scatterer according to time-dependent acoustic wave propagation

Abstract

This paper investigates the approximate solutions to the time-dependent acoustic scattering problem with a point-like scatterer under some basic assumptions and provides a simple method to reconstruct the location of the scatterer. The approximations of the solution to the forward scattering problem are analysed utilizing Green's function and the retarded single-layer potential. Then, based on the approximate solutions, a sampling method is proposed to solve the inverse scattering problem for the location of the scatterer. The proposed method is easy to implement since no equations or matrices have to be computed for the reconstruction. Numerical experiments are provided to show the effectiveness of the method.

Keywords:

• Point-like scatterer
• time-dependent
• acoustic
• inverse scattering problem
• sampling method

2010 Mathematics Subject Classifications:

• 35L05
• 65M32
• 65M80

Acknowledgments

The work of Bo Chen was supported by the National Natural Science Foundation of China (NSFC) [grant number 11671170] and the Scientific Research Foundation of Civil Aviation University of China [grant number 2017QD04S]. The work of Yao Sun was supported by the NSFC [grant number 11501566].

Disclosure statement

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

Additional information

Funding

The work of Bo Chen was supported by the National Natural Science Foundation of China (NSFC) [grant number 11671170] and the Scientific Research Foundation of Civil Aviation University of China [grant number 2017QD04S]. The work of Yao Sun was supported by the NSFC [grant number 11501566].