Open AccessFourier method for reconstructing elastic body force from the coupled-wave field
Author(s) -
Guiling Wang,
Jiaqi Zhu,
Minghui Song,
Wei Wu
Publication year - 2022
Publication title -
inverse problems and imaging
Language(s) - English
Resource type - Journals
eISSN - 1930-8345
pISSN - 1930-8337
DOI - 10.3934/ipi.2021052
Subject(s) - fourier transform , fourier series , robustness (evolution) , computer science , fourier analysis , body force , inverse problem , inverse , mathematical analysis , acoustics , mathematics , physics , classical mechanics , geometry , biochemistry , chemistry , gene
This paper is concerned with the inverse source problem of the time-harmonic elastic waves. A novel non-iterative reconstruction scheme is proposed for determining the elastic body force by using the multi-frequency Fourier expansion. The key ingredient of the approach is to choose appropriate admissible frequencies and establish an relationship between the Fourier coefficients and the coupled-wave field of compressional wave and shear wave. Both theoretical justifications and numerical examples are presented to verify the validity and robustness of the proposed method.