Factorization method for near-field inverse scattering problems in elastodynamics

作者：Chun Liu, Guanghui Hu, Yin Tao, Bo Zhang · 发表于：Inverse Problems and Imaging · 年份：2025 · DOI：10.3934/ipi.2025054 · 被引用次数：2 · 研究领域：Numerical methods in inverse problems、Microwave Imaging and Scattering Analysis、Ultrasonics and Acoustic Wave Propagation

Consider a time-harmonic elastic wave scattering problem with a bounded rigid obstacle embedded in a homogeneous and isotropic elastic medium. This work is concerned with the inverse problem of recovering the location and shape of the obstacle from near-field data generated by infinitely many incident point source waves at a fixed energy. An outgoing-to-incoming operator is defined for facilitating the factorization of the near-field operator. Necessary properties of the factorization of the composition of the outgoing-to-incoming operator and the near-field operator are shown to apply the range identity to construct an indicator function for the reconstruction. Numerical examples in 2D are presented to show the validity and accuracy of the inversion algorithm.