Inverse source problems in elastodynamics. (15th March 2018)

• Record Type: Journal Article
• Authors: Bao, Gang; Hu, Guanghui; Kian, Yavar; Yin, Tao
• Is Part Of: Inverse problems. Volume 34:Number 4(2018:Apr.)
• Publication Date: 2018-03-15
• Subjects: inverse source problems -- Lamé system -- uniqueness -- Landweber iteration -- Fourier transform; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aaaf7e
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We are concerned with time-dependent inverse source problems in elastodynamics. The source term is supposed to be the product of a spatial function and a temporal function with compact support. We present frequency-domain and time-domain approaches to show uniqueness in determining the spatial function from wave fields on a large sphere over a finite time interval. The stability estimate of the temporal function from the data of one receiver and the uniqueness result using partial boundary data are proved. Our arguments rely heavily on the use of the Fourier transform, which motivates inversion schemes that can be easily implemented. A Landweber iterative algorithm for recovering the spatial function and a non-iterative inversion scheme based on the uniqueness proof for recovering the temporal function are proposed. Numerical examples are demonstrated in both two and three dimensions.