Inverse source problems in elastodynamics
Provides theoretical guarantees and practical algorithms for inverse source problems in elastodynamics, which is important for applications like seismology and non-destructive testing.
The paper addresses time-dependent inverse source problems in elastodynamics, proving uniqueness and stability in recovering spatial and temporal source functions from wave field data, and proposes inversion schemes with numerical examples in 2D and 3D.
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 interval. Stability estimate of the temporal function from the data of one receiver and uniqueness result using partial boundary data are proved. Our arguments rely heavily on the use of the Fourier transform, which motivated 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.