2019/11/11 by Michael V. Klibanov, Klibanov, Michael V., Thuy T. Le +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1911.04581
openalex publication_date 2019/11/11 · openalex created_date 2019/11/22 · openalex updated_date 2026/07/28
We propose a new numerical method to solve the linearized problem of travel time tomography with incomplete data. Our method is based on the technique of the truncation of the Fourier series with respect to a special basis of L2. This way we derive a boundary value problem for a system of coupled partial diffeerential equations (PDEs) of the first order. This system is solved by the quasi-reversibility method. Hence, the spatially dependent Fourier coefficients of the solution to the linearized Eikonal equation are obtained. The convergence of this method is established. Numerical results for highly noisy data are presented.