On the travel time tomography problem in 3D
This work provides a theoretical stability result and a globally convergent algorithm for an underdetermined inverse problem in geophysics or medical imaging.
The paper addresses the 3D travel time tomography problem with non-overdetermined data, obtaining a Lipschitz stability estimate and constructing a globally convergent numerical method using a Carleman estimate for an integral operator.
Numerical issues for the 3D travel time tomography problem with non-overdetemined data are considered. Truncated Fourier series with respect to a special orthonormal basis of functions depending on the source position is used. In addition, truncated trigonometric Fourier series with respect to two out of three spatial variables is used. First, the Lipschitz stability estimate is obtained. Next, a globally convergent numerical method is constructed using a Carleman estimate for an integral operator.