Scalar and vector tomography for the weighted transport equation with application to helioseismology

Abstract

Motivated by the application to helioseismology, we demonstrate uniqueness and stability for a class of inverse problems of the weighted transport equation. Using A-analytic functions, this inverse problem is expressed as a Cauchy problem. In this form, we show that, for a finite even trigonometric polynomial weight function, the resulting system is well-conditioned numerically and permits a Carleman-like estimate with boundary terms.