Helioseismic tomography is a new rapidly developing field of solar
physics to study the physical properties of the solar interior.
It is based on inversion of travel time perturbations of acoustic
waves stochastically excited by turbulent convection near the
Sun's surface and propagating through the solar interior.
The main challenges to the inverse problem are the large amount of
data and the high level of noise. We review the current mathematical
models, inversion methods and algorithms of helioseismic tomography,
discuss various regularization options, and present results of test
inversions and 3D images of the solar interior obtained by analyzing
data from the space mission SOHO.
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