Tomography of cool giant and supergiant star atmospheres - I. Validation of the method K. Kravchenko, S. Van Eck, A. Chiavassa, A. Jorissen, B. Freytag and B. Plez A&A, 610 (2018) A29 Published online: 21 February 2018 DOI: 10.1051/0004-6361/201731530