Structural inversion for Star A: the sound speed a), density b), and buoyancy frequency c). Dashed green lines show a (re-scaled) model taken as an initial guess; solid green lines display the inverted result. Thin blue lines result from adding the measured frequencies with Gaussian noise, of variance corresponding to the reported uncertainties, in 10 realisations, to address the sensitivity of the inversion to random errors in the input data.