"This new magnetic inversion approach relies on the spectrum synthesis calculations over the full wavelength range  covered by observations and does not assume that the LSD profiles behave as a single spectral line with mean parameters."

and if you are reluctant to overlook details, you may well find a perfect fit between the observed phase-dependent mean profiles and the mean profiles synthesised from the recovered abundance map; virtually all the individual lines can however exhibit bad to very bad fits.

In the example shown below I plot the differences (normalised to the continuum) observed minus predicted for 10 lines at 10 different phases. These differences for individual lines can get as large as 6% -- positive and negative -- whereas they are about 10 times lower for the mean line (in red) for which the rms scatter is better than 10^-3. It is clear that a kind of compensation is at work to the detriment of the ZDM afficionado.

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