@hamster3null: the inmarsat press document with the doppler graph describes the method. It does not say that the AES adjusts transmit freq. Instead, it suggests freq search is done by the ground station. The ground station computes the expected sat down link doppler shift, any residual doppler shift is logged as the offset due to a/c + up link motion.
I have verified the qualitative Match to the published graphs, as have you. My calculations result in shifts 250% of those charted. By coincidence, this is the conversion factor for Hz to mph, so I wonder if in the hurry to publish, someone labelled the graph with the wrong unit or forgot about a conversion factor in the spreadsheet.
If there was any other kind of compensation going on, or the modeling was more sophisticated, I don't think we could Get such a good qualitative match. If anything, thus supports their calculation and their conclusion as to likely flight path.