Example of the synthetic time series generated to validate the 3SD approach when noise equals magnetic activity plus long-term trends, granulation, and WGN. Top: averaged periodograms of the two-day GOLF solar observations used in Sect. 2.4 (green) and the associated MHD training data (red), Harvey model fit to the MHD PSD (yellow), and averaged periodogram of the final synthetic data (GP+Harvey, black). Bottom: example of synthetic RV data generated with a regular sampling (black) based on a GP noise modeling for the magnetic activity (red). For the study, the dataset was also sampled irregularly (gray).