The connection between the initial vertical velocity v_0, z(τ) and the velocity dispersion σ_z. Upper panel: computed initial vertical velocity v_0, z(τ) (which satisfies the condition of Eq. (4)) as a function of Galactic age τ for the SSPs born at different evolutionary times shown as the solid magenta line. Data for the age–velocity dispersion σ_z relation in the solar vicinity from Sharma et al. (2021) and Mackereth et al. (2019) are drawn with the grey line and diamond blue points, respectively. Middle panel: orbit in the meridional plane (R, Z) for the SSP born in the Galactic plane (z = 0 kpc) at 8 kpc (labelled with a star) at the Galactic time t_B = t_G − 1 Gyr and integrated for 1 Gyr. The colour-coding stands for the modulus of the vertical velocity component |v_z|. Lower panel: the 1 Gyr evolution of the modulus of the vertical velocity component |v_z| for the same SSP as the lower left panel. The starred symbol indicates the vertical velocity associated at birth v_0, z(τ = 1 Gyr) (also indicated in the other panels with the same symbol) which also corresponds to the maximum value of the vertical velocity component |v_z| (see red dashed horizontal line).