  We study the radial metallicity gradient $\Delta[M/H]/\Delta R_g$ as a
function of [Mg/Fe] and $|Z|$ with the help of a guiding radius based on the
Apache Point Observatory Galactic Evolution Experiment and Gaia and then
analyze the radial migration effect on the radial metallicity gradient and
metallicity-rotation gradient between the Galactic thin and thick disks. The
derived trend of gradient $\Delta[M/H]/\Delta R_g$ versus [Mg/Fe] shows a
transition at [Mg/Fe] $\sim 0.18$ dex, below which the gradient is negative and
varies a little as [Mg/Fe] increases; however, it changes sharply in [Mg/Fe]
ranges of 0.16-0.18, above which the gradient increases linearly with
increasing [Mg/Fe], being a positive value at [Mg/Fe]$\gtrsim 0.22$ dex. These
positive gradients in the high-[Mg/Fe] populations are found at $|Z| < 0.8$
kpc, and there are nearly no gradients toward higher $|Z|$. By comparing the
metallicity distributions, the radial metallicity gradients $\Delta[M/H]/\Delta
R$ and the metallicity-rotation gradients between the total sample and
$|R-R_g|<2$ kpc subsample (or $|R-R_g|>2$ kpc subsample), we find that, for the
thick disk, blurring flattens the gradient $\Delta[M/H]/\Delta R$ and favors
metal-poor high-eccentricity stars. These stars are responsible for the
measured positive metallicity-rotation gradient of the thick disk.
