I present the mean metallicity distribution of stars in the Milky Way Galaxy based on photometry from the Sloan Digital Sky Survey. I utilize an empirically calibrated set of stellar isochrones developed in previous work to estimate the metallicities of individual stars to a precision of $0.2$ dex for reasonably bright stars across the survey area. I also obtain more precise metallicity estimates using priors from the $Gaia$ parallaxes for relatively nearby stars. Close to the Galactic mid-plane ($|Z|<2$ kpc), a mean metallicity map reveals deviations from the mirror symmetry between the northern and southern hemispheres, displaying wave-like oscillations. The observed metallicity asymmetry structure is almost parallel to the Galactic mid-plane, and coincides with the previously known asymmetry in the stellar number density distribution. This result reinforces the previous notion of the plane-parallel vertical waves propagating through the disk, in which a local metallicity perturbation from the mean vertical metallicity gradient is induced by the phase-space wrapping of stars in the $Z$-$V_Z$ plane. The maximum amplitude of the metallicity asymmetry ($Delta$[Fe/H]$sim0.05$) implies that these stars have been pulled away from the Galactic mid-plane by an order of $Delta|Z|sim80$ pc as a massive halo substructure such as the Sagittarius dwarf galaxy plunged through the Milky Way. This work provides evidence that the $Gaia$ phase-space spiral may continue out to $|Z|sim1.5$ kpc.
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