  We perform radiative magnetohydrodynamic calculations for the solar quiet
region to investigate the dependence of statistical flow on magnetic properties
and the three-dimensional (3D) structure of magnetic patches in the presence of
large-scale flow that mimics differential rotation. It has been confirmed that
strong magnetic field patches move faster in the longitudinal direction at the
solar surface. Consequently, strong magnetic patches penetrate deeper into the
solar interior. The motion of the deep-rooted magnetic patches is influenced by
the faster differential rotation in the deeper layer. In this study, we perform
realistic radiative magnetohydrodynamic calculations using R2D2 code to
validate that stronger patches have deeper roots. We also add large-scale flow
to mimic the differential rotation. The magnetic patches are automatically
detected and tracked, and we evaluate the depth of 30,000 magnetic patches. The
velocities of 2.9 million magnetic patches are then measured at the
photosphere. We obtain the dependence of these values on the magnetic
properties, such as field strength and flux. Our results confirm that strong
magnetic patches tend to show deeper roots and faster movement, and we compare
our results with observations using the point spread function of instruments at
the Hinode and Solar Dynamics Observatory (SDO). Our result is quantitatively
consistent with previous observational results of the SDO.
