Additional Evidence Supporting a Model of Shallow, High-Speed Supergranulation

Recently, Duvall and Hanasoge ({\it Solar Phys.} {\bf 287}, 71-83, 2013) found that large distance $[\mathrm{\Delta }]$ separation travel-time differences from a center to an annulus $[\delta t_{\mathrm{o}\mathrm{i}}]$ implied a model of the average supergranular cell that has a peak upflow of $240\mathrm{m}{\mathrm{s}}^{-1}$ at a depth of $2.3\mathrm{M}\mathrm{m}$ and a corresponding peak outward horizontal flow of $700\mathrm{m}{\mathrm{s}}^{-1}$ at a depth of $1.6\mathrm{M}\mathrm{m}$. In the present work, this effect is further studied by measuring and modeling center-to-quadrant travel-time differences $[\delta t_{\mathrm{q}\mathrm{u}}]$, which roughly agree with this model. Simulations are analyzed that show that such a model flow would lead to the expected travel-time differences. As a check for possible systematic errors, the center-to-annulus travel-time differences $[\delta t_{\mathrm{o}\mathrm{i}}]$ are found not to vary with heliocentric angle. A consistency check finds an increase of $\delta t_{\mathrm{o}\mathrm{i}}$ with the temporal frequency $[\nu ]$ by a factor of two, which is not predicted by the ray theory.