Seismic boundaries caused by phase transitions between olivine polymorphs in Earth's mantle provide thermal and compositional markers that inform mantle dynamics. Seismic studies of the mantle transition zone often use either global averaging with sparse arrays or regional sampling from a single dense array. The intermediate approach of this study utilizes many densely spaced seismic arrays distributed around the globe. We systematically compute teleseismic P-to-S receiver functions for each seismic array and invert for the 1-D seismic velocity structure of the mantle transition zone beneath each array to facilitate a comparison between densely sampled regions. We stack 3,600 receiver functions on average at 67 arrays in total. The stack is used in a probabilistic inversion to estimate the mantle transition zone interface depths and velocities beneath each array. We focus on the 410-km discontinuity (410) because it is a prominent seismic interface that is clearly linked to a single mineral phase transition between olivine and wadsleyite. The depths and velocity contrasts of the 410 are mapped to temperatures and compositions using mineral physics constraints. The depth of the 410 ranges from ∼405–440 km, which is consistent with a ∼360 K temperature range in a dry mantle and a ∼260 K temperature range in a wet mantle (2 wt. % water). The Vs contrast across the 410 ranges from ∼2.5–8 %, which is consistent with ∼20–70 vol. % olivine composition in a dry mantle and ∼25–80 vol. % in a wet mantle. The bulk composition of the upper mantle near the 410-km discontinuity is typically considered to be well-mixed because there is no thermodynamic impediment to convection at the olivine to wadsleyite phase transition. However, the wide range of inferred olivine content from our study suggests that there are large lateral variations in the bulk composition of the upper mantle near the 410-km discontinuity.