Two-stage gas-gun ballistic experiments are performed to investigate the feasibility of stratified mixtures with variable global equivalence ratios Φglobal for the formation of sphere-induced oblique detonation wave (ODW) and quantify their critical behaviors, which include local quenching and transitional structure to ODW, by testing conventional detonation criteria for uniform mixtures. 2 Φglobal H2 + O2 + 3Ar mixtures are tested with different concentration gradients for each fuel-lean/fuel-rich global composition. Opposite responses are observed depending on the global equivalence ratio: the lean mixture of Φglobal = 0.7, which forms ODW in the uniform mixture, fails partly in the strongest stratification, whereas the richest mixture of Φglobal = 2.0 turns to ODW in the strongly stratified conditions. As elucidated in the authors' previous work, Chapman–Jouguet (C–J) theory, including the curvature effects, reproduces the wave angles of the stable ODWs, as well as provides a good prediction on the local quenching of ODW occurring in the area with less reactive composition. Comparison of different wave regimes observed in the explored conditions reveals that wave curvature governs the critical behaviors of ODW far away from the projectile, whereas the initiation structure around the projectile is also influenced by the non-dimensional diameter. Surface energy theory is proven to quantify well the initiation structure on the projectile using a local equivalence ratio. These results indicate a new possibility of controlling the methodology of ignition and stabilization of detonation in aerospace engines, in which perfect mixing is difficult and non-stoichiometric and non-uniform mixtures are expected.