The leakage and coupling of solar global oscillations to the overlaying magnetized solar atmosphere is investigated in this paper. Solar global acoustic oscillations may couple through resonant absorption to atmospheric local magnetic eigenoscillations (i) resulting in small shifts of the order of μHz in the real part of their frequencies as compared to their non-magnetic counterparts, and (ii) causing dissipation of wave energy and a consequent line broadening of the modes. Alternatively, global modes may also penetrate deeply into the magnetized solar atmosphere through leakage along magnetic field lines causing small-scale structuring in the transition region and low corona. By analyzing the dynamic fragmentation generated by direct wave propagations, one may deduce diagnostic information about the geometric and physical properties of the local magnetic environment in the atmosphere. A few numerical examples are presented here to demonstrate the leakage of global oscillations and its influence and omnipotence on the dynamics of the lower solar atmosphere.