  Recently, scanning tunneling microscopy on Bi-2212 cuprate superconductor has
revealed a spatial variation of the energy gap that is directly correlated with
a modulation of the apical oxygen position. We identify two mechanisms by which
out-of-plane oxygens can modulate the pairing interaction within the CuO_2
layer: a covalency between the x^2-y^2 band and apical p-orbital, and a
screening of correlation U by apical oxygen polarization. Both effects strongly
depend on the apical oxygen position and their cooperative action explains the
experiment.
