  We analyze how the coherence peaks observed in Scanning Tunneling
Spectroscopy (STS) of cuprate high temperature superconductors are transferred
from the cuprate layer to the oxide layers adjacent to the STS microscope tip.
For this purpose, we have carried out a realistic multiband calculation for the
superconducting state of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi2212) assuming a
short range d-wave pairing interaction confined to the nearest-neighbor Cu
$d_{x^2-y^2}$ orbitals. The resulting anomalous matrix elements of the Green's
function allow us to monitor how pairing is then induced not only within the
cuprate bilayer but also within and across other layers and sites. The symmetry
properties of the various anomalous matrix elements and the related selection
rules are delineated.
