  Impurities that are present on the surface of a metal often have internal
degrees of freedom. Inelastic scattering due to impurities can be revealed by
observing local features seen in the tunneling current with scanning tunneling
microscope (STM). We consider localized vibrational modes coupled to the
electronic structure of a surface. We argue that vibrational modes of
impurities produce Fermi momentum $k_F$ oscillations in second derivative of
current with respect to voltage $\partial^2I(\br, V)/\partial V^2$. These
oscillations are similar to the well known Friedel oscillations of screening
charge on the surface. We propose to measure inelastic scattering generated by
the presence of the vibrational modes with STM by imaging the
$\partial^2I/\partial V^2$ oscillations on the metal surface.
