  Love waves are dispersive interfacial waves that are a mode of response for
anti-plane motions of an elastic layer bonded to an elastic half-space.
Similarly, Stoneley waves are interfacial waves in bonded contact of dissimilar
elastic half-spaces, when the displacements are in the plane of the solids. It
is shown that in slow sliding, long wavelength Love and Stoneley waves are
destabilized by friction. Friction is assumed to have a positive instantaneous
logarithmic dependence on slip rate and a logarithmic rate weakening behavior
at steady-state.
  Long wavelength instabilities occur generically in sliding with rate- and
state-dependent friction, even when an interfacial wave does not exist. For
slip at low rates, such instabilities are quasi-static in nature, i.e., the
phase velocity is negligibly small in comparison to a shear wave speed. The
existence of an interfacial wave in bonded contact permits an instability to
propagate with a speed of the order of a shear wave speed even in slow sliding,
indicating that the quasi-static approximation is not a valid one in such
problems.
