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Love waves are dispersive interfacial waves that are a mode of response foranti-plane motions of an elastic layer bonded to an elastic half-space.Similarly, Stoneley waves are interfacial waves in bonded contact of dissimilarelastic half-spaces, when the displacements are in the plane of the solids. Itis shown that in slow sliding, long wavelength Love and Stoneley waves aredestabilized by friction. Friction is assumed to have a positive instantaneouslogarithmic dependence on slip rate and a logarithmic rate weakening behaviorat steady-state.  Long wavelength instabilities occur generically in sliding with rate- andstate-dependent friction, even when an interfacial wave does not exist. Forslip at low rates, such instabilities are quasi-static in nature, i.e., thephase velocity is negligibly small in comparison to a shear wave speed. Theexistence of an interfacial wave in bonded contact permits an instability topropagate 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 suchproblems.

Destabilization of long-wavelength Love and Stoneley waves in slow sliding