Abstract:

A unified treatment is given of the class of low-frequency P--SV modes whose complex phase velocities do not approach zero as fast as the frequency when the frequency is decreased toward zero. Utilizing the analyticity of the dispersion function, a complete characterization is given of these modes and the linearly viscoelastic fluid--solid media in which they occur. The two Lamb plate modes and the classical interface waves (Rayleigh, Scholte, Stoneley) all appear in a general setting, and asymptotic low-frequency expressions are given for modal slownesses and mode forms. The corresponding phase velocities will either tend to a nonzero constant or approach zero like the square root of frequency. In addition, slow modes appear whose phase velocities approach zero like three other powers of frequency: 1/3, 3/5, and 2/3. Concerning 1/3, a correction is made to a paper by Ferrazzini and Aki; 3/5 and 2/3 appear for certain bending-type waves that are slower than the classical bending wave. A less known type of interface wave also emerges from the analysis, and precise conditions for existence and uniqueness are obtained. The results are extended to interface conditions with slip. In an extreme case, yet another kind of interface wave is obtained.