A CLASS OF LOW-FREQUENCY MODES IN LATERALLY HOMOGENEOUS FLUID-SOLID MEDIA

By a fundamental wave mode in a laterally homogeneous fluid-solid medi um, we mean a propagating mode that continues to exist as a propagatin g mode down to arbitrarily low frequencies. In underwater acoustics wi th a fluid medium having a pressure-release surface, there is no funda mental mode since each mode has a lower cutoff frequency. In plate aco ustics there are two fundamental Lamb modes, a symmetric one (the quas i-longitudinal wave) and an antisymmetric one (the bending wave). Ther e is also a fundamental mode for a fluid plate with rigid boundaries. In seismology, interface waves of Rayleigh-, Scholte-, and Stoneley-ty pe are well known for certain media with one or two homogeneous half-s paces. The purpose of this paper is to give a unified treatment of a c lass of modes that is related to the fundamental modes. Specifically, we consider low-frequency P-SV modes whose complex phase velocities do not approach zero as fast as the frequency when the frequency is decr eased towards zero. Utilizing the analyticity of the dispersion functi on, a complete characterization is given of these modes and the linear ly visco-elastic fluid-solid media in which they occur. All the mentio ned particular waves appear in a general setting, and we give asymptot ic low-frequency expressions for the modal slownesses and mode forms. As the frequency approaches zero, the phase velocities of these waves will either tend to a nonzero constant or approach zero like the squar e root of the frequency. In addition, slow modes appear whose phase ve locities approach zero like three other powers of the frequency: 1/3, 3/5, and 2/3. (The power 1/5 is possible as well, but only for certain leaky modes.) Concerning the power 1/3, we make a correction to a pre vious study by Ferrazzini and Aki. The powers 3/5 and 2/3 appear for c ertain bending-type waves that are slower than the classical bending w ave. A less-known type of interface wave also emerges from the analysi s. In the nonleaky case, we give precise conditions for its existence and uniqueness. The results can be directly extended to interface cond itions with slip. In an extreme case with vanishing specific normal st iffness, we get yet another kind of interface wave.