SIMPLIFIED EXPRESSIONS FOR THE DISPLACEMENTS AND STRESSES PRODUCED BYTHE RAYLEIGH-WAVE

In many cases involving Rayleigh wave propagation along the free surfa ce of a solid, the ratio between the normal and transverse displacemen t components, i.e., the aspect ratio of the elliptical particle trajec tory on the surface, is of great importance. Surprisingly, this aspect ratio is exactly the same as the ratio between the vector and scalar displacement potential amplitudes. More importantly, the aspect ratio is also identically the same as the ratio between the shear and normal stresses in any plane parallel to the surface at any depth, i.e., exa ctly the same ratio also shows up between two fundamental physical qua ntities. It is shown that the identical amplitude ratio, which apparen tly has not been pointed out in the otherwise very comprehensive liter ature on Rayleigh wave propagation, is a direct result of the requirem ent that just below the surface even the oscillating power, i.e., the imaginary component of the Poynting vector, be parallel to the surface (of course, the average power, i.e., the real component of the Poynti ng vector is everywhere parallel to the surface). (C) 1998 Acoustical Society of America. [S0001-4966(98)06211-0].