PROPAGATION OF ELASTIC WAVES IN LAYERED MEDIA BY ...

392 BULLETIN OF THE SEISMOLOGICAL SOCIETY OF AMERICA2.0, 3.0 and 5.0. When p2/pl = 0, which is the special case of a free surface, we againfind the Rayleigh wave. As p2 increases, the interface wave continues and arrives attimes expected for either the Stoneley wave or the "second surface wave."* Sincethe phase velocity of Stoneley waves is very nearly v,1, and that for the "secondsurface wave" is exactly v~, the pulses overlap and are not resolved. As p~/pl increasesup to 1.0, the amplitudes of the horizontal and vertical components of theinterface waves decrease. At p2/o~ = 1, the amplitudes are zero and no interfacewave is found. Recall that these are still different media with different velocities.The horizontal component decreases more rapidly than the vertical component as16.0A×R 212.0AxR z8.0& :0,o 2: .2p~AxR 2P2 = .4p,AxR 24.0gI22= ,.oe,-4.Cz.'ot"vs,/d_B×R 2t~ -BXR24:0 ~ ~---B×R 2--7 I8.0FIG. 17. Horizontal and vertical displacements on the interface separating two semi-infiniteelastic media. A compressional point source of pulse width .8 is located in the upper medium(vc~ = ~/1.05vct , v~2 = %/~v,1). The observation point is located on the interface at a distanceof four times the height of the source above the interface measured from a point directly belowthe source. The four curves are for density contrasts o2/ol given by 0, .2, .4 and 1.0.the density contrast increases from 0 to 1. For the Rayleigh wave the ratio of thehorizontal to the vertical component is approximately .68, while for the interfacewave the ratio is smaller. For p~/pl larger than 1 and increasing, the amplitude of theinterface wave increases again and it appears mainly in the vertical component.Notice that there is a phase change of 180 ° in this component in passing through thevalue P2/pl = 1.The phase velocity of Stoneley waves is a root of an equation originally derived byhim (1924). The region in which these roots exist is given in the book by Ewing,Jardetzky and Press ( see p. 113) and also in the book by Cagniard. ( See Figures 4-6,p. 49. In this figure the vertical scale is incorrect and should be changed to* A name used by Cagniard (1962) for the surface wave that travels along the interface withthe shear velocity v,t •