PROPAGATION OF ELASTIC WAVES IN LAYERED MEDIA BY ...

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394 BULLETIN OF THE SEISMOLOGICAL SOCIETY OF AMERICAappearance of Stoneley-like pulses for values of the elastic parameters outside thisregion has also been noted by Gilbert and Laster (1962). The interface wave mayalso include the "second surface wave." However, it should be remembered that inthose cases where the Stoneley equation does not have solutions (and hence theStoneley wave should not exist), that other solutions do exist provided differentRiemann sheets are permitted. Also, as mentioned by Roever, Vining and Strick(1959), the pole causing the Stoneley wave in the first place may still influence the~ P2= 1.3p,x4.0- ~ 4.0 ff~, fd<
PROPAGATION OF ELASTIC WAVES IN LAYERED MEDIA 395layer and lower medium are X~ = /~1, vc2 = 1.5v~ and v,2 = 1.5v,1. Hence vc2 > vc~ >v82 > v~. The density contrast p2/Pl between the two media is permitted to take onthe values .8, 1.3, 3.0 and 6.86. The range of densities selected are typical of anumber of interesting cases. The choice of P2/pl = 6.86 corresponds to the case ofbrass and plexiglas, materials used in model studies. In Figure 19 the observationpoint is located on the surface at a distance equal to twice the layer thickness from4.04.C3,C3.0&=,3f,,2,£2.0h£1,0f,.>.06.0 8.0-{.(1.5-I.C1.0BxR/o2 = 6.86 P II.C.5I:-,5_BxR2~W//B-I,(-I.0FIG. 20. Horizontal and vertical displacements on the interface of a layered half-space. Acompressional point source of pulse width 1.6 is located midway between the surface and interface.(vc2 = 1.5vol, v~2 = 1.5v~, .) The observation point is located on the interface at a distanceequal to twice the layer thickness from the point directly below the source. The four curvesare for density contrasts p2/pl given by .8, 1.3, 3.0 and 6.86. Compare with Figure 19.the epicenter. When p2/f~l = .8, the horizontal component in the dimensionless timerange t(v~i/d) = 4 to t(v81/d) = 6 is similar to the horizontal component of aRayleigh wave in a half-space but has slightly larger amplitude. The vertical componentis also similar to the vertical component of the Rayleigh wave in a half-spacebut has about twice the amplitude in the same range 4 to 6. When P2/p2 -= 1.3, thehorizontal component in the range 4 to 4.5 is similar to the horizontal component ofa Rayleigh wave in a half-space. In the range 4.5 to 6.0, where the maximum occurs,it is modified by reflections from the interface. The vertical component is similar to
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