Propagation of a compressional pulse in a layered solid

In this investigation we solve the problem of propagation of a compressional pulse in a solid half‐space which is overlain by a solid layer of different properties. The point source is situated at the depth ½H, H denoting the thickness of the layer. Theoretical seismograms of the vertical displacement w at the surface are evaluated out to ranges r = 20H. The solution is obtained by the exact ray theory. The displacement W_o due to the source was assumed to have a shape which at large distances reduces to a sawtooth. The once‐reflected waves from the interface, PP and PS, are strongly marked. The Rayleigh wave is already recognizable at r = 5H and is fully developed at r = 20H. The method of ‘ray theory’ was applied here far into the region where the normal mode theory converges well. The theoretical seismograms are illustrated. The properties assumed for the layer (1) and for the half‐space (2) are λ₁ = μ₁ μ₂ = 2μ₁c_s2 ≡ c₂ = 1.1c_s1 ≡ 1.1c₁c_p2 > c_p1 > c₂ > c₁