Movement of the ground in Rayleigh waves produced by underground explosions

Analytic representations are obtained for the displacement and stress fields in the Rayleigh surface wave ($R$-wave) generated in an elastic half-space by an internal source that produces the same seismic $P$-wave as an underground explosion. Oscillograms, particle trajectories, and stresses in the half-space and on its surface are calculated. Relations for the energy flux in the $R$-wave are obtained. For rock salt, the fraction of the explosion energy transferred to the $R$-wave is estimated. It is established that this fraction can reach values of about 1% of the total explosion energy if the explosion is a contained one. As the charge depth is increased, the energy of the $R$-wave decreases in approximately inverse proportion to the depth.