A formal integral transform solution is obtained for the response of an elastic half-space to a radially symmetric pressure signature of variable pressure and variable velocity. An asymptotic approximation to this solution is developed and expressed in terms of the known solution for the response of a half-space to a two-dimensional pulse moving with constant velocity plus a correction that is important only if the blast-wave speed directly above the point of observation is close to the Rayleigh-wave speed.

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