Analytic approximation for the elastic radiation from a contained underground explosion

A simple analytic function involving only an exponential and a polynomial is found to give a rather good fit to the experimental curves of the reduced displacement potentials for nuclear explosions in four different mediums as given by Werth and Herbst. By using this function, the near field and radiation field terms in the total energy integral and the energy spectral density of the radiation field are evaluated in closed form in terms of simple algebraic functions.