Seismic moment and long-period radiation of underground nuclear explosions

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Abstract
The moment function of an explosion is introduced, using the equivalence of an explosive point source and three mutually perpendicular linear dipoles. The seismic moment of an explosion is the final value, for large times, of the moment function. Its relation to source parameters is similar to that of the moment of an earthquake: M1 = (λ + 2μ)S1D1 (λ, μ = Lamé's parameters, S1 = surface area of a sphere surrounding the explosion in the elastic zone, D1 = static radial displacement on this sphere). From strain observations of other authors (Romig et al., 1969; Smith et al., 1969), the moment of the underground nuclear explosion BENHAM is estimated to be about 1024 dyne cm. This moment value supports the assumption that the source-time function for the long-period radiation from large nuclear explosions (periods greater than about 10 sec) is essentially a step-function. On the other hand, a quantitative estimate of the long-period P-wave spectrum of the explosions JORUM, HANDLEY and MILROW and a comparison with observed spectra of Molnar (1971) for JORUM and HANDLEY and Wyss et al. (1971) for MILROW support the assumption of an impulsive source-time function. This discrepancy, which is typical of current opinions among seismologists, is not resolved. It is concluded that an explosive point source is possibly not a sufficient model for the long-time radiation and the static displacement field of a nuclear underground explosion whose elastic radius is about equal to its depth and which is detonated in a prestressed medium.