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The teleseismic amplitude resulting from an underground explosion is proportional to the asymptotic value of the reduced displacement potential (ϕ∞) or, in physical terms, to the permanent change in volume measured anywhere beyond the range at which the outgoing wave has become elastic. It is known that ϕ∞ decreases with increasing initial cavity size (r0) until the cavity is large enough to preclude inelastic behavior in the surrounding rock, at which point no further decrease occurs. Earlier numerical calculations suggested that ϕ∞ was not a monotonic function of the initial energy density and that the seismic amplitude might actually be decreased, in certain cases, by decreasing the initial cavity size. We have examined this question from an analytical point of view and derived the seismic response for a simple linear‐elastic, perfectly plastic medium as r0 → 0. In this limit, an exact, power law relationship is found between ϕ∞/W and r0W−⅓, where W is the yield, a result which implies that ϕ∞ vanishes altogether for an explosion in which the initial cavity radius is vanishingly small. The physical explanation for this curious behavior is shown to derive from the unique inability of a Hooke's law medium to generate thermal pressure. A similar, but less dramatic, effect is demonstrated with more realistic material models. The significance of these results is that the estimation of yield from measurement of seismic amplitude may be a less accurate process than previously suspected.
The teleseismic amplitude resulting from an underground explosion is proportional to the asymptotic value of the reduced displacement potential (ϕ∞) or, in physical terms, to the permanent change in volume measured anywhere beyond the range at which the outgoing wave has become elastic. It is known that ϕ∞ decreases with increasing initial cavity size (r0) until the cavity is large enough to preclude inelastic behavior in the surrounding rock, at which point no further decrease occurs. Earlier numerical calculations suggested that ϕ∞ was not a monotonic function of the initial energy density and that the seismic amplitude might actually be decreased, in certain cases, by decreasing the initial cavity size. We have examined this question from an analytical point of view and derived the seismic response for a simple linear‐elastic, perfectly plastic medium as r0 → 0. In this limit, an exact, power law relationship is found between ϕ∞/W and r0W−⅓, where W is the yield, a result which implies that ϕ∞ vanishes altogether for an explosion in which the initial cavity radius is vanishingly small. The physical explanation for this curious behavior is shown to derive from the unique inability of a Hooke's law medium to generate thermal pressure. A similar, but less dramatic, effect is demonstrated with more realistic material models. The significance of these results is that the estimation of yield from measurement of seismic amplitude may be a less accurate process than previously suspected.
Recently released Russian data on two underground nuclear explosions in an Azgir salt dome allow comparison for the first time with similar U. S. explosions. In both cases, highly tamped explosions were employed to form cavities and, after a period of several years, much smaller explosions were then carried out in these same cavities. The seismic decoupling factor obtained from the Russian tests appears to be a factor of 4 less than is predicted, based on the U. S. experience. However, the Russian data are found to be entirely consistent with smaller scale U. S. experiments with chemical explosives. These results can be explained by the extent of damage in the immediate vicinity of the cavity walls, but it remains unclear why the damage should exist at the Russian site, and not at the U. S.
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