Th e explosio n seismi c sourc e functio n i s th e potentia l which satisfie s th e spherica l P-wav e equation. I t i s completel y described b y fou r properties. The y ar e th e steady-stat e value , roll-off , overshoot, an d corne r frequency. I n on e approac h t o describin g th e potential, th e spectral roll-of f is specified and the other properties ar e determined b y fittin g th e dat a a t prescribe d times. I n a variatio n o f this approach , th e roll-of f is specified by assumin g a radial stress o f a known for m i s applie d uniforml y over a spherica l surface , locate d a t a rang e wher e th e motio n i s assume d t o b e linear. I n thi s review , i t was foun d tha t o f th e fou r properties , les s uncertaint y exist s abou t the steady-state valu e an d th e corne r frequency than abou t th e othe r two. A majo r proble m ha s bee n scalin g th e result s fro m on e yiel d to another. Ne w result s ar e presented tha t sho w that , whe n th e geophysical propertie s o f th e sho t poin t ar e take n i n account , cube-roo t scaling o f th e yiel d i s appropriat e fo r th e steady-stat e valu e an d th e corner frequency , i.e. , yiel d t o th e firs t an d one-thir d powers , respectively. Th e ne w result s als o suggest tha t previou s assumption s abou t the for m o f th e applie d radia l stres s ar e probabl y no t appropriate. Finally, chemica l an d nuclea r explosion s appea r i n th e ne w result s to b e indistinguishable , suggestin g tha t experiment s usin g chemica l explosions coul d ai d i n reducin g th e remainin g uncertaint y i n th e seismic sourc e functio n properties. Explosion Sourc e Phenomenolog y Geophysical Monograph 6 5 Copyright 199 1 America n Geophysica l Unio n a 2 dt 2 respectively, wher e A and / i ar e th e Lame' s constants , a i s th e compressional wav e speed, an d
As part of a larger joint effort by the Defense Advanced Research Project Agency and the Department of Energy to study the seismic source problem, a comprehensive reevaluation of the 1964 Salmon and 1966 Sterling nuclear explosions in dome salt was carried out. The Sterling source function originally estimated by Springer et al. (1968) conveys the impression that the cavity was badly overdriven; on reexamination this does not appear to be the case. The work of Glenn et al. (1987) on the Sterling free-field data is expanded upon, confirming that the cavity response was close to the theoretical expectation. Sterling's source function is estimated and is found to be comparable to Patterson's (1966) slightly weakened salt model. A source model for Salmon is derived from the Sterling source model and the five seismic stations that recorded both events. The new source model has a reduced displacement potential • of about half that previously estimated. A temporary nonlinear two-wave system developed during the Salmon explosion as the compressional wave evolved from a shock wave; the separation of these two waves resulted in a high-frequency roll-off of the reduced velocity potential of a• -3. In addition, it is shown that the corner frequency is much higher and is created much closer to the cavity than the eigenfrequency. For both Salmon and Sterling the radial stresses are approximately a low-passed damped sinusoid superimposed on a small step function. The decoupling value of 72 obtained by Springer et al. (1968) is confirmed. A revision of Patterson's (1966) partial decoupling curve shows that the value for full decoupling in a shot-generated cavity would be only slightly higher. Contrary to previous studies, decoupling as a function of frequency for the surface waves is found to be the same as for the P waves. A new definition of decoupling appropriate to threshold test-ban treaty monitoring is also proposed.
In a recent paper Springer et al. [1968] present results concerning the Sterling nuclear decoupling experiment. At this time, I would like to present additional theoretical analyses verified with datg obtained over a wider frequency band. The additional data indicate that the alecoupling at low frequencies is somewhat less than that indicated by the data in the vicinity of 1 Hz. An analysis is performed that satisfactorily explains the observed frequency dependence in terms of a simple analytic expression. As shown in Figure 3 of the referenced paper, the seismic instruments used to record the events Salmon and Sterling are characterized by low-frequency rolloffs. In particular, the NC-21 velocity meter employed by the U.S. Coast and Geodetic Survey has a second-order rolloff at I Hz. Using an analog correction circuit [Watson, 1967], the inverse of this response function was programmed on an analog computer resulting in an effective instrument response that gives reliable information down to 0.3 Hz. We employed this circuit in the processing of the Salmon and Sterling measurements and thereby obtained data over the frequency range of 0.3-100 Hz. As mentioned by Springer et al. [1968], narrow bandpass filtering can be used to approximate Fourier analysis. We agree with this concept and routinely employ analog filters characterized by the following transfer function [Lynch, 1965]: + + S,o where $ is the Laplace transform variable, and •o is the center frequency of the filter. The
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Spectral ratio discrimination studies carried out on events located in the western United States and Soviet Union (S.U.) illustrate that pronounced differences in radiated explosion‐source spectra relative to nearby earthquakes exist between the two regions. Nevada Test Site (NTS) explosions are characterized by the existence of more low‐frequency and/or less high‐frequency energy (greater low‐to high‐frequency spectral ratios) than western U.S. earthquakes. The opposite pattern is observed in the S.U. with nuclear explosions appearing to have more high‐frequency (and/or less low‐frequency) energy than earthquakes. These observations may be caused by at least two principal effects that are probably acting in parallel: (1) variations in depth‐dependent effects of attenuation acting between the shallow explosions and deeper earthquakes and (2) differences in the dynamic response of the near‐source geology to the passing explosion shock wave. Anelastic synthetic seismogram calculations illustrate that depth‐dependent attenuation effects may explain the spectral observations. However, a number of observations using near‐ and far‐field data from NTS explosions suggest that near‐source effects are the dominant factor. A quasi‐empirical explosion source model is proposed that simultaneously fits the spectral ratio data from both the U.S. and S.U. relative to earthquakes in each of the respective regions. Additionally, the model fits the trends of the spectral ratios observed as a function of magnitude. The key to the model is the shape of the pressure time history acting at the elastic radius. For explosions detonated in weak, porous rock, the radiated shock wave divides into a two‐wave system consisting of an elastic precursor followed by a plastic wave. The generation of this two‐wave system introduces a rise time into the pressure time history. In the frequency domain a second corner frequency is established in a third‐order model (with an ω−3 high‐frequency decay) whose value is inversely proportional to the time separation of the two waves. In higher‐strength, saturated rocks (or for overburied explosions) the effective rise time is short, and a second‐order model is appropriate (with an ω−2 high‐frequency decay). The second‐order model provides a good fit to the S.U. data. In contrast, a hybrid model is required to fit the NTS data with an ω−3 high‐frequency decay for shallow explosions detonated in unsaturated tuff that evolves to an ω−2 decay as depth of burials reach higher‐strength, saturated rocks below the water table.
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