This author cannot judge whether the formula is appropriate for the tectonic conditions of Pokhran, but from Wallace's own report it appears that it is actually on the low end of available formulas the extreme low value for the formulas given by Wallace would make Pokhran-I a 3. Even this extreme low yield is much higher than the yield estimate implied by Wallace's interpretation of the crater evidence about one kiloton or less.
But Wallace's interpretation of the crater features is not valid, being based on several erroneous beliefs. In a shallow underground explosion the cavity formation goes through phases as depicted in [Teller et al , p. Images made only moments after the shot was fired which match verbal accounts by witnesses show that the test was too large to be fully contained -- that is, no significant surface disturbance prior to subsidence collapse. In this image we see the uplift mound thrown up briefly by Pokhran-I. Descriptions of this test by the scientists involved [Chengappa , p.
Studying the images of this crater show that is has an unusual complex set of features, not comparable to any other underground nuclear test this author has been able to find. The crater proper, which contains fissures characteristic of settling and subsidence as Wallace observed, is surrounded by fissures and uneven broken ground stretching well away from the crater perimeter. These fissures were presumably created by stretching when the mound was heaved upward. Images of subsidence craters at the Nevada Test Site available to this writer entirely lack the pronounced fissures surrounding the outside of the crater that are so striking in images of Pokhran-I.
Largest artificial non-nuclear explosions
In the NTS images of pure subsidence craters, the fissures are confined to the crater interior see the Storax and NTS underground test pages for examples. On the other hand, clear evidence of ejecta - material thrown from the crater - is impossible to find in the pictures. Taken together these indicators show that the blast, though apparently contained, was only very marginally so. The upheaval was either not quite violent enough to actually break through and create a "throw out crater" the typical blast-type crater , or if it did break through it was without sufficient force to throw material out of the crater.
All of the material propelled upward remained within the crater. These phenomena match the craters shown here with burial depths of equivalent to diagram e. Clearly, if the yield had been significantly greater an obvious surface rupture with ejecta would certainly have occurred. The wide shallow crater produced reportedly it had a 47 m radius and was 10 m deep; recent high resolution commercial satellite imagery indicates a crater radius of 60 m is also characteristic of a marginal cratering explosion rather than a contained subsurface detonation.
True subsidence craters have dimensions similar to the underground cavity, which for this yield range would be a radius of 30 m or less. The fact that this explosion marks a transition between surface and subsurface explosions accounts for its unusual distinctive and complex structure. Based on the surface effect diagram he uses, Wallace expects that a shallowly contained explosion would necessarily produce a permanent "retarc" a mound of rubble - this is "crater" spelled backwards and is the actual terminology used. But the formation of a retarc is not general behavior - it is dependent on the characteristics of the medium in which it is fired, and the characteristics of any overburden that may be present see The Effects of Underground Explosions for a detailed discussion of the issues.
Retarcs only occur if the shot is fired in a medium that bulks up when shattered by the explosion, and can hold the mounded form as occurred in granite and basalt with the Whetstone Sulky shot at NTS 18 December Retarc formation is also rather sensitive to the depth of firing - in fact Sulky is the only retarc formed in the entire history of US nuclear testing.
Direct calibration of the yield of nuclear explosion - Page 55 of 73 - Digital Library
A relatively deep shot produces greater bulking because the rock is broken into large blocks with a greater amount of void between them. A shallow detonation produces higher stresses and smaller particles with low bulking even in a bulking-prone medium [Teller et al , p.
And if the shot is instead fired in a stratum that becomes compacted to the sides and below by the explosion creating a cavity , but is overlaid with material that does not bulk up substantially from the explosion, then an uplift mound followed by a subsidence cavity is exactly what would be expected - but the phenomenon involved are rather different from the permanent cavity formation, followed by chimney formation progressively climbing to the surface seen in "classic" subsidence craters. This appears to be the situation with Pokhran-I.
From the available descriptions that are available about the shaft digging operations at Pokhran, it is clear that while the test shaft may have been above the water table, it was plagued by continual seepage and flooding, so that the porous moisture bearing rock is perhaps similar to the tuff at NTS. But the surface of the Pokhran site is clearly covered by a layer of sand - a material that does not bulk at all, and efficiently fills subsurface voids. It may also be that below the sandy surface of this area of the Thar Desert there is a layer of alluvium - a loose material that also does not bulk.
Also the obviously shallow depth of the detonation would have shattered the rock overburden into small pieces reducing or eliminating bulking in any material prone to it. Thus the formation of a subsurface partial cavity, a temporary uplift mound, followed by cavity collapse and permanent subsidence crater formation in entirely consistent with an explosion that was large enough to be only marginally contained. Using this understanding to calibrate the yield is complicated by the scaling problems noted above. But by marshalling the available data on deep cratering experiments done for Plowshare a tight boundary on the yield can be obtained.
Sulky provides the closest analogy to Pokhran-I in the US nuclear test program. This shot was a hard rock deep cratering test that was marginally contained - it failed to throw out any material, but it did rupture the surface. As [Allen et al ; pg. Sulky had a yield of 0. The surface rupture produced by Sulky had a radius of 12 m, and took the form of a retarc - a pile of rubble - 4 m high.
The formation of a retarc rather than a shallow subsidence crater is an artifact of the unusually strong rock in which the test was conducted, granite overlaid by basalt. The granite shattered into large blocks, producing a large permanent volume increase. If the strata had been softer causing it to shatter into finer pieces; or if the scaled depth had been slightly shallower producing a stronger shock and greater shattering effect; then Sulky would likely have produced a subsidence crater also.
The retarc formation had come as a surprise, a shallow crater was the expected, and Sulky was the only retarc producing shot in the entire US nuclear test program. A Plowshare shot that provides another constraint on conditions for containment is Palanquin which was a 4. Palanquin was a deep cratering shot that excavated a 73 m by 24 m crater with an ejecta boundary extending 82 m from the center [Gibson ; pg. This gives a scaled depth for Palanquin ranging from The dimensions of Palanquin can be compared to the dimensions of Pokhran-I, 94 m by 10 m. The generally similar wide shallow form of the two craters suggest a similarity in their mechanism of formation.
If the rock in which Pokhran-I was fired matched the dry rhyolite of Palanquin in containment strength, this immediately establishes an easy upper limit to P-I's yield. Figure 1 below is adapted from one by Nordyke which appears in [Teller et al , p. The graph plots cratering results for basalt and has been altered by adding data points for an additional Plowshare cratering shot Palanquin , and also the positions for Pokhran-I scaled for 8 and 13 kt.
In addition the data point for Sulky has been replotted. The original data point gives it a "zero radius". The thinking for plotting it this way was no doubt that since it wasn't defined as a crater, it couldn't have a "crater radius". However it did produce a surface rupture of considerable size, which missed being a depression simply due to the upper strata's failure to recompact.
If the graph is considered a plot of surface rupture features of all types, then Sulky should be plotted at the position labelled "actual". Note also, the original diagram placed Sulky slightly too high on the depth scale. Click here to see x version 20 k Figure 1. Scaled Depth vs Radius for Cratering Shots. It can be seen in Figure 1 that Sulky and Palanquin occupy almost the same spot on the graph, with Sulky being located slightly farther from the crater vs radius curve.
In looking for reasons that two shots with almost identical scaled characteristics produced quite different surface effects it should be noted that they are falling on opposite sides of the point of containment, but just barely. Sulky was fired in a notably strong rock - granite - which would be expected to cause rather better containment than basalt. The rhyolite used for Palanquin is a strong hard rock it has the same chemical composition as granite but with a finer crystal structure , probably stronger than basalt but not quite as strong as granite.
Thus both shots should be expected to fall slightly below the scaled radius curve for basalt i. Also the fact that Palanquin produced a throw-out crater while Sulky did not, even if it was slightly deeper, is explicable given the stronger rock used with Sulky. The scaled depth difference between Sulky and Palanquin 1.
The Yield of Pokhran I (Smiling Buddha)
But the fact that these two shots - with a fold yield difference - tightly bracket the threshold conditions for containment places tight constraints on the plausible yield for Pokhran-I. It can be seen that with an 8 kt yield Pokhran-I clusters closely with Sulky and Palanquin. Pokhran-I was slightly deeper than Palanquin and was barely contained, suggesting that the rock in which it was fired was roughly similar in strength to the rhyolite of Palanquin. On the other hand the claim of 13 kt puts Pokhran-I in a strikingly anomalous position. It is much farther below the curve than any over the other shots, and at a much shallower scaled depth than the evident cutoff region for containment.
In effect this requires Pokhran-I to have been fired in rock with remarkable properties - offering far better containment than basalt, rhyolite, or granite. The actual test site rock sandstone and shale was soft, porous and moisture bearing - quite significantly weaker than the granite strata in which Sulky was emplaced. Chidambaram asserts that rock mechanics calculations employing measurements of the physical properties of the Pokhran rocks support the 13 kt yield for Pokhran-I [Sikka et al ].
With due respect to Chidambaram, in light of the scaling data presented here this is an extraordinary claim, and is impossible to credit. From this analysis, it appears that the yield of Pokhran-I has been tightly constrained to value close to 8 kt, in accordance with recent statements made by PK Iyengar.
It has been reported [Chengappa ; p. Since Chadambaram presumably consulted the Plowshare test results Palanquin was conducted 14 April , he would have been aware that a shot that scaled to Palanquin would be very unlikely to be contained. Thus if Chidambaram really planned complete, or nearly complete containment, a planned yield would have had to have be no more than 9 kt, and very likely less.
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The 8 kt yield range suggested by comparison with US cratering data is well within the range that seismic scaling laws provide - which extends from 3. Log in to Wiley Online Library. Purchase Instant Access. View Preview. Learn more Check out. Volume , Issue 5 May Pages Related Information. Close Figure Viewer. Browse All Figures Return to Figure.
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