IN response to an article in Frontline (September 25, 2009) on the revival of the controversy over the yields of the May 11, 1998, Pokhran-II nuclear tests, one of the issues raised in informal discussions is the fact that while the fission device (of 12-13 kiloton) in the Pokhran-I test of 1974 produced a prominent crater, the Pokhran-II thermonuclear device of a much greater yield did not produce a distinctly larger crater morphology. An explanation for this is, therefore, in order.
A study of the surface topography after an underground nuclear test also provides a method to estimate the yield of the test. Western analysts have tried to use the images of post-shot crater morphology to debunk the yield values put out by the Department of Atomic Energy (DAE). The crater morphology would obviously depend on the depth of burial (DOB) and the manner of emplacement of the device in relation to the surrounding earth.
Qualitatively speaking, if the DOB is shallow a more voluminous crater is created. In an underground explosion, there are two effects: the confining effect of the material overburden causes the energy to be directed downwards and is thereby a negative influence on cratering, and at the same time the confining strata are blown upwards by the expanding gas. As the DOB increases, the confining effect obviously increases and the average material pushed upwards decreases as the mass of the overburden increases. As a result a larger and larger fraction of the material thrown upwards falls back. This also traps and buries much of the radioactivity.
At a particular depth, the increasing overburden is exactly balanced by the force of the volume being thrown out. This depth is called the optimum depth of burial and varies with the geology of the site, being greater for less dense and structurally weaker surrounding material (for example, alluvium) and shallower for dense rock.
At depths greater than the optimum DOB, the crater size begins to reduce as less and less material now gets ejected. There would be upheaval within the crater boundary but nothing is thrown out. At these depths a great amount of broken rock is produced, which was seen in the Pokhran-II thermonuclear explosion, whose DOB was about 230 metres compared with Pokhran-Is 107 m.
The observed effects would depend on the properties of the surrounding strata and the emplacement of the device. According to S.K. Sikka, formerly of the Bhabha Atomic Research Centre (BARC) and one of the key scientists involved in the tests, the geology of the Pokhran test site is such that at depths corresponding to that of the Pokhran-I device of 1974, the surrounding material is more like alluvium, comprising sandstone and shale. But as one goes deeper the geology changes, and at depths corresponding to that of the 1998 thermonuclear device and lower the material is pink granite.
The crater sizes (depths, cavity radii, etc.) are empirically determined to be governed by a scaling law, which goes as Y0.295, where Y is the explosive yield in kt. That is, cratering explosions at different depths and yields (under similar surrounding geology) can be compared by scaling them to a standard yield, say 1 kt. For example, a 1 kt explosion at 20 m may be similar to a 50 kt explosion at 100 m. This relation has been fully characterised for Pokhran by BARC scientists. From this relation, the corresponding scaled comparisons can be made for different yields.
The Pokhran-I explosion actually resulted in a shallow crater (where the crater radius and cavity radius are roughly equal) following a raised mound with a crater radius of 47 m and a cavity radius of 30 m. Without knowing the geology of Pokhran, Western analysts have assumed the Pokhran-I test to have resulted in what is known as a subsidence crater and an equation for scaled depths (122 x Y0.295) that is not applicable to Pokhran. They also used a known value of a U.S. test which resulted in a subsidence crater, and estimated a low value for the Pokhran-I yield. For estimating Pokhran-II, they have used this low Pokhran-I yield to calibrate the Pokhran geology and estimated the thermonuclear yield to be lower.
Now, according to studies at BARC for the design yield of the Pokhran-II thermonuclear device, the DOB was exactly in the region where the crater size falls at the minimum of the scaling curve. And this is exactly what was observed. In fact, according to Sikka, exact simulations were done to eliminate completely the venting of radioactivity and the DOB was chosen accordingly. He further points out that the little mound that is seen in the picture of the cratering by the thermonuclear weapon is actually owing to the strong reflection of the shock waves from the granite stratum below the DOB.
In this revived debate over the Pokhran-II yields, Sikka has come up with yet another proof to show why Western analysts were wrong to ascribe low yield values based on seismological parameters. As explained in the earlier article (Frontline, September 25), underground explosions set up seismic waves analogous to earthquakes. These waves comprise body waves that travel through the body of the earth and those that travel along the surface. The body waves are short period (about 1-2 seconds) waves that include both compressional or P waves (which are longitudinal) and shear or S waves (which are transverse). At short distances (less than 2,000 km) body waves travel through the crust and top portion of the upper mantle and are called regional seismic waves. Beyond 2,000 km, body waves travel through the mantle and the core and are called teleseismic waves.
P waves travel faster than S waves (with speeds of about 5-10 km/s) and these arrive at the detectors first. The P-wave amplitudes are used to determine what is called the body wave magnitude m(B). The yields of explosions (as in the case of energy released in earthquakes) are given by a relation between m(B) and the explosive yield Y. This has the form m(B) = a + b log Y, where a and b are site-specific constants. While there is considerable variation in the a values from site to site, variations in b are much less.
In a paper published soon after the tests (in the September 10, 1998, issue of Current Science), Sikka and others pointed out that owing to the simultaneity of the Pokhran-II (fission and thermonuclear) explosions in shafts that were a kilometre apart, the network-averaged m(B) values would be lower than the true values because of the significant interference effects in the direction of the line joining the two shafts (east-west). They showed that if interference effects are corrected for, the averaged m(B) value was 5.39, compared with 5.0 of the Arlington-based International Data Centre (IDC) network and 5.2 of the U.S. Geological Survey (USGS) network.
They also pointed out that the constants a and b, in the m(B)-Y relation, that were appropriate for Pokhran were those pertaining to the hard rock conditions of the Nevada Test Site (NTS) and not those of the Shagan River Test Site (SRTS) at Semplatinsk of the former Soviet Union, which were used by Western analysts. Sikka and co. reiterated this fact by a detailed analysis of 64 NTS observations and 74 SRTS observations, which was published in Current Science in 2002 (Frontline, September 25).
The earliest analyses contesting the yield claims made by the BARC scientists were those of Brian Barker and others in the September 25, 1998, issue of the journal Science and T.C. Wallace in the September 1998 issue of Seismological Research Letters. In their analyses, while Barker and co. used the IDCs m(B) of 5.0, Wallace used the USGSs m(B) of 5.2. Further, arguing that the observed P-wave spectrum from Pokhran-II, averaged over 20 seismic stations of the IDC network, was remarkably similar to those of tests at the SRTS, but inconsistent with those of the NTS, they applied the SRTS constants (a= 4.45 and b= 0.75) for Pokhran and determined the yield to be 12-15 kt. This, according to the BARC scientists, was incorrect. Besides, Barker and co.s paper did not provide details of the P-wave spectra or the averaging technique they had used.
Countering this, the BARC scientists sent their comments to Science, which, however, were not published. Instead, the journal sent a plot of the spectra that Barker and co. used for arriving at their assumptions regarding the constants but did not include in their paper (Figure 1). Admittedly, from Figure 1, the Pokhran curve appears closer to the SRTS curve than to the NTS curve.
Revisiting the issue now, Sikka has shown how the Pokhran-II spectrum used by Barker and co. is actually consistent with appropriate NTS constants and a yield of around 60 kt. In doing so he has demonstrated two things: one, the method of comparing network-averaged P-wave spectra is not unambiguous; and, two, careful selection of spectra should be made for choosing appropriate constants because even for a given region (NTS or SRTS or Pokhran) the geological conditions can vary from test to test depending on the depth of burial and emplacement of the device. This analysis also re-emphasises the fact that yield estimation on the basis of P-wave characteristics, including m(B), is not a precise method.
The geology of the Pokhran test site is such that at depths of around 100 m, corresponding to the emplacement of the Pokhran-I device, the surrounding material is more like alluvium, made of rocks of sandstone and shale. But at depths corresponding to the emplacement of the Pokhran-II thermonuclear device and lower, the material is pink granite. Shock physics experiments done at the Terminal Ballistic Research Laboratory (TBRL) of the Defence Research and Development Organisation (DRDO) to characterise the Pokhran granite have shown that these Pokhran rocks are very similar to the granite at the French Hogger Testing Site (HTS) in Sahara.
Fortunately, says Sikka, in 2001 J.R. Murphy and B. Barker published the P-wave spectrum of the French 58 kt Rubis explosion at HTS on October 20, 1963. The same paper also published the spectrum of the 62 kt Pile Driver test of the U.S. at NTS. Further, Murphy and Barker also proved in their paper that the coupling of granite with the explosive source at the NTS was close to that of the HTS granite.
Simply plotting together the P-wave spectra of Pokhran-II, Rubis and Pile Driver, as given by Barker himself, shows the striking similarity between them (Figure 2). This is what Sikka has done in his recent exercise to drive home why Western estimates of Pokhran-II yield were lower. From the plot one can directly infer that the Pokhran-II yield would be in the ballpark of the yields of Rubis and Pile Driver, which is around 60 kt.
Specifically, applying the constants a= 3.93 and b= 0.89, corresponding to the HTS and NTS granites, for Pokhran-II m(B) gives a yield of about 47 kt. The actual values of a and b for Pokhran, as determined by the BARC scientists, are 4.04 and 0.77 respectively and this gives a yield of 58 + 5 kt. The original estimate of combined yield of the May 11, 1998, tests was about 60 kt, with 45 kt for the thermonuclear weapon and 15 kt for the fission weapon that were set off simultaneously.
