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On May 28, Pakistan's Prime Minister, Nawaz Sharif, announced that his country had conducted five nuclear tests of its own and "settled the score" with India. Although Pakistan had voted in the UN to adopt the CTBT, it had declared it would not sign it as long as India did not. Unlike nuclear tests conducted by the five major nuclear powers, which in the past were shrouded in secrecy, both the Indian and Pakistani governments held several press conferences and announced explosive yields, how many explosions were involved in each test, and even the types of the nuclear weapons. This provided a unique opportunity to compare seismic analysis with governmental pronouncements. This is especially timely, as the U.S. begins debates about ratifying the CTBT. Seismology is the main monitoring technology for buried explosions, and the India and Pakistan tests provide a ground truth test of the as yet incomplete International Monitoring System (IMS), the role of seismic stations which are not part of the IMS, and rapid access through real-time data links.
| India May 11, 1998 | Pakistan May 28, 1998 | Pakistan May 30, 1998 | |||||||
| OT | Lat | Lan | OT | Lat | Lon | OT | Lat | Lon | |
| REB | 10:13:44.2 | 27.072 | 72.761 | 10:16:17.0 | 28.903 | 64.893 | 06:54:57.1 | 28.495 | 63.781 |
| USGS | 10:13:42.0 | 27.102 | 71.857 | 10:16:15.2 | 28.862 | 64.818\ | 06:54:54.9 | 28.487 | 63.787 |
| JHD | 10:16:17.8 | 28.856 | 64.906\ | 06:54:57.1 | 28.499 | 63.741 | |||
The constant C in (1) is very dependent on the seismic attenuation of the source region, in particular the attenuation associated with the upper mantle beneath the explosion source. It is possible to determine C by measuring the seismic spectra at teleseismic distances. In general, C is smaller for tectonically active regions, like the Basin and Range Province, as compared to stable tectonic environments like the Indian Shield. The value of C varies from about 3.9 to 4.5. If mb is well determined (averaged over a large number of stations), it is possible to get a robust estimate of explosive yield.
The Indian test site lies within a very stable tectonic province, the Indian Shield. Examination of the spectra from the May 11 explosion indicates that attenuation in the test region is very similar to that seen beneath the former Soviet Union test sites in Kazakhstan. The standard relationship used for stable environments is (Ringdal et al., 1992):
This relationship was developed from mb calculated with the traditional definition, which requires a period of approximately 1 Hz. Great care must be taken in applying this formula, especially since many of the mb measurements that are now reported are not made at 1 Hz.
The USGS reported a mb = 5.2 for the May 11 explosions (preliminary magnitudes were slightly higher). This implies a yield of approximately 10 kt. Considering uncertainty in the yield relation and magnitude variability, we determine that the May 11 event had a yield of 10-15 kt. This value is much smaller than that reported by the Indian government; if all three reported tests were detonated simultaneously, the yield would be the sum of the individual explosions as announced by the Indians, or approximately 55 kt (55 kt corresponds to a mb = 5.76). On the other hand, if the explosions were delayed by several tenths of a second, then the mb would only represent the largest of the explosions. However, the reported yield of the thermonuclear device was 43 kt, which is still much larger than expected from the observations.
Although there is uncertainty in the absolute determination of the seismic yield, the relative yield between two tests can be calculated with a much higher precision. If Equation (2) is used to calculate the yield from two explosions at the same test site, then the differences in magnitude can be expressed as
where Y1 and Y2 are the yields of the first and second events respectively. The mb reported for the 1974 Indian test was 4.9; applying Equation (2) gives a ratio of yields of 2.4. If the yield determination of May 11 is correct, then the yield of the 1974 explosion would be 4 to 6 kt. The Indian government announced the yield for 1974 as 8 to 12 kt; however, there have been reports that the actual yield of the 1974 test was really less than 5 kt, and possibly as small as 2 kt.
The goal of the U.S. nuclear test program was to design the collapse chimney to assure no release of radioactive by-products of the explosion into the atmosphere. The optimal design is for the chimney to reach the surface and form a subsidence crater. Experience from the Nevada Test Site (NTS) led to the development of a scaling relation between depth of burial and optimal containment of radioactive gases:
where d is the depth of burial in meters and Y is the yield of the explosion in kilotons. In other words, at the NTS a 1 kt explosion would be buried 122 m, and it would be expected that a clear subsidence crater would be developed. The relationship in Equation (3) does depend on rock type. However, rock type, and consequent rock strength, influence the depth-of-burial relation, although only by a relatively small factor. When a test is designed, the device is buried at the maximum credible yield, which is larger than the expected yield.
The Indian government released a photograph of the crater formed by the 1974 explosion. In that photo it was possible to identify tension cracks, and therefore the crater was classified as a subsidence crater. BARC stated that the depth of burial for the 1974 event was 107 m. Using the U.S. depth-of-burial formula, the 1974 test implies a subkiloton size. Even allowing a factor of two adjustment for the strength of materials at the Pokharan test site, the announced depth of burial and subsequent crater indicate a yield of < 5 kt. This is very consistent with the seismic estimates of the yield using the teleseismic mb determination of 4.9.
The Indian government released several photographs of the test areas for the May 11 explosions. At least one of the tests was accompanied by a subsidence crater; it is likely that this crater is associated with the largest of the tests on May 11. Assuming that the Indian scientists used the same depth-of-burial formula for 1998 as they did in 1974, one can infer that the seismic and crater estimates of yield for 1974 can be used to calibrate the 1998 explosion/yield relationship. Thus, the magnitude difference formulation (Equation 2) implies a total yield for May 11 of <12 kt. In summary, the seismic yield equation, character of subsidence crater, and comparison with the 1974 explosion all give a consistent value of yield of 10 to 15 kt.
We conducted two simple tests to look for multiple explosions within the waveforms of the May 11 event. First, we examined the teleseismic determination of mb as a function of azimuth. We took all values of mb reported in the USGS EDR (Earthquake Data Report) and looked for trends; if two explosions were separated by a kilometer the relative arrival times of the P waves would shift as function of azimuth. There should be two azimuthal ranges for which the interference is optimal and the magnitude is enhanced. We did not observe any coherent trend. This does not preclude separated explosions, but does limit the tempo-spatial distribution of sources to be a fraction of the period of the mb measurement (1 second). The second procedure we tried was a comparison of the May 11 waveforms with the 1974 waveforms at stations which recorded both. An examination of the EDR suggests that this comparison should be possible at approximately 10 stations. However, we could only make the comparison at one station, Yellowknife (YKA) in Canada. We deconvolved the 1974 waveform from the May 11 waveform and found a very high degree of similarity and no evidence for source multiplicity.
We performed two types of analysis to try and identify a signal from the May 13 events. First, we filtered the data in the frequency band of 5-15 Hz and then passed the data stream through a detection algorithm which triggered at a signal-to-noise ratio of 3 to 1. Although this procedure detected three Hindu Kush earthquakes, nothing was detected that could be have an explosion. Next we used the May 11 explosion as a filter and cross correlated it with the entire 12-hour NIL data stream. There were no windows with correlation coefficients which were large enough to signify a detection. Figure 3 shows a comparison of the time windows on May 11 and 13 which correspond to the expected seismic arrivals at NIL. The net result of the analysis is that there is no evidence of any explosions on May 13.
The null result can be used to place some constraints
on the size of the May 13 explosion. We calculated a mb (Lg) of 5.1 for
the May 11 event; assuming a signal-to-noise ratio of approximately 1000, the
detection capability at NIL for the Pokharan test site is mb (Lg) = 2.5.
Using the yield difference equation (Equation 2), the detection capability can
be expressed in terms of the yield of the May 11 event: Yield (May 11) / Yield
(May 13) = 1800. Conservatively, this implies that the yield of May 13 events
were at least three orders of magnitude smaller than the May 11 yield, or 10-15
tons.
It is possible to increase the maximum possible size of the May 13 events by
assuming that they were detonated in very porous (and dry) media (recall the
press reports that the event was detonated in a sand dune). This could increase
the allowable yield by an order of magnitude, or 100-150 tons. This yield is
still much smaller than the combined announced yield for the two explosions of
0.8 kt.
Two days later, on May 30, Pakistan announced that it had tested two warheads with yields of approximately 12 kt. The official announcement was later changed to read that Pakistan had tested a single nuclear weapon with a yield of 15-18 kt. Within a week of the May 30 test, the Pakistani government announced that it had completed its test program and no further explosions were planned.
Unlike the Indian test site, there is a level of background seismicity in the Chagai Hills area. Because of the monitoring interest in the area, several of these earthquakes have been studied; two of the earthquakes (December 4, 1997, and January 5, 1998) were relocated by the PIDC using all available teleseismic arrivals and are listed as calibration events (the locations in Figures 4 and 6 are labeled CEB, or "calibration event bulletin"). We used the teleseismic arrivals for the CEB events and the explosions on May 28 and 30 to perform Joint Hypocenter Determinations (JHD) using the algorithm of Dewey (1983). The method simultaneously calculates all the hypocenters relative to a reference event; we chose the December 4, 1997 CEB event as the reference. Three of the events were recorded at the same 22 seismic stations located at teleseismic distances ; the May 30 explosion was recorded at 21 of the 22 stations. These stations provide good azimuthal coverage . The JHD locations (white stars, Figures 4 and 6) clearly indicate that the May 28 and May 30 explosions were located at distinct test sites separated by about 100 km. Figure 6 shows an enlargement of the May 28 test region. The contours on the map are spaced at 500 m, and it is apparent that the JHD location is on the face of a steep mountain. This observation is consistent with statements by Pakistani officials that indicate that the test occurred in a horizontal rather than a vertical shaft. Subsequent satellite photos shown in various press accounts indicate that the tunnel adit may have been on the south side of the hill within the JHD error ellipse. Perhaps the first recognition that the tunnel was on the south side of the hill was by Frank Pabian: he correlated the time of day with the broadcast images of the tunnel to draw the conclusion that the tunnel entrance was located on the southern side of the Koh Kamaran massif. Subsequently, Pabian provided the following information on the geology of the area: "The mountainous area , identified as the Koh Kambaran massif, rises to a maximum elevation of 2700 meters east and north of the Rayo (seasonal) river valley. It consists of intrusive diorites and syenites of the Post-Paleocene and Pre-middle Eocene Ras Koh formation. These have intruded through the older Cretaceous Kuchakki volcanic group. The Kuchakki formation, in turn lies conformably against the younger Paleocene Rakhshani formation (consisting of shales, limestones, sandstones, and volcanic sediments) on the southeast, and faulted against the same Kuchakki formation. The Kuchakki formation that is situated on this faulted side is also intruded by a wedge of ultabasic rocks of the Bunap formation. A number of old chromite mines are located within the Bunap formation. The geology and the associated steep mountainous terrain of the Ras Koh massive are indicative of very hard rock of substantial thickness."
The USGS reported a mb of 4.8 for the May 30 test. The Chagai Hills region appears to have a slight attenuation bias compared to the Indian test site, and a more appropriate formula for the yield relation is:
This gives a seismic yield of approximately 9 kt. Applying the same uncertainty used in the Indian analysis our estimate of the yield of the May 28 explosion is 9-12 kt.
The seismic waveforms for the May 28 explosion appear much more complex than those from the Indian explosion. Even at teleseismic distances the P wave does not appear simple, and many stations have a significant coda which lasts approximately 25 seconds . This complexity may be the result of source multiplicity, although there are several other possible explanations including scattering from the complex topography in the source region. We attempted to use the waveforms from the May 30 explosion (described below) to isolate source multiplicity within the May 28 waveform. We were able to find a second "event" in the coda, but it was delayed by 22 seconds from the first P wave. This would seem to be a highly unlikely multiple explosion scenario, and so the significance of this event was discounted.
The PIDC reported a magnitude for both the May 28 and May 30 events, which makes it possible to use the magnitude difference to derive a yield. The delta mb = -0.2, which translates to the May 30 event being a factor of ~1.9 smaller than the May 28 explosion (in other words, a yield of 4-6 kt). The difference in emplacement procedures between the two tests may introduce some error. However, experience at NTS, where it is possible to make many comparisons between tunnel and vertical shaft events, indicates that the yield relationship should not change much.
As discussed earlier, the May 30 explosion shows some seismic waveform complexity at regional distances. The apparent simplicity of the source of the May 30 event (a single announced explosion of 15 to 18 kt) cast doubt on interpreting the waveform complexity of May 28 in terms of multiple sources. At this time it is not known if the May 30 test created a crater, or whether such a crater was of the throw-out or subsidence type.
The May 11 India test had a seismic yield of 10-15 kt. This is a factor of 4 smaller than that announced by the Indian government, and there have been several attempts to explain the discrepancy. In June the Bhabha Atomic Research Center (BARC) released their own analysis. They state that "an elaborate analysis, now completed, gives an mb of 5.4. This means that our earlier quoted yield values perhaps were underestimates. It may be noted that the USGS average estimate is 5.4, which corresponds to a yield of 65 kt." In actuality, the USGS magnitude is 5.2, but the larger issue is how BARC arrived at the yield of 65 kt. It turns out this is what would be expected at NTS for a similar explosion where the yield relation is given by:
However, it is clear from the frequency content of the teleseismic P waves from the Pokharan test site that it is not a region of high attenuation. Further, the explosions appear to be well coupled. The reports of a combined yield of 0.8 kt for the May 13 test is even more perplexing. Even if the yield relationship for NTS is used, the expected mb would be 3.88. This would produce a signal at NIL which would be at least a factor of 50 times larger than the noise. If the test were indeed detonated in a sand dune, seismic waves could be reduced, but the expected mb would still be larger than 3.0.
The Pakistan test of May 28 had a seismic yield determination of 9-12 kt. As with the Indian tests, this yield appears to be much smaller than the official announcement of 40-45 kt. The seismic yield of the May 30 event is 4-6 kt; again this is smaller than the official announcement.
The May nuclear tests are not the first time that seismological results have been at odds with government statements. However, it is the first time that seismologists have said that the yields are smaller than announced by the government conducting the test. Although the seismic analysis presents a consistent picture, it is not definitive. It is always possible to construct arguments about coupling that would reduce the seismic efficiency. On the other hand, the seismic yields provide invaluable constraints on the nature of the weapons tested. For example, conventional wisdom states that 10-15 kt would be too small to have been a full test of a thermonuclear weapon.
In the future the International Monitoring System will grow to a larger number of seismic stations. In addition, plans by various organizations, such as IRIS, and individual nations' networks will lead to hundreds of very high quality seismic stations which will be available on the Internet within the next few years. This global, real-time monitoring system will add a new dimension to discouraging clandestine nuclear testing stations.