Seismic Source Size and Yield for Nuclear Explosions

Abstract

The relationship between the seismic size of a nuclear explosion and yield has been an important factor in test ban negotiations since these began in 1958. Initially the interest was in the short-period magnitude/yield relationship which was required so that estimates could be made for any given area, of the number of earthquakes that could be expected to occur each year with magnitude equal to or greater than that of an explosion of some chosen yield. The first magnitude-yield relationship was based on the results from a series of chemical explosions and one underground nuclear explosion, Rainier, fired at the Nevada Test Site, USA. The relationship is referred to as the Rainier law. Observations from a further series of explosions — the Hardtack II series — suggested however, that the Rainier law is wrong. Disagreements over what was the correct magnitude/yield relationship to use was one of the factors that led to the abandonment of the early talks on a Comprehensive Test Ban Treaty (CTBT).

Since the early discussions the arguments on the relationship of seismic source size and yield have continued. The relationship assumed particular importance when the US and USSR agreed in the bilateral Threshold Test Ban Treaty (TTBT) on 3 July 1974 that the yields of underground nuclear weapon tests after 31 March 1976 would not exceed 150 kt. For, although by March 1976 the treaty had not been ratified by the US Senate, both the US and USSR separately stated their intention to abide by the Treaty.

To verify compliance with the TTBT both sides had to devise ways of estimating the yield of explosions at the other’s test sites. To assist with the process the Treaty contains provisions for exchanging test site information and yields of calibration explosions but this exchange could only take place after ratification by the two sides. As, by 1976, the Treaty was not ratified seismologists had to devise ways of verifying compliance without test site or calibration data. As it has turned out, the treaty was only ratified in 1990 after the inclusion of a new protocol. The protocol was only negotiated after the Joint Verification Experiments (JVEs) where each party was given access to the other’s test site to make hydrodynamic measurements close to one test to verify its yield. One reason why the JVEs were carried out and the treaty amended was that on the magnitude/yield relationship based on US experience at the NTS, the USSR appeared to be testing at yields greater than 150 kt. Thus again uncertainties in the magnitude/yield relationship hampered agreements to limit nuclear testing.

Techniques now exist for estimating seismic source size in absolute terms (eg seismic moment) at least for large sources. In general this would be the ideal way of measuring the seismic size of explosions. Nevertheless, the seismic magnitude has been used almost exclusively for the estimation of explosion yield. In principle the determination of magnitude/yield relationships is straightforward given the magnitude of explosions of known yield. The number of explosions for which yields have been published however, is small and most of these are NTS explosions. Three magnitude scales have been used in studies of the magnitude/yield relationships: the body wave magnitude (m _b ); the surface wave magnitude (M _S ); and the body wave magnitude m _b (Lg), estimated indirectly from the short period surface wave Lg.

Initial studies were principally on m _b /yield. However, discrimination studies showed that for a given M _S , m _b for explosions at NTS is 0.3–0.4 magnitude units (m.u.) lower than m _b for USSR explosions. Further, it appears that M _S is less sensitive to differences in firing medium and test site structure than m _b . M _S is effectively an unbiased measure of yield. If this is so the m _b /yield relationship for NTS must be different from that for the main test sites in the USSR. Several reasons have been suggested for this but the most widely accepted explanation is that the anelastic attenuation under the NTS is greater than at other test sites. The apparent differences in the m _b /yield curves for the NTS and other test sites has become known as “NTS bias”.

There was much argument particularly in the US about the size of the bias and many experiments to estimate it were devised. For example magnitude corrections for stations situated in the western US (which includes the NTS) were compared to those in eastern US (where the crust and upper mantle structure is thought to be similar to that at the main USSR test site at Shagan River, E Kazakhstan, STS). These studies showed differences between the two areas ranging from around 0.1 to about 0.3 m.u. The figure of 0.30–0.40 m.u. seems only to have been widely accepted after the publication of studies by Nuttli on the use of m _b (Lg) for yield estimation. Like M _S , m _b (Lg) turns out to be insensitive to test site structure. The work showed for NTS explosions that m _b (Lg) is 0.31 m.u. greater than m _b determined from P and for STS explosions m _b (Lg)-m _b is 0.04 m.u. implying an overall bias between the NTS and the STS of around 0.35 m.u. More recently m _b (Lg) has been used to study variations in the bias in m _b within test site. The evidence is that m _b (Lg) is the magnitude least sensitive to test site structure and thus the most reliable for determining at least relative yields.

The presence of bias was finally confirmed by the JVEs. For the first of these experiments scientists from the USSR visited the NTS to make hydrodynamic measurements on the underground nuclear explosion Kearsage (17 August 1988) to verify its yield. In the second experiment scientists from the USA made similar measurements for the explosion of 14 September 1988 at the STS. The yields of the explosions used in the JVEs have not yet been published but they were required to be in the range 100–150 kt. Based on the assumption that the yield of the JVEs were indeed in the required range, the NTS bias using data from the experiments is in agreement with earlier estimates.

The JVEs show that the NTS bias estimated by seismologists from long range is essentially correct. However, because of the scatter in magnitudes the uncertainties in yield estimates particularly from m _b is significant: usually quoted as a factor of 2. The US thus asked that the TTBT be revised and a new protocol on verification be added to the treaty to improve the reliability of yield estimates. This was agreed to by the USSR and the revised treaty was finally ratified by the US on the 12 December 1990 over 16 years after the agreement was first signed.

The protocol to the TTBT that was signed in 1990 allows the advantages of estimating reliable relative yields from Lg to be exploited. Thus the verifying party has the right to make seismological recordings from explosions with yields of 50 kt or greater at Designated Seismic Stations (DSSs) within the territory of the testing party. In the US the DSSs are: Tulsa (TUL), Oklahoma; Black Hills (RSSD), South Dakota; and Newport (NEW), Washington. In the USSR the stations are Arti (ARU); Novosibursk (NVS); and Obninsk (OBN). These stations are at regional distances from the test sites they are intended to monitor, so Lg should be well recorded from explosions with yields around the 150 kt threshold. With such recordings reliable relative yields should be obtainable. The protocol also provides for hydrodynamic measurements of yield to be made by the verifying party again for explosions with yields of 50 kt and greater. Given a few hydrodynamic yield estimates the m _b (Lg)/yield relationship could be calibrated.

With the strong possibility of a CTBT being negotiated in the next year or two the TTBT looks as though it will be superseded. The estimation of yield for treaty verification will thus no longer be required. The principal interest in future for magnitude/yield is to derive maps that show the yield which can be detected and identified by a monitoring network as a function of position. The research that has been done on monitoring the TTBT makes this now feasible although it appears no such maps have yet been produced.