Chapter 7

Estimating the Yields ofNuclear Explosions

CONTENTS

PageIntroduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...........113Measuring the Size of Seismic Signals.. . ............................113Determining Explosive Yield From Seismic Magnitude . ...............115Sources of Uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...........,.116Bias Correction for Soviet Nuclear Explosions. . . . . . . . . . . . . . . . . . . . . ...117Reducing Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..............120

Random Uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ... ... ... ..120Systematic Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .........,122

Yield Estimation Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..122Soviet Test Practices and Test Ban Compliance . . . . . . . . . . . . . . . . . . . . ..124

BoxBox Page7-A. Calculations of the Six Largest East Kazakhstan Explosions.

By Sykes et al., Based on Unclassified Data . ....................124

FiguresFigure No. Page7-l. Computation of P-Wave Magnitude . . . . . . . . . . . . . . . . . . . . . . .......1147-2. Explosions in Granite . . . . . . . . . . . . . . . . . . . . . . . . .................1157-3. Yield Data From the Nevada Test Site . . . . . . . . . . . . . . . . . . . . .. ....1167-4. Yield Estimate Distribution . . . . . . . . . . . . . . . . . . . . . ...............1167-5. Schematic Illustration of Attenuation-Related Magnitude Bias .. ....1187-6. Comparisons of Explosions in Eurasia With Explosions in North

America. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..1197-7. Uncertainty in Yield Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . .......1217-8. mb Versus Time for Large Soviet Explosions . . . . . . . . . . . . . . . . . . . . .1257-9. U.S.S.R. Nuclear Tests 1966-86 According to Sykes and Davis .. ....126

Chapter 7

Estimating the Yields of Nuclear Explosions

For treaties that limit the testing of nuclear weapons below a specificthreshold, the yield of the explosion must also be measured.

INTRODUCTION

Once a seismic event has been detected andidentified as a nuclear explosion, the next stepis to estimate the yield of the explosion. Thisis particularly important for monitoring trea-ties that limit the testing of nuclear weaponsbelow a certain threshold. The process of esti-mating the yields of Soviet explosions involvesthree steps: 1) calculate the magnitude of theseismic signal; then, 2) make corrections to ad-just for the different geology at each test site;and finally, 3) convert the magnitude into ayield estimate.

The final yield measure describes the explo-sive energy of a nuclear explosion in terms ofkilotons, where 1 kiloton (kt) was originally de-fined as the explosive power equivalent to1,000 tons of TNT. This definition was foundto be imprecise,’ however, and so it was agreedin the United States during the Manhattanproject that the term “kiloton” would refer tothe release of 1012 calories of explosive energy.

1 kiloton = 1,000,000,000,000 = 1012 calories

While this convention is also followed in theSoviet Union, it does not necessarily mean that

*The definition is not precise for two reasons. First, there issome variation in the experimental and theoretical values ofthe explosive energy released by TNT (although the majorityof values lie in the range from 900 to 1,100 calories per gram).Second, the term “kiloton” could refer to a short kiloton (2x106

pounds), a metric kiloton (2.205x106 pounds), or a long kiloton(2.24x10 6 pounds).

the United States and the Soviet Union calcu-late explosive yields in the same way. Only thatpart of the total energy released in a nuclearexplosion that is immediately available (the so-called prompt energy release) is counted in theyield, and there does not appear to be any gen-erally accepted precise definition of what energyrelease time scale is considered “prompt.” Alsoa complication arises in determining the yieldof underground nuclear explosions due toenergy released by interaction of the neutronsfrom the explosive device with the surround-ing ground. Consequently, there might beslight differences in how the United States andthe Soviet Union measure yields.

Yields can be estimated not only throughseismic means, but also by other methods. Theother methods are based on analysis of the nu-clear byproducts of the explosion (radiochem-ical methods) or measurements of the speedof the shockwave generated by the explosionin the surrounding rock (hydrodynamic meth-ods). Neither radiochemical nor hydrodynamicmethods are currently used by the UnitedStates to measure routinely the yields of So-viet explosions because they require access tothe test site during the test, and in the caseof radiochemical methods, may require infor-mation about the weapon design that could re-veal sensitive information concerning the char-acteristics of the weapon.

MEASURING THE SIZE OF SEISMIC SIGNALS

At present, U.S. estimates of Soviet yields waves, Rayleigh waves, and Lg waves.2 Theare generally made using seismic waves re- various magnitudes are averages based oncorded at teleseismic distances (distancesgreater than 2,000 km). Seismic magnitudes 2A description of the various types of seismic waves is pre-can be determined from the ampl i tudes o f P sented in Chapter 3, The Role of Seismology.

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recordings at several stations. The magnitudesare then converted to explosive yields usingformulas developed through past experience.The formulas used are based on testing experi-ence at the Nevada test site and at the testsite operated in the Sahara by France in the1960s. The three magnitude measures mostoften used in yield estimation are: the P-wavemagnitude mb the surface wave magnitudeMs, and the Lg-wave magnitude mb(Lg).

The mb is computed from measurements ofP-wave recordings by the use of the formula

m b = log (A/T) + B.

As illustrated in figure 7-1, A is the largestP-wave amplitude in nanometers (0.000000001meters) measured peak-to-peak from a seismicshort-period recording during the first few se-conds of the P wave and correcting it for theinstrument magnification, T is the duration ofone cycle of the wave in seconds near the pointon the record where the amplitude was meas-ured (for P waves the period is typically 0.5to 1.5 seconds), and B is a distance-dependentcorrection term that compensates for the changeof P-wave amplitudes with distance.

The surface wave magnitude is determinedby measuring the Rayleigh-wave amplitudenear the point where the dominant period ofthe wave is nearest to 20 seconds on long-period vertical component records. The for-mula used is

Figure 7-1.–Computation of P-Wave Magnitude

A

s e c o n d so 1 2 3 4 5

Measurement made on P waves to obtain the magnitude ofa seismic event. The peak-to-peak amplitude (A) in the firstfew seconds of the P wave is corrected for the instrumentmagnification at the dominant period T.

Ms = log (A/T) + D,

where A and T are the amplitude and theperiod measured off long-period vertical com-ponent seismic recordings, again in nanometersand seconds, and D is a distance-dependent cor-rection term for Rayleigh waves.

The magnitude measure derived from meas-urements of Lg waves is computed from theformula

mb (Lg) = 5.0 + log [A(10km)/110],where A( 10 km) is the maximum sustained am-plitude of Lg on short-period vertical recordsin nanometers extrapolated backwards to a dis-tance 10 km from the source by dividing bythe geometrical spreading factor of d-5/6, whered is the source-to-receiver distance, and by theestimated attenuation along the path. The em-pirical mb(Lg) v. log Yield (Y) relationship alsoincludes a small second-order term, givingmb(Lg) = 3.943 + 1.124 log Y -0.0829 (log Y)2

for explosions in water saturated rocks suchas those at the Nevada Test Site.

The mb magnitude is routinely used at tele-seismic distances for yield estimation becauseP waves are detectable at large distances, evenfor small seismic events. This measure canalmost always be obtained for any seismicevent that is detected. The measurement ofMs requires a larger event, because Rayleighwaves are small for nuclear explosions. For ex-plosions below 50 kt, Ms may be missed al-together at teleseismic distances. The Lg am-plitude is similarly weak for small explosions.Consequently, it maybe important for seismicstations to be close to the explosion if surfacewaves and Lg waves are to be used for yield esti-mation of explosions less than 50 kt. This is oneof the reasons why seismic stations within theterritories of the treaty participants are desira-ble. The distance correction factors can be quitevariable regionally, and hence, some of themagnitude-yield relationships will need to beadjusted for different regions.

In addition to the conventional surface wavemagnitude Ms, a new measure of sourcestrength for surface waves is coming into wide

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use. Called seismic moment (MO), it is an esti-mate of the strength of a compressional (ex-plosion-like) force at the explosion site. Seis-mic moment gives a direct description of theforce system, acting in the Earth, that wouldmake seismic waves of the size and shape ac-tually recorded. The advantage of using seis-mic moment is that the computation can cor-rect for the estimated effects of contaminationof the seismic signals due to earthquake-likemotion triggered by the explosion. This is use-ful because nuclear explosions often releasestress that has been built up in the area of the

explosion by geological processes. The releaseof built-up stress by the explosion creates asurface wave pattern similar to that observedfor earthquakes, which is seen superimposedon the signals of the explosion. Characteris-tics of an earthquake, such as Love waves andreversed polarities in the Rayleigh waves, areoften observed from a nuclear explosion, in-dicating release of pm-existing stress. If notremoved, this release of natural stress by theexplosion, called tectonic release, can distortyield estimates obtained from conventionalMs.

DETERMINING EXPLOSIVE YIELD FROM SEISMICMAGNITUDE

Once the seismic magnitude measurementshave been made, the next step is to relate themagnitude measurements to the yield of theexplosion. Because we know the actual yieldsonly of U.S. tests and some French nuclear ex-plosions (the Soviets have announced yieldsonly for a few of their tests), our knowledgeis based on data other than Soviet data. Theactual data used to derive this relationship areshown in figure 7-2. The relationship betweenthe yield of a nuclear explosion and the meas-

Figure 7-2.—Explosions in Granite

I

4.0

I

Yield (kt)

Data for explosions in granite from which the magnitude v.yield equation is derived.SOURCE: Modified from Air Force Technical Application Center.

ured seismic magnitude can be described usingan equation of the general form

M = A + B log Y + Bias Correction

where M is a magnitude measure (or moment)from surface waves, body waves, or Lg waves,A and B are constants that depend on whichmagnitude measure is used, and Y is the yieldin kilotons. The specific constants used by theUnited States for these calculations are clas-sified. The “Bias Correction” term is an ad-justment made to correct for the differencesin how efficiently seismic waves travel fromthe various test sites. This correction is par-ticularly important for mb, because short-period body waves are strongly affected by thephysical state (especially temperature) of themedium through which they travel.

The empirical magnitude-yield relationshipsfor mb that are used to estimate yields at in-accessible test sites in the U.S.S.R. and else-where have been revised several times duringthe last two decades. These revisions were im-provements in yield formulas and computa-tional procedures to correct for such problemsas difficulties in merging magnitude sets fromdifferent station configurations and instru-ments, clipping (limiting the maximum record-able amplitudes) of large signals by the record-ing systems, and not correctly accounting for

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differences in the geology at different test sites.The early magnitude-yield formulas were basedon the simplifying assumption that all nuclearexplosions in granite at any site follow a simple

linear relationship between mb and log(yield).After the factors listed above were properlyconsidered, however, it became obvious thatbias corrections for each test site were needed.

SOURCES OF UNCERTAINTY

Under the ideal conditions of a perfectly uni-form and symmetrical Earth, it would be pos-sible to estimate yields of nuclear explosionsat any site from measurements at a singleseismic station. In practice, however, seismicmagnitudes and magnitude-yield plots showscatter. Using data from the InternationalSeismological Centre3 as an example, individ-ual mb measurements typically have a stand-ard deviation of 0.3 to 0.4 magnitude units be-fore station corrections are applied. Whenstation corrections are applied, the standarddeviation is reduced to 0.1 to 0.15 units. Fig-ure 7-3 illustrates typical scatter in a magni-tude-yield plot.

‘The International Seismological Centre is an organizationbased in England that gathers data for the research commu-nity from thousands of seismic stations operated all over theglobe.

Figure 7-3.— Yield Data From the Nevada Test Site

7 . 0

6.0

5.0

4.0

Yield (kt)

Mb versus yield for explosions at the Nevada Test Site. Thescatter is characteristic of yield measurements when onlyP-wave magnitudes are used.SOURCE: Modified from Air Force Technical Applications Center.

One reason for this variation is the small-scale geologic contrasts in the Earth that causefocusing and scattering of seismic waves. Fo-cusing effects near the recording seismometerscan create differences in estimated magnitudeseven when the stations are closely spaced.Focusing effects near the explosion can causebroad regional variations of seismic amplitudesso that seismic observatories over whole con-tinents may observe higher or lower averageamplitudes than the global average. Fortu-nately, the uncertainty introduced by focusingeffects can be reduced by averaging measure-ments from numerous stations if the stationsare well distributed around the test sites inboth distance and direction.

In addition to the scatter due to focusing,geological structures under individual stationsmay amplify seismic waves. Such effects may

Figure 7-4. —Yield Estimate Distribution

95% oftotal area

—

o 75 150 225 300 375

Yield estimate. in kilotons

50 % of

Yield estimate, in kilotons

Probability of yield estimates for a 150 kt explosion meas-ured with a factor-of-2 uncertainty.

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be corrected for by applying statistically de-rived station corrections that compensate forany such local effects.

After averaging many measurements andapplying appropriate corrections, estimates ofthe yield of a nuclear explosion are expectedto be distributed about the “true” value in themanner indicated in figure 7-4. The horizontalaxis in this figure is the yield estimate whilethe vertical axis is the probability that the esti-mate is correct. The area under the curve be-tween 2 yield values represents the probabil-ity that the actual yield is in this interval (thepercentage chance is 100 times the probabil-ity and the total area under the curve is 1, giv-ing a 100 percent chance that some value ofmagnitude will be measured). This figure showsthat it is most likely that the central yield value(150 kt in this case) will be close to the actualvalue and that outcomes become increasinglyless likely the larger the difference between theestimated value and the central value (see chap-ter 2 for a more detailed discussion of uncer-tainty and what it represents). The yield dis-tribution is asymmetric due to the normaldistribution of mb and the logarithmic rela-tionship between the yield of the explosion andthe measured seismic magnitude. Figure 7-3

is a typical empirical magnitude-yield curveobtained from actual data at the Nevada testsite that shows the measurements do not fol-low a single line but scatter around it becauseof measurement errors and variations in rockssurrounding the explosions.

Some of the uncertainty described above isdue to variations in how well explosions arecoupled to the surrounding rock. Also, explo-sion depth can influence the amplitudes of theseismic waves emitted, as can variations in thephysical properties of the Earth. For inacces-sible test sites, these effects result in increaseduncertainty in estimating yields. However, ifdata were exchanged and calibration shots per-formed, corrections could be made that wouldgreatly reduce the uncertainty. Nevertheless,there will always be some uncertainty in esti-mates of the yields of Soviet explosions, as inestimates of any physical quantity. This is notunique to seismology. Some uncertainty willexist no matter what type of measurement sys-tem is used. Such uncertainty should not nec-essarily be considered to represent opportuni-ties for cheating. Chapter 2 discusses themeaning of the various uncertainties and theirimplications for cheating.

BIAS CORRECTION FOR SOVIET NUCLEAR EXPLOSIONS

In estimating the yields of Soviet explosions,a major concern is how well the magnitude-yield formula for U.S. tests can be applied toSoviet test sites. Geophysical research hasshown that seismic P waves traveling throughthe Earth’s mantle under the main U.S. testsite in Nevada (and many other areas of theworld as well) are severely attenuated whencompared to most other continental areas,especially those with no history of recent platetectonic movements. If not corrected for, thisattenuation will cause a sizable systematic er-ror in estimates of the yield of Soviet ex-plosions.

The apparent reason for this attenuation isthe high temperature in the upper mantle un-

der Nevada and many other tectonically ac-tive regions. Regions of high temperatureschange the elastic and absorptive propertiesof the rocks, causing a large loss in the ampli-tudes of seismic waves traveling through them.Similar phenomena are thought to occur un-der the French test sites in Algeria and thePacific, though not under either the Soviet testsites in Kazakh and Novaya Zemlya or the U.S.test sites in Mississippi and Amchitka. If theP-wave magnitudes observed from U.S. testsin Nevada are used as a basis for estimatingyields, most Soviet explosions which have beenexploded in areas where the upper mantle iscool and there is little attenuation of P waveswill appear considerably larger than they ac-tually are.

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The evidence for such attenuation effectscomes from many studies, including:

●

●

●

●

comparisons of P-wave amplitudes ob-served at the Nevada test site with obser-vations made at other sites in areas un-derlain by colder mantle;studies of short period S-wave amplitudes,which are very sensitive measures of man-tle temperature variations;studies of the frequency content of bothP and S waves, i.e., the relative loss of highfrequency energy in waves travelingthrough the upper mantle in both direc-tions under Nevada; andstudies of P- and S-wave velocities, which

In addition, there is a large amount of inde-pendent geophysical evidence supporting thenotion of anomalously high temperatures un-der most of the western United States. Thisevidence includes:

●

●

●

measurements of anomalously high heatflow,measurements of electrical conductivity,andthe low velocity P waves (Pn) and the ab-sence of S waves (Sn) that propagate justunder the Earth’s crust.

These “symptoms” of high attenuation havebeen observed in many other areas of the worldand are recognized as such by most geophysi-

are also influenced by temperature. cists. The sketch in figure 7-5 illustrates how

Figure 7-5.—Schematic Illustration of Attenuation. Related Magnitude Bias

Signal from Signal fromSoviet test U.S. test

Soviet Union’stest site

Us.test site

Seismic body waves crossing parts of the upper mantle with high temperatures become anonymously reduced in amplitude.Seismic signals from the Soviet Union’s test site appear much larger than signals from an identical explosion conducted atthe U.S. test site.

SOURCE: Modified from Defense Advanced Research Projects Agency.

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this attenuation is created in the Earth andaffects estimates of the size of the wave source.Seismic body waves crossing the hatched highattenuation zones in the upper mantle are re-duced in amplitude and high frequency com-ponents of wave motion relative to waves thatbypass such zones.

Magnitudes derived from Rayleigh wavesand Lg waves are less influenced by tempera-ture variations in the mantle because theytravel along the surface and largely bypass thehigh attenuation zones in the upper mantle.A plot of P-wave magnitudes (rob) against sur-face wave magnitudes (Ms) should, therefore,show the attenuation of P waves relative tosurface waves. By plotting the Ms - mb ratioof explosions for different test areas, the at-tenuation indifferent regions can be compared.Figure 7-6 shows the results of an early studythat compared the Ms - mb for explosions inEurasia with the Ms - mb for explosions inNorth America. It can be seen that the twogroups are offset, with explosions of the sameMs value having lower mb values in NorthAmerica than in Eurasia. Results like this ledto early speculation about the existence of highattenuation zones in the upper mantle.

In general, if the P-wave magnitudes areplotted against the Rayleigh or Lg magni-tudes for the Nevada and Soviet test sites, the2 sets of data are offset by about 0.3 to 0.4magnitude units (or an amplitude factor ofabout 2 for P waves).4 The most likely expla-nation for this offset is the reduction of P-wavemagnitudes due to attenuation at the Nevadatest site. Such data constitute additional sup-port for the idea of an attenuation bias for Pwaves. Offsets can also be brought about byother factors such as contamination of the MS

measurement by tectonic release. However,such contamination can be detected by thestrong Love waves the release generates, and

“See for example P. Il. Marshall and P. W. Basham, “Dis-crimination Between Earthquakes and Underground ExplosionsEmploying an Improved M. Scale, ” GeophysicaZJoumal of thelibyzdAstronomicaJ Soa”ety, vol. 28, pp. 431-458,1972, and OttoW. Nuttli, “L~ Magnitudes of Selected East Kazakhstan Un-derground Explosions, ” BulZetin of the Seismological Societyof Ame~”ca, vol. 76, No, 5, pp. 1241-1252, October 1986.

Figure 7-6.—Comparisons of Explosions in EurasiaWith Explosions in North America

7.0

6.0

5.0

I I 1 I3.0 4.0 5.0 6.0

M s

Explosions

● Eurasia o North America

Explosions with the same MS value have lower mb values inNorth American than in Eurasia. This led to early specula-tion about the existence of high attenuation zones in theupper mantle.

SOURCE: Modified from P.D. Marshall and P.W. Basham, Geophysical Journalof the Royal Astronomical Society, 1972, vol. 28, pp. 431-458.

reduced by using seismic moment instead ofsurface wave magnitude (Ms) for yield esti-mation.

Various government-supported scientificpanels of seismologists, after considering thetotality of the geophysical evidence, haverepeatedly recommended during the last dec-ade that U.S. yield estimates of Soviet explo-sions be reduced by subtracting a larger “BiasCorrection” term from the magnitudes to ac-count for the attenuation effect on mb. As aresult, the bias correction has been increasedon several occasions over the last decade asnew scientific evidence indicated that suchchanges are appropriate.

The size of the bias correction was deter-mined simply by averaging the correction in-ferred from a number of independent or semi-independent estimates of the attenuation ef-fect made by different researchers. Most evi-dence for an attenuation “bias” has been in-direct thus far, although the evidence from

76-584 0 - 88 : QL 3 - 5

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global seismic studies and seismological experi-ence gives strong support to the idea. Moredirect measurements of this bias may soon be-come available. The United States and SovietUnion have recently agreed on experiments tocalibrate seismic yield estimation methodsthrough measurements at each others testsites. Explosions will be measured with seis-mic methods and the yields confirmed inde-pendently by hydrodynamic methods. In addi-tion, several seismic stations have been set uprecently in the Soviet Union near the Kazakhtest site by a group of U.S. scientists supportedthrough the Natural Resources Defense Coun-

cil. Data from these stations will help improveestimates of the bias correction and assess theefficiency of seismic wave propagation at highfrequencies to regional distances.

The bias correction is currently used as a sim-ple, yield-independent adjustment to the in-tercept, A, in the rob-log Y curve. The valuecurrently used by the U.S. Government is in-tended to be the most appropriate value foryields near the 150 kt threshold of the 1974Threshold Test Ban Treaty. A different biasmay be appropriate for yields that are eithermuch larger or much smaller.

REDUCING UNCERTAINTIESThe estimated yield of an underground of nu-

clear explosion, like any quantity derived frommeasurements, has some error associated withit. The error comes from a variety of sources.Some of the error is considered to be randomin that it varies unpredictably from one meas-urement to another. Other errors are not ran-dom but are systematic. Systematic errors arethose that always act in the same way, for ex-ample, the bias between test sites. If system-atic errors are understood, corrections can bemade to reduce or eliminate the error.

The distinction between random and system-atic errors, however, has no clear boundary.If everything about the Earth and seismicwaves were known, almost all errors in seis-mology would be systematic. In general, ran-dom errors usually turn out to be systematicerrors once the reason for the error is under-stood. However, if the systematic errors arenot understood, or if there are lots of system-atic errors all operating indifferent ways, thenthe systematic errors are often approximatedas random error. In such cases, random uncer-tainties are inflated to encompass the unex-plained systematic uncertainties.5

‘As discussed in Chapter 2, random errors do not provide op-portunities for cheating. However, if systematic errors are foundto be 1) of sufficient size, 2) usable for an advantage by one side,and 3) unrecognized as being systematic by the other side, thensuch errors can be exploited under some situations. A treatyshould, therefore, contain provisions to reduce the uncertaintyof yield estimates and counter evasion opportunities.

Random Uncertainty

Different methods of yield estimation havedifferent accuracies and uncertainties. At theNevada test site, the most precise method usesP-wave magnitudes (rob). Less precise meth-ods use Lg waves (mb(Lg)), surface waves (MS),

Ms)and seismic moment ( At the Nevada testsite, yields estimated from mb alone have arandom uncertainty factor of 1.45 at the 95percent confidence level, whereas those frommb(Lg) have an uncertainty factor of 1.74, andthose from Mo have an uncertainty factor of2.13.

Recently, the Defense Advanced ResearchProjects Agency (DARPA) has been able toreduce the random uncertainty in seismic yieldestimates at the Nevada test site by combin-ing measurements made by the three differ-ent methods. Scientists have shown, usingdata from U.S. explosions at the Nevada testsite, that the random errors of the three typesof magnitude measures for a given event canbe considered statistically independent. Con-sequently, an improvement in the accuracy ofyield estimates can be achieved by combiningseveral methods to produce a “unified” mag-nitude measure. By forming a weighted aver-age of the three magnitudes, a “unified seis-mic magnitude” with an uncertainty factor of1.33 (figure 7-7) has been derived. Most seis-mologists believe that if this method were now

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Figure 7-7.—Uncertainty

6.2

5.4

1.74

in Yield Estimates

/100 200 300400

/2.13

Yield (kt)

95%Factor

1.33

1 I100 200300400

Yield (kt)

Uncertainty in yield estimates can be greatly reduced through the use of a unified seismic yield estimate. On the left are threeplots of mb, mb(Lg), and MO versus yield at the Nevada Test Site. On the right is a similar plot of the unified seismic yield esti-mate versus the actual yields. The 95 percent uncertainty factors are shown to the right of each plot.SOURCE: Modified from Defense Advanced Research Projects Agency.

applied to estimating yields at the Soviet testsite in Eastern Kazakh, the uncertainty wouldbe reduced to a factor of 1.6- 1.5 for explosionsaround 150 kilotons.6 What limits the uncer-tainty from being reduced to the level of the

‘Consider, as an example, the situation where there are 3 sta-tistically independent methods of calculating the yield of anexplosion, all of which (for the sake of this example) have a fac-tor of 2 uncertainty in a log normal distribution:

# of Methods Resulting Uncertainty1 2.02 1.63 1.5

By combining methods, the resulting uncertainty can be re-duced. This methodology, however, can only reduce the randomuncertainty. Systematic uncertainty such as differences betweenthe test sites will remain and limit the extent to which the un-certainty can be reduced unless calibration is performed.

Nevada test site (a factor of 1.3) is the system-atic uncertainty or bias correction. As we willsee later, however, this systematic uncertaintycan be reduced through calibration shots.

The expected precision given above are onlyfor explosions where all waves are used for theestimation. For smaller explosions, the re-gional Rayleigh and L waves are not always

strong enough to travel the long distances re-quired to reach seismic stations outside the So-viet Union. Consequently, for monitoring low-yield explosions, stations within the SovietUnion may be necessary to obtain the improvedaccuracy of the “unified seismic yield” esti-mation method. The relationship between mag-nitude and yield for the stations within the So-viet Union will also have to be established.

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As noted above, the formulas derived fromthe Nevada test site data that describe the rela-tionships between yield and mb(Lg) and mo-ment MO are not directly applicable to the So-viet test site in Kazakh without some as yetunknown adjustments. The values of these ad-justments can be determined if stations areplaced within the Soviet Union and the Soviettest sites are calibrated. Test site calibrationssuitable for lower yields could only take placeafter an internal network is installed. If themb(Lg) and MO v. yield curves are suitablycalibrated, the absolute yields of explosionsat Kazakh should be measurable with the “uni-fied seismic method” just as accurately as atthe Nevada Test Site.

The above analysis applies only to explosionsat known test sites observed by a large set ofwell-distributed seismic stations for which theappropriate station corrections and bias cor-rection have been determined. The accuracywith which the yields of “off-site” nuclear testscould be estimated would be less than thatstated above. Therefore, to maintain high ac-curacy in yield estimation, nuclear testingshould be prohibited outside specified, cali-brated test sites.

Most yield estimation research has concen-trated on yields around 150 kt, so the accuracythat could be achieved by seismic methods atlower yields is not yet well known. In any fu-ture low threshold test ban treaty, it might beexpected that the initial uncertainties in yieldestimation for explosions below 10 kt wouldbe large. These uncertainties would then be re-duced as more data were gathered, as ourknowledge of wave propagation properties forvarious paths in the monitored regions was re-fined, and as calibration information was ob-tained.

Systematic Uncertainty

The yield estimation precision describedabove for teleseismic data are limited becauseof systematic uncertainties. As discussedabove, the systematic uncertainty can be re-duced by calibrating the test site. Calibratinga test site involves exploding devices whoseyields are either known or accurately deter-mined by independent means, and then meas-uring the magnitudes at a large number ofmonitoring stations. By doing so, the yieldsof other events can be determined by compar-ing the amplitudes of the seismic waves at com-mon seismic recording stations with thoseoriginating from the events with known yields.

This approach reduces the systematic uncer-tainties caused by having to estimate the vary-ing properties of the rocks surrounding theexplosion and any focusing effects near the ex-plosion sites. As long as these factors remainapproximately unchanged within a geologi-cally uniform area, the calibration improvesthe estimation of yields.

The sizes and numbers of geophysically dis-tinct subdivisions in any test site depend onthe geological structures of the area. A spe-cific calibration maybe valid only for a limitedarea around the shot if, at larger distances, therock properties and focusing effects change.The distances over which the relevant condi-tions change vary, depending on the local ge-ology. Testing areas that are large or containvarying geology would obviously need morecalibration shots than areas that are geologi-cally uniform. If calibration were performedat the Soviet test site, the expected seismicyield estimation capability would be compara-ble to the existing seismic capability at the Ne-vada Test Site.

YIELD ESTIMATION CAPABILITIES

In considering the capability of all methods is radiochemical methods. Radiochemical meth-of yield estimation, it must be kept in mind ods of yield estimation have an uncertainty ofthat it is never possible to determine a yield about 10 percent (a factor of 1.1). Also, experi-without some uncertainty. The standard against mental devices often detonate with yields thatwhich yield estimation methods are measured are slightly different from what was predicted.

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This uncertainty in predicted yield was recog-nized during the negotiations of the Thresh-old Test Ban Treaty and provisions were estab-lished for unintended breaches (see ch. 2).

The yields of Soviet underground explosionscan be seismically estimated with a much bet-ter capability than the factor-of-2 uncertaintythat is commonly reported.7 New seismic meth-ods have greatly improved yield estimation ca-pabilities. Further improvements would occurif the test sites were calibrated and, for smalltests, if stations were present within the So-viet Union during the calibration. The capa-bilities depending on these variables can besummarized as follows:

●

●

Without Calibration: For large explosions(above 50 kilotons) seismic yield estima-tion could be improved with the additionaluse of the other methods including: sur-face waves, Lg waves, and seismic mo-ment. Through such a combined method,it is estimated that without calibration So-viet yields can be seismically measuredwith present resources to a factor of 1.6to 1.5 uncertainty.With Calibration: Further reductions inthe uncertainty of yield estimates can beaccomplished if the Soviet test site werecalibrated. At a defined, well-calibratedSoviet test site, it is estimated that yieldscould be seismically measured with thesame factor of 1.3 uncertainty that isfound for seismic estimates at the Nevada

‘See, for example, VerifyingIVuclear TestingLim.itations: Pos-sible U.S.-Soviet Cooperation (Washington, DC: U.S. Depart-ment of State, Bureau of Public Affairs, Special Report No. 152,Aug. 14, 1986)

●

Test Site. In fact, Soviet seismologistshave told U.S. seismologists that they areable to estimate yields seismically at theirown test site with only a factor of 1.2 un-certainty.Small Explosions: For small explosions(below 50-kt), the regional seismic waves

may not always be strong enough to travellong distances to seismic stations outsidethe Soviet Union. Consequently, seismicstations within the Soviet Union may benecessary (in addition to calibration) to ob-tain the 1.3 factor of uncertainty fromcombined seismic methods for explosionwith yields below 50 kt. At yields below10 kt small variations of the physical envi-ronment may produce greater uncertainty.Therefore, at yields below 10 kt, the un-certainty may be inherently greater.

A 1.3 factor of uncertainty (for yields above50 kt) is the claimed capability of the hydro-dynamic yield estimation method using CORR-TEX data8 that has been proposed as an alter-native means for improving yield estimation.Consequently, hydrodynamic yield estimationwill not provide a significantly superior yieldestimation capability over what could be ob-tained through well-calibrated seismic means(also a 1.3 factor of uncertainty). Hydrody-namic yield estimation is, however, one of themethods that could be used to provide inde-pendent estimates of the yields of calibrationshots to improve seismic methods. Once a testsite was calibrated using hydrodynamic meth-ods, there would be no need to continue theuse of those intrusive methods.

‘See appendix, Hydrodynamic Methods of Yield Estimation.

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SOVIET TEST PRACTICES AND TEST BAN COMPLIANCESpecific concern over compliance with test 1. The mb of several Soviet tests at their

ban treaties has been heightened with findings Shagan River (E. Kazakhstan) test site areby the Reagan Administration that: significantly l arger than the mb for U.S.

Soviet nuclear testing activities for a num- tests with yields of 150 kt.ber of tests constitute a likely violation of the 2. The pattern of Soviet testing indicateslegal obligations under the Threshold Test that the yields of Soviet tests increasedBan Treaty.9 after the first 2 years of the treaty.

Such findings are presumably based on netassessments of all sources of data. In measur-ing yields near the 150 kt limit of the Thresh-old Test Ban Treaty, however, seismic evidenceis considered the most reliable basis for esti-mating the yields of Soviet underground nu-clear explosions.10 It is, therefore, the seismicevidence that has received particular attention.

Concern about whether the Soviet Union isactually restricting its testing to a maximumyield of 150 kt is motivated by two arguments:

“’The President’s Unclassified Report on Soviet Noncompli-ance with Arms Control Agreements, ” transmitted to the Con-gress Mar. 10, 1987.

Conclusion of the Defense Intelligence Agency Review Psnelas stated in a letter from Roger E. Batzel, Director of LawrenceLivermore National Laboratory to Senator CMbome Pen onFeb. 13, 1987.

The validity of the first argument is depen-dent on how the Soviet yields are calculated.Because of the uncertainty in measuring theyields of Soviet tests using only mb and be-cause of differences in opinion as to what thecorrect bias value for Soviet tests should be,there is disagreement as to whether the mb

values of the largest Soviet tests do, in fact,represent violations of the 150 kt limit of theThreshold Test Ban Treaty. For example, whencalculations such as those in table 7-1 are madeusing both mb and MS measurements and abias correction of 0.35, they indicate that thefew remaining yields estimated as above 150kt are well within the expected random scat-ter, and do not support claims of a violation.

The second argument is dependent on as-sumptions about probable Soviet behavior.Two years after the signing of the Threshold

Box 7-A.—Calculations of the Six Largest East Kazakhstan Explosions. By Sykes et al.,Based on Unclassified Data

6 Largest East Kazakhstan Explosions 1976-1986Yield from Yield averaged from

Date mb only mb & MS

23 June 79. . . . . . . . . . . . . . . . . . . . . . . . . . 152 14914 Sept 80 . . . . . . . . . . . . . . . . . . . . . . . . . . 150 150*27 Dec 81 . . . . . . . . . . . . . . . . . . . . . . . . . . 176 1614 July 82 . . . . . . . . . . . . . . . . . . , . . . . . . . . 158 158*14 July 84 . . . . . . . . . . . . . . . . . . . . . . . . . . 140 140*27 Oct 84. . . . . . . . . . . . . . . . . . . . . . . . . . . 140 140*

Average: 152.7 (± 13.4 kt) Average: 149.7 (± 8.8 kt)(*based on mb only; no Ms determined)All estimated yields are well within the uncertainty expected for observance of the 150 kt threshold limit.

SOURCE: Calculations of the six largest East Kazakhstan explosions made by Sykes et al., based on unclassified data. Body wave measure-ments from International Seismological Centre Bulletins and United States Geological Survey Reports. Station corrections deter-mined to be 0.02 to 0.04 from mean. Surface wave calculations made by Sykes et al. Calibration corrected for bias using a valueof 0.35 to make body wave data consistent with surface wave data.

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Test Ban Treaty, the size of the largest Sovietexplosions at their eastern Kazakh test siteincreased markedly (see figure 7-8).11 This in-crease has been interpreted by some to inferthat the Soviets have been violating the 150kt threshold limit in the later tests. The argu-ment assumes that the Soviets were testingup to the limit for the first 2 years and, there-fore, by inference, have been testing above thelimit in violation of the treaty ever since 1978.Alternate interpretations for this apparentyield increase have been offered. It has beenpointed out that a similar pattern of testingoccurred at Kazakh for the 2 years prior to thetreaty. It has also been speculated that thisincrease in yields may reflect a Soviet decisionto move their high yield testing from the NovayaZemlya test site to the Kazah test site.12 As

~There w= &IO speculation that this increase was coincidentwith a change in the U.S. official method of yield estimation.For example, Jack Anderson, “Can’t Tell If Russia Cheats OnTest Ban,” The Waslu”ngton Post, Aug. 10, 1982, p. C15.

‘*See for example, “Nuclear Test Yields” (Letter to the Edi-tor), J. F. Evemden and L. R. Sykes, Science, vol. 223, Feb. 17,1984, p. 642.

anon-technical consideration, it can be arguedthat if the Soviets had tested above the limitof the Threshold Test Ban Treaty at the Kazakhtest site, they would never have offered to al-low the United States to calibrate their testsite using CORRTEX and Soviet test explo-sions. The calibration will reduce the uncer-tainty of yield estimates, a reduction that ap-plies to past as well as future explosions andhence can provide more accurate evidence con-cerning past compliance.

Because of the statistical nature of all yieldestimates, the question of compliance can beaddressed best not by looking at individualtests but rather by examining the entire pat-tern of Soviet testing. It is particularly usefulto compare the testing programs of the UnitedStates and the Soviet Union. It can be seenfrom figure 7-9 that if a bias value lower than0.35 is used, there appears to have been about10 (out of over 200) Soviet tests since the sign-ing of the Threshold Test Ban Treaty in 1974with yield central values above the 150 ktthreshold limit. When the same method of yield

Figure 7-8.— mb Versus Time for Large Soviet Explosions

E

5.0 ‘

4.4 “ ‘

*o ● .

I I I I 1 I1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 198’1 1982 1983

. Kazakhstan O Novaya Zemlya

The m b versus time for all large Novaya Zemlya and Kazakhstan explosions. It can be seen that a large increase of the maxi-mum yield for explosions at the Eastern Kzazkh test site occurred about 2 years after the Threshold Test Ban Treaty was signed.

SOURCE: T.C. Bache, S.R. Bratt, and L.B. Bache, “P Wave Attenuation mb Bias, and The Threshold Test Ban Treaty,” SAIC-86-1647, submitted to AFGL, March 1966, p. 5.

126

Figure 7-9.—U.S.S.R. Nuclear Tests 1966-86 According to Sykes and Davis5,000

2,000

1,000

500

100

50

201966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985

● Kazakhstan O Novaya ZemlyaThese yields were calculated by combining P-wave and surface-wave magnitudes and using a bias correction of 0,35. Barsdenote the estimated standard deviations of the estimates. The few tests that do appear to have exceeded 150 kt are wellwithin the expected scatter. If a lower bias correction is applied and only P-wave determinations are used, then slightly higheryield estimates will result and additional central values will be greater than 150 kt.

SOURCE: Modified from L.R. Sykes and D.M. Davis, Scientific America, vol. 258, No. 1, January 1987, pp. 29-37.

estimation is applied to U.S. tests, approxi-mately the same number of U.S. tests also ap-pear to be above the 150 kt threshold limit.This, however, does not mean that one or theother or both countries have cheated; nor doesit defacto mean that seismology is an inade-quate method of yield estimation. It is inher-ent in any method of measurement that if bothcountries are testing up to the yield limit, theestimated yields of some tests will have cen-tral values above the yield limit. Because ofthe uncertainty of measurements using anymethod, it is expected that about half the So-viet tests at 150 kt would be measured asslightly above 150 kt and the other half wouldbe measured as slightly below 150 kt.

All of the estimates of Soviet tests are withinthe 90 percent confidence level that one wouldexpect if the yields were 150 kt or less. Exten-sive statistical studies have examined the dis-tribution of estimated yields of explosions atSoviet test sites. These studies have concludedthat the Soviets are observing a yield limit.The best estimate of that yield limit is thatit is consistent with compliance with the 150kt limit of the Threshold Test Ban Treaty .13

I$such gtatistic~ studies have been carried out extensivelyby Lawrence Livermore National Laboratory, The conclusionof these studies was reported in open testimony before the Sen-ate Armed Services Committee on Feb. 26, 1987 by Dr. MiloNordyke, Leader of the Treaty Verification Program.