Seismometric Estimates of Underground Nuclear Explosion Yields

FOA 4 Happort C 4464-26 Juni 1971

SEISMOMETRIC ESTIMATES OF UNDERGROUND NUCLEAR EXPLOSION YIELDS

U Ezdcsson

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FOA Repro Stockholm 1970 Försvarets forskningsanstalt FOA 4 rapport Avdelning 4 C 4464-26 Stockholm 80 Juni 1971

SEISMOMETRIC ESTIMATES OF UNDERGROUND NUCLEAR EXPLOSION YIELDS by Ulf Ericsson

Antal blad 84

FOA kostnadsnr: 473 A1 61

Nyckelordt Kärnladdningsexplosioner, seisroologi, detektering Nuclear explosions, seismology, detection

Rapporten utsänd till: UD/Pol IV (3 ex), Fst, FortF, FHS (2 ex), MHS, SkyddS, Fysiska inst Sthlm univ, Seism inst Uppsala (2 ex), Inst f geodesi KTH (2 ex), Inst f geofysik Uppsala (2 ex), FOA 3 (2 ex), FOA P FOA 4: 420, 470 (100 ex), 471 (3 ex), 472 (2 ex), 473 (3 ex), 478 (3 ex), 48

J_ Page la

Summary A linear and stochastic model of the connection between seismic surface and body wave magnitudes ana the energy yield of underground nuclear explosions is adapted to the maximum likelihood estimation of yields from magnitudes measured in seismograph station networks. Standard deviations and confidence ranges are also obtained.

Application to the calibratea situation of explosions in the yield range from 70 to 1200 kilotons in the Pahute Mesa at the Nevada Test Site and magnitudes from Canadian stations shows that the precision of such estimates, as measured by the standard deviation of the logarithm of the yield, ranges from 0,3 with one average body wave statior to 0.03 when 19 body vave stations and 19 surface wave stations are used, the latter precision being well comparable with radiochemical yield determinations. The yield estimate from one average surface wave station is as precise as the joint estimate from four average body wave stations.

Applications to a few explosions with known yields outside the Pahut-t. Mesa but at the Nevada Test Site and also in New Mexico and Colorado had an average logyield accuracy of very roughly * 0.2. For explosion? under Amchitka Island the model was numerically unsuitable.

The ratio of yields estimated from surface and body vaves is employed as a yield independent indicator of departure from the conditions at the reference sources in Pahute Mesa. The surface wave yields from explosions under Yucca Flat at Nevada Test Site are systematically only half of the body wave yields. The possibility of such source area biases reduces the yields seismometrically estimated for other source areas than Pahute Mesa, to equivalent yields. Such yields are affected by the explosion depth and by the explosions medium.

Several formulae of secondary or tertiary reliability are obtained for the seismometric estimation of the yields of US and USSR explosions when only some of the current single station or average network magnitudes are available, including provisional formulae for tha Hagfors Observatory. Accuracy and precision are estimated.

Applications are made to some of the US and USSR explosions, for which the official yields have not been published. l.b

Sammanfattning En linear och stokastisk modell för sambandet mellan seismiska magnituder från djup- och ytvågor och explosionsstyrkan hos underjordiska kärnladdnings- explosioner tillämpas på att enligt maximimetoden uppskatta explosionsstyrkor ur i stationsnät mätta magnituder. Standardavvikelser och konfidens- intervall beräknas.

Tillämpning på den kalibrerade situationen med explosioner mellan 70 och 1200 kiloton i Fahute Mesa på Nevada-provplatsen och magnituder från stationer i Kanada visar att precisionen, mätt i enheter för logaritmen av explosionsstyrkan, varierar från 0.3 för en genomsnittlig mätstation för djupvågor till 0.03 för 19 djupvågsstationer och 19 ytvågsstationer tillsammans. Denna precision är väl jämförbar med den hos radiokemiska styrkebestämningar. Uppskattningar med hjälp av en genomsnittlig ytvågs-station är lika precisa som med fyra genom- snittliga djupvågsstationer tillsammans.

Vid tillämpning på några explosioner i USA men utanför Pahute Mesa och med kända styrkor, erhölls e;i noggrannhet av ungefär * 0.2 i logstyrkan. Modellen passar dock inte för explosioner under Amchitka-ön i Aleuterna.

Kvoten mellan de ur yt- och djupvågor uppskattade styrkorna användes som ett av styrkan oberoende mått på avvikelser från referens-förhållandena i Pahute Mesa. De ur ytvågorna uppskattade styrkorna hos explosioner under Yucca Flat på Nevada-provplatsen är i genomsnitt endast hälften av de ur djupvågorna uppskattade styrkorna. Möjligheten av sådana snedställningar reducerar de för andra kallområden än Pahute Mesa uppskattade styrkorna till relativa eller ekvivalenta styrkor. Sådana ekvivalenta styrkor påverkas av mediet för och djupet hos explosionen.

Flera formler med sekundär eller tertiär pålitlighet härleds för seismometrisk uppskattning av den ekvivalenta styrkan hos explosioner i USA och Sovietunionen för de iall där endast någon eller några av de vanligare magnituderna från nät- verk eller enskilda stationer är tillgängliga. Däribland anges provisoriska formler för Hagfors-observatoriet. Uppskattningar av formlernas precision och noggrannhet anges. Formlerna tillämpas på ett antal av de explosioner i USA och Sovietunionen, för vilka officiella styrkor inte har publicerats. Page 2

Page 0. Summary 1 1. Introduction 4 1.01 The basic model 4 1.02 The, present applications 4 1.G3 Remarks on surface wave magnitudes 6 1.04 Notations 6 2. Primary seismometric estimates of the yields of some U S underground nuclear explosions with published official yields 8 2.01 The tables 8 2.02 The predicted standard deviation due to coupling variability and channel noise 9 2. "*3 Confidence ranges ior K and C 10 2.04 The calibration explosions Chartreuse, HaIfbeak, Greely, Scotch, Knickerbocker and Boxcar in the Pahute Mesa 12 2.05 The explosion Benham in the Pahute Mesa 13 2.06 The explosions Rex and Dureya in the Pahute Mesa 13 2.07 The extension of the model to include source area bias 14 2.08 The explosions Discus Thrower and Pile Driver 15 2.09 The explosion Gasbuggy in New Mexico 16 2.10 The explosion Rulison in Colorado 16 2.11 The explosions Long Shot and Milrow under Amchitka Island in Alaska 17 2.12 Precision and accuracy of the model 19 3. Primary seismometric estimates of the yields of some U S underground nuclear explosions with unpublished official yields 20 3.01 The tables 20 3.02 Nuclear explosions under the Yucca Flat in the Nevada Test Site 20 3.03 The explosions Pin Stripe and Diluted Waters near French- man Flat in the Nevada Test Site 21 3.04 The explosion Faultless in central Nevada 21 3.05 Remarks on the bias C 22 3.06 Station corrections 23 Page 3

4. Secondary seismometric estimates of the yields of underground nuclear explosions in the U S 29 4.01 Estimates by mean Canadian magnitudes 29 4.02 Estimates by LRSM and CGS body wave magnitudes 31

4.03 Estimates by n^,FS body wave magnitudes 33 4.04 Estimates by HL, and n*™, 34

4.05 Estimates by mCT1T 34 4.06 Estimates by m, «. 35 5. Tertiary seismometric estimates of the yields of underground nuclear explosions in the USSR 37 5.01 Use of the experience with explosions in the Pahute Mesa 37 5.02 The data and their reduction 37 5.03 Accuracy and precision 38 5.04 The estimated yields 39 6. Discussion and conclusions 40 6.01 The material 40 6.02 The maximum likelihood seismometric estimates of the yields of explosions in the Pahute Mesa at the Nevada Test Site 40 6.03 The maximum likelihood seismometric estimates of the seismometric yields for U S explosions outside the Pahute Mesa 42 6.04 Secondary seismometric estimates of the yields of ex-* plosions in the U S 45 6.05 Tertiary seismometric estimates of the yields of explosions in the USSR 46 6.06 Conclusions about event identification by the internal bias between equivalent logyields. 47 7. Acknowledgements 47 8. References 48 Tables 1-15 50-79 Figures 1-5 80-84 Page 4

1) Introduction 1.01 The Basic model In an earlier paper (Ericsson 1971), here referred to as paper II, the author applied a simple linear and stochastic model to the connection between seismometric surface and body wave magnitudes M. and m. observed at station i in a network of seismograph stations and the nuclear yield or energy W of an underground nuclear explosion. In a notation fully explained below, the model is

M. • a. + b K i i m. + b"K * ai

K - log10W where the intercepts aT and a'.1 and the slopes b" and b" are constants and the residuals e" and e" are normally distributed with zero means. The residuals describe noise and variations between explosions of the coupling of energy into the ground. The case treated in paper II was a series of nuclear explosions in the Pahute Mesa in the Nevada Test Site, for which the official radiochemical yields W had been published by Higgins (1970) and for which M. and m. from 19 Canadian stations had been published or made available by Basham (1969a). The average standard deviations of e~ and e" were 0.19 and 0.30 at all Canadian stations, cor responding to the UNSPLIT variant of the model in paper II.

1.02 The present applications Paper II contains a description of how the linear network model can be employed to obtain maximum likelihood estimates of the yields from the station magnitudes. In the present paper that procedure is elaborated and applied to magnitudes measured by the Canadian network by other network and by some single stations and generated by underground nuclear ex plosions in the US and the USSR.

The maximum likelihood estimates, as defined in paper II, can be made when magnitudes from individual stations in a calibrated network are available. Such estimates are here called primary estimates. They are weighted means over channels, with weights inversely proportional to the channel variances. Such estimates minimize the influence from the variability in the individual magnitude measurements. This is a valuable feature in seismology, where the Page 5 variability of magnitudes is rather large. The maximum likelihood technique maximizes the repeatability or precision of our estimates and throughout this paper efforts are made to estimate this precision, by standard deviations or by confidence intervals. The maximum likelihood estimates are accurate or without systematic error when the conditions at the source and along the wave transmission paths and in the instruments ar*> essentially the same as in the calibration or reference situation. In such situations the seismic estimates are estimates of the radiochemical yield. But as we apply the model also to other situations, the estimated yields are in most cases only equivalent yields, referring to some reference explosions in a reference source area measured at reference stations with reference instruments. Occuring departures from the reference situation are therefore important and are traced by estimation of internal bias between body and surface wave data. This bias also appears as a promising tool for the identification of explosions and earthquakes. The limitations of accuracy due to a limited number of calibration explosions are measured by confidence intervals.

Some applications of the primary formulae to US explosions with unpublished yields are given.

Primary estimates can be obtained only with detailed network data and such are not always available. We therefore also construct some less reliable, secondary formulae for the estimation of US explosion logyields from mean Canadian magnitudes and, by regression of mean Canadian body wave magnitudes, also for estimation by some other widely published network magnitudes and from some single station magnitudes. Applications to explosions in the US are given, with estimates of precision and accuracy.

Finally some tertiary formulae are constructed for the estimation of the yields of underground nuclear explosions in the USSR, with rough estimates of precision. These formulae rest on the assumption that the relationship between mean Canadian body wave magnitudes and explosion yields in the Pa hute Mesa in the Nevada Test Site also holds for explosions in the USSR, an assumption for which there is some experimental support, but only from one explosion. Applications to a number of Russian explosions are given. Page 6

1.03 Remarks on surface wave magnitudes Apart from Bashams extensive set of Canadian station surface wave magnitudes for US explosions, the author has found only relatively small and rather disparate sets of surface wave magnitudes from cor* inental or overseas measurements on nuclear explosions in the US and USS J. This is so because of the technical difficulties in measuring thi weak surface waves from underground nuclear explosions. This scarcity of coherent data, together with the important differences in upper earth structure along various surface wave paths and with the differences between instrumentation and magnitude definit: ~is employed by various investigators, seems to

prevent, for the r»i«:.;v..t, the direct and confident construction of K(M) relationships for other than the US/Canada situation.

It is of course possible to construct K(M) relationships indirectly, via the K(m) relationships obtained in this paper and the m(M) relationship appropriate to the situation. The establishment of such relationships between m and M ^'vjuires, however, straight line fitting in a case where both variables are subject to appreciable error and is not a trivial matter. The matter is also clos y related to the identification of explosions and earthquakes by means oi m and M. Both topics deserve separate papers.

1.04 Notations

a risk level, corresponding to the confidence level 100(l-a)%. a intercept A zero to peak amplitude b slope and yield scaling exponent of amplitude/period A C bias defined as K'-K" 6 a-a and the negative of a station correction öm magnitude difference d differential D disc itninant e residual success parameter, equ&l to 1 or 0 depending on whether the measuring station or channel indicated by superscript and index provided a magnitude or not Y measure of station intercept bias relative to intercepts for explosions in the Pahute Mesa l first or second index, indicating station or measuring channel I number of stations or channels » first or second index, indicating explosion J number of explosions J Page 7 k first or second index, indicating source area K the logyield log.-W i station correction m or m body wave magnitude from vertical short period P or P wave amplitude/period, at station i due to explosion j. In cases the m.. refer to body or surface wave magnitudes, as appropriate to channel i. M or M surface wave magnitude measured from the maximum amplitude of the vertical Rayleigh wave amplitude/period at station i due to explosion j. n number of operating channels r estimate of correlation coefficient or first or second index indicating station or measuring channel R number of reference stations or channels s estimated standard deviation T period 12 W explosion energy or yield, in kiloton units of 4.18*10 Joule each m 95ZK 95ZC 95% confidence intervals for K, C and K, the latter con- and 95ZKcc sidering not only channel variability but also calibration variability ( } large parentheses are around factors ( ) small parentheses are around interjections in the text or around arguments to a function the cap superscript indicates a seismometriw estimate, like the estimate K of the radiochemical K the prime superscript indicates surface waves " the double prime superscript indicates body waves the bar superscript indicates an arithmetic mena of the set whose index it replaces CAN, b' etc subscripts like CAN, b~ etc refer to seismometric station networks and stations, as explained in the text the dot subscript indicates an arithmetic mean over the subscript or index it replaces Page 8

2) Primary seismometric estimates of the yields of some U S underground nuclear explosions vith published official yields

2.01 The tables Table la lists the published official radiochemical kiloton yields of contained underground nuclear explosions at the Nevada Test Site, as given by Higgins (1970). Table lb gives this for a few other explosions and both tables give also other official explosion parameters, such as epicenter, medium etc. Table 2 reproduces the surface and body wave magnitudes obtained by Basham from 19 Canadian seismograph stations and used by him in an earlier publication, Basham (1969a). Table 2 also gives magnitudes for the explosion Benham, from the U S Coast and Geodetic Sur- vey Earthquake Data Report 105/1968, for the explosion Rulison, from a report by Jordan (1970) and for the explosion Long Shot, from Jensen et al (1966), Currie et al (1967) and from Lambert et al (1969). Table 3 lists the estimated logyie.lds R'and K", the estimated bias C and its standard deviation s(C), the 95% confidence range 95%C for C, the joint estimate K of the seismic logyield, its standard deviation s(£) for a single determination, the 95% confidence range 95%K for K considering only channel variability, the 95% confidence range 95%Kcc considering both channel and calibration variability and, finally and for comparison, the published official logyields K. The estimates of K were obtained from formulae given in paper II. The other quantities in table 3 are defined in the following subparagraphs, were also the numerical contents of table 3 are discussed in more detail.

Table 4 contains rounded off values of the maximum likelihood estimates W of the kiloton yields for eleven of the 31 U S explosions listed in table 3,their standard deviations s(W) for single determinations, the 95% confidence intervals 95%W and 95% Wcc for W considering only channel variability and both channel and calibration variability. For the other explosions only the significantly different yield estimates by body and surface waves are listed. For comparision table 4 also gives the published official yields W. The seismic and the official yields can also be compared in figure 1. Page 9

2.02 The predicted standard deviation due to coupling variability and channel noise The maximum likelihood estimates K of future K, made on the basis of the particular calibration in paper II of the Canadian station channels i for measuring m. from Pahute Mesa explosions, are expected to contain systematic errors due to misealibrations, tource area bias etc and stochastical errors due to coupling variability and channel noise.

2 - The standard deviation s(K) and the variance s (K) of these stochastical errors were estimated, approximately, by

s2(K) where the estimates b./s. have been employed instead of the population values. The particular form of this variance stems from the use, in K, of weights inversely proportional to the channel variances. Similarily

2 * 2 Ä was used for the variance of C. These predicted variances s (K) and s (C) refer to the stochastical errors expected from coupling variability and channel noise when one calibration, as in paper II, is made and applied to a series of repeated K or C.

A In the expression for s2 (K) we can observe one good property of the estimate 2 " K: the variance s (K) is always decreased if a new channel is added to network, even if the new channel is a bad one because of large s./b.. The new channel 2 - x x must, however, be unbiased. We also observe that s (C) is small only when both 2 * 2 * s (K~) and s (K") are small. Further we may point out that the estimate K has a minimum variance in the sense that no other weighted mean of the K. has a smaller variance than s (K), see e g the treatise by Cramer (1946). Our last two remarks are important for the design of efficient networks and discriminants for the identification of explosions and earthquakes. When C is used for event identification, the separation of explosions and earthquakes is properly measured A A in units of s(C), so that small s(C) make efficient identification.

A The s(K) measure the precision of the network, as distinct from its accuracy, which can be afflicted with systematic errors due to channel bias and calibration bias. The following list, obtained from the model data in paper II for 19 Canadian bichannel stations, illustrates the range of precision available

J Page 10 in various combinations of these stations and their channels:

One bad tn-channel (SPLIT) s(K) 0.40 One average m-channel (UNSPLIT) 0.32 One bad M-channel (SPLIT) 0.22 One good m-channel (SPLIT) 0.19 One average M-channel (UNSPLIT) 0.16 One good M-channel (SPLIT) 0.09 The ten best m-channels (SPLIT) 0.06 The five stations PNT, SCH, GWC, MBC and HAL with both m and M channels good (SPLIT) 0.04 19 Canadian stations (UNSPLIT) 0.03 The eleven best M-channels 0.03 19 Canadian stations (SPLIT) 0.02

The terms SPLIT and UNSPLIT refer to two different ways of assigning variances to the individual 2x19 Canadian channels. The SPLIT variant exploits the particular possibilities in Canada more than UNSPLIT, by splitting the channels in high and low variance groups. UNSPLIT averages over all stations and should be more representative of networks in general.

The precision obtainable from the joint use of 38 independent seisms- graphic channels is quite high. Employment of the whole or the better half of the Canadian network indeed gives a precision of the same order as the errors the radiochemical K-values. In paper II errors of radiochemical W-values were quoted, which were unspecified as to their nature but which were equivalent of K errors between 0.02 and 0.06.

2.03 Confidence ranges for K and C In paper II we defined a confidence range for K that takes into account the expected variability or noise in future repetitions of both the multi- channel measurement on the unknown event and the calibration by Pahute Mesa. The numerical values are obtained first after somewhat lengthy calculations. For some of our purposes it is sufficient to have a confidence range that considers the calibration as fixed and only considers future variability in re- determinations of the unknown event. Such a confidence range measures precision. We have here used the range b. Page 11 1

K t «s(K) / n-1

. • 1 if channel i is operating, otherwise • 0

m.-a. K.i yi b.

t » the two tailed Students t with n-1 degrees of freedom 2 at the risk level a.

These confidence ranges, as well as "hose defined in paper II, are some-* what optimistic by being made on the assumption that the relative values of the estimates s. are essentially correct. The present confidence range A is also approximate by hiving K instead of K under the square root. This makes a numerical simplification but underestimates the range by about 100/n percent, if n is the numbe- of channels involved. Another condition for their relevance, and an important one, is that all the channels must be unbiased. The expectation of m./b. - a./b. must be K in all channels. v liii For the Pahute Mesa source area our calibration in paper II determined the a. and b. so that this condition is satisfied for the set of calibration i i explosions. The idea with the model in paper II is of course, that it shall hold also for other Pahute Mesa explosions and, hopefully, for explosions before the estimates of the K themselves are found to be unbiased. For explosions outside the Pahute Mesa one must, of course, expect bias. It is therefore desirable to have a test for the unbiasedness of the magnitudes observed through the channels.

A A In view of the behaviour of K" and K" in tables 3 and 4 we have calculated

A A A C • R"*-K" and have used a confidence range for C to test for the presence A of bias. The calculation of C and the confidence range of C has the advantage that it does not require knowledge of the real logyield K. The grouping of the channels into surface wave channels and body wave channels is also expected to make C a physically significant description of the source area and the wave paths. C can be interpreted as the logratio of the nuclear explosion yields required occur in the Pahute Mesa in order to reproduce the observed surface and body wave magnitudes. This interpretation or definition can also be applied to earthquakes. The bias C is therefore also important in the identification of explosions and earthquakes. The confidence range for C, Page 12 as given below, has the disadvantage that equal bias in all the channels will not be detected. Such a case simply means a change in overall energy coupling and can be observed only when non-seismometric K measurements also are available. For the calculation of the confidence range for C we used the expression

C « C * t -s(C)« / a n-2 n

KV - •V(m.-a.)/b. i iv i i' i

2 K- - i

K" where t is Students two-tailed t on the risk level a with n-2 degrees of 1 freedom. These expressions were constructed in the same approximate way as the K-range above, from the normally distributed K-K and the chi-square distri buted (KT-K)2 etc.

When the 95% confidence range 95% C calculated from this expression contains 00, we have some support for the hypothesis that the channels are unbiased, so that we probably can trust the confidence ranges for K defined in this paper and in paper II. They then give us the two K interval estimates in tables 3 and A, one marked 95% K and considering only channel variability and the other marked 95% Kcc and considering both channel variability and calibration variability.

2.04 The calibration explosions Chartreuse, Halfbeak, Greely, Scotch, Knicker- bocker and Boxcar in the Pahute Hesa The explosions Chartreuse, Halfbeak, Greely, Scotch, Knickerbocker and Boxcar were used in paper II to calibrate our magnitude (yield) model for Pahute Mesa. The estimated logyields K in table 3 are thus only reestimates, they show how the model would work if it were applied to explosions very like the calibration explosions. The obtained precision s(K) of the joint channels was quite high. The 95% confidence ranges of the precision correspond to a factor of only 1.14 Page 13 up or down in yield. The surface wave/body wave bias C appears in most cases as insignificantly different from zero. The C for Halfbeak, and Greely appear as not insignificantly different from zero, but in opposite senses. This shows that the data basic to paper II are not ideal and that tests for inhomogeneity should be made when more data from the Pahute Mesa become available. The difference between the confidence ranges 95Z K and 95% Kcc reflects the quality of calibration, introducing another factor 1.7 up or down in yield and representing the not very high accuracy.

2.05 The explosion Benham in the Pahute Mesa The explosion Benham in the Pahute Mesa at the Nevada Test Site was not employed for the calibration, in paper II, of the magnitude (yield) model for explosions in Pahute Mesa. With its official radiochemical yield 1100 kt ,ust inside the upper limit of the yield range of the model, it can provide ä direct check on the model. Table 2 shows that only body wave measurements were available, so that the above described test for the presence of surface wave/body wave bias could not be applied. The estimate R«3.O7 of K is quite near the official radiochemical K-3.04. Benham thus confirms our model but from the high s(K) and the rather wide confidence range for K in table A its should be clear that the close numerical fit is only fortuitous. The precision was low and the ranges wide because data from only four Cana- dian stations were available from the reference employed.

2.06 The explosions Rex and Dureya in Pahute Mesa The W-range from 70 to 1200 kg of the model in paper II is somewhat narrow. For many applications it is desirable to have a model also for body and surface wave magnitudes from lower W. In this subparagraph we therefore consider indirect evidence for a simple extrapolation downwards of our model for body waves.

In paper II we observed that the same b" can be assigned to all Canadian stations measuring body wave m. from Pahu^e Mesa explosions. Now the bulletin data from the International Seismological Centre in Edinburgh about the log (amplitude/period) observed for the Pahute Mesa explosions Halfbeak and Chartreuse provide material for the calculation of the mean 6m. of the differences 6m. between these explosions over a worldwide network of 17 stations outside Canada (see table 5). One obtains 6m. * 0.77 with an estimated standard deviation 0.23 between the stations, not significantly different from the corresponding mean difference between the 17 Canadian stations in table 2 giving body wave m. for both of these two explosions, 6m. • 0.87 with the estimated standard deviation 0.25 between stations. This fits with a hypo- Page 14 thesis by the author that the b" for a certain source area is rather independent of network composition also on a global network scale. Further below, in the discussion of the explosions Longshot and Milrow, we describe other observations in support of this hypothesis.

On this basis we then can employ worldwide International Seismological Centre bulletin data on log (amplitude/period) for the Pahute Mesa explosions Rex, Dureya, Halfbeak and Chartreuse for an estimate of the Rex and Dureya logyields by an extrapolation of our model with blla!0.93 from Halfbeak and Chartreuse downwards. Then we can check the extrapolation against the known logyields of Rex and Dureya, log 16 and log 65 respectively. From the data in table 5 and from

6m. i alfbeak etc we obtain

K" extrapolated from Official Chartreuse Halfbeak K Rex 1.1 1.4 1.21 Dureya 1.5 1.9 1.81

The extrapolated K" straddle the official K and thus provide some indirect support for an extrapolation of our K" model down to about 10 kt explosions in Pahute Mesa. Other support for such an extrapolation to low yields in quoted in the discussion and conclusion part of this paper.

2.07 The extension of the model to include source area bias The magnitude(yield) model of paper II was made for nuclear explosions in the Pahute Mesa in the Nevada Test Site. For other source areas we must admit the possibility of significant changes in all parameters of the model and even of deviations from linearity. To keep matters simple at this stage we use the evidence in figure 3 of paper II to restrict Che first model changes to the intercepts a.. When the source area is moved to some place outside the Pahute Mesa, the intercepts are assumed to change from a. to a.+b.y.. The a. and b. are as for Pahute Mesa and the y. are station dependent measures of bias of the new source area relative to Pahute Mesa. The factor b. is introduced for conveni- ence. With generalized magnitudes and with the index i denoting channels in general, we get

m. » a. • b. K • e. • b.y. ill i ii Page 15 for an explosion with unknown K in the new source area. If we now estimate K by K, K~ and K" as if it were for an explosion in Pahute Mesa and then use our model m.(K) to eliminate the observed m., we obtain

K - K + e + E$.(b./s.)2«Y./r$.(b./s.) Yi^ i 1/ i Tiv- i iJ and, if we introduce 4>T and 4>V,

Tfb./s.)2?. I^fb./s.)2 '^(b./s. K » K • e • I*:(b./S.)2 ^.(b./S.)^ 1^(^/8.) (/s and

2 2 :(b./s.)v Y- Z4>V(b./s.)T Y. « A i i x' i i^ i i/ i C • K* - K" - O «• e • (/ lv 1 1 Introducing the weighted means

of the channel biases, we get

K - K • e ^.(b./s.)

C - e • y" - Y" where e indicates residuals which are not necessarily the same in all formulae but which have the expectation zero.

2.08 The explosions Discus Thrower and Pile Driver The 21 kt explosion Discus Thrower in tuff under the Yucca Flat about 50 km south east of the Pahute Mesa showed significant bias and its K « log 21 « 1.32 was moderately well estimated as K • 1.13 by the model for the Pahute Mesa. The estimate K" « 1.33 by body waves, however, was quite accurate and the low joint estimate K was due to the low estimate K~ • 1.04 by surface waves. We will return to Discus Thrower when we discuss other explosions under Yucca Flat.

y Page 16

Pile Driver was an explosion in granite just north of Yucca Flat» with K - log 56 • 1.75. The joint estimate K • 1.85 is moderately accurate but the bias C is significant, the estimates by surface and by body waves only being K" • 1.74 and K" • 2.27. The earlier explosion Hardhat in granite near the Pile Driver epicenter should provide interesting opportunities to study b" etc in granite» but sufficient data are not available to the author.

2.09 The explosion Gasbuggy in New Mexico For the 29 kt explosion Gasbuggy in shale in Colorado, about 800 km from Pahute Mesa, the joint precision s(K) of 16 Canadian channels employed here was estimated at 0.06. The point estimate C of the surface wave body wave wave bias was 0.04, insignificantly different from zero. The maximum likelihood estimate of the real K • 1.46 was K • 1.43, quite accurate. The 95% confidence interval estimate for K was 1.22 to 1.63 when only channel variability was considered and 1.01 to 1.66 when channel variability and calibration variability was considered. Gasbuggys £ and K* and K" would have been well predicted by our model for explosions in the Pahute Mesa at the Nevada Test Site.

2.10 The explosion Rulison in Colorado For the 40 kt explosion Rulison in shale and sandstone in Colorado, about 800 km from the Pahute Mesa and about 300 km from the explosion Gasbuggy, 29 Canadian channels are employed here. Their joint precision for logyield measurement was estimated at s(K) * 0.04. The point estimate Ö of the surface wave/body wave bias was -0.22 but insignificantly different from zero. The maximum likelihood estimate of the real K » 1.60 was K » 1.40. The estimates of the confidence intervals for K were 1.29 to 1.52 when only channel variability was considered and 1.19 to 1.52 when channel variability and calibration variability were considered, not covering the official yield. K" from body waves was 1.59 and very near the official K, but the K' • 1.36 from surface waves was noticeably smaller. The explosion Rulison was measured with high precision but did not behave quite as predicted by the model for explosions in the Pahute Mesa at the Nevada Test Site. The estimate of K by body waves was accurate but that by surface waves was not.

y Page 17

2.11 The explosions Long Shot and Milrow under Amchitka Island in Alaska For the 85 kt explosion Long Shot under Amchitka Island in the Aleutians two somewhat different interpretations of the same records were used, they are reproduced in table 2. For the data set Long Shot D readings by Lam- bert et al (1969) were used, as explained in table 2. The data set Long Shot G consists of the vertical short period body wave data published by Jensen et al (1966) and the vertical long period surface wave magnitudes published by R G Currie et ai (1967). In both cases the surface wave readings appear to have been confined to the period range from 16 to 24 seconds so that the surface wave magnitudes are by definition not strictly comparable to the M obtained by Basham. Even if they had been comparable by definition, we should have expected departures from our model because of the ex- change of the purely continental wave paths from Nevada, New Mexico and Colo- rado to the Canadian stations for oceanic or pseudooceanic paths with various oblique crossings of the border of the North American continent.

The estimates obtained are given in table 3, they are all well off the mark. Both sets show strong C bias relative to Pahute Mesa, negating a calculation of our confidence intervals. The estimates K • 1.62 and 1.69 are rather pre- A cise (s(K) - 0.04 and 0.04) but not accurate. Estimates by m" alone were also precise (s(K') - 0.05 and 0.05) but well below the mark (K' - 1.29 and K~ « 1.21). Estimates by m" only were still precise (s(£") - 0.08 and 0.07) but A well above the mark (K" * 2.44 and 2.71). In contrast with the at least moderately successfull applications of the Pahute Mesa model to the explosions Discus Thrower, Pile Driver, Gasbuggy and Rulison, all outside the Pahute A Mesa, we have here a complete failure of our model. The failure of K" could have been expected from the changes of paths and definitions but the reasons for the failure of the body wave part of the model are not so obvious. One could of course use Long Shot for an attempt to recalibrate the model for Amchitka but the support of only one explosions is somewhat weak for such an adjustment of the aT and aV. In addition it is also rather doubtful whether the Pahute b* and b" apply to Amchitka, as we will explain presently.

On the not unreasonable assumption that the megaton-strength of Milrow mentioned in press releases will mean an official yield somewhere between 800 and 1200 kt, Basham (1970) concluded that the mean body wave magnitude difference 0.6 between Long Shot and Milrow, (obtained from the Longshot data by Jensen et al (1966) and from in detail unpublished measurements on Milrow at a set of some 15 Canadian stations) mean a slope b" of about 0.6 over the K range from 1.9 to 3.0. In view of the expected standard deviations one should Pare not draw too firm conclusions from only two explosions but a b" below 0.9 is indeed indicated by these Canadian measurements. On the same assumption about the Milrow W, Bashams conclusion about b" is further supported by Longshot and Hilrow m"-data obtained from a worldwide network of stations outside Canada and reproduced in table 6. The mean magni- fide difference between 19 stations is again 0.6 and th«2 standard deviation of the differences is 0.4. More data for the construction of a proper model for AmchiL a will be available when the yield of the megaton-size Milrcw explosion under Amchitka is published.

papei IJ and the above it appears as if the slope or yield scaling exponent b" were rather independent of the particular teleseismic station but possibly dependent on the source area. The data suggest that the slope decreases from 0.9 to 0.6 when the sources are moved from Nevada Test Site to Amchitka Island. From the rather few data published about experimental source functions (displacement potentials) near nuclear explosions, see the paper by Haskell (1967), it appears that the slope b" would show such a decrease if the roll off towards high frequencies of the Fourier spectrum of the source function were increased. From Haskells analytical approximations of some of the source functions it seems to follow that such an increased roll off could be connected with a slower excursion to the source function overshoot. A recent nutt^rical investigation by Cherry and Petersen (1970) demonstrated the strong dependence of the source function on the unloading properties of the medium at low stress levels. The importance of the low or intermediate stress level region to waves from explosions was pointed out already in an early study by Kiesslinger (1963). Further studies of how the composition and structure of the source area influences the source function should be quite rewarding and publication of the official yields of other than the U S explosions would create more opportunities to investigate these phenomena.

The Long Shot data sets D and G were obtained from the same records but by different analysts working in nominally the same way. The differences between their results offer an opportunity to estimate the noise introduced by variations in analysis. From a fitting of straight lines to these data on the hypothesis that the two variations are uncorrelated and have equal standard deviation, as described by York (1969) and also in a forthcoming note by the present author, it appeared that the standard deviation of channel noise due to variations in analysis in these cases were about 0.3 for surface wave magnitudes and about 0.15 for body wave magnitudes. Page 19

2.12 Precision and accuracy of the model The precision or repeatability of the yield estimates can be measured by the standard deviation between repeated measurements of the logyield. It is expected to be quite good, about 0.03, when 19 bichannel Canadian stations are employed, but as bad as 0.40 when only one of the worst m, -channels is employed. Single stations have rather low precision, a network greatly increases the precision and preference of low variance surface wave channels gives a still higher precision.

The accuracy or correctness of the seismic yield estimates can be measured by the standard deviation between the residuals of the estimated logyields relative the official radiochemical logyields. For explosions in the calibrated Pahute Mesa the observed accuracy is about 0.08. This rather high accuracy corresponds to i 20% of the yield. Rather limited data from explosions elsewhere in the Nevada Test Site, in New Mexico and in Colorado indi- cate a not much lower mean accuracy of about 0.14 in a joint estimate using both body and surface wave magnitudes from ten to twenty stations. This correspondings to about 35% of the yield. For the explosions under Amchitka Island in Alaska the model is useless. Page 20

3. Primary seismometric estimates of the yields of some U S underground nuclear explosions with unpublished official yields

3.01 The tables The table 4 contains maximum likelihood estimates of the yields for 19 U S underground nuclear explosions, for which the official yields are unpublished at the time of writing. The table 3 gives the corres-

A A A ponding logyields K and, where obtainable, the K* and K". The estimates were obtained by application of the UNSPLIT variant of the magnitude (yield) model in paper II to basic Canadian magnitude data reproduced in table 2.

Tables 3 and 4 also give measures of precision and accuracy. In table 3 A the precision is given by the standard deviation s(K), the inhomogeneity of the observations is ''escribed by the surface wave/body wave bias function OK"-K", by its standard deviation s(C) and by the 95% confidence range 95% C of C. The precision is also described by the 95% confidence range 95% K of K considering only channel variability and by the 95% confidence range 95% Kcc of K, considering channel variability as well as calibration variability.

3.02 Nuclear explosions under the Yucca Flat at the Nevada Test Site For 15 of the explosions with unpublished official yields in table 3 the epicenters have been published and are reproduced in table lb below. They were in the Yucca Flat, part of the Nevada Test Site and about 45 km southeast of the Pahute Mesa. For explosion Zaza no such information was available, it has here been sorted with the explosions under Yucca Flat. The hypocenter media for these explosions are not always disclosed, they are probably dry alluvium, dry or wet tuff or paleozoic rock. The Nevada Test Site geology has been described in a collection of papers edited by Eckel (1968).

Most of the Yucca Flat explosions appear to have a surface wave/body wave bias that is significantly different from zero. That applies also to the Yucca Flat explosion Discus Thrower, in tuff and with the published yield 21 kt. The mean bias of these explosions, weighted in inverse proportion to 2 * the individual bias variances s (C), was -0.35 and the mean standard deviation of these biases was about 0.13. This means that the seismic body wave yields of the explosions under Yucca Flat were about twice the seismic surface wave yields. The results for Discus Thrower, K"« 1.04 and K" « 1.33 for a radiochemical K <• 1.32, suggest that this Yucca Flat bias possibly is due to small K' and that the K" possibly are better estimates of K than K". The Page 21 opposite holds for explosion Pile Driver in granite just north of Yucca Flat. Figure 2 shows C * K -K as a function of K, for these and other explosions.

Here we should remark that we have calculated seismometric yields equivalent to rather strong explosions deep in rhyolite in the Pahute Mesa. We have no primary data to estimate the influence of alluvium as an epicenter medium. Neither is there material to check on the influence of explosion depth. Usually the underground containement of radioactivity is ensured by exploding the nuclear devices at depths not less than 100 meters times the third root of the yield in kilotons. For large explosions this pre- caution keepts the energy release well coupled to wet and by overburden pres- sure compacted rock. For weak explosions, however, in more dry and less compacted media near the surface, quite different conditions might apply. Spri- nger (1966) used two short distance (235 to 285 km) and short period body wave channels to Mina in Nevada and to Kanab in Utah to obtain amplitude(yield) data for weak explosions in various media at the Nevada Test Site. He found that coupling correlates inversely with the porosity of the hypocenter medium. His data were from yields below 20 kt. In the yield range from 1 to 12 kt his data are well described by the slope 0.83 for amplitude/period versus logyield. In that yield range the short period amplitudes from explosions in high porosity alluvium are about 0.6 of those from low porosity alluvium. One explosion in underlying valley tuff gave amplitudes 1.6 times higher and another explosion (Hardhat) in the granite just north of Yucca Flat gave about 20 times large amplitudes. More material on the influence of the medium is given in a following subparagraph on secondary yield estimates by

3.03 The explosions Pin Stripe and Diluted Waters near Frenchman Flat in the Nevada Test Site The explosions Fin Stripe and Diluted Waters in undisclosed media under or near Frenchman Flat, part of the Nevada Test Site and about 60 km southeast of the Pahute Mesa, showed both the same kind of behaviour as the explosions under Yucca Flat. Diluted Waters is rather extreme. It is the weakest of the explosions, with 3 and 18 kilotons as our estimated equivalent yields, its bias C - - 0.83 is the most negative of all and its published epicenter the by far southernmost.

3.04 The explosions Faultless in central Nevada The explosion Faultless was in tuff in an auxilarly test site in central Nevada, about 150 km north of the Pahute Mesa. The estimated body wave yield W" was 1010 kt and the estimated surface wave yield was only W - 710 kt. The rage difference of the logyields, however, does not appear to be significantly different from zero and the joint estimate of the logyield is K - 2.88 corresponding to a seismic yield of 760 kt. The confidence ranges for K were 2.80 to 2.96 and 2.74 to 3.07, without and with the calibration variability, corresponding to the yield »anges 630 to 920 kt and 550 to 1180 kt.

3.05 Remarks on the bias C From the extension, in § 2.07 above, of our model to include source area A A A bias, we obtain that the quantity C • K* - K" from a certain network is independent of the yield and normally distributed, with mean y" - y" and estimated variance s 2 (C*) as defined in § 2.02.

In the bichannel case with just one surface wave channel i and one body wave channel r we obtain

eT e" C - — - — + v* - v" ir bT b" Yr i r which is yield independent and normally distributed with mean y* ~ y" and 9 o » i r variance (sT/bT) + (s"/b") . The quantity C. is simply related, by

C.l r - D.l r /br" to the yield independent quantity

D. » a" - b" • aT/bf + b"M./b: - m lr r r ii rii r which was defined already in paper II but with opposite sign. The. present D. has the mean lr

bM(y- - yV xK x \ and the estimated variance

22 22 (b-;/b:):) (9-.)-) • (s^)

In 6 2.07 the y" and y" were defined as weighted means of the channel biases yT and yV. This makes the y* and y" dependent on which particular network channels that happened to be operating during the explosion. We now simplify our biased model further, by assuming that all the y". are exactly equal to y' and all the yV are exactly equal to y". Physically such an assumption means that the move from Pahute Mesa to a new source area only would change the Page 23 general levels of energy coupling from the explosion to the surface waves and the body waves. In terms of Pahute Mesa explosions such an effect can be described by an increase of the real logyield K by y" for surface wave magnitudes and by y" for body wave magnitudes or by an multiplication of the real yield by 10y" and 10 y" respectively. In our simplified model the expectation of C is then independent of the selection of operating channels.

The 14 estimates of Yucca Flat C in table 3 were obtained from measurement by differently composed networks, each with its standard deviation s(C) given in table 3, as predicted from the properties of the involved channels and ranging from 0.08 to 1.9. Weighting the C in inverse proportion to their variances 2 * s (C) gives the maximum likelihood estimates -0.35 of the mean Yucca Flat bias t" - YV11» , with 0.03 as the estimated standard deviation of this mean.

3.06 Station corrections In this subparagraph we discuss properties of the station corrections and present some justification for the use of source area independent station corrections but also examples of clear departures from the underlying assumption of independent and additive corrections for station and source area.

There is a physical interpretation of the simplifying assumption in the pre- ceding subparagraph, that a move of the explosive sources from the reference source area (Pahute Mesa) to some other source area (like Yucca Flat) gives the expected logyields an internal bias between the expected surface wave yields and the expected body wave yield, which is independent of the measuring station. Physically the assumption means that any consistent assymmetry in the radiation patterns from the reference area, as generated by geological, topo- graphical and geographical structures in and around the reference source area and accounted for by the differences between the station intercepts a., is assumed to be unchanged when the sources are moved to another area. Clearly real situations could easily be different. The assumption is, however, equivalent to the often used assumption that magnitude corrections for station and source area are independent and additive.

Bashams Canadian material provides an opportunity to test this simplification. It is insufficient to determine numerically meaningful source area corrections, as only one explosion with proper seismic data and published official yield is available to us for each of the outlying source areas on Amchitka Island in Alaska (Long Shot), in Colorado (Rulison), in New Mexico (Gasbuggy), in central Nevada (Faultless), in the granite area just north of Yucca Flat at the Nevada Test Site (Pile Driver) and in Yucca Flat (Discus Thrower). For the time being Page I we must be content with the bias estimates C signalling whether overall level changes are probable in these source areas or not. We can, however, use our material to investigate whether or not the station corrections are independent of the move of sources from the Pahute Mesa southeastwards to the about 50 km distant Yucca Flat. We will, as before, assume that the slopes b" « dm/dK and b* • dM/dK are not affected by this particular move. The experience with Amchitka Island shows that this is not necessarily so in general but in the particular case of Yucca Flat we can found our assumption on the invariance of b"/b* in figure 3 of paper II.

In our model

m.. • a. + bK. + e.. in paper II the a. were split according to

a. = a + 6. where the reference level a is the mean of the a. in the reference station i or channel set {i}, containing R stations. This reference set {i} is usually chosen to comprise all available stations, R"I, as done by Basham (1969a) and by the present author in paper II. That choice is, however, not necessary and there is indeed some advantage in selecting a smaller reference set, with one or a few reference stations, as will be shown in this subparagraph. We therefore assume that (i) contains at least one but not necessarily all stations or channels and that the a of these constitutes our reference level. The -6. are « i then station or channel corrections to this reference level. To show the influence of the source area we now introduce the area index k and write a • by, where "by,, already defined in subparagraphs 2.07 and 3.05, takes the place of a station correction for source area which is zero for the reference source area Pahute Mesa. Hence our model becomes

m. ., »a by, + 6. • bK. + e. ., ljk k i j ljk where j now is subindex to k, an explosion must have one source area but one source area can have several explosions. Averaging over the reference set (i) of stations for one event j and one source area k, we get Page 25

m .. - a • by. • 6 • bK. • e . .JK .. K * J • J K-

The station correction £-«k is a quantity to be added to the observation at station i to adjust it, on the average, to the reference level. Hence

2..., —m ., —in... ijk .jk ljk or £...,• 6 - 6. + e .. - e. ., ljk . i .jk ljk

The variance of an £... generated by the just described process depends on whether the station i belongs to the reference set (i) or not. If it belongs to {i}, then e ., and e... are not independent of each other so that . J K 1J K -1 R I.. 6 - 6. + R Z e. .. - e. .. i . . ljk ijk is suitably written

R-l -1 1... « ( ljk , to make the last two e-terms independent. According to paper II we can take 2 the variance o (e...) as independent of i (corresponding to the UNSPLIT model IJK for the Canadian stations) and get

If i instead is outside {i}, the original e-terms are independent and we get

If we now instead of one event in area k have J events there, we average them and get

for a reference station and

0 (£i \? " 1 for a non-reference station. From these: two expressions we conclude that many events make a precise station correction but also that the advantage in having many reference stations is limited, the usage of making R as large as possible by taking R»I is not required for precision. The advantage of this practice is merely that the reference level is centrally situated in the whole station set and thereby is representative of an average station. Thexe is indeed an advantage in employing a small R instead, one is more likely to obtain measurements from all of a few R than from all of many R. With a small R it is therefore easier to obtain a large J and thereby precise i. . Clearly one should select sensitive and re- i. k liable stations for such a reference set.

In table 7 the station corrections -6., as obtained in paper II for Pahute Mesa and 19 Canadian bichannel stations, can be compared with the corrections obtained by Basham (1969a). He obtained his corrections by presumably the present formulae and by merging the source areas Pahute Mesa, Yucca Flat, Frenchman Flat, Pile Driver, Faultless and Gasbuggy whereas the -6. were obtained as a byproduct in the course of fitting K. and m. to our model for Pahute Mesa only. The two sets are not very different but in order to obtain well comparable station corrections from two distinct source areas, we calculated separate station corrections strictly for Pahute Mesa and for Yucca Flat and in both cases from the formulae in the present subparagraph, see table 7. The reference station set was intended to be R»I for each kind of magnitude, but because of the difficulty in always having data at all the 19 stations in this rather large reference set, the conditions were eased to include also cases with only 17 or 18 stations recording. This illustrates the already mentioned disadvantage with large R. The number of explosions J and the standard deviations as estimated from the data are also given in table 7.

No significant differences appeared between the station corrections for surface magnitudes but for body wave magnitudes the station corrections at PNT, SFÅ and SES for explosions under Yucca Flat appear as significantly or very significantly larger than for explosions in Pahute Mesa, according to Students t-test at the 99% and 99.9% levels. These three cases of very probable departure from the simple model with additive and source area represent a complication in principle that is also quite important in practice if a few isolated stations are used for the estimation of K but fortunately of less concern when many stations are used in parallell.

One purpose with station corrections is to reduce the variation between magnitudes obtained at different stations. When many stations are used in parallell, this reduction can be measured by the standard deviations between magnitudes before and after the application of the corrections. Before correction we have, at station i and for event j,

2 2 2 s (n»i.) - s (a^ + s (ei.) where e.. is from noise and from coupling variations between explosions in the same source area. We have also

s so that s2Ca..} -

After application of the corrections -6. we instead have

2 2 s (m.. - 6.) • s (e..) and the ratio of standard deviations or efficiency of the corrections is about

1/2 s(m.. - s(e.. ,..

With the numerical values for s(e..) and s(6.) obtained in paper II we find that for Pahute Mesa sources and Canadian stations the application of station corrections 6. reduces the standard deviation between station i magnitudes not more than by 30% for surface waves and 40% for body waves.

This rather small effect is due to the dominance of the large variability in coupling and station noise and would be even further reduced if station corrections I. with considerable errors are employed. The situation is illu- strated by the standard deviation between magnitudes before and after application of the Pahute Mesa station corrections -6., listed here below in order of increasing distance from the Pahute Mesa:

V s(mT) sOnT-öT) I" s(mV) s(mV-6V) i i i i i i Pahute Mesa, Chartreuse 14 0.22 0.27 17 0.43 0.22 Boxcar 14 0.16 0.16 15 0.25 0.37 Yucca Flat Pile Driver 17 0.33 0.25 18 0.42 0.32 Dumont 17 0.21 0.12 17 0.47 0.36 Nevada Faultless 19 0.29 0.23 17 0.52 0.33 Colorado Rulison 16 0.31 0.32 13 0.54 0.41 New Mexico Gasbuggy 4 0.39 0.49 12 0.41 0.37 Alaska Long Shot D 10 0.27 0.28 16 0.50 0.51 Page 28

Our yield estimates are based on many stations and not much affected if a few station corrections are not proper or if all corrections are somewhat incorrect in a random way.

When station corrections are calculated by averaging over a reference area and several outlying areas, the various by. could cancel out and make the corrections to be nearly the same as for the reference area, barring a few exceptional cases like SES above. An example of such a canceling effect are the snail differences, in table 7, between the -6. from Pahute Mesa and the I. obtained by Basham (1969a) by averaging over Pahute Mesa, Yucca Flat, Pile Driver, Faultless, Rulison and Gasbuggy. Another instance of such insensitiveness to source areas are the surface wave station corrections calculated by Basham (1969a) from earthquakes in the south western U S. In a case like that one must, however, expect an increase in the standard deviation s(by, ) between the source areas. This is perhaps visible in the difference between the average standard deviations for earthquakes and explosions given by Basham. Page 29

4. Secondary seismometric estimates of the yields of underground nuclear explosions in the U S

4.01 Estimates by mean Canadian magnitudes In the UNSPLIT variant of our model for the magnitudes of explosions in the Pahute Mesa, the same standard deviation s" is assigned to all Canadian surface wave channels and the same standard deviation s" to all Canadian body wave channels. In such circumstances we can express the maximum likelihood A A A __ estimates K, K' and K" very simply in terms of one arithmetic mean M of the station corrected magnitudes M.-6T and one similar mean m of the m.-6V:

K' - (M-a'j/b'

ic" «s (m-I")/b" and A M-ä m-a" n"fb"/s") K where n n are the numbers of contributing channels of each kind. Now these mean magnitudes M and m differ only by differences in the station corrections from the

Canadian means M_.x. and m...T published by Bas ham (1969a). In our notation he -CAN CAN uses

MCAN

mCAN where the station corrections I. were obtained by Basham (1969a) not only from the explosions in the Pahute Mesa but also from other explosions in Nevada and New Mexico. We have

Table 7 shows the £.+6. as obtained from Basham1s (1969a) table 4 and from table 4 in our paper II. For explosions with most of the Canadian network involved, we can ignore the expectation of £.+6. and replace M Mid m by M_

and m_4 T. The variance of the 1.+6.t however, lessens the average precision u j i i Page 30 by introducing an extra variance

0.011/n* • 0.020/n" because of the somewhat different station corrections.

With the numerical values given in paper II we obtain the following formula for the estimate Kof the logyield K from Basham mean Canadian CAN magnitudes M^.M and m_AM, each obtained from n" and n" stations respec- wAN CAN tively 53n* 13n" CAN 1.19 53n'+13n" 0.93 53n'+13n"

The precision can be estimated by the variance

1 0.011 0.020 TAN' 39n'+9.6n" n n

When man-' of the Canadian stations are involved, K_AN should be as precise as the maximum likelihood estimate K but accurate only for Pahute Mesa.

M m As an example we obtain, from the data n'»13, CAN*6.1, n"»15, CAN*6,3 given by Basham, Weichert and Anglin (1970) for the explosion Benham in the Pahute

Mesa, that KPA »2.90 0.06, corresponding to a yield W *790 kt and a standard CAN CAM deviation of 15%. This seismometric estimate of the yield of Benham looks somewhat lower than the official yield 1100 kt (Higgins 1970) but comparison of the difference between these logyields 3.04-2.90*0.14 with the standard deviations s(e'.)s0.11 and s(e".)*0.13 obtained in table 6 of paper II between the coupling of Pahute Mesa explosions shows that the difference is not exceptional. In other words, also according to WPAM Benham supports the Pahute Mesa model of paper II.

From the K M formula we can construct less precise and less accurate but sometimes useful formulae for the estimation of K from other magnitudes, if or proper regressions of mrAN *VAN on these other magnitudes can be obtained. This will be attempted in the next few subparagraphs. Page 31

4.02 Estimates by LRSM and CGS body wave magnitudes are The body wave magnitudes ILRSM published by the Seismic Data Labora- tory in Alexandria, Virginia and the body wave magnitudes m_ _ by the U S Coast and Geodetic Survey in Rockville, Maryland. Both are network magnitudes, calculated as unweighted and uncorrected means over some ad hoc selection of stations among a fixed network of stations. The selection of stations is available in the original publications but is not always quoted. The LRSM network is on the North American continent, the CGS network is there and overseas. Relative to explosions in Nevada the networks include stations at local and regional as well as at teleseismic distances (larger than 20°). The waves recorded at local and regional distances are strongly dependent on the particular crustal structure between source and station. The crustal magnitudes routinely obtained from recordings at lo-al and regional distances therefore scatter much. This can be seen from the standard deviations of the

iadividual determinations in the n*rRSM quoted by Basham (1969a), they are nearly twice the standard deviations of the individual and corrected values in the m . In addition they are not always comparable with magnitudes at teleseismic stations, depending on what crustal wave phase happened to be picked for the magnitude calculation. With weak explosions the crustal magnitudes dominate over the teleseismic magnitudes and make the mean CGS and LRSM magnitudes of weak events unreliable. Evernden (1967) made an instructive study of the crustal disturbances in the LRSM magnitudes.

The LRSM and CGS magnitudes HLRSM and m_ _ are hence not well defined enough to be treated by a statistical model like ours for the Canadian means m CAN and M,,.M. We can, however, obtain some empirical regressions of m_.M or M_.M LAN LAN LAN on QWf^cM or mrr>c ami use them to construct formulae for the estimation of K, formulae wich are admittedly unreliable for weak events but useful when no better magnitudes are available. From 16 IL values between 4.5 and 6.1, reproduced by Basham (1969a) for explosions in the Nevada Test Site, we obtain the regression

»CAN "LRSM " 0< with an estimated correlation coefficient r-0.94 and with the estimated variance 0.021 between the residuals. Inserting this into the expression

KCAN * U0S »CAN " 3-75

obtained from our expression above for *vAN but with n"«0, we get Page 3:

KLRSM "LRSM

We can check the performance of this K_ -formula directly against the official K for five explosions in the Pahute Mesa. On the average the A estimated KrRSM turn out to be too low by 0.20 units or the seismometrically estimated yields W" cu too small by a factor 0.6. The explanation ot this bias can be that most of the HL employed in the regression refer not to explosions in the Pahute Mesa but under the Yucca Flat. The standard deviation of the residuals was estimated to be 0.15, corresponding to a factor 1.4 up or down in yield. These results illustrate the accuracy A and precision of our expression for *C M«

No m_ values seem to have been published for most of the Nevada explosions for which Bas ham et al have published m_.M and M_..T. As a provisional measure CAN CAN until better data are accumulated, we use the data for the explosion Boxcar giver by Basham (1969a) and for the explosion Benham and its aftershocks given by Basham, Weichert and Anglin (1970). The latter are not explosions but have the advantage of being very weak events nearly colocated with Benham hereand ,Boxca thery covein thr e thPahute rangee Mesas 3..8 Ths.e 1m5 data6. 3point and s 4ar ae m reproducei 6.3d. Thein ytabl give e8 CAN the regression

»CAN -CGS with the estimates 0.975 for the correlation coefficient and 0.039 for the variance of the residuals. The latter is not grossly different from the estimate 0.023 of the variance of the residuals in the direct K^Ync**) regression found above. These residuals concern precision, the author cannot see any mean- m m ingful way of estimating the accuracy with the present n»crs data. The rAv( (vje) regression obtained is such that at m_. =6 the two kinds of magnitude are nearly Li AN equal and that mo__ is about half a unit larger than m_4M when m,,. "4. CGb CAN CAN

Combining this regression of m^k%. with our estimate K" . we obtain CAN CAN

for the range 4.0 m 6.3. This expression is a provisional description of the regression of K on m___ for nuclear explosions in the Pahute Mesa at LGS the Nevada Test Site. The formula reproduces the Benham and Boxcar K with a negative bias of about 0.15 units, the author has no other material to check on its accuracy. Even after adjustment for this bias the accuracy of the formula would have to be regarded as quite low at lower magnitudes. The precision is perhaps of the same order as for the estimate Kj1 _ . As an application, we have listed, in table 9, the K" and W" obtained in this un~ CGS CGb certain way from the m_-,s in the U S Coast and Geodetic Survey Earthquake Data Reports for 23 of the explosions during 1969 at the Nevada Test Site. In view of the widespread uses of the m_ _ magnitudes, the collection of a better data base for K" in very desirable. This is of course also the LGb case for the estimates RJL, IL and Kr>RK derived in the following subparagraphs from the present expression for K" _. LGb

4.03 Estimates by M,TFr body wave magnitudes The Research Institute of National Defence in Stockholm operates the Hag- fors Observatory (HFS) in western Sweden and obtains body wave magnitudes m^ and surface wave magnitudes M^ from there. Until direct experience on the regression of U S explosion K on HL... and nL,_<, has been obtained, we can make a preliminary formula from the concurrent m <,an< * ^Hrpc va^ues published by Dahlman (1970) for 1969 explosions at the Nevada Test Site, reproduced here in table 9. Excluding the simultaneous explosions Blenton and Thistle, we obtain the regression

0.970 + 0.017 mCGS from 18 points in the ranges 4.4 * m _ i 6.2 and 4.6 i m^ £ 6.4. The coefficient of correlation was estimated as 0.947 and the standard deviation of the residuals as 0.16. Combining this regression with our provisional expression for K" _ we obtain Lbb

1.24 - 5.07 "HFS

An estimate of the precision of such an estimate is the variance 0.07-(0.27) , obtained from the compounded residual variances 0.026 and 0.021 in the regressions mCGS (nijjpg) and mCAN G^j^)» the latter in lieu of the residual variance for m (m _o). The accuracy is not estimated for this provisional and L

As an application we have listed, in table 9, the K|L_ and ft"g obtained from HFS observations of Nevada Test Site explosions in 1969. They can be compared with the corresponding K" _ and W" _ in the same table. \\ b rage J**

4.04 Estimates by m^ „ and In the same way and on similarly shaky grounds regressions were obtained of Nevada Test Site explosion m_ _ on the magnitudes m_Ac issued by the

Seismological Laboratory of Pasadena and m_ov. issued by the Seismographic Station in Berkeley, both ir. California. From data published by Lander (1969, 1970) and reproduced in table 10, we obtained

1.19 m CGS with the estimated variance of residuals 0.05 and

m CGS n BRK with the estimated variance of residuals 0.02. The numbers of points and the estimated coefficient of correlation were 21 and 0.862 for PAS and 14 and 0.970 for BRK. The formulae for estimation of K became

0.97 "PAS - 3.58

No applications are given.

4.05 Estimates by mOTtt The monthly Seismological Bulletin from the Seismological Institute in Uppsala was searched for magnitudes of explosions in Nevada which occurred before 1968 and for which Higgins (1970) had published official yields higher than 20 kt and also for those for which Bas ham (1969a) had published m_AXT. The data found are reproduced in table 11. The magnitudes are according to the procedures employed at the Seismological Institute for events before 1968, they are a weighted mean of magnitudes obtained at the stations UPP and KIR and are here for- mally treated as body wave magnitudes and denoted by ^CTIJ' After 1967 the Seis- mological Institute in Uppsala has employed a revised procedure for the determination of magnitudes, these new mCTr. are not covered by our study. o AU

The ten points for the regression of m_AN on give, in the narrow range

6.0 mCTI. £ 6.464, that

m CAN with the correlation coefficient estimate 0.703 and the variance of residuals Page 35 estimate 0.039. With our expression for K" we obtain CAN

1.57 m - 7.30 SIU siu

A direct comparision with the official K for three explosions in the A

Pahute Mesa shows that K y is only slightly biased, by being about 0.09 units too low, and that the variance is quite low, 0.04A or (0.07) . The control consists, however, of only three points and tha data range is narrow. For the explosion Pile Driver in granite the K . is 2.28, olU much higher than the official K « 1.75. 4.06 Estimates by PL „ Evernden (1967) reformed the calculation of magnitudes from crustal body waves at local and regional distances (less than 20 ) in the U S, by ex- tending a procedure by Romney to determine the teleseismic magnitudes of weak events at the Nevada Test Site from measurements on an identified crustal phase by fixed regional stations. He identified the various crustal phases by their velocities and established empirical formulae to obtain from them magnitudes consistent with the magnitudes obtained at teleseismic distances (farther out than 20°) from the Gutenberg-Richter tables. His crustal magnitudes differ significantly from the crustal magnitudes obtained from the Gutenberg-Richter tables and from the tables employed for the cru- ital contributions to the nLRt,M magnitudes. Evernden employed measurements by the LRSM network on the North American continent and published the unweighted mean m, ^ of teleseismic and crustal magnitudes, without station corrections, for some earthquakes in the U S, and for a number of underground nuclear explosions in the U S. Table 12 below reproduces the m, , for those Nevada Test Site explosions for which Basham (1969a) published m CAN and also for a number of the explosions for which the official yields are published by Higgins (1970).

From 11 points, in the range 4.8 i m, „ i, 5.9, the regression of mfAN on m, .. is obtained as

m CAN V * with the estimates 0.973 for the correlation coefficient and 0.013 for the A variance of residuals. With our expression for K" M we get CAN V 1.01 m^ - 3.26 Page 36

This expression can be directly checked against the official K for a number of explosions in table 12. For three explosions in the Pahute Mesa, with yields 16, 70 and 300 kt, the »stimate Kj^ is about 0.05 units too high and the standard deviation of the true residuals of Kj*^ is about 0.2. These numbers are unchanged if we also include 7 explosions in the tuff under the Yucca Flat or in mesas nearby. The explosion Hardcar in dolomite is also well estimated by our expression for K|"^. The K of eleven explosions in the alluvium of the Yucca Flat are all significantly underestimated, in the mean by 0.44 units, corresponding to a factor of nearly 3 in yield, the standard deviation of the K residuals is again about 0.2, corresponding to a factor 1.6 up or down in yield. For the two explosions in granite just north of Yucca Flat, the KjJ.. over- estimate by 0.35, or a factor of nearly 2 in yield. The standard deviation of the true residuals is about 0.13, corresponding to a factor 1.3 up or down. The K of the explosion Shoal in granite near Fallon in northern Nevada also fits into this picture, being well estimated if the bias 0.35 is taken into account. The estimated and official W are compared in figure 3. Other experi- ences with the influence of the medium are described in the an earlier subparagraph dealing with primary estimates of Yucca Flat explosions.

As an application the KV^ are given for some events without official logyields K in table 12. rage

5. Tertiary seismometric estimates of the yields of underground nuclear explosions in the USSR

5.01 Use of the experience with explosions in the Pahute Mesa There is only one specific underground nuclear explosion in the USSR (66 09 30 near Buchara in Uzbekistan) for which some Russian statement about the yield seems to have been published, by Khedrovsky et al (1970), and even that is inferred from a newspaper article by Gubarev (1970) and thus indirect. No official yields are available for this explosion or for any of the many explosion near 50 N and 78 E between Semipalatinsk and Karaganda in eastern Kazachstan or for the explosions on Novaja Zemlja or elsewhere in the USSR. We therefore simply assume that the relation

K" " U0B "CAN * 3'75 observed to hold well for the mean m_AM of station corrected magnitudes CAN obtained by Basham (1969*>) from Canadian stations and for nuclear explosions in the Pahute Mesa at the Nevada Test Site in the US, also holds for nuclear explosions in the USSR, now with other station corrections than for explosions in the Pahute Mesa. Our assumption involves the intercepts and slopes of our simple linear model for the connection between magnitude and yield. The assumption means that the mean of the intercepts at Canadian stations is taken to be the same as for explosions in the Pahute Mesa, which is merely a way of referring the seismometric yields of explosions in the USSR to explosions in the Pahute Mesa. The assumption means, however, also that we take the slope dm/dK to be the same as for the Pahute Mesa and from the experience with Aleutian explosions we know that this assumption can be quite wrong.

5.02 The data and their reduction In table 13 body wawe magnitudes for some of the explosions in the USSR have been compiled. The mCAN were obtained by Basham (1969b), the mCGg were taken from the Earthquake Data Reports or their predecessors from the

US Coast and Geodetic Survey, the nL,p<, from a report by Dahlman (1970) , the mYKA* ^KA'm rBA an<* "WRA were kindly made available by dr H Thirlaway at the UKAEA in connection with the 1968 SIPRI conference on seismic monito- ring, the mc refer to the mean magnitude from stations UPP and KIR published in the monthly Seismological Bulletin from the Seismological Institute in Uppsala. The magnitudes m^^, m^ and mK£V were computed from amplitude/ Page 38 period data in the bulletins from the Seismological Institute in Helsinki and from the International Seismological Center in Edinburgh.

The magnitudes for the test site east of Karaganda in eastern Kazachstan

(here called KAR) were reduced to m_AM by simple station corrections for LAN YKA, EKA, GBA, WRA, SIU, NUR, KJN and KEV and from m.AM to K". For m._c, LAN LGb however, it was necessary to employ a linear regression of m M on m . LAN LGo

For niy-g an intermediate regression of ni--- on HL,_S was necessary. The formulae and standard deviations of precision obtained and the data ranges covered are given in table 14. Table 15 shows the K" obtained by appli cation of table 14 to table 13. 5.03 Accuracy and precision The accuracy of the K" values in table 16 can be checked against the Buchara explosion on 66 09 30, for which Khedrovsky et al (1970) give W«30 kilotons or K-1.48. Our table 15 has K"«1.49 1.27 2.39 and 1.40, partly in good numerical aggreement with the stated K. This is our only but not very solid support of the basic assumption about the applicability of K(m_A .) to explo- LAN sions in the USSR. It should be stressed that it is founded on only one explosion in a separate area and, according to Khedrovsky et al (loc cit), at the depth of 2440 m,rather large when compared with most explosions in Neva- da.

We can estimate the precision expected in the K" values in table 15. From the number n of station magnitudes behind each m and from the average LAN 0.12 of the standard deviations between the station magnitudes, as obtained by Basham (1969b), one obtains the expected standard deviation

S(KCAN

The average value of n is 13 in Bashams data, making the average s(K" ) to LAN be about 0.04, which corresponds to about * 9Z in yield. The K" are rather LAN precise, indeed as precise as radiochemical logyields appear to be. The other K"-values in table 15 were forced to be unbiased relative to K" ... CAN A A From the differences between K" c and K" we then obtain that the average LGo LAN value of s(K" ) is 0.16. From the 1966 and 1967 KAR data at YKA, EKA, GBA, LG 5e WRA, SIU, NUR, KJN and KEV the average standard deviation of the K" at these stations was also estimated to be about 0.16. A standard deviation 0.16 in the logyield corresponds to a factor of nearly 1.5 up or down in yield. The standard deviation 0.16 can be provisionally assigned also as the HFS precision. The Page 39 weight of K" can hence be estimated to be, on the average, 13 (0.16/0.13) or nearly 20 times higher than the weight of each of the other logyields.

5.04 The estimated yields In its last columns table 15 gives the weighted means K of the various

K estimates K" in the table, obtained by assigning the weight 20 to PAM and unity to each of the other logyields. The corresponding standard deviations s(K") also given in table 15 are for single measurements and estimate, very roughly, the precision. Finally the table also gives the seismic yields obtained in this way. Page 40

6. Discussion and conclusions

6.01 The material The official radiochemical yields of contained underground nuclear explosions and the associated epicenter and time data necessary for the making of yield(magnitude) formulae ha/e.so far been published only for 45 explosions. They were all in the U S fnd only about one third of them were strong enough for widespread teleseismic measurements of their short period body wave magnitudes. The necessary combination of extensive many- station data for one narrow source area was available only for six explosions in the Pahute Mesa in the Nevada Test Site but from as many as 19 stations in Canada. These six explosions are our calibration explosions but they were somewhat inhomogeneous in coupling and their number was less than desirable. Several smaller sets of worldwide data from networks and single stations could be used for the establishment of secondary yield(magnitude) formulae for explosions in the U S. Data on the connection between USCGS and Canadian body wave magnitudes for weak explosions are, however, lacking and were simulated by body wave magnitudes for the aftershocks of explosion Benham. For explosions in the USSR the extent of available body wave magnitudes was similar but Russian data on yield were found only for one of the events. The difficulty in measuring the weak Rayleigh waves for surface wave magnitude determinations on explosions restricted the data re- ally useful for direct yield estimates from surface waves to one but extensive set of such magnitudes from the same six explosions in the U S and the same 19 Canadian stations as above.

6.02 The maximum likelihood seismometric estimates of the yields of explosions in the Pahute Mesa at the Nevada Test Site Our maximum likelihood estimates of the logyields are weighted means over K estimates from available body and surface wave channels, weighted in inverse proportion to the K estimate variances of the channels. Thus the variances must be known or estimated and the channels must also have been made unbiased relative to some standard, by application of station correction!. These corrections are independent of yield if the magnitude/logyield slope b~ and or b" is the same at all channels of the same kind. For surface wave magnitude slopes we have used the value b" « 1.19, determined as a mean slope in paper II. This find- ing and use is also supported by the b* slopes in a recent publication by Wagner (1970) about the determination of yields from Rayleigh wave magnitudes. He used nearly the same set of explosions at NTS and the same kind of surface wave magnitudes but measured at nine stations in the U S, the 3lopes obtained by him were Page 41

Station Slope

COL b' 1.14 OXF 1.10 WES 1.13 LUB 1.32 SMA 0.87 LON 1.29 ATL 1.26 GEO 1.C3 SCP 1.15

Their mean is 1.14 and their standard deviation is 0.17, well compatible with our value 1.19. Wagner's observations also support our use of a surface wave model simply linear in logW. For the body wave magnitude/logyield slopes we used the value 0.93, also determined as a mean slope in paper II. Some extraneous support for this particular value for b" can be found in a recent publication by Mitchell (1970), where unspecified body wave magnitudes m are plotted against yields W in the range from 3 to 1200 yield. Be- sides our calibration explosions Boxcar, Greely, HaIfbeak, Scotch and Chart- reuse, Mitchells points for explosions on the North American mainland also comprise Benham at 1100 kt and Dureya, Rex, Shoal, Salmon, Hardhat and Gnome, ranging from 65 to 3 kt. The points are well fitted o^er the whole range by our expression m • 3.49 + 0.93 logW.

On the assumption that the explosive to earth coupling is the same as for the calibration explosions in the Pahute Mesa, our model gives two seismometric

A, Ä estimates, K" by surface waves and K" by body waves, of the logyield K«logW of the radiochemical yield W of a nuclear explosion in the Pahute Mesa at the Nevada Test Site. They are calculated from the surface and body wave magnitudes M. and m. at certain Canadian seismograph stations. The two estimates are generally somewhat different from each other, but as they are unbiased relative to the radiochemical yield and therefore also to each other, they differ only by stochastic residuals. A confidence range can be used to test the internal bias estimate C « K~ - K" for this state cf affairs. In the present material the internal biases of Halfbeak and Greely appeared as not insignificantly different from zero (table 3), thus indicating some inhomogeneity in our material. When zero internal bias is indicated-, the two estimates can be combined to a joint

A unbiased seismometric estimate K of the radiochemical logyield. When the internal

A bias C is significantly different from zero, then the joint seismometric estimate A K of the radiochemical iogyield is very probably biased. In tables 3 and 4 such Page 42

explosions are marked by being without confidence ranges for K and W.

Our estimates are such that their standard deviations are minimized and their precisions maximized relative to other linear combinations of the channels. The joint precision increases when channels are added to the network. Surface wave stations give more precise estimates than body wave stations, one average surface wave station is about as precise as four average body wave stations together. Estimates of the precision available with Canadian stations depend on the stations involved and range from standard deviations of about 0.4 for one single and bad body wave station to possibly about 0.02 for 19 body wave and 19 surface vave stations together. Thus the logyields from ten or twenty good Canadian stations together are as precise as the radiochemical yield precisions quoted in paper II.

For internally unbiased explosions, confidence ranges for the radiochemical logyield K and yield W can be estimated as further measures of precision. In tables 3 and 4 such two such 95% ranges are given, one without and the other with the variability of calibration included. Their difference measures the quality of calibration.

The accuracy of the maximum likelihood estimates for Pahute Mesa could be in- dependently checked only against explosion Benham, whose logyield was estimated as 3.04, insignificantly different from the official 3.07.

From some extra-Canadian and worldwide short period amplitude/period data on some Fahute Mesa explosions the slope b" appeared to be rather independent of the station, provided that similar instruments are used. Extension of the Pahute Mesa model to other stations would then be by simple station corrections

6.03 The maximum likelihood seismometric estimates of the yields for U S explosions outside the Pahute Mesa The applicability of the maximum likelihood formulae for logyields of Pahute Mesa explosions to explosions elsewhere was investigated by calculation of station correction changes, by tests for internal bias between surface wave and body wave logyields and by direct checks against single control explosions with published yields. The data were not sufficient for separate checks on the applicability of the intercepts and slopes of the Pahute Mesa model.

The move of the explosions from the Pahute Mesa to the nearby Yucca Flat made significant changes in the station corrections only for body waves and there Page 43

only at three of nineteen seismograph stations. These were only a small minority and were therefore not excluded from the application of the Pa- hute Mesa model to other source areas.

The Yucca Flat explosions showed significant internal bias between the surface wave and the body wave logyields, with surface wave yields about half of the body wave yields. One control explosion there, in tuff, supported the body wave yield. Explosions near the nearby Frenchman Flat showed similar bias. A nearby control explosion in granite also had significant negative biaj but supported the estimate by surface waves. The explosion Faultless in tuff in central Nevada showed insignificant internal bias. The control explosion Gasbuggy in shale in New Mexico had no bias and supported the model very well. The control explosion in shale and sandstone in Colorado had insignificant bias but supported the model only moderately well. The control explosion in andesite under Amchitka Island in Alaska showed significant bias and did not support the model. This failure is attributed to an altered short period source function and to the introduction of oceanic surface wave paths.

The Pahute Mesa model of course retains its high precision also when applied to other source areas, as long as many stations are employed. Its overall accuracy, however, appears to be only moderate, about one third or one half of the yield for explosions in the US mainland. In other words we can say that cur seismometric estimate of the radiochemical logyielcl can not be expected to be unbiased for explosions outside the Pahute Mesa. Even so we must assume that the Pahute Mesa yield scaling exponents or slopes also apply to the new source areas, an assumption which appears as false at least for Amchitka. We must therefore adopt a few distinctions and limitations, in order to avoid misunderstanding and confusion of our estimates.

After the basic assumption about unchanged yield scaling, the Pahute Mesa model can be applied to other and uncalibrated source areas only with at least the following two restrictions:

a) an assumption of the same coupling or intercept level as with the calibration explosions in the Pahute Mesa would have no particular basis, so that any coupling must be assumed, even when the Pahute Mesa model indicates zero internal bias. The explosions Gasbuggy and Rulison in table 3 can serve as examples of either kind. b) also the relative excitation of body and surface waves can have changed. Such a change will in most '~ases be indicated by the Pahute Mesa model givivig an observed internal bias significantly different from zero. The explosion Pile Driver and others in table 3 are examples of such situations Page 4s

Because of restriction a the seismometric estimates K, K' and K" for an explosion in an uncalibrated source area differ by an unknown constant, an external bias of unknown size, from the radiochemical logyield K, even if th?

A internal bias C is insignificantly different from zero. Such seismometric estimates are here called estimates of equivalent logyields, to avoid confusion with the externally unbiased estimates of the radiochemical or real logyield obtainable from seismometrically calibrated source areas. The equivalent estimates are equivalent in the sense that they estimate the logyield that should be exploded in the Pahute Mesa to make nearly the same estimates by the Canadian stations considered. This operational definition gives the equivalent logyields some physical meaning. In addition they have the advantage that any not empty subset of the Canadian station set studied gives equivalent estimates which are unbiased to each other and thus readily comparable also between explosions. When available, station corrections proper to the new source area can be employed to improve on the original model. Another advantage with our method of estimating the logyield from several stations or channels jointly is that they have minimum variance or maximum precision.

In cases where restriction b applies, we get two significantly different estimates K* and K", so that two different equivalent explosions in the Pahute Mesa are required to simulate the real explosion. In such situations the joint esti-

A mate K according to the Pahute Mesa model has lost its simple equivalent meaning and is reduced to a formal condensation of the observations. In tables 3 and 4 such explosions are marked by not having confidence ranges for K and W assigned to them.

When the estimate C of the non-zero bias is precise enough, it can be used to construct a new and internally unbiased model for the new source area. Addition of C to the Pahute Mesa formula for K" makes a new formula which together with

A the original formula for £' makes the new model with a new joint estimate K. We

A can of course also take the other alternative and make a new formula for K by subtracting C from the Pahute Mesa formula for K" etc. We obtain two alternative and different but unique operational definitions of an equivalent explosion in the Pahute Mesa with the real logyield K. Such model changes appear attractive for attempts to determine relative yields. The new models will, however, only provide equivalent yields and the external bias or systematic error will remain unknown. Only calibration or reliable calculation can make the external bias known and permit a switch from precise or accurate seismometric estimates of equivalent yields to accurate seismometric estimates of the real yields. Page 45

In the absence of trustworthy calibration or calculation it appears prefe- rable to retain the two significantly different estimates K' and K"*. Their difference then signals the situation and also shows how explosion-like the events happen to be. The present Canadian data for explosions under the Yucca Flat in the Nevada Test Site are an example here. In general these explosions appear as more explosion-like than the calibration explosions in the Pahute Mesa, the estimate of their mean internal bias was negative, C « - 0.35. It was also rather precise, s(C) = 0.03 but the estimates were not reduced to K" as the existing support for K" by only one explosion was considered as being too weak.

Tables 3 and 4 contain seismometric estimates, by our maximum likelihood model for the Pahute Mesa, of the logyields and yields of 24 explosions outside the Pahute Mesa. 23 of these were in the U S mainland. Estimates of the internal bias were available for 22 explosions and of these 15 had internal bias not insignificantly different from zero. 12 of those were under the Yucca Flat in the Nevada Test Site. For the biased explosions both estimates of W are given in table 4, they are equivalent yields. Seven of the explosions in the U S mainland showed zero bias, they were Rulison in Colorado, Gasbuggy in New Mexico, Faultless in central Nevada, Pin Stripe near Frenchman Flat in the Nevada Test Site and Cup, Lampblack and Yard under the Yucca Flat. For these unbiased explosions only the joint estimates of W are reproduced in table 4. They are, however, not sufficiently well calibrated, if at all, to be regarded as other than equivalent yields.

We can compare some of our estimates W* with estimates obtained by Wagner (1970) from surface waves at eight seismograph stations in the U S. For the explosions Dumont, Bronze, Pirahna and Tan his estimates are essentially in agreement with ours but for Buff, Faultless and Corduroy Wagners eitimates are not insignificantly different from curs.

6.04 Secondary seismometric estimates of the yields of explosions in the U S From the primary model secondary models for seismometric estimation of the yields of explosions in the Novada Test Site were obtained for use with less detailed data than separate raw magnitudes from several of certain Canadian stations. The main secondary model was made for use with the currently published averages Mo... and m_.., of station corrected Canadian magnitudes. The other secondary formulaCAeN then vAextendeN d the main secondary model for m in a much less precise way to situations with the same source areas but with other stations or station networks, by means of regressions of mean Canadian magnitudes on the kind of magnitudes to be used. The secondary estimates are of equivalent or of real Page 46 yields, as the case may be according to the calibration. In our present secondary estimates only those for Purse, Jorum and Pipkin in table 9 and for Rex in table 12 can be regarded as estimates of real logyields, as they were in the calibrated Pahute Mesa. The estimates from different stations are designed to be unbiased between each other. With simultaneous data from several stations the precision can be estimated also for uncalibrated situations. The accuracy or difference between the equivalent and the real yield remains, how-* ever, unknown until calibration.

The secondary estimates from the mean Canadian magnitudes are as accurate as our primary estimates and only little less precise. The other secondary estimates are much less reliable. For the explosion Purse our two secondary estimates 180 and 190 kilotons for the real yield were obtained from the body waves at the HFS station and in the worldwide USCGS network and they compare well with Wagners (1970) estimate 173 * 24 kilotons obtained from surface waves at five stations in the US but despite this coincidence our formulae for estimation by CGS and by HFS and also those for PAS and BRK should as soon as possible be re- constructed on a better data base.

The secondary formulae obtained are rather disparate and the very wide range of magnitudes which according to these formulae lead to the same estimate of K illustrates well the fallacy in equating numerically equal magnitudes from various stations and networks. Conversely our secondary formulae offer an imperfect but useful instrument to avoid this difficulty by reduction to the corresponding logyield. Such reductions to equivalence with an explosion in the Pahute Mesa should be useful also with earthquakes.

6.05 Tertiary seismometric estimates of the yields of explosions in the USSR As with US explosions the formulae for the reductions of various magnitudes to 3eismometric logyields of explosions in the USSR are rather disparate and again the same logyield is obtained from a wide range of magnitude values. The accuracy of these logyields was not well established and can be very low. They are only equivalent logyields. The formulae were designed to be unbiased between each other, so that meaningful joint estimates could be formed. The data were numerous enough to permit rough internal estimates of the precisions. The mean precision of the joint estimates of the logyields was 0.09, corresponding to about 2A percent of the yield.

The listing is not exhaustive but comprises 69 explosions, with equivalent yields ranging from 3*5 to 1300 kilotons. Half of them fall between 50 and 200 kilotons. Our estimates of the equivalent yields of explosions in the USSR are lower than 47 the yields usually appearing in public discussions.

6.06 Conclusions about event identification by the internal bias between equivalent logyields The logyield bias, defined as the difference between the maximum likelihood estimates of the equivalent logyield by surface waves and by body waves, has a physical interpretation, is normally distributed, is efficient by having a minimum variance, is independent of the yield and is easily defined for any station network. Its expectation is independent of the network, its variance is network dependent and decreases with network enlargement. It has also some physical meaning with earthquakes and ooks like a suitable generalization, for discrimination by networks, of the usual surface wave body wave criterion for the discrimination between explosions and earthquakes.

7. Acknowledgements The author has been much aided by the programming and computational work of I Eriksson , by the secreterial work of G Esko and by discussions with 0 Dahlman and H Israelson at this institute. The investigation was made possible by the extensive magnitude data kindly supplied by dr P Basham at the Earth Physics Branch in Ottawa, Ontario, of the Canadian Depart- ment of Energy, Mines and Resources and by dr H Thirlaway at the Black- nest Data Analysis Centre for Seismology of the United Kingdoms Atomic Energy Authority. Page 48

8. References Basham, P.W. (1969a): Canadian Magnitudes of Earthquakes and Nuclear Explosions in Southwestern North America, Geop J R Astr Soc 17, p 1-13. Basham, P.W. (1969b): Station Corrections for Canadian Magnitudes of Earthquakes and Underground Explosions in North America and Asia. Paper 1969-3 in the Seismological Series of the Dominion Observa- tory, Ottawa, Ontario. Bauham, P.W. (1970): Seismic Magnitudes of High Yield Underground Ex- plosions, Canadian J of Earth Sci 7, p 531-534. Basham, P.W., Weichert, D.H. and Anglin, F.M. (1970): An Analysis of the Benham Aftershock Requence Using Canadian Recordings. J Geoph Res 75, p 1545-1556. Cherry, J.T. and Petersen, F.L. (1970): Numerical Simulation of Stress Wave Propagation from Underground Nuclear Explosions. Proc of the IEAE Conference on Peaceful Uses of Nuclear Explosions in March 1970 in Vienna, Austria. Corbishley, D.J. (1970): Some Seismic Results of the U S Gasbuggy and Rulison Underground Nuclear Explosions, Report AWRE 0 46/70, Alder- maston, Berkshire. Cramer, H. (1946): Mathematical Methods of Statistics, Princeton Univer- sity Press. Currie, R.G., Ellis, R.M., Russel, R.D. and Jensen, O.G. (1967): Addendum- analysis of Canadian Long Shot Data. Earth Planet Sci Letters 2, 75, 1967. Dahlman, O. (1970): Hagfors Observatory 1969 (in Swedish), Research Insti- tute of National Defence Report A 4497-26, Stockholm, Sweden. Eckel, E. (Editor) (1968): Nevada Test Site. Memoir 110, Geological Society of America, Boulder, Colorado. Ericsson, U. (1970): Event Identification for Test Ban Control, BSSA 60, p 1521-1546. Ericsson, U. (1971): A Linear Model for the Yield Dependence of Magnitudes Measured by a Seismographic Network, Research Institute of National Defence Report C 4455-26, Stockholm Sweden. Evernden, J.F. (1967): Magnitude Determination at Regional and Near-regional Distances in the United States, BSSA 57, p 591-640. Evernden, J.F. (1969a): Identification of Earthquakes and Explosions by Use of Teleseismic Data. J Geoph Res 74, p 3828-3856. Evernden, J. (1969b): Precision of Epicenters Obtained by Small Numbers of Worldwide Stations. BSSA 59,p 1365-1398. Page 49

Gubarev, V. (1970): Taming of the Underground Fire, the Peaceful Work of the Nuclear Explosion, Komsomolskaja Pravda, Moscow, September 24, 1970. Haskell, N.A. (1967): Analytic Approximation for the Elastic Radiation from a Contained Underground Explosion, J Geoph Res 72, p 2583-2587. Higgins, G. (1970). Summary of Nuclear Explosion Data for Underground Engineering Applications, Report USRL-72346, Lawrence Radiation Laboratory, Livermore, California. Jensen, 0., Ellis, R.M. and Russel, R.D. (1966): Analysis of Canadian Long Shot Data, Earth and Planetary Science Letters 1, p 211-221. Jordan, J. (1970): Seismic Data from Rulison U S Coast and Geodetic Sur- vey Report. Kedrovskij, O.L., Ivanov, I.J., Mjasnikov, K.K., Mangusheev, K.I., Valen- tinov, J.A., Leonov, E.A., Musinov, V.I. and Dorobnov, V.F. (1970): Basic Technical Aspects of the Use of Underground Nuclear Explosion for Economic Purposes, in Atomic Explosions for Peaceful Purposes (X.D. Morochov, Ed), Atomizdat, Moscow. Kiesslinger, C. (1963): The Generation of the Primary Seismic Signal by a Contained Explosion. VESIAC State of the Art Report 44lO-*8-C Univ of Michigan, Arbor, Michigan. Lambert, D.G., von Seggern, D.H., Alexander, S.S. and Galat, G.A. (1969): The Long Shot Experiment, Report 234, Seismic Data Laboratory, Alex- andria, Virginia. Lander, J.F. (Ed), (1968, 1969, 1970): Seismological Notes, BSSA 58, 59, 60. Mitchell, M. (1970): Physical and Biological Effects, Milrow Event, NVO-79, USAEC, Las Vegas, Nevada. Niazi, M. (1969): Use of Source Arrays in Studies of Regional Structure, BSSA 59, p 1631-1643. Von Seggern, D. and Lambert, D.G. (1970): Theoretical and Observed Rayleigh- Wave Spectra for Explosions and Earthquakes. JGR 75, pp 7382-7402. Springer, D.L. (1966): P-wave Coupling of Underground Nuclear Explosions, BSSA 56, p 861-876. Wagner, D. (1970): Nuclear Yields from Rayleigh Waves. Earthquake Notes 41, no 3, p 9-20. York, D, (1969): Least Squares Fitting of a Straight Line with Correlated Errors. Earth and Planetary Science Letters 5, p 320-324. Page 50

Table la Underground and contained Nevada Test Site explosions with official and official preliminary yields (marked x) and other parameters reproduced from Higgins (1970). Date North lat West long DOB Yield o Medium Name y m d m kt 58 10 29 37 11 41 116 12 17 Tuff 258 0.03 Evans 58 10 08 37 11 43 116 12 02 tuff 100 0.072 Tamalpais 61 12 13 37 07 36 116 02 56 all 181 0.46 Mad 62 07 11 37 07 20 116 19 59 all 0.50 Johnie Boy 65 06 11 37 00 34 116 01 01 all 181 1.2 Petrel 64 12 16 37 02 05 116 00 44 all 180 1.2 Parrott 68 03 14 37 02 52 116 00 39 all 209 1.4 Pomraard 57 09 19 37 11 45 116 12 11 tuff 274 1.8 Rainier 62 02 19 37 02 57 116 01 46 all 150 1.8 Chinchilla I 62 04 14 37 13 19 116 09 27 tuff 191 1.85 Platte 61 09 15 37 11 17 116 12 28 tuff 402 2.6 Antler 64 12 16 37 10 40 116 04 01 tuff 152 2.7 Mudpack 62 02 08 37 07 38 116 03 10 all 181 3.0 Stillwater 62 03 28 37 07 28 116 02 02 tuff 189 3.4 Hoosic 62 02 15 37 13 35 116 03 34 gran 286 4.8 Hardhat 62 01 09 37 02 41 116 02 06 all 302 4.8 Stoat 58 10 16 37 11 03 116 12 04 tuff 253 5.1 Logan 62 01 18 37 02 50 116 02 04 all 261 6.0 Agouti 62 02 09 37 02 37 116 02 20 all 239 6.6 Armadillo 62 04 05 37 02 49 116 02 22 all 261 10.0 Dorprime 62 02 23 37 07 44 116 02 54 all/tuff 305 11.9 Cimatron 64 11 05 37 10 28 116 04 01 dol 402 12.0 Handcar 61 12 03 37 02 45 116 01 40 all 364 12.4 Fisher 66 05 05 37 03 02 116 02 16 all 304 13.0 Cyclamen 66 02 24 37 16 19 116 26 02 tuff 671 16.0 Rex 66 05 27 37 10 42 116 05 52 tuff/pal 337 21.0 Discus Thrower 58 10 30 37 11 09 116 12 07 tuff 301 22.0 B lane.a 62 05 12 37 03 55 116 01 49 tuff 434 38.0 Aardvark 64 10 09 37 09 05 116 04 37 all 406 38.0 Par 62 06 27 37 02 30 116 02 07 all 408 45.5 Haymaker 66 06 02 37 13 37 116 03 20 gra 463 56.0 Piledriver 66 04 14 37 14 34 116 25 51 rhy 542 65 x Dureya 66 05 06 37 20 53 116 19 19 rhy 666 70 Chartreuse 67 05 26 37 14 53 116 28 49 rhy/tuff 635 71 x Knickerbocker

continued! Page 51 Table la (cont)

Date North lat West long DOB Yield Medium Name y m d o ti o tn kt

67 05 23 37 16 30 116 22 12 Tuff 977 150 X Scotch 63 09 13 37 03 38 116 01 18 tuff 705 200 Bilby 66 06 30 37 18 57 116 17 56 rhy S19 300 X Halfbeak 66 12 20 37 18 07 116 24 30 tuff 1215 825 X Greely 68 12 19 37 13 53 116 28 25 tuff 1402 1100 Benham 68 04 26 37 17 44 116 27 21 rhy 1161 1200 X Boxcar Page 52

Table lb

U S explosion data from USCGS Earthquake Data Reports, from Higgins (1970), from Niazi (1969), from Evernden (1969a) and from von Seggem and Lambert (1970).

Date North lat West long Depth Yield II i II Medium Name y m d O I 0 m kt 65 03 03 37 03 32 116 02 14 Wagtail 65 03 26 37 08 51 116 02 34 Tuff 750 Cup 65 06 16 36 41 05 115 57 22 Diluted Waters 65 07 23 37 05 52 116 01 59 tuff 530 Bronze 65 09 10 37 02 52 116 08 59 Charcoal 65 10 29 51 26 17 -179 10 57 andesite 702 85 Long Shot 65 12 03 37 10 17 116 03 57 tuff 680 Corduroy 65 12 16 37 04 21 116 01 45 Buff 66 01 18 37 05 30 116 01 07 Lampblack 66 04 25 36 54 30 115 54 07 Pin Stripe 66 05 13 37 05 03 116 02 01 Pirahna 66 05 19 37 06 40 116 03 29 tuff 670 Dumont 66 06 03 37 04 06 116 02 07 Tan 67 01 19 37 08 37 116 08 07 Nash 67 01 20 37 06 00 116 00 14 tuff 560 Bourbon 67 05 20 37 08 00 116 04 14 Commodore 67 09 07 37 09 11 116 03 10 Yard 67 09 27 Zaza 67 10 18 37 06 56 116 03 27 Lanpher 67 12 10 36 40 40 107 12 30 shale 1292 29 Gasbuggy 68 01 19 38 38 03 116 12 55 tuff 975 Faultless 69 09 10 39 24 22 107 56 53 sandst 2568 40 Rulison 69 10 02 51 25 02 -179 10 56 1200 Milrow Page 53

Table 2 (a to d) Canadian magnitudes for U S explosions The stations are Canadian. The event numbers refer to US explosions named in tables 3 and 4. The magnitudes for explosions 1-28 are raw magnitudes used by Basham (1969a). For explosion 29 (Benham) they are from the U S Coast and Geodetic Survey Earthquake Data Report 105/68 and for explosion 30 (Rulison) from Jordan (1970). The data set with index 31 (data set Long Shot D for the explosion Long Shot) the body wave magnitudes are from Lambert et al (1969) and the surface wave magnitudes were caluclated as log(A/T) + 0.3 + 1.66 log (A) from data published by Lambert dt al. Explosion index 32 is also for Long Shot but with the data set Long Shct G with surface magnitudes as published by Currie et al (1967) and with body wave magnitudes as published by Jensen et al (1966). The Long Shot D and Long Shot G surface wave magnitudes are intercomparable but are, because of a different definition, not comparable with the surface waves obtained t,y Basham for explosions 1-28. Table 2 a Surface wave magnitudes M..

Station Station Explosion index index j » 1 2 3 8 10 11 12 13 14 15

ALE 1 = 1 4.62 4.70 — 5.05 — 4.82 4.92 MBC 2 4.64 - 4.66 5.02 - 4.81 4.98 5.40 - 5.12 4.86 RES 3 4.44 4.53 3.53 4.56 4.30 4.83 4.38 4.25 3.63 44.7.75 4.79 5.45 3.93 _ 5.23 CMC 4 4.45 - 4.57 4.90 4.57 - - 4.70 4.70 5.11 3.96 4.88 FBC 5 4.22 - 4.61 4.73 - 4.53 4.85 4.99 - 4.76 4.78

BLC 6 4.93 4.53 — 4.51 4.83 5.15 3.83 5.15 4.95 YKC 7 4.02 4.62 — 4.62 - 4.64 4.72 4.98 - 4.70 4.62 SCH 8 4.60 - - 4.90 4.96 - 4.79 :>.01 GWC 9 - — 4.95 3.83 - 4.71 5.14 - 4.95 4.84 FSJ 10 4.42 3.96 4.02 - 4.31 3.66 4.35 4.59 5.11 3.93 4.29 4.70

STJ 11 4.65 — 5.03 - 4.83 4.95 FFC 12 4.41 - 4.48 4.35 4.61 4.76 - 4.41 4.28 PHC 13 4.47 4.55 — - 4.43 4.64 4.68 4.73 3.82 4.11 4.31 HAL 14 4.76 — 4.87 4.96 5.27 - 5.04 5.24 PNT 15 4.68 - 4.59 4.17 4.37 3.83 5.07 4.77 4.98 4.01 4.24 4.37 00 SFA 16 5.12 4.18 5.02 5.27 - 4.71 5.10 VIC 17 4.51 4.07 - 4.33 3.63 4.75 4.70 4.82 3.87 4.26 4.44 SES 18 3.86 - 4.63 OTT 19 4.72 4.55 4.72 4.34 4.97 4.62 3.84 4.54 4.86 5.20 - 5.09 5.18 Table 2 b Surface wave magnitudes M. . Station Exolosion index index 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 1 5.67 6.12 5.40 5.22 4.76 — 4.91 — 6.18 6.21 4.53 4.20 4.20 2 5.81 6.40 5.29 5.55 5.16 — 5.02 4.65 6.41 6.37 4.61 3.95 4.00 3 6.31 6.60 5.33 5.90 5.33 4.28 _ 4.77 6.53 6.31 4.54 4.10 4 5.93 6.02 5.35 4.75 4.3? 5.31 5.10 6.21 6.28 4.06 4.34 4.10 5 5.78 5.96 5.29 5.27 5.04 - 5.21 4.90 4.38 6.18 4.57 4.01 4.20

6 5.80 6.11 5.40 5.4V 5.00 4..20 5.25 4.95 6.15 4.49 4.38 3.60 7 5.52 6.04 5.38 5.20 4.86 - 5.02 4.80 5.71 6.04 4.41 4.68 4.30 8 5.81 6.23 5.42 5.44 4.81 - 5.23 5.20 6.40 6.30 4.60 4.06 4.20 9 5.71 6,11 5.44 5.32 5.06 - 5.31 4.88 5.98 6.39 3*90 10 5.83 6.26 5.25 5.62 5.09 4.17 5.15 4.73 6.04 6.39 3.64

11 5.53 6.00 5.49 5.37 5.19 - 5.01 - 6.18 6.22 12 5.06 5.91 5.17 4.85 4.59 4.16 4.90 4.65 3.92 3.99 3.84 4.10 13 5.41 5.84 5.15 4.66 4.12 4.86 5.47 - 14 5.97 6.39 5.37 5.51 - 4.12 5.38 4.88 6.14 4.67 15 5.31 5.92 5.37 5.02 4.59 4.12 4.73 4.56 4.82 5.67 6.06 3.99 "0 0Q n 16 5.70 6.07 5.62 5.26 5.15 4.45 5.36 5.02 6.38 6.20 4.54 17 5.48 5.99 5.17 4.50 4.13 4.86 4.72 5.79 6.27 4.13 18 5.47 6.09 5.34 5.21 4.78 4.09 4.83 4.75 4.01 5.71 6.69 4.19 19 6.01 6.31 5.36 5.60 5.46 4.25 5*41 4.26 6.09 6.37 4.20 4.19 4.50 Table 2 c Body wave magnitudes m..

Stat ion Explosion index index j « 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 5.34 4-92 - 5.37 4.98 5.62 5.13 4.87 4.14 5.22 5.38 5.65 - 5.68 5.61 5.37 - 4.81 5.50 4.96 5.36 5.19 5.18 4.67 5.01 5.55 5.61 '*.79 5.34 5.24 5.29 4.94 4.36 5.37 5.13 5.45 5.32 5.03 4.35 4.70 5.17 5.32 4.64 5.30 5.39 5.42 5.03 5.25 5.33 5.32 - 4.81 4.73 4.95 4.60 4.73 4.94 5.18 5 5.16 4.78 4.65 5.25 4.99 5.32 5.09 4.91 4.58 5.25 5.48 5.65 4.54 5.33 5.62

6 - 4.74 5.38 5.12 4.89 4.57 5.11 5.25 5.08 4.59 5.44 5.35 7 5.07 5.00 4.29 5.07 4.82 5.47 5.04 4.72 4.44 5.38 5.47 5.43 4.72 5.89 5.03 8 5.29 4.99 - 5.37 5.04 5.47 5.20 4.91 - 5.07 5.65 5.90 4.48 5.54 5.83 9 5.61 5.43 - 5.43 5.08 - 5.27 5.71 10 5.31 4,78 5.26 4.69 4.52 4.70 4.30 4.21 4.78 5.17 4.89 4.89 5.05

11 5.10 - 5.50 5.09 5.55 5.21 - - 5.47 6.17 6.51 4.84 6.35 6.27 12 4.44 5.10 4.88 5.33 5.31 4.71 4.44 5.50 5.43 5.15 4.82 5.79 5.60 13 5.37 4.43 - 5.27 4.83 4.86 - 4.68 5.01 5.42 - 5.45 5.18 14 4.89 - 5.18 4.68 5.35 4.97 5.00 - 5.07 5.16 5.40 4.96 5.44 5.32 15 5.89 6.27 4.58 6.28 6.13 +0 5.09 - 5.07 4.67 5.83 4.90 4.31 6.06 0> 09 (B 16 5.35 4.81 - 5.27 4.91 5.40 4.91 4.69 5.50 5.43 - 5.64 5.82 17 5.60 5.48 4.75 5.39 5.18 5.48 5.33 5.07 5.57 6.01 5.02 6.24 5.89 18 4.68 5.62 19 - - - 4.92 5.50 4.97 5.40 5.22 Table 7 d Body wave magnitudes m.. Station Explosion index index j - 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 = 1 5.91 5.78 5.26 4.82 5.73 5.39 4.88 4.86 5.61 5.63 5.05 - 6.21 6 .0 5.25 5.12 5.50 2 5.53 5.66 5.02 4.72 5.51 5.30 4.87 4.78 5.47 5,46 5.04 6.38 6.04 5 .9 4.48 - 6.10 3 5.66 5.67 4.76 4.55 5.77 5.07 4.58 5.38 5.34 4.62 5.54 6.22 6 .0 - 5.75 5.80 4 5.46 5.10 4.55 4.43 5.30 4.96 4.63 5.17 - 6.40 6.37 — 5.99 G.10 5 6.10 6.07 5.13 4.94 5.71 5.60 5.11 5.78 5.53 4.34 6.33 6.03 4.84 6.22 6.20

6 5.98 5.63 4.86 4.78 5.55 5.58 4.48 - 5.55 5.38 4.27 6.09 6,23 5.15 - 6.30 7 6.29 6.14 5.33 4.93 5.90 5.51 5.35 4.79 5.71 5.72 4.46 6.58 5.95 4.90 5.80 6.00 8 6.07 6.50 4.93 5.05 5.92 5.62 5.25 5.10 5.91 5.74 4.73 6.35 6.21 5.12 6.37 6.50 9 5.78 6.22 4.59 5.09 5.99 5.27 4.86 - 5.96 5.54 - 5.92 6.30 - 6.65 6.70 10 5.65 5.88 4.82 4.12 5.48 4.96 4.90 4.93 5.22 5.10 4.71 6.18 6.58 4.61 5.11 5.20

11 6.53 6.61 5.57 5.64 6.52 6.17 5.58 - 6.50 6.44 — 6.74 5.99 - 6.21 6.40 12 5.92 5.39 5.18 5.01 5.76 5.77 5.46 4.79 5.72 5.58 4.53 6.22 - 3.95 5.07 5.50 13 5.55 5.54 4.63 - 5.60 4.60 4.89 5.13 5.42 5.38 - 5.69 6.17 4.36 4.95 5.40 14 6.08 6.18 5.37 4.91 5.59 5.52 - 4.91 5.69 5.48 - 6.06 - - 5.70 6.20 15 6.83 6.98 5.91 5.66 6.42 6.36 6.11 4.81 6.26 0.34 5.59 7.45 6.71 5.68 5.82 6.00 •X CO 0Q A 16 6.45 6.50 5.36 4.89 5.89 6.03 5.38 4.82 5.82 5.85 _ 5.94 — - 6.05 6.00 17 6.28 5.80 5.56 5.22 5.31 5.30 5.49 5.35 - 5.99 - 6.28 - 5.24 5.50 5.40 18 6.59 6.76 5.14 5.04 6.01 5.97 5.55 4.94 5.77 5.75 4.95 - 6.73 5.95 19 6.11 6.51 - - 5.73 5.70 - - 5.58 5.37 6.21 6.55 6 .7 5.07 5.55 6.10 Table 3

Primary estimates of logyields K of U S explosions

Index Name Area K' K" s(C) 95%C K s(K) 95%K 95%Kcc K j * 1 Wagtail Yucca 1.37 2.16 -0.78 0.15 -1.18 -0.39 1.83 0.074 2 Cup •i 1.47 1.59 -0.12 0.10 -0.40 0.16 1.50 0.046 1.38 1.62 1.13 - 1.74 3 Diluted Waters ¥ F 0.43 1.25 -0.83 0.21 -1.38 -0.27 0.93 0.10 4 Bronze Yucca 1.59 1.93 -0.34 0.09 -0.61 -0.08 1.66 0.037 5 Charcoal 1.22 1.55 -0.33 0.11 -0.63 -0.02 1.36 0.054 6 Corduroy 1.82 2.17 •0.36 0.10 -0.56 -0.15 1.89 0.041 7 Buff 1.48 1.87 •0.39 0.10 •0.63 -0.16 1.62 0.046 8 Lampblack 1.03 1.55 -0.52 0.19 -1.08 0.05 1.43 0.078 1.20 1.65 0.80 - 1.72 9 Pin Stripe F F 0.S4 1.17 •0.33 0.12 -0.73 0.07 0.94 0.055 0.77 1.12 0.35 - 1.28 10 Chartreuse Pahute 1.69 1.82 •0.14 0.09 •0.33 0.06 1.72 0.038 1.64 1.80 1.36 - 1.93 1.85 11 Pirahna Yucca 1.78 2.07 -0.29 0.09 -0.46 -0.12 1.85 0.036 12 Dumont 2.03 2.24 -0.22 0.09 •0.38 -0.05 2.07 0.035 13 Discus Thrower 1.04 1.33 •0.29 0,10 •0.57 -0.01 1.13 0.048 1.32 14 Pile Driver 1.74 2.27 •0.53 0.09 -0.74 -0.33 1.85 0.035 1.75 15 Tan 1.79 2.24 -0.45 0.08 -0.61 -0.29 1.88 0.034 16 Halfbeak Pahute 2.54 2.76 •0.22 0.08 •0.32 -0.12 2.58 0.033 2.48 17 Greely it 2.90 2.77 0.14 0.08 0.02 0.25 2.88 0.033 2.92 18 (Nash) Yucca 1.77 1.77 0.075

19 Bourbon 1.55 1.55 0.077 00 20 Commodore 2.25 2.47 -0.22 0.0S •0.39 -0.06 2.30 0.035 21 Scotch Pahute 2.24 2.19 0.06 0.08 •0.03 0.15 2.23 0.033 2.20 2.27 1.99 - 2.46 2.18 22 Knickerbocker 1.91 1.81 0.11 0.09 -0.03 0.24 1.89 0.034 1.84 1.95 1.63 - 2.10 1.85 23 (Yard) Yucca 1.29 1.51 -0.22 0.10 •0.52 0.07 1.34 0.042 1.22 1.45 0.96 - 1.60 continued! Table 3 (cont)

Index Name Area K" s(C) 95%C K s(K) 95ZK 95%Kcc j - 24 (Zaza) Yucca 2.06 2.39 -0.33 0.08 -0.48 -0.19 2.12 0.034 25 (Lanpher) •t 1.82 2.34 -0.52 0.09 -0.70 -o.:-> 1.94 0.037 26 Gas Buggy N M 1.45 1.40 0.04 0.12 -0.39 0.47 1.43 0.061 1.22 1.63 1.01 - 1.66 i.46 27 Faultless Nevada 2.85 3.01 -0.16 0.09 •0.36 0.04 2.88 0.034 2.80 2.96 2.74 - 3.07 28 Boxcar Pahute 3.03 3.06 -0.03 0.09 •0.24 0.17 3.03 0.038 2.95 3.11 2.84 3.28 3.08 29 Benham •i 3.07 3.07 0.16 3.04 30 Rulison Col 1.36 1.59 -0.22 0.10 •0.53 0.08 1.40 0.037 1.29 1.52 1.19 - 1.52 1.60 31 Long Shot D Amch 1.29 2.44 -1.15 0.10 •1.47 -0.83 1.62 0.043 1.93 32 Long Shot G 1.21 2.71 -1.50 O.Ot •1.79 -1.21 1.69 0.042 1.93

(Naae) inferred from date. (") near Yucca Flat

00 Page 60

Table 4

Primary seismometric estimates of yields of U S Explosions

W" W s(W) 95ZW 95%Wcc W

1 Wagtail 23 145 2 Cup 32 4 24 - 42 13 - 55 3 Diluted Waters 2.7 18 4 Bronze 39 85 5 Charcoal 17 36 6 Corduroy 66 150 7 Buff 30 74 8 Lampblack 27 5 16 - 45 6.3 - 53 9 Pin Stripe 8.8 1 5.9 - 13 2.2 - 19 10 Chartreuse 52 5 44 - 63 23 - 85 70 11 Pirahna 60 120 12 Dumont 110 170 13 Discus Thrower 11 21 21 14 Pile Driver 55 190 56 15 Tan 62 170 16 Halfbeak 350 580 300 17 Greely 790 590 825 18 (Nash) 59 19 Bourbon 35 20 Commodore 180 300 21 Scotch 170 10 160 - 190 98 - 280 150 22 Knickerbocker 78 6 69 - 89 43 - 130 71 23 (Yard) 22 2 17 - 28 9.1 - 40 24 (Zaza) 110 250 25 (Lanpher) 66 220 26 Gas Buggy 27 4 17 - 43 10 - 46 29 27 Faultless 760 60 630 - 910 550 - 1200 28 Boxcar 1100 100 890 - 1300 690 - 1900 1200 29 Benham 1200 1100 30 Rulison 25 2 19 - 33 15 - 33 40 31 Long Shot D 20 280 85 32 Long Shot G 16 510 85 Page 61

Table 5

at ion Rex Dureya Chartreuse Halfbeak BMO 1.0 1.5 - - LON 1.1 - 1.9 2.5 SPO 1.5 - 1.9 2.6 COL 0.6 1.2 1.6 - NP- 1.2 - 1.9 - B8L 0.9 l.A 1.6 2.4 CLK 0.7 - 1.2 1.8 ALQ 1.2 - - 2.0 BOZ 1.2 2.1 - RCD 1.9 1.8 - CNN 1.9 1.9 2.8 SJG 1.8 2.1 2.4 KJN 1.3 1.4 2.0 SEO 1.6 1.5 - BHA 0.4 1.1 - GDH 1.4 2.5 CAR 1.8 2.6 TRN 1.6 2.1 LPB 1.7 2.5 EKA 1.0 - LHN 1.2 - NUR 1.3 1.9 BNS 1.6 2.5 MOX 1.2 2.1 KHC 1.0 2.1 BKG 0.3 1.4 PRE 1.5 2.4

Data are log(amplitude/period) values for short period vertical P-waves and were obtained from the bulletins of the International Seismological Centre in Edinburgh.

J_ Page 62

Table 6

Station [ilrow Long Shot

KIP mr »6.9 m" - 6.A HMO 6.A 5.6 GUA 6.6 6.1 LAO 6.9 6.2 TUC 6.6 6.0 ALQ 6.8 6.1 KTG 6.6 5.6 RAB 6.0 5.9 AAM *5.3 6.2 DAV 6.1 5.7 CPO 6.7 6.2 NUR 6.5 5.8 PMG 6.6 5.6 GEO 6.A 5.A WES 6.8 6.2 NDI 6.5 6.0 BNS 6.6 5.5 GRF 6.0 5.8 RIV 7.2 6.2

Milrow data from USCGS Earthquake Data Report 6A/1969. Long Shot data from Lambert et al (1969). Page 63

Table 7

Pahute Basham Pahute Yucca paper II

Station Channel -6. £ *s<[1 ) £. +6. J* £. . *s(i. J ) i i.. i.. i.. i l.k i l.k i .k ALE i - 1 0.07 0.02 i' 0.13 -0.05 4 0.08 * 0.08 3 0.03 * 0, 16 MBC 2 -0.17 -0.21 0.16 -0.04 4- 21 07 ./— 10 20 RES 3 -0.35 -0.47 0.08 -0.12 4- 52 10 2- 40 04 CMC 4 0.01 -0.06 0.15 -0.07 4 01 18 2- 12 13 FBC 5 0.04 -0.01 0.11 -0.05 4 01 13 3 00 10 BLC 6 -0.03 -0,13 0.13 -0.10 4- 08 06 3- 12 05 YKC 7 0.13 o.n 0.10 0 4 12 05 3 12 05 SCH 8 -0.07 0.14 -0.02 4- 05 12 3- 07 17 GVC 9 -0.07 -**>, 06 0.11 0.01 4- 03 07 3- 1C 09 FSJ 10 -0.16 -0.03 0.19 0;13 4- 18 07 3 01 08 95% STJ 11 -0.02 -0.04 0.15 -0.02 4- 03 19 2- 03 17 FFC 12 0.40 0.35 0.17 -0.05 4 42 18 3 35 16 PHC 13 0.21 0.37 0.15 0.16 4 26 04 3 36 13 HAL 14 -0.29 -0.25 0.11 0.04 3- 24 06 3- 30 13 PNT 15 0.26 0.34 0.11 0,08 4 31 08 3 30 18 SFA 16 0.09 -0.13 0.16 -0.22 4- 02 14 3- 25 06 VIC 17 0.15 0.28 0.10 0.13 4 24 13 3 29 06 SES 18 0.00 0.19 0.10 0.19 4 13 08 2 22 07 OTT 19 -0.20 -0.28 0.16 -0.08 4- 32 15 3- 27 13

ALE 20 0.32 0.3< >' 0.13 -0.02 5 0.15 * 0.13 9 0.00 * 0.09 95% MBC 21 0.30 0.1 0.19 -0.14 5 31 14 9 11 17 RES 22 0.38 0.30 0.20 -0.08 5 45 08 9 20 18 95% CMC 23 0.49 0.47 0.3C -0,02 5 61 20 8 45 29 FBC 24 0.01 -0.02 0.10 -0.03 5- 04 05 9- 02 09 BLC 25 0.20 0.20 0.18 0 5 23 30 9 21 11 YKC 26 -0.07 -0.08 0.21 -0.01 5- 15 10 9 03 21 SCH 27 -0.09 -0.13 0.17 -0.04 5- 12 21 9- 15 17 GWC 28 0.12 0.08 0.27 -0.04 4 15 22 9 00 30 FSJ 29 0.34 0.47 0.23 0.13 5 46 32 9 50 18 STJ 30 -0.36 -0.61 0.24 -0.25 5- 49 14 9- 67 27 FFC 31 -0.04 -0.01 0.25 0.03 5- 02 42 9 01 15 PHC 32 0.46 0.38 0.22 -0.08 5 53 24 8 30 12 HAL 33 -0.05 0.07 0.14 0.12 4- 02 10 9 10 16 PNT 34 -0.81 -0.77 0.17 0.04 5- 88 07 9- 66 10 99% SFA 35 -0.40 -0.16 0.7.4 0.24 5- 39 11 9- 09 17 99% VIC 36 -0.02 -0.24 O."2 -0.22 5 00 27 8- 28 31 SES 37 -0.52 -0.27 0.24 0.25 4- 53 13 6- 10 07 99.95 OTT 38 -0.27 0.00 0.27 0.27 4- 26 17 4 17 17 95% mean {I* • 61) - 0.00 010 i. • i 1 . . mean <4V • 6V) « 0.01 s(£V • 67) - 0.14 i.. i i.. i

J Page 6A

Table 8

mCAN mCGS Benham: 6.3 6.3 Benham aftershocks: 3.A A. 2 3.6 A. 3 3.7 A. 1 3.,7 A.0 3.,7 A. 3 3..8 A.,2 3..8 A..A 3,.9 A,,2 A,.0 A,.A A,.1 A,.2 A ,3 A,.6 A.A 5.0 A.5 A .9 Boxcar: 6.3 6.3

Data from Basham, Weichert and Anglin (1Q7°) and from Basham (1969a). Page 65

Table 9

CGS CGS CGS ^IFS ^IFS HFS

69 01 15 Wineskin 5.3 1.63 43 5.4 1.63 43 y 69 01 30 Vise 4.8 1.00 10 5.2 1.38 24 y 69 03 20 Barsac 4.6 0.74 5.5 4.5 0.51 3.2 y 69 03 21 Coffer 4.9 1.12 13 5.1 1.25 18 y 69 04 30 Thistle + Blenton 5.3 1.63 43 y 69 05 07 Purse 5.8 2.27 190 5.9 2.25 180 p 69 05 27 Torrido 5.0 1.25 18 5.3 1.50 32 y 69 06 12 Tapper 4.4 . 0.49 3.1 4.8 0.88 7.6 y 69 07 16 Ildrin 4.7 0.87 7.4 4.9 1.01 10 y 69 07 16 Hutch 5.6 2.01 100 5.8 2.12 130 y 69 08 27 Pliers 4.7 0.87 7.4 y 69 09 12 Minute Steak 4.5 0.62 4.2 4.7 0.76 5.8 y 69 09 16 Jorum 6.2 2.77 590 6.4 2.87 740 p 69 10 08 Pipkin 5.5 1.89 78 5.6 1.87 74 p 69 10 29 Cruet 5.1 1.38 24 y 69 10 29 Pod 5.0 1.25 18 y 69 10 29 Calabash 5.7 2.14 140 5.6 1.87 74 y 69 11 21 Picallilly 5.0 1.25 18 5.1 1.25 18 y 69 12 05 Diesel Train 5.0 1.25 18 5.0 1.13 13 y 69 12 17 Grape A 5.5 1.89 78 5.6 1.87 74 y 69 12 17 Lovage 4.8 1.00 10 4.7 0.76 5.8 y 69 12 18 Terrine 5.2 1.50 32 5.3 1.50 32

Magnitudes m from the U S Coast and Geodetic Survey's Earthquake Data Reports, magnitudes HL.-^ from Dahlman (1970). Page 66

Table 10

mCGS "'PAS "BRK 68 04 26 Boxcar 6.3 6.4 p 69 01 30 Vise 4.8 4.7 y 69 07 16 Ildrin 4.7 4.7 4.6 y 69 07 16 Hutch 5.6 5.4 5.3 y 69 08 27 Pliers 4.7 4.4 y 69 09 12 Minute Steak 4.5 4.8 y 69 09 16 Jorum 6.2 6.3 6.1 p 69 10 08 Pipkin 5.5 . 5.5 5.5 p 69 10 29 Cruet 5.1 4.3 y 69 10 29 Pod 5.0 4.7 y 69 10 29 Calabash 5.7 5.7 y 69 11 21 Picallilly 5.0 5.2 5.0 y 69 12 05 Diesel Train 5.0 5.0 y 69 12 17 Grape A 5.5 5.6 5.2 y 69 12 17 Lovage 4.8 5.1 y 69 12 18 Terrine 5.2 5.2 5.0 y 70 01 23 Fob 4.6 4.6 4.4 y 70 01 30 Ijo 4.6 4.7 y 70 02 04 Grape B 5.6 5.8 5.5 y 70 02 05 Labis 4.7 4.7 4.5 y 70 02 11 Diana Mist 4.6 4.8 4.5 y 70 02 25 Cunmarin 5.2 5.6 y 70 02 26 Yannigan 5.3 5.2 4.8 y

Data from the Seismological Notes by J Lander in volumes 58, 59 and 60 of the Bulletin of the Seismological Society of America. Page 67

Table 11

K K mCAN mS1U SIU

66 05 13 Pirahna 5.37 6.0 2.12 y 66 05 19 Dumont 5.51 6.3 2.59 y 66 06 02 Pile Driver 5.56 6.1 2.28 1.75 66 06 03 Tan 5.55 6.1 2.28 y 66 06 30 Halfbeak 6.04 6.2 2.43 2.48 p 66 12 20 Greely 6.29 6.4 2.75 2.92 p

67 05 20 Commodore 5.77 6.2 2.43 y 67 05 23 Scotch 5.51 6.0 2.12 2.18 p 67 09 27 Zaza 5.70 6.3 2.59 y 67 10 13 Lanpher 5.66 6.1 2.28 y

Magnitudes m from Basham (1969a) and magnitudes mCTII from the Monthly Bulletins of the Seismological Institute in Uppsala, area and yield data from Higgins (1970). Page 68

Table 12

m'CAN V K ifV" medium area 61 09 15 Antler 4.03 0.41 0.80 mesa tuff y 61 12 03 Fisher 3.45 1.09 0.22 all y 61 12 13 Mad 2.37 -0.34 -0.87 all y

62 01 09 Stoat 3.38 0.68 0.15 all y 62 01 18 Agout i 3.55 0.78 0.32 all y 62 01 30 Dormouse 3.64 0.41 all y 62 02 08 Stillwater 3.46 0.49 0.23 all y 62 02 09 Armadillo 3.51 0.82 0.28 all y 62 02 15 Hardhat 4.15 0.68 0.93 gra y 62 02 19 Chinchilla 3.16 0.25 -0.07 all y 62 02 23 Cimarron 3.98 1.07 0.75 all y 62 04 05 Dorprime 3.73 1.00 0.50 all y 62 04 14 Platte 3.44 0.27 0.21 mesa tuff y 62 05 12 Aardvark 4.55 1.58 1.33 valley tuff y 62 06 27 Haymaker 4.52 1.66 1.31 all y

63 09 13 Bilby 5.61 2.30 2.41 valley tuff y 63 10 26 Shoal 4.62 1.08 1.40 gra Fallon 63 12 10 Gnome 4.4 0.48 1.18 salt Carlsbad

64 10 09 Par 4.6 1.58 1.38 tuff y 64 10 22 Salmon 4.27 0.72 1.05 salt Hattisburg 64 11 05 Handcar 4.19 1.08 0.97 dolom y

65 03 03 Wagtail 5.32 5.2 1.99 y 65 03 26 Cup 4.94 4.9 1.69 tuff y 65 07 23 Bronze 5.26 5.0 1.79 tuff y 65 09 10 Charcoal 4.91 4.8 1.58 y 65 12 03 Corduroy 5.43 5.4 2.19 tuff y 65 12 16 Buff 5.17 5.0 1.79 y 66 02 24 Rex 4.50 1.20 1.28 mesa tuff p 66 05 06 Chartreuse 5.15 4.9 1.84 1.69 rhy p 66 05 19 Dumont 5.51 5.4 2.19 tuff y 66 06 02 Pile Driver 5.56 5.4 1.75 2.19 gra y 66 06 03 Tan 5.55 5.5 2*29 y 66 06 30 Halfbeak 6.04 5.9 2.48 2?70 rhv p

Data from on K from Higgins (1970), on m-... from Basham (1969a) and on m, .. and media from Evernden (1967, 1969b), on media from von Seggern and Lambert (1970). Page 69

oo Os co > oo o sr vD o w o CN • vD 4 m vo m m m

O> vO sr CN r-< in vO co o^ • • m vo m m i<~

vO vO sr sr vO sr r-* CO CM CO CO CN m co • • • \O m m m m m m

CN O rH O 00 m 00 r-* vO vD r-i co • in • VD VD vO 1i in il m m vO l vO vD vD m vo VO vO vO

CM sr f—i m CM o m m co sr sor vO • • • • • • • • • vO« m sr m m m sr sr m sr co sr sr vO co m co o CM o o u i—i CO co OmN m • • m cmo sr m • o sr m

vO CM r^ c vO m o cc in m vo o CM c O 00 so vo in m m in vo • • vo m

m CO o sr o> vO co o vo r co r-t• • • • vO • • • vO m m sr m

CO ft.

co vomo covocMsrmvor^oo co CM m I-. vO r- co vO O • •• •••••••• • • • • • O mmvo vominmsrminm m vD vO m m m m sr m m

m r» er» ON sr co vO 00 CM CO CM co CM 00 vO sr co m CN CO rH CM O CN Sf CM CO vO • « rH CO m CM m m m vo m • • • vO vO m m in in in m m

m C7\ vO co r~t r». 00 rH Sf CO O m CO 00 i—i m r-4 o O CM CN CM CN CM CN o r-t r-t r-* r-t O a> r-t o CM co r» rH r-t CO m VO |x* 'JN O CM CN CO sr m vO r». oo CO O CM CM O o fH O o O O O rH O O o o O O Q o o o sr sr sr m m m m m in m in in vO vO vO vO vO vO vO vO vO vO vO o vO vO vO vO vO vO vO vO vO vO vO vO vO vO vO vO vO vO vO vO vO vO vO vO Page 70

55 3

sO ON CO CM CO i—I O .... o o o so m so so sO m* sO so sD sO

ft CO O ,-. sO CO m C4 sO os CO

sf CO •

fo r I ^^ 5.5 8 5.8 3 4.8 5 5.1 1 5.0 4 5.0 9 5.2 9 GB A m m ibl e 1 m H B

o in sO sO m 00 o CM i—i co m •st m sO

EK A sO m m m m m m m m sO m m

sO CO sO i—i m CO sO ON ON sO sD ON sO in CM so £t* m m m m m m m sr m m m

CO ft,

co o sO m in in

CM sO co CM co O m m CM sr co 1 co f-l sO • • B sO in m • • m • • m sr m m m

sO o CO ON m sO CM p». o CM CO f-i CM O CO CM i-i t-* ft f-» m o CM CM CM l-l o CM co CM O O CM CM

Dat i o px r>. r». P*. CO CO 00 CO CO COCOCOCO sO sO sO sO sO sO sD sO sO sO sO sO sO sO sO sO sO sO sO sO sO sD Page 71

o tf co

pq o O 14-1 tö H B

en CO co 32 m m m m

CO in o co o O m m m m m m & m

ro CO co o CN o OJ CM CN co m o o o o o Page 72

to vO I

wS N CO O 53 l JO

CO ^X>

CO O r-t

(^ (N S fi CO O\ ro sr • • • vO lO IO

CO r» i-i r*. sf CM CM O r-t CT\ O O O rH O O rH r-( rH sr sr vo r^ co ^0 ^0 ^0 ^0 ^0 Page 73

CU cd CO CO CD H 2 ^J U CO w u < cu u

Di vO

O CO

Q) 0) o X o < o ro H CO u O o 00

o •ef

CO <• sr o cs • * • m io vo

co \O CO O in in i/i u

CM o CM CO CM O o CM o sr ON ON ON ON CM o o O o O vO

J_ Page 74

Table 14

Formulae employed for the seismometric estimation of logyields K for explosions in the USSR by various magnitudes m.

range of "YKA6" •'CAN-1-08 KAR 5.5-6.1

KAR 11 0 45 0 10 5.7-6.6 "EKA" - * - "EKA"4'24 KAR 10 s m +0.11*0.10 5.1-6.0 OTGB1A KAR 11 « 1^-0.50*0.11 5.3-6.2

KAR 8 1^+0.09*0.07 5.2-6.1 "HUR"3*66 KAR 7 - 0^^0.13*0.13 5.5-6.2 •VJN"3-89

KAR •» = 1^^0.14*0.20 5.1-6.1 "KEV"3-60 KAR 20 3S mSIU-0.59*0.13 5.5-6.7 msiu"4-39

KAR+NOVZEM 36 -1.13 m 91±0 14 4.5-6.3 4 73 CGS-°- - "CGS" - SOV 13 .02 11^^-0.56*0.05 "CGS^1 SOV "CAN"1 .15 n. -1.54*0.15 •SIFS"1-24 VS"5-41 Page 75

CM CO NO r-~ O O O CO tf\ O o i—oi o o f—o1 o o sr m o o m c sr c o CM NO NO c CM m NO OS ft sT c f—1 i—t m CM t—t —i CM f—1 CM f—1 f-l oo in t—t f-t CM

00 00 00 r-^ CM in ro m o NO O» in cr> I-» CO CO a> t-t f—1 o NO NO CO t-l NO f—4 f-si in CM 00 m CO CM m NO NO O"! NO r-» in CM m Os. CO o f-4 CM CM (0

m O sr CO CM NO 00 r-l CM 00 CO m CO NO t—1 o i—i o CO o CO CO 00 O CM CO r-. Os. t—t c C O r-1 CO o f—1 CO CM CM CM CO CM r-1 f-l o r-4 CM CM r-l CM CM r-l i—1 CM r-4 CM f—1 t—i CM r-1 CM

•n 00 CN CM CM m m C i—1 m sr us CM CM CM CM CM CM

O r-1 CM 00 NO NO CO CO r-1 t—1 CM CO O CM m

CM CM i—1 CM f-l CM CM CM

NO 00 CM CO f-l C sr m ON sD O r-l f-l CO • • • c CM CM CM CM CM CM CM CM mcd O\ O m O sr sr o co t—i CO O CM O CO m co r^ r~» CM c sr vO OJ CM CM r-4 O CO CM CM CM CM CM CM CM r-t CM CM CM .O. CM H CO m CM oo CM vO 00 m r- oo NO o C r-l sr co CM CM CM CM r-i CM CM CM CM

CM vO NO 00 cx> f—1 CM o f—1 f—1 o ON O sr 00# • • • • • o i—l CM CM • CM r-1 O CM CM

sr O oo NO 00 sr m NO co co co r-l ON CM ON O sr W CM CM CM CM

m r- sr CO sr CO CO o m CO m co CM CM CM o CM CN r-l HF S 33* 3 33* 3 co sr 1.9 8 1.6 1 2.1 0 2.5 9 2.9 6 1.8 6 1.9 8 2.1 0 2.1 0 2.3 5 2.9 6 2.8 3 1.2 5 2.2 2 CG S 1.4 9 2.1 0 0.7 6 CM CM

O sr z sr 2.1 4 2.0 5 2.2 9 3.0 4 1.3 6 1.8 2 1.7 8 2.0 4 2.0 2 2.0 1 1.3 7 2.9 5 2.7 4 1.9 6 2.1 0 1.9 5

2.2 1 CM a 0.8 7 CM

ON NO co 1-4 o> CO PH sr co O r-4 I—1 m C\ o> CO cc m r-t r-t m o r-t r-l i—t O CM CM CM O CM CM o r-t o f-H 01 CM CM r-t f—l w r-t r-4 o CO r». i—1 r-l co m NO r^ ON o r-t CM CM CO sr NO NO r*. 00 CO o CM CN O i—1 o o r-t r-4 o O O o r-t c— u O O o o O 1—1 O O O o o r-4 sr s* SJ" m m m m m m m m m NO NO NO NO NO NO NO NO NO NO NO sO i NO NO NO NO NO NO NO NO NO NO NO NO NO vO NO NO NO NO NO NO NO NO NO NO Page 76

o m c C CO O CN sD o CN O CO c O C m er» so sO sO CO m m ON m CM sO CO CN CM in r-l o1—1 t—1 •—I i—l CO

00 r—1 ON ON 1—1 sO O CM GN CN o CO smo m ON Or*N. ON ON CO soO CN CO CM CN CO O r-4 r-4 rO co

00 o O O o m CO CO CO m CO CN CM CO o CM CO CO co CM m CN cr. o c CM CM CM • CM CM CM CN CN CM

m CO r-4 r-4 O CN CO C 00 o O r-4 r-4 O in CN r-l CN CM CM r-l CN CN CN CM CD ca H CO CN CM co ON ON i—1 r-l CO C CO O c CO i—1 CO CM CN r-4

CN CM CM CM CN r—l CN i—1 CM 1-4 CM

CO C r-l i—1 O O 00 m CO O 00 CO CN CM m PQ oo O CM CN CN CM CM

CM vO SO CN 1—1 CO m co CO co ON CN CO CO o CN CN CM CM CN

CO o ON m i—i m CO m CO i—l CM o

CO X

CN O CN Cj CO sO

CO CO CN vO CN m CO CM m r-l CN O CO r-4 CO CM O m é • CN CN CN CM CN CN CN

sO CO CN in sO CN O CO P-. r-t ON CM O m ON co CN CmM CoN CM CN i—i O r-l CM CO CM O CN l—1 i—t i—1 CN o v O CN r-l 4J CN co sO 00 CN O CN r-4 SO sO CO ON ON CN m i—1 O O O i—1 O(Q O o o o O O o O O O O O o o ,^ f^. 1^ r». ,^, CO CO CO 00 00 00 co CO CO sO sO sO sO SO sO sO sO sO vO vO sO vO sO sO vO sO sO sO Page 77

m 00 00 00 m m O o cr» vC 5 0 m m CM m en

00 m oo co r^. CM CJN 6 0 CM co CM 6 0 CM m vO

00 vO CT> CO CO CO in i-i CO • • CM CM O

u m

0) O 14-1 CO

co i-i co m o> CO p** CTN r^- m 1—1 CM CM d

CO co r^ CT\ CM CO CO CO CM 00 o CT\ CO m o CM CM

O CO r-t r-t O CO ON O co o CM i-l O CO CM CM 01 4J CO m m r* ON o i—l CM CM CO o o o o o O r-4 r-4 i-t Q o> cr* O>> O» O\ as CTi vO vD vD VO o Page 78

in CO O CM oin o ion CoO CO oin in

CM m m m CM r-t 00 4

CM CM O m CO i—I m • » « • • c r-l CO CM CM CM

W m CvJ

r-t C/5 CM

CO H

(4 YK A

CM HF S SO D 2.4 7 2.5 9 2.9 6 1.2 5 0.5 2 CM 2.5 4 2.7 0 3.1 5 0.5 4 1.3 2 CA N

CO m CM CM O 0) CM U O O r-t O CO Page 79

st CO 00 __j ^o^ CM

vO 37 1 51 0 02 8 19 1 02 8 04 9 CO O O O O O O O

CM t-» CM 00 CM CM ro CM CM

P-4 CM •C CO CO H u SM PM CM CO o O M Pwu Pwu CO

o sr

ro CM

(U CX CO o

O CO u o ro 00 d

ro oo CO CM CM 00 Ä CM CM

CM rH CO m • • CM 1.2 5 1.4 9 1.2 5 CG S CM CM

CM O CM 00 VO vO IT» CM ro O CM O CM 0) O st CT. CM O O O o O r-t O vO CTi CT* Os O\ o ^«0 \0 Page 80

Figure 1

10' W kt 104

Figure 1 A Primary and joint seismometric estimates W and official yields W for the calibration explosions (0) in the Pahute Mesa, for one control explosion (•) there and for five control explosions (D) in other source areas. Page 81

Figure 2

C=K -K H

O o 2 o 3 K -h o O FF

-1-

Figure 2 The internal bias C • K* - K" as a function of the surface wave A logyield K', for explosions in the Pahute Mesa (0), under Yucca Flat (•) , near Frenchman Flat (FF) and for the explosions Pile Driver (PD), Faultless (F), Gasbuggy (G), Rulison (R) and Long Shot (L). The dashed line is at the mean Yucca Flat bias. Page 82

Figure 3

o K

Figure 3 Secondary seismometric estimates of the ljgyield Kj^ and official log yields K for explosions in tuff (•), alluvium (C) and granite (G) in Nevada. Page 83

Figure 4

4 5 6 magnitude m 7

Figure 4 Nomograms for the seismometric estimates W" for explosions in the USSR from various station and network magnitudes m. For SIU it applies to magnitudes issued before 1968. Figure 5

W or W kt

LRSM

m BRK PAS

10'

\ SIU

HFS

CGS

4 5 6 magnitude

Figure 5 Nomograras for the seismometric estimates W* or W" for explosion? at the Nevada Test Site in the US from various station and network magnitudes m and M. For SIU it applies to magnitudes issued before 1968.