The accurate location of seismic events is a basic discriminant for underground

nuclear test monitoring (Bolt, 1976; Dahlman and Israelson, 1977; Blandford, 1982).

Of particular interest are determining epicentral confidence regions and providing

constraints on estimated focal depths. In this study, only routine teleseismic P

travel-time data are used, as provided by worldwide stations reporting to the

International Seismological Centre (ISC). This lessens the need to model the effects

of crustal and shallow-mantle velocity variations, as is necessary with seismographic

networks operating at regional distances (Blandford, 1981; Evernden et al., 1986)

Johnson, Lane R.

Tralli, David M.

Caltech Authors - Main

Bulletin of the Seismological Society of America, Vol. 77, No. 6, pp. 2212-2217, December 1987 
SHORT NOTES 
EPICENTRAL CONFIDENCE REGIONS OF NUCLEAR TEST EVENTS 
AT TELESEISMIC DISTANCES 
BY DAVID M. TRALLI AND LANE R. JOHNSON 
The accurate location of seismic events is a basic discriminant for underground 
nuclear test monitoring (Bolt, 1976; Dahlman and Israelson, 1977; Blandford, 1982). 
Of particular interest are determining epicentral confidence regions and providing 
constraints on estimated focal depths. In this study, only routine teleseismic P 
travel-time data are used, as provided by worldwide stations reporting to the 
International Seismological Centre (ISC). This lessens the need to model the effects 
of crustal and shallow-mantle v locity variations, as is necessary with seismographic 
networks operating at regional distances (Blandford, 1981; Evernden et al., 1986). 
A method for source location in a tectonically regionalized earth (Tralli and 
Johnson, 1986b) is calibrated for events in the Nevada Test Site (NTS) in the 
south-central Basin and Range province. The locations are demonstrated in the 
context of epicentral confidence regions. The site calibration, in the form of a 
travel-time bias estimation, incorporates the effects of the crustal and shallow- 
mantle velocity structure, and is determined asa function of slowness. The principle 
is somewhat similar to the "master" event location scheme (Evernden, 1969; 
Blandford, 1977; Douglas, 1981). 
Disclosed or accurately known locations are needed in order to estimate a travel- 
time bias. Calibration for sites outside the United States is more difficult since 
knowledge of the locations of a handful of events, as for example the "1004" 
experiment in Eastern Kazakh (Nordyke, 1975; Gubarev, 1976, 1978; Rodean, 1979; 
North and Fitch, unpublished data, 1980), is required. In view of this limitation, 
the calibration determined for NTS is used for Eastern Kazakh, both sites being in 
active continental regions. A similar method of travel-time bias estimation for 
seismogenic zones can also be undertaken if the earthquake locations are con- 
strained by local seismographic networks. 
Given the interest in developing discriminants hat can be used to monitor small 
explosions from outside the country conducting the testing, the study has been 
restricted to teleseismic P-wave data only. This is a realistic situation for Eastern 
Kazakh, where travel-time data are unavailable within a range of about 15 ° (Rodean, 
1979; North and Fitch, unpublished ata, 1980). The problem of focal depth 
estimation cannot be approached using such data. In principle, pP-P and sP-P 
times could be used to constrain focal depths, but the differences are small and 
difficult to analyze for shallow sources (Douglas, 1981). It is assumed that the 
location discriminant considered here would be used to supplement o her discrimi- 
nation criteria such as mb: Ms magnitude ratios, first motions, and spectral methods. 
An on-site approach, as discussed by Evernden et al. (1986), may allow an even 
more complete set of criteria to be applied. Nevertheless, it should be pointed out 
that accurate location remains one of the more robust discriminants a  the size of 
the explosion decreases and is a necessary ingredient in many other discrimination 
criteria. 
2212 
SHORT NOTES 2213 
DATA REDUCTION 
P-wave travel-time data in the epicentral distance range 15 ° to 95 ° were obtained 
from the Bulletin o/the ISC for the period March 1978 through October 1981 for 
nuclear test events in NTS (36.6 ° to 37.4°N and 115.9 ° to 116.6°W) and events in 
the eastern portion of the Eastern Kazakh Nuclear Testing Ground (NTG) (49.3 °
to 50.3°N and 77.8 ° to 79.3°E) in the Soviet Union. A listing of the disclosed 
hypocentral parameters of NTS events is provided by Howard and Richardson 
(1984). 
The method of estimating the P travel times is based on the tectonically region- 
alized tau functions and slowness-dependent source and receiver corrections ob- 
tained by Tralli and Johnson (1986a, b), and is not reviewed here. The hypocenter 
parameter estimation code is a standard nonlinear least-squares algorithm which 
follows the general approach of Levenberg (1944) and Marquardt (1963) as cited by 
Brown and Dennis (1972). 
Slowness and azimuthal biases were determined empirically from the apparent 
functional form of the travel-time residuals for hypocentral parameters fixed at the 
disclosed values of NTS events using both Pahute Mesa and Yucca Flat data. A 
slowness-dependent travel-time baseline correction of -2.43 + 0.092p (sec), where 
p is the horizontal slowness, is obtained from these residuals and is used for 
relocation of both NTS and NTG events. In addition, an azimuthal correction of 
the form -0.52 cos ~b - 0.29 sin ~b (sec) is obtained, where ~b is the receiver-to-source 
azimuth, measured east of north. This azimuthal correction is applied only to the 
NTS data. The residuals in slowness and azimuth are shown, respectively, in Figure 
1, a and b. The differences in the distribution of data between slowness and azimuth, 
particularly the more uniform sampling in slowness, are discussed further by Tralli 
and Johnson (1986a). 
Although the above corrections are used in this study, travel-time biases were 
also determined separately from 1677 Pahute Mesa residuals and 1504 Yucca Flat 
residuals. This yielded combined slowness and azimuthal corrections of the form 
-2.58 + 0.110p - 0.58 cos ¢ - 0.38 sin ¢ (sec) and -2.30 + 0.076p - 0.46 cos ¢ - 
0.18 sin ~ (sec), respectively. The azimuthal terms suggest slow directions at about 
33 ° and 21 ° azimuth. This does not agree with the more detailed studies of Spence 
(1974) and Taylor (1983). However, a mean global baseline bias is still present in 
the correction terms (see Tralli and Johnson, 1986b), and only a comparison of bias 
estimates using travel-time residuals from other source regions would help isolate 
regional variations. 
EPICENTRAL CONFIDENCE REGIONS 
Epicentral confidence llipses are obtained from the sums of the weighted station 
residuals, or estimates of the sample variances, and the covariance matrices of the 
epicentral parameters. The station weights are determined using Jeffreys' (1961) 
method of uniform reduction, where the residuals are assumed to be random 
variables which follow a quasi-Gaussian distribution. No a priori knowledge of the 
station data is invoked, and only first arrivals as given bythe ISC are used. Stations 
yielding residuals greater than about 4 sec are essentially weighted null. Focal depth 
is not a free parameter in the locations, as all focal depths are fixed at the surface. 
However, the disclosed burial depths and elevations of NTS events were used for 
the site calibration. For epicenter determination, the geographical orientation and 
ratio of the axes of the ellipse are then related only to the distribution of stations 
2214 SHORT NOTES 
5.0 
3.0 
1.0 
"i. 0 
' :  ~ ~ ! .~  , 
. : . :  ~:,;~.~ ~ .~: 
i if: 
•! 
• . ' :> .  ' i . ,  . 
~. ::v'~ ! :.~ 
[ :  .. " 
-3.0 
8 
-5.0 
.5 
5.0 
3.0 
1.0 
I I ~ _ _  I 
5.5 6.5 7.5 8.5 
SLOWNESS (S/D%) 
g. 5 
:~ • ' . . ,  . 
• } • . :  • 
• ,@ . . . ::..?..~:. . , !; 
:." "'.i "i; 
-I.0 , : 
-3.0 
b 
-5.0 I I 
1.0 72.0 144.0 216,0 288.0 360.0 
AZIMUTH (DEG) 
FIG. 1. (a) NTS travel-time residuals as a function of slowness p given hypocentral parameters fixed 
at the disclosed values. Uniform reduction is not used to weigh the residuals for bias estimation. Only 
ray paths with slownesses of 9.5 to 4.5 sec/deg are used in order to avoid the effects of upper mantle 
heterogeneity. The corresponding correction, -2.43 + 0.092p (sec), is used for all events. (b) NTS 
residuals as a hmction of azimuth, yielding a travel-time correction of the form -0.52 cos ¢ -0.29 sin 
which is applied only to the NTS events. Azimuth (¢) is measured east of north. 
about the epicenter. The appropriate expressions are given by Flinn (1965) for 
confidence llipses linearized about the epicenter. 
Briefly, the confidence ellipses are scaled by an F statistic according to the 
number of stations (N) and the number of hypocentral parameters estimated (K), 
at a chosen confidence level w. The scaling term CK is given by 
CK 2 = KF(w;  K ,  N - K )s  2 
where see 2 is the estimate of the sample variance. Sample variances for events 
located in this study are typically less than 0.50 sec 2 with a mean of 0.32 sec 2 for 
NTS events and 0.60 and 0.34 sec 2, respectively, for NTG events (Tralli and 
Johnson, 1986b). At NTS, the mean epicentral mislocation is 3 km. Confidence 
ellipses are shown in Figure 2. The F statistic used is at the 95 per cent confidence 
SHORT NOTES 2215 
37.,~ 
37." 
37. l 
37.[ 
a 
-i16.6 
50.0 
49.9 
c~ 
.~ 49.8 
49.7 
AHUTE MESA 
YUCCA FLAT 
-ll6.2 -116. 0 
LONG ITUI)E (C'E) 
i 49. 61 
-i16.4 
i , I r , l , , , , i  
b 
J l l l m J l l l l l ~ J f  
78. 0 78.5 79. 0 
LONGITUDE {°El 
F[6. 2. (a) Ninety-five per cent confidence ellipses of NTS events. Mislocation vectors are relative 
to the disclosed locations. (b) Ninety-five per cent confidence ellipses of Eastern Kazakh events. 
level. The linearized confidence regions in a small neighborhood about he estimated 
epicenter behave statistically as the exact regions, which they approach asymptot- 
ically as the number of stations becomes large (Flinn, 1965). The axes of the 
confidence llipses obtained here are typically on the order of 10 kin, and the 
approximation is valid. 
DISCUSSION OF RESULTS 
The mean area of the epicentral confidence regions of the 18 NTS events with 
greater than 100 observing stations is 48.6 ± 12.9 km 2. With less than 100 stations, 
the mean area is 369.4 ± 188.5 km 2, determined from nine events. Almost all 
mislocation vectors relative to the disclosed locations fall within the 95 per cent 
confidence bounds. The largest uncertainties, with areas greater than 500 km 2, 
correspond to events with mb less than about 4.8 and data from about 50 stations 
only. Confidence ellipses are typically elongated at a NW-SE trend due to the 
azimuthal station distribution (Figure lb). 
For comparison with NTS,  14 Eastern Kazakh (NTG) events with 100 to 200 
stations yield a mean epicentral confidence region area of 162.7 _ 103.2 km 2, and 7 
events with less than 100 reporting stations yield a mean area of 208.6 ± 102.3 km 2. 
This corresponds to mean ellipse axes of 7 to 8 kin. Twenty-four events with greater 
than 200 station observations yield a mean area of 29.5 ± 12.3 km 2. 
As the number of measurements is increased, the location uncertainties should 
indeed decrease. However, an additional likely interpretation of the inverse rela- 
tionship between location uncertainty and number of stations is that the number 
of stations reporting an event decreases as the signal-to-noise ratio decreases and 
that the scatter in the reported arrival times increases correspondingly. In this 
sense, the confidence ellipses are a measure of the magnitude of the event. 
2216 SHORT NOTES 
True event locations in Eastern Kazakh are not known. However, the event of 
15 January 1965 (Nordyke, 1975; Gubarev, 1976, 1978), discussed as a "master" 
event by Rodean (1976) and North and Fitch (unpublished ata, 1980), allows for 
some comparison of accuracy. The relocation of this event, determined from 75 
stations, yielded a presumed mislocation of 7.83 km and an azimuth of 44.54 °
relative to the coordinates of the crater (49.917°N, 79.000°E), whereas the ISC 
mislocation is 5.02 km with an azimuth of 214.95 °. However, the ISC lists a standard 
deviation of station residuals of 1.25 sec, whereas the scheme used here yields a 
standard deviation of 0.50 sec. The area of the 95 per cent confidence llipse is 
about 108 km 2. The estimate of the origin time is now 1 sec before the hour, which 
would agree more with the indications of Rodean {1979) for a nuclear test event. 
Adjustments in the tectonic regionalization i  and about Eastern Kazakh would 
be appropriate. This would not affect the receiver corrections as there are no data 
within about 15 °. However, if Eastern Kazakh were to be regionalized as stable 
continent for example, a systematic shift of about +0.3 sec in the source corrections 
would translate to an earlier shift in the origin times {e.g., Tralli and Johnson, 
1986a). The epicentral coordinates are not affected. 
Well-constrained locations are a useful discriminant in nuclear test monitoring 
programs and a necessary supplement to other discrimination criteria. Clearly, there 
are limitations on the resolution and level of confidence attainable imposed by the 
number of observing stations, the magnitude of the event, and the accuracy of the 
reported readings. On the other hand, the resolution is a robust measure of the 
source magnitude. The small uncertainties in epicenter determinations shown by 
confidence regions at the 95 per cent level are not unexpected after removing the 
observed travel-time bias, particularly at NTS. However, the level of confidence in 
the results when using the slowness-dependent portion of this baseline to locate 
events in Eastern Kazakh is encouraging. 
It is worth noting the indication of Pavlis {1986) that the F statistic may not be 
reliable in cases where the error estimates include systematic model biases. In the 
results presented in this study, a systematic bias in travel times is removed by the 
slowness and azimuthal corrections, and uniform reduction is then applied in the 
location algorithm to ensure a Gaussian distribution of station residuals. The 
confidence llipses obtained are therefore xpected to mainly reflect data error. A 
measure of accuracy is then the fact that mislocation vectors at NTS for the most 
part remain within the 95 per cent confidence llipse, this also suggesting the 
success of tectonically regionalized travel-time estimates in characterizing the 
effects of lateral velocity variations in the crust and mantle. 
ACKNOWLEDGMENTS 
Special thanks are in order to Dr. Timothy H. Dixon of the Jet Propulsion Laboratory for providing 
an opportunity ofinish and present these results. This research was supported by Grant EAR-84167902 
of the National Science Foundation and by the Director, Office of Basic Energy Sciences, Division of 
Engineering, Mathematics, and Geosciences, of the U.S. Department of Energy under Contract DE- 
AC03-76SF00098. All computations were carried out at the Center for Computational Seismology of the 
Lawrence Berkeley Laboratory. 
REFERENCES 
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Francisco, California. 
Blandford, R. R. (1977). Discrimination between earthquakes and nuclear explosions, Ann. Rev. Earth 
Planet. Sci. 5, 111-122. 
SHORT NOTES 2217 
Blandford, R. R. (1981). Seismic discrimination problems at regional distances, in Identification of 
Seismic Sources--Earthquake or Underground Explosion, E. S. Husebye and S. Mykkeltveit, Editors, 
695-740. 
Blandford, R. R. (1982). Seismic event discrimination, Bull. Seism. Soc. Am. 72, $69-$88. 
Brown, K.. M. and J. E. Dennis (1972). Derivative free analogues ofthe Levenberg-Marquardt and Gauss 
algorithms for nonlinear least squares approximation, Numer. Math. 18, 289-297. 
Dahlman, O. and H. Israelson (1977). Monitoring Underground Nuclear Explosions, Elsevier Scientific 
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Evernden, J. F. (1969). Identification of earthquakes and explosions by use of teleseismic data, J. 
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Evernden, J. R., C. B. Arehambeau, and E. Cranswick (1986). An evaluation ofseismic decoupling and 
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Pavlis, G. L. {1986). Appraising earthquake hypocenter location errors: a complete, practical approach 
for single-event locations, Bull. Seism. Soc. Am. 76, 1699-1717. 
Rodean, H. C. (1979). ISC events from 1964 to 1976 at and near the nuclear testing round in eastern 
Kazakhstan, UCRL-52856, Lawrence Livermore Laboratory, University of California, Livermore, 
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Spence, W. (1974). P-wave residual differences and inferences on an upper mantle source for the Silent 
Canyon Volcanic Centre, Southern Great Basin, Nevada, Geophys. J R. Astr. Soc. 38, 505-523. 
Taylor, S. R. (1983). Three-dimensional crust and upper mantle structure at the Nevada Test Site, J. 
Geophys. Res. 88, 2220-2232. 
Tralli, D. M. and L. R. Johnson (1986a). Estimation of slowness-dependent source and receiver 
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heterogeneous Earth, Phys. Earth Planet. Interiors 44, 242-256. 
JET PROPULSION LABORATORY 
CALIFORNIA INSTITUTE OF TECHNOLOGY 
PASADENA, CALIFORNIA 91125 (D.M.T.) 
CENTER FOR COMPUTATIONAL SEISMOLOGY 
UNIVERSITY OF CALIFORNIA, BERKELEY 
BERKELEY, CALIFORNIA 94720 (L.R.J.) 
Manuscript received 8January 1987 


Epicentral confidence regions of nuclear test events at teleseismic distances

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Epicentral confidence regions of nuclear test events at teleseismic distances

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