## Summary

Analysis of variance is used to estimate the measurement error and path effects in the P times reported in the Reviewed Event Bulletins (REBs, produced by the provisional International Data Center, Arlington, USA) and in times we have read, for explosions at the Chinese Test Site. Path effects are those differences between traveltimes calculated from tables and the true times that result in epicentre error. The main conclusions of the study are: (1) the estimated variance of the measurement error for P times reported in the REB at large signal-to-noise ratio (SNR) is 0.04 s^{2}, the bulk of the readings being analyst-adjusted automatic-detections, whereas for our times the variance is 0.01 s^{2} and (2) the standard deviation of the path effects for both sets of observations is about 0.6 s. The study shows that measurement error is about twice (∼0.2 s rather than ∼0.1 s) and path effects about half the values assumed for the REB times. However, uncertainties in the estimated epicentres are poorly described by treating path effects as a random variable with a normal distribution. Only by estimating path effects and using these to correct onset times can reliable estimates of epicentre uncertainty be obtained. There is currently an international programme to do just this. The results imply that with P times from explosions at three or four stations with good SNR (so that the measurement error is around 0.1 s) and well distributed in azimuth, then with correction for path effects the area of the 90 per cent coverage ellipse should be much less than 1000 km^{2}—the area allowed for an on-site inspection under the Comprehensive Test Ban Treaty—and should cover the true epicentre with the given probability.

## 1 Introduction

The International Data Centre, Vienna (IDC) is being set up to take *inter alia*, data from the seismological network of the International Monitoring System (IMS) to produce a bulletin of seismic disturbances (the Reviewed Event Bulletin, REB) rapidly, and as far as possible automatically. The REB is for use by States Parties to the Comprehensive Test Ban Treaty (CTBT) to check for possible violations of the Treaty. The IDC also makes available to States Parties the seismograms from the IMS. Should a possible violation of the Treaty be detected there is provision for an on-site inspection (OSI): an international team will search the area around the epicentre of the suspicious disturbance to determine if a nuclear test really took place.

The Treaty states that ‘the area of an OSI shall be continuous and its size shall not exceed 1000 km^{2}. There shall be no linear distance greater than 50 km in any direction’. For an OSI to be effective it is essential for a seismic disturbance that is truly a nuclear explosion, that the area of search covers the true epicentre. This requires not only that the epicentre be unbiased but also that the area allowed by the Treaty for any possible OSI, covers the true epicentre with high confidence. In practice this seems to be interpreted by the IDC as meaning that what is termed the 90 per cent coverage ellipse on epicentres published in the REB, should have an area of less than 1000 km^{2}.

The IDC uses standard methods of hypocentre and origin time estimation which requires the minimization of the sum of the squared differences between observed and predicted times. Observed traveltimes from true hypocentres and origin times differ from those predicted from traveltime tables (or earth model) because of measurement error (the wrong onset is picked) and errors in the tables. Tables usually only give times as a function of focal depth and epicentral distance whereas, because of lateral heterogeneity in the earth, times depend on the specific source-station path. In general, the traveltime differences show a baseline shift (the average difference over the stations used is not zero) with times being early or late relative to this baseline for paths to each station. It is the relative path effects—called by the IDC, model error—that introduces errors into the estimates of epicentres.

In the absence of path effects the size of any area of uncertainty around an estimated epicentre depends on the geometry of the observing network and the variance of the measurement error. This variance is usually estimated from the time residuals; the difference between the observed times and the times calculated from the estimated hypocentre and origin time. This gives the sample variance. For large numbers of residuals the sample variance should approximate to the population variance of the measurement error—which is what is required. (Note, however, that in practice variances estimated in this way will always be contaminated by path effects.) When the number of times is small (say <10) the uncertainty in the sample variance as an estimate of the population variance, is large, and this is reflected in the uncertainties in the epicentre estimates when these are determined by the standard method of Flinn (1965). Evernden (1969), argues that such wide limits are overestimates because upper bounds can be placed on the error variance from previous experience, and that this prior knowledge should be used in estimating the variance of the population of measurement errors. Evernden (1969) suggests measurement error is around 0.1 s and this is supported, at least for P times for explosions by the studies of Douglas (1997).

The obvious way to deal with path effects is to estimate them and use the estimates to correct observed times. In the 1960s and 1970s a number of attempts were made to estimate such corrections for times to teleseismic distances (e.g. Cleary & Hales 1966; Herrin & Taggart 1968; Lilwall & Douglas 1970; Poupinet 1979) but new studies are needed to obtain corrections for stations established more recently, particularly for those of the IMS. There is currently an international programme to do this, that is, to determine what are termed ‘source-specific station corrections’ (SSSCs). Meanwhile the IDC uses an *a priori* variance to estimate uncertainties that has two components: one for measurement error and the other for path effects. In this way it is hoped that the region of uncertainty around the estimated epicentre will cover the true epicentre with the specified probability. However, Bondár (1998) shows that there are epicentral regions where the area of uncertainty almost always fails to cover the true epicentre.

There are few published estimates of the variance of measurement error or path effects—particularly for onsets measured at the IDC. Douglas (2005) do give estimates of the variances for P times from explosions at the Nevada Test Site observed out to distances of 20° but these times are from explosions in the 1960s, not IDC observations. Here we investigate errors and path effects in times reported in the REBs for the four 1995/96 Chinese underground tests. In 1995/96 the IDC, Vienna had not been established; the REBs used here were produced by the provisional IDC, Arlington, USA. However, there is little difference in the procedures used by the two IDCs so the conclusions arrived at here should apply to current REBs.

We follow Douglas (2005) and use analysis of variance to estimate, among other things, measurement error and path effects for the P times reported in the REB for the distance range 20-100°, for three of the four 1995/96 Chinese tests (Table 1Table 1): two in 1995 (May 15 and August 17), and one in 1996 (June 8). The three explosions (ISC *m*_{b}≥ 5.7, Table 1Table 1) were fired in boreholes drilled within a few kilometres of each other in the main test area (MTA). The fourth 1995/96 explosion (1996 July 29, ISC *m*_{b}4.7) was fired in a tunnel driven into a range of mountains about 30 km north-west of the main test area. (Below, the individual explosions are referred to by date in the form given in Table 1Table 1).

Inspection of the P seismograms from the four explosions shows, as expected from the differences in magnitude, that the signal-to-noise ratio (SNR) for the tunnel explosion is much less than that for the MTA explosions (Fig. 1). Hence the measurement error is likely to be greater for the tunnel explosion than for the other three. There is also the possibility that path effects differ between the two test areas. The possible differences in path effects for the two test areas and in measurement error with magnitude are investigated.

Ideally this analysis would be carried out using the true hypocentres and origin times of the explosions but these have not been published. However, Fisk (2002) has determined the epicentres of 11 Chinese tests including the four 1995/96 tests, using satellite imagery combined with locations estimated from P times. The Fisk (2002) epicentres (Table 1Table 1) are taken to be the true epicentres. Only by using onset times from clusters of seismic disturbances can path effects and measurement error be separated. To allow comparisons of onsets picked by the IDC and those of an analyst, we have re-read many of the onset times of P recorded at IMS stations for the four explosions. We refer to our readings as the BKN observations.

The path effects obtained here are estimates of the SSSCs. Applying the corrections to the times for any future disturbances in the vicinity of the test site, should result in estimated epicentres with negligible systematic bias.

## 2 Hypocentre Estimation At The Idc

Hypocentres published in the REB are estimated principally from times of direct P, but times from some supplementary phases (and vector slowness estimates from array readings when the number of times is small) may also be used. Most of these phases are detected automatically, and initially the onsets of these signals are read also automatically. The onsets are then reviewed by an analyst and may be adjusted, but (provided any adjustments are small) they are still flagged as being automatic picks. If a phase is found and read by an IDC analyst and was not detected automatically it is flagged as a manual pick. The measurement error is estimated on the basis of the SNR (Bondár 1998). For onsets picked automatically and reviewed by an analyst the standard deviation (SD) of an observation is assumed to vary from 1.66 s when the SNR is 2.0, to 0.12 s when the ratio is 17.7 or greater. For unreviewed picks the SD is assumed to vary from 1.72 s at a SNR of 4.0 to 0.69 s at a SNR of 18.0 or greater. This measurement error is combined with a path effect to give an overall estimate of the uncertainty in the onsets. The path effect for most of the distance range beyond 20° is assumed to have a SD of 1.0-1.5 s. The equations of condition are weighted inversely as the standard deviation of the *a priori* error and hypocentre and origin time estimated by least squares. (SNR measurements are made by the automatic system, so if a signal is not detected initially, then, although the onset may be picked manually later, there is no estimate of SNR. Such readings are assigned a SD of 0.55 s.) For the explosions considered here the number of P times for each explosion is greater than 40, so no azimuth observations are used. Not all onsets reported in the REBs are used by the IDC in estimating location and origin time; those that are, are referred to as time-defining phases. To be time defining the residuals must be less than 2 s.

The REB gives measures of uncertainty on hypocentre and origin time estimates, of which the coverage ellipse on the epicentre is of most interest here. Flinn (1965) gives expressions for the standard method of estimating confidence regions on epicentres based on the sample variance. The coverage ellipse given in the REB is calculated in a similar way to the confidence ellipse but using an *a priori* variance for the combined effect of measurement error and path effects.

## 3 Methods

The difference between the observed traveltime (O) from explosion *i* to station *j*, and the time (C) calculated for the true hypocentre and origin time (assumed here to be the Fisk 2002, epicentres with zero depth and origin time set to the nearest minute, see below) from the IASPEI 91 Tables (I91, Kennett & Engdahl 1991) gives the O−C residual *T*_{ij}+ɛ_{ij}, where *T*_{ij} is the difference between the true and predicted times and ɛ_{ij} measurement error. It is then assumed that *T*_{ij} can be written as:

*E*

_{i}is that part of

*T*

_{ij}that is common to stations recording explosion

*i*, and

*S*

_{j}is the part common to explosions recorded at station

*j*.

*E*

_{i}is referred to here as the explosion effect and

*S*

_{j}is the path effect. Both effects as defined here, have zero mean. is then an average baseline shift common to all

*T*

_{ij}. If all the explosions are recorded by all stations, least-squares estimates of

*E*

_{i},

*S*

_{j}, and are simply obtained, thus: the estimate of, is the average over all the O−C residuals; the average over station

*j*minus the estimate of

*S*

_{j}; and the average over explosion

*i*minus the estimate of

*E*

_{i}. However, all stations used do not report P times from all the explosions, so least-squares estimates of

*E*

_{i},

*S*

_{j}, and have to be found by forming and solving the normal equations, with the condition that to ensure that the average explosion effect and average path effect is zero. (The method is the same as that used by Carpenter 1967, to analyse magnitudes for explosions at a test site.) In addition to estimates of

*E*

_{i},

*S*

_{j}, and, estimates of the variance of the measurement error and of the mean square due to the explosion and path effects can be obtained. These can be used to test for the statistical significance of

*E*

_{i}and

*S*

_{j}.

If the explosions are fired at the same height, *h*, above sea level in the same structure, *T*_{ij} will include the constant baseline shift between the IASPEI times for zero depth and a source at height *h*. This shift is taken up in . Any variation in *h* with explosion and any differences from some average in the variation in *P*-wave speed with depth below each explosion, will give rise to variations in traveltimes that will be taken up in the explosion effects. As the maximum range of *h* and the variation in structure are likely to be small, the explosion effects are also expected to be small.

The most important contribution to *T*_{ij} is expected to be the path effects, *S*_{j} (the IDC's model error). It is this component of *T*_{ij} that increases the uncertainty in epicentre estimates. Formally Σ*S*^{2}_{j}/(*m*− 1) is an estimate of the variance of the path effects; *m* being the number of stations used.

## 4 The Bkn Times

The BKN times were read by one analyst from the seismograms obtained from the provisional IDC. A total of 260 P times are reported in the REB from the four explosions, for stations in the distance range 20°-100°. Attempts were made to get all 260 seismogram segments covering the expected arrival times of the P signals from the four explosions; 251 were obtained. As the seismograms are not all recorded on systems with a common response we converted the seismograms as recorded, to ones that simulate the signal as it would be recorded on one system; this has the amplitude response of a widely used SP system, which has a fall-off below 1 Hz of ω^{3}, whereas above 1 Hz the response is proportional to ω; ω being angular frequency. All the conversions were carried out satisfactorily except for those seismograms where the original recordings are from a high-frequency channel (e.g. MJAR). Stations with such recordings were therefore dropped from the analysis. In addition some seismogram segments have data errors or do not cover the full time-bracket requested so they were also dropped from the analysis. Inspection of the seismograms shows another problem with attempting to repeat the IDC readings: there is no obvious signal on some recordings for which the REB reports a P time. Fig. 1 shows examples of such recordings together with the examples of observed signals.

Five P onset times reported in the REB have O−C residuals that are too large to be taken as time defining by the IDC. These large residuals do not seem to be the result of misreading at the IDC: our re-reading shows similar residuals. The most likely explanation of the large residuals seems to be timing (clock) errors. The times reported for station AAE for 950515 and 960608 have large errors (O−C residuals of 6.1 s and 16.8 s respectively) yet in the reports of the National Earthquake Information Center, the O−C residuals are around a second or less.

Preliminary results from the analysis of variance gave further evidence of clock errors: the O−C residuals for a given station should be roughly the same across explosions if measurement error is only a few tenths of a second, but differences between residuals of 1-2 s are seen for several stations, one of which is ARCES. Kværna (2000) reports clock errors at ARCES. Israelsson and McLaughlin (personal communication, 2001) also note that there are intermittent clock errors in REB times. Five further readings are, therefore, dropped from the analysis because of possible clock errors.

For observations from a station to be included in the analysis of variance, times are required from at least two explosions. Stations reporting times from only one explosion even though they may be reliable cannot be used. After all the winnowing, 206 BKN times (all read from seismograms corrected to the common response) are available for analysis. The distribution around the test site of the stations used, is shown in Fig. 2.

## 5 Results Of The Error Analysis

The origin times of Fisk (2002) are set so that for a given network of stations, the average difference between the traveltimes calculated from the epicentre (with depth zero) and the observed traveltime, is zero. Inspection of the origin times (Table 1Table 1) shows that the three MTA explosions all have origin times about 0.6 s before the minute suggesting that they might have been fired on the minute. The origin time of the explosion at the tunnel site (960729) is also close to a minute. For the purposes of the analysis described here it is assumed that all the explosions were fired on the minute nearest the Fisk (2002) origin time.

Table 2Table 2 gives the statistics of the analyses of the REB and BKN observations, from the three MTA explosions (i.e. leaving out readings from 960729); the REB readings used being those for which there is a BKN reading. For both the analyses the path effects are highly significant—the mean square due to path effects is at least 16 times greater than the variance of the measurement error—and the variance of the path effects is around 0.3 s^{2}. For both REB and BKN observations the measurement error is small (SD 0.1-0.2 s) with the error in the BKN reading being somewhat smaller than those of the REB.

An unexpected difference in the REB and BKN observations is in the explosion effect. For the BKN analysis, the explosion effects are insignificant. For the REB observations on the other hand the explosion effects have a range of 0.3 s (Table 1Table 1) and are significantly different from zero at less than the 0.005 per cent level. These differences are discussed in .

The effect on the sample variance of the O−C residuals, of correcting for path effects is shown in Table 3Table 3. When the epicentres of the four explosions are estimated with no corrections for path effects the sample variance of the time residuals ranges from 0.21-0.32 s^{2} for the REB readings and 0.19-0.30 s^{2} for the BKN observations. After correction for path effects the sample variances for the three MTA explosions ranges from 0.01-0.03 s^{2} for the REB times and are negligible for the BKN readings.

For the tunnel explosion the sample variance is larger than for the MTA explosions—almost certainly because the SNR is much lower for the tunnel explosion than for the other explosions. Some evidence for this can be seen in the estimates of sample variance obtained by dividing the 960729 observations into two groups: those for which the time given in the REB is a manual reading (the M stations); and those (the A stations) for which P is detected and the onset read automatically, but where the automatic reading may have been adjusted by the analyst (Table 3Table 3). The REB times for the 15 M stations have significantly lower variance (0.03 s^{2}), than the 16 times read for the A stations (0.10 s^{2}). For the same two sets of stations the sample variances for the BKN readings (all read manually) show the opposite effect: the A stations have lower variance than the M stations. The explanation of the differences in sample variance between the two groups of stations obtained with the BKN readings seems to be that the SNR is greater at the A stations (which are mainly arrays) than at the M stations. The differences in variance at the A and M stations obtained with the REB observations seems to be that IDC analysts do not consistently adjust the automatic readings, leaving unadjusted such readings if they are within a few tenths of a second of what the analyst would read. Overall however, the differences in the estimates of sample variance with station set, suggest that it is reading error (due to low SNR) rather than errors in the path effects that explains why the sample variance is larger for the tunnel explosion than the MTA explosions.

Figs 3(a) and (b) shows the epicentres estimated using the REB times, relative to the true (Fisk) epicentres for each of the four explosions: Fig. 3(a) is without correction for path effects; Fig. 3(b) with correction. The 90 per cent coverage ellipses on the epicentres without correction for path effects are calculated using 0.35 s^{2} for the *a priori* variance of the combined measurement error and path effects; with correction for path effects an *a priori* variance of 0.05 s^{2} is used to allow for measurement error. (These variances are from Table 2Table 2 rounded to the nearest 0.05 s^{2}).

The estimated epicentres without correction for path effects (Fig. 3a) are displaced to the NE of the Fisk (2002) epicentres along, as might be expected, the major axes of the ellipses. There are no stations in the azimuth quadrant 35-125° and only one station (in Africa) to the SW. Control in the SW-NE direction is thus poor. However, as all the epicentres are displaced to the NE and three of the coverage ellipses do not cover the true epicentres this indicates that the times to stations on azimuths between 0° and 35° are relatively fast. Correcting for the appropriate path effects removes the large systematic bias and the coverage ellipses for the three MTA explosions cover the true epicentres (Fig. 3b; note the difference in scale of Figs 3+c and 3b+d).

The epicentres estimated using the BKN times with and without correction for path effects are shown in Figs 3(c) and (d). The 90 per cent coverage ellipses without correction use an *a priori* variance for the combined measurement error and path effects of 0.30 s^{2}. For the coverage ellipses with correction for path effects a measurement error of 0.01 s^{2} is assumed for the MTA explosions and 0.05 s^{2} for the tunnel explosion. Again correction for path effects removes systematic bias from the epicentres of the MTA explosions. Nevertheless, the coverage ellipse for 960608 fails to cover the true epicentre. Similarly for both the REB and BKN times the coverage ellipse on the tunnel explosion does not cover the true epicentre, although the distance from the ellipse boundary is small. These failures of the ellipses to cover the true epicentres could have many causes. They may be a chance effect, error in the statistical model, or evidence that the Fisk epicentres are in error. Whatever the explanation the discrepancy is so small (∼2 km) that for the purposes of Test Ban verification they can be neglected.

## 6 Discussion

The results show that the bulk of the REB times are reliable, although measurement error is probably greater than assumed by the IDC (SD ∼0.2, rather than ∼0.1 s) at large SNR. Nevertheless, the study confirms the IDC assumption that, neglecting gross errors (e.g. clock error), the contribution of measurement error to the overall error (at least for P from explosions) is insignificant (variance over seven times smaller than the path effects).

The explosion effects turn out to be insignificant for Analysis 2 (BKN), showing that the hypothesis that the three MTA explosions were fired on the minute is acceptable. (This assumes of course, that there is a baseline shift, between the times from the test site to the stations used here and the IASPEI 91 traveltimes of −0.3 s, Table 2Table 2. This shift could also contain any analyst bias that is constant over the three explosions.) Assuming the baseline shift for the tunnel explosion is the same as for the three MTA explosions, the origin time of the tunnel explosion estimated from the BKN readings is within 0.05 s of the minute suggesting that it may be that all the explosions were fired on the minute.

If the firing times were truly on the minute, then the significant explosion effects found in the analysis of the REB times implies systematic measurement errors in the times for each explosion. This may be an analyst effect, if the times for each explosion were read or adjusted by one analyst, and a different analysts was assigned to each explosion. Alternatively, it may be that differences in the form of the signal onset of the explosions results in the P times for each one being read relatively early or late by the automatic system—but only by around ±0.1 s.

Pavlis (1986), Billings (1994) and Douglas (2005) among others point out that treating path effects as a normally distributed random variable is unsatisfactory when estimating uncertainties in epicentres, because it does not allow for any systematic bias in the estimated epicentres resulting from the effects. This is demonstrated by the results presented here. For, consider a sequence of explosions at the MTA all recorded by the network of stations used here. None of the estimated epicentres would ever fall outside the coverage ellipse calculated by treating the path effects as a random variable: 90 per cent would be expected to lie within a coverage ellipse calculated using the variance of the measurement error with its centre offset from the true epicentre by the bias for the path effects. This is why the epicentres of the explosions are so tightly clustered in Figs 3(a) and (c), and do not show the scatter implied by the size of the coverage ellipses. Further, if the variance of the path effects is simply inflated to ensure that the coverage ellipse covers the true epicentre then this ellipse will cover the true epicentre 100 per cent of the time.

Whether or not the coverage ellipses cover the true epicentres is unimportant when the epicentres with correction for path terms differ from the true epicentres by only a few kilometres and the probability that the true epicentre lies outside a circle of area 1000 km^{2} is vanishingly small. Further, with correction for path effects an OSI would only need to search a small fraction of the 1000 km^{2} allowed, to make sure that the true epicentre is covered.

Usually depth estimates for shallow sources have large uncertainty if P times from only teleseismic distances are used, as is done here: the rate of change of traveltime with depth is almost constant with distance in the teleseismic range, so origin time and depth are almost linearly dependent. Consequently the estimates of epicentre error shown in Fig. 3 have been made with focal depth restrained to zero. Removing the constraints demonstrates some of the difficulties with depth estimation with teleseismic networks of stations. Thus, whereas with the depth restrained a solution is obtained for the three MTA explosions in two to three iterations, without the restraint more than ten iterations are usually required. Further, for the REB and BKN times without correction for path effects the depth estimates range from −18 to 15 km and the 90 per cent confidence limits range from ±11 to ±27 km. With the REB times corrected for path effects the depth estimates range from −5 to 20 km and the uncertainties from ±5 to ±12 km. Clearly then these depth estimates have little value.

With the BKN times corrected for path effects however, the uncertainties are reduced to around ±5 km and the depth range to −2 to 5 km; the sources are thus shown to be shallow. In practice of course any suspicious disturbance is likely to be of low magnitude and so recorded by only a few stations. Then, with say a tenth of the number of stations used here, the uncertainty would increase to around ±15 km, assuming that the uncertainty depends only on *n*^{−1/2}, where *n* is the number of times used. However, the uncertainty also depends on the range of distance covered by the stations. As the distance range decreases the linear dependence of the origin time and depth, and hence their uncertainties, increases. In the limit, when all the stations are at the same epicentral distance, there is no solution—the confidence limits are infinite. Depth estimates with teleseismic networks will thus usually be unreliable except in the ideal circumstances such as is available here with the BKN times corrected for path effects—large numbers of stations well spread in distance, and with reading error of 0.1 s. An epicentre however, can almost always be estimated if the depth is restrained to zero—which is anyway, presumably the best epicentre to use for an OSI.

Although the estimated 90 per cent confidence limits on depths of the MTA explosions is small for the BKN times with path corrections, it is significantly greater than the limits on the epicentres, which are around ±1 km. Thus, when the number of stations is reduced by a factor of 10 (as assumed in the discussion on depth estimates above) the confidence limits on the epicentre would be expected to increase by about a factor of three, which is still negligible in a target for an OSI. That epicentres can be estimated to within a few kilometres with small numbers of stations is confirmed by the results of Douglas & Young (2005). The results show that with a measurement error of a few tenths of a second as found here, reliable epicentres can be estimated with P times from only three or four stations (with depth restrained), given correction for path effects and stations well distributed in azimuth—the 90 per cent coverage ellipse covers the true epicentre with the specified probability and the area is much less than 1000 km^{2}.

The initial purpose of the study of the REB P times from the 1995/96 Chinese explosions was to estimate measurement error and path effects and in particular to estimate errors in onsets picked automatically. It was expected, as the 1995/96 explosions have magnitudes well above *m*_{b} 4.0, that most of the P times published in the REB would be automatic picks. However, as the study proceeded and particularly from a comparison of the REB with its precursor bulletins (called by the IDC, Seismic Event Lists) it became clear that many of the times specified as automatic are indeed analyst-adjusted times. In addition a significant number of the REB times, are specified as manual picks—particularly as discussed above for 960729, the explosion with the lowest magnitude of the four. Manual picks are not all for signals with low SNR, however. For 950817 and 960608 with magnitudes around *m*_{b}6.0, the YKA P onsets are given as manual, yet supplementary phases (PKPPKP and PKP2 respectively) are reported as being detected automatically. Further, readings have been included in the REB where there are clock errors, and from stations where we can find no signal. Times from such stations if not read on a true signal might be expected to introduce above average errors. (Conversely, if the analyst is guided by a predicted time such times may have an apparent O−C residual that is below average.) All this means that it is not possible to estimate the performance of the automatic system free from analyst intervention.

A more systematic analysis than is possible here could be made if the recordings were reprocessed to obtain as large a set as possible of automatic detections and onset readings, without any adjustment by an analyst. In addition to testing the current processing system—to investigate why, for example, some signals with large SNR are not detected—the recordings could be used to compare the performance of detection and onset-time-measuring algorithms in general, with those of analysts. Perhaps the recordings should be collected into a data library and made available to research groups that would like to test new or different systems. Ideally, the recordings in such a library would be corrected for any timing errors and would include at least 24 hr of data (say 12 hr before the onset of P from the explosion and 12 hr after) to allow any processing system to settle down and be tested on more than one signal. More urgently of course the source of the timing errors needs to be identified and eliminated, if this has not already been done.

Similar studies are possible using observations from groups of shallow earthquakes (ideally with epicentres that have been reliably determined from close-in observations). However, it seems unlikely that the onsets of P from earthquakes can be read as reliably as those of explosions either automatically or by an analyst (see Douglas 1997)). What is required from such studies is reliable estimates of path effects. Given this, the capacity of the network to locate explosions can be estimated using the *a priori* variance for the measurement error of explosion times inflated slightly to allow for residual path effects.

Whatever the measurement error turns out to be for P times from earthquakes published in the REBs, it should be significantly smaller than that of times routinely reported by non-IMS stations to the NEIC and ISC (once clock errors have been eliminated). Including the REB times in tomographic studies—weighted appropriately to reflect the higher reliability of such readings over normal bulletin data—should therefore improve the resolution of the earth models.

## 7 Conclusions

Analysis of variance is used to estimate the measurement error and path effects in the traveltimes of P for the three 1995/96 Chinese explosions at the MTA. Two sets of onset times are analysed: those reported in the REB; and times (the BKN times) read as part of this study by one analyst. The main conclusions of the study are:

- (i)
the estimated variance of the measurement error at large SNR is 0.04 s

^{2}for the REB onsets (the bulk of the readings being analyst-adjusted automatic-detections) and 0.01 s^{2}for the BKN readings; - (ii)
the formal variance of the path effects is around 0.3 s

^{2}(a SD of about 0.6 s, about half that assumed at the IDC) but uncertainties in the estimated epicentres are poorly described by treating these effects—as they are at the IDC—as a random variable with a normal distribution; - (iii)
it is systematic bias due to path effects—estimated for the Chinese Test Site to be about 11 km to the northeast—that alone increases the uncertainty in epicentre estimates; if bias is insignificant the uncertainty is controlled purely by the measurement error whatever the variance of the path effects;

- (iv)
the hypothesis that the three MTA explosions were all fired on the minute (or at least a common time relative to the minute) is acceptable;

- (v)
for the analysis of the REB observations the explosion effects for the three MTA explosions have a range of 0.3 s and are significantly different from zero at less than the 0.005 per cent level, which implies (if the explosions were fired at a common time relative to the minute) that the times for some explosions are being picked systematically early and for others systematically late;

- (vi)
the path effects for the one 1995/96 Chinese test at the tunnel site (about 30 km northwest of the MTA) are little different from those of the MTA;

- (vii)
the study confirms what is assumed by the IDC, that at large SNR path effects are much greater than measurement error, so that once SSSCs (the equivalent of path effects) are available for IMS stations, errors in REB epicentres for explosions should be no more than a few kilometres even with times from only a few stations.

## Acknowledgments

We thank Dr David Bowers for his helpful comments which resulted in significant improvements to the paper.