High-precision location and yield of North Korea's 2013 nuclear test
Laboratory of Seismology and Physics of Earth's Interior; School of Earth and Space Sciences, University of Science and Technology of China, Hefei, Anhui, China
Corresponding author: M. Zhang, Laboratory of Seismology and Physics of Earth's Interior; School of Earth and Space Sciences, University of Science and Technology of China, Hefei, Anhui 230026, China. (firstname.lastname@example.org)
 Using North Korea's 2009 nuclear test as reference and satellite imagery, we show that the location and yield of North Korea's 2013 nuclear test can be quickly and accurately determined based on seismic data. North Korea's 2013 nuclear test site is pinpointed by deriving relative location of North Korea's 2009 and 2013 nuclear tests and using the previously determined location of the 2009 nuclear test, while its yield is estimated based on the relative amplitude ratios of the Lg waves recorded for both events, the previously determined Lg-magnitude of 2009 nuclear test and burial depth inferred from satellite imagery. North Korea's 2013 test site is determined to be located at (41°17′26.88″N, 129°4′34.68″E), about 345 m south and 453 m west of its 2009 nuclear test site, with a geographic precision of 94 m. Its yield is estimated to be 12.2 ± 3.8 kt.
 On 12 February 2013, the Democratic People's Republic of Korea (North Korea) announced, without providing information of exact time, location, and yield, that it conducted a third nuclear test. On that day, the United States Geological Survey (USGS) reported detecting a magnitude 5.1 event in an aseismic region in North Korea (http://earthquake.usgs.gov/earthquakes/eventpage/usc000f5t0#summary).
 In the event of a nuclear test, source discrimination, location determination, and yield estimate of the test are the immediate issues facing the scientific monitoring community. Rapid and accurate determination of these parameters is, however, still hindered by many factors. In location determination, the traditional ways to locate an event still suffer large uncertainties due to our imperfect knowledge of seismic heterogeneities in the Earth's interior and lack of efficient methods to simulate high-frequency wave propagation in three-dimensional heterogeneous media at large distances. For example, the horizontal uncertainties of North Korea's 2013 nuclear test location reported by USGS and the Comprehensive Nuclear-Test-Ban Treaty Organization are ±11.2 km and ±16.2 km, respectively. In yield estimate, our lack of knowledge of burial depth, inaccurate consideration of path and station effects of wave propagation, and uncertain relationship between the seismic amplitude and yield could result in a large range of yield estimation. For example, the yield of North Korea's 2013 test is estimated at 19.8 kt, with minimum and maximal yields of 14.8 and 39.5 kt by some research groups (http://www.iris.edu/dms/nodes/dmc/specialevents/2013/02/12/north-korea-nuclear-explosion/); while the Federal Institute for Geosciences and Natural Resources, a state-run geology research institute in Germany, places the estimate to be 40 kt (http://www.bgr.bund.de/DE/Gemeinsames/Oeffentlichkeitsarbeit/Pressemitteilungen/BGR/bgr-130212_Kernwaffentest-Nordkorea.html).
 In this study, we show that, by combining modern methods of high-precision relocation and satellite imagery, and using the knowledge of a previous test (North Korea's 2009 test) as reference, it is possible to rapidly and accurately determine the location and yield of North Korea's 2013 test. In section 2, we review the previously determined location, magnitude, and yield of North Korea's 2009 test; in section 3, we present detailed analyses of relative location and magnitude difference between North Korea's 2009 and 2013 tests, and determine the location and yield of North Korea's 2013 nuclear test.
2 Review of the Previously Determined Location and Yield of North Korea's 2009 Nuclear Test
2.1 Location of North Korea's 2009 Nuclear Test
 North Korea's 2009 test was located by Wen and Long  to be at (41°17′38.14″N, 129°4′54.21″E) (Table 1), with a geographic precision of 140 m. The location was derived based on the relative location between North Korea's 2006 and 2009 tests and satellite image identification of the 2006 test site [Wen and Long, 2010] (http://cryptome.org/eyeball/dprk-test/dprktest.htm). The relative location was obtained by minimizing arrival time differences of seismic Pn wave, the first arriving compressional wave that diffracts along the Earth's crust-mantle boundary, between North Korea's 2006 and 2009 tests, using seismic data recorded at seismic stations in the Global Seismographic Network and F-net in Japan. North Korea's 2009 nuclear test was located about 723 m north and 2235 m west of 2006 test (Figure 3). Similar results were also obtained by others using different methods [e.g., Murphy et al., 2010; Selby, 2010].
Table 1. Location, Time, Lg-Magnitude, and Yield of North Korea's Nuclear Tests
2.2 Yield Estimation of North Korea's 2009 Nuclear Test
 Much effort has been devoted to estimate the yield of North Korea's 2009 test. Murphy et al.  estimated the yield of the 2009 test to be 4.6 kt, if detonated at a depth of 550 m. However, they pointed out that there was a significant trade-off between the assumed burial depth of the test and yield estimation. The observed seismic data could not distinguish between an explosion with a 2.7 kt yield at a depth of 200 m and a 4.8 kt yield at a depth of 800 m. Rougier et al.  combined the results from the hydrodynamic simulation and near-field observations and obtained the minimum yield and depth of burial for the 2009 test as 5.7 kt and 375 m. Chun et al.  obtained mb(Lg) of the 2009 test to be 4.86 ± 0.13 and yield to be 6.51 kt under the minimum burial depth assumption based on a magnitude-yield relationship used by Bowers et al. . Zhao et al.  investigated the yield of North Korea's 2009 test using a regional network in northeast China and South Korea. They first estimated the Lg-magnitude of the event based on the Lg-wave amplitudes observed in the seismic data. They then employed a modified fully coupled magnitude-yield relationship [Bowers et al., 2001] to estimate the yield of the 2009 test. In their study, the Lg-wave amplitudes were corrected for the path effects using a crust attenuation Q model [Xie et al., 2006], and the Lg-magnitude was further calibrated for the station effects using a historical event dataset related to the seismic network. They estimated Lg-wave magnitude of the 2009 test to be mb(Lg) = 4.53 ± 0.12 and the yield approximately 2.35 kt under the minimum burial depth assumption.
3 Determining the Location and Yield of North Korea's 2013 Nuclear Test Using its 2009 Test as Reference and Satellite Imagery
3.1 Location of North Korea's 2013 Nuclear Test
 We first use the observed arrival time difference of Pn phase between the two tests to infer the relative location and origin time of North Korea's 2009 and 2013 nuclear tests. Such approach allows high-precision determination of relative location and origin time between the two tests. We then determine the location of the 2013 test, based on the inferred relative location of the two tests and the location of the 2009 test identified by Wen and Long  (Table 1).
 We use a method developed by Wen  to determine the relative location and origin time of the two tests. The method uses the arrival time difference of a particular seismic phase between a waveform doublet, defined as a pair of seismic events occurring at different times but in close location and exhibiting similar waveforms, to determine the relative location and origin time of the doublet. It is similar to the modern methods using the information between earthquake doublets [e.g., Poupinet et al., 1984] chemical explosions [Phillips et al., 2001] and nuclear tests [e.g., Waldhauser et al., 2004]. Because the doublets occur very close in location, the relative travel time and waveform difference between the waveform doublets are sensitive primarily to the relative change of event location. Waveform doublets also allow accurate travel time measurements to be made by the waveform cross-correlation technique because of similarities of the waveforms. It is thus a powerful tool for high-precision studies of relative location and time of the doublets. In the present case, North Korea's 2013 and 2009 tests essentially constitute a nuclear doublet, and the available observational pairs between the two tests recorded in Chinese National Seismic Network in China and the F-net stations in Japan provide good azimuthal coverage for high-precision determination of the relative location of the two tests (Figure 1).
 The travel time differences of the Pn phases between the two tests are obtained by cross-correlating the observed waveforms between the two tests (Figure 2a and Table 2). The data time series of the two tests are time interpolated to an evenly spaced time series with a time sampling rate of 0.0025 s before the cross-correlations are performed. The seismograms in each pair are aligned according to the cross-correlation travel time shifts and are further eye-checked for possible cycle skipping. We search for the best-fitting relative location and origin time for the 2013 test that minimize the travel time residuals of the Pn observations between the two events. The search region for the relative location of the 2013 test is a 10 km (N-S direction) × 10 km (E-W direction) centered at the identified location of the 2009 test. The search grid intervals are 0.1 m in N-S and E-W directions. The relocation procedure places the best-fitting location of the 2013 test to be 345 m south and 453 m west of the 2009 test (Figure 3a). The best-fitting origin time for the 2013 test is 12 February 2013, 02:57:51.331 UTC. The best-fitting location and origin time of the 2013 test significantly reduce the root-mean-square (RMS) travel time residual to 8 ms (Figure 3a), and the travel time residuals at each individual station to a maximum of 13 ms (station IMG), between the two tests (Figure 2b and Table 2). The precision of the relative location between the two tests is determined to be 94 m based on the 95% confidence ellipse of the relocation travel time residuals (Figure 3a). The inferred location of the 2013 test is at (41°17′26.88″N, 129°4′34.68″E) (Table 1) and is shown on Google Earth (image on 23 January 2013), along with the locations of two previous nuclear tests (Figure 3b).
Table 2. Pn Differential Travel Times at Each Seismic Stationa
“Δt0” measured differential travel time with a zero mean; “Δt1”differential travel time after corrected for the best-fitting location of 2013 test.
 Our relocation results are affected little by the uncertainties of the reference Earth's velocity models that we used. Using the Preliminary Earth Reference Model [Dziewonski and Anderson, 1981] or AK135 [Kennett et al., 1995] as the Earth's reference model essentially yields the same results. The Pn differential travel times are affected by the compressional wave velocities assumed in the top of the Earth's mantle, which has been reported to vary from 7.7 to 8.3 km/s. Such two end-member velocities would introduce an uncertainty of 88 m in the relocation result. The uncertainty is within the range of the travel time residuals in each individual station after the relocation (Table 2). We attribute those differential travel time residuals partially to the uncertainty of compressional velocities in the top of the mantle.
 With the actual locations of the tests identified (Figure 3), we estimate their burial depths based on elevation data as derived from Google Earth, using the difference of the surface elevations between the associated tunnel entrances and the identified test locations. The surface elevations of the inferred 2009 and 2013 test locations are 2010 m and 1830 m, respectively. Although three tunnel entrances have been previously identified in the immediate vicinity as being capable of supporting underground nuclear testing, only one tunnel entrance, “the west portal” as identified and suggested by Pabian and Hecker , could be associated with (and most likely used to support) both of these tests. The elevation of that identified tunnel entrance is 1400 m. The burial depths of the 2009 and 2013 tests are thus determined to be about 610 m and 430 m, respectively, based on the elevation differences between the test locations and the tunnel entrance.
3.2 Yield of North Korea's 2013 Nuclear Test
 The yield of a nuclear test can be estimated using different portions of seismic signals [e.g., Murphy, 1977; Nuttli, 1986]. In the present case, we use regional Lg-wave amplitude to estimate the yield of the 2013 test for the following reasons: (1) Lg waves exhibit large and stable amplitudes in the regional distances for the seismic data recorded in China, while the teleseismic body wave amplitudes could be affected by strong scattering from the surface topography near the test sites, (2) the path and station effects have been carefully corrected in their estimation of Lg-magnitude of the 2009 test [Zhao et al., 2012], and (3) the Lg-magnitude-yield relationship was also calibrated with several known chemical explosions in the region [Zhao et al., 2012]. There is a difference in Lg-magnitude estimates between the studies of Chun et al.  and Zhao et al. , because different Lg Q models and seismic stations were used between the two studies. We use Zhao et al.  study as reference, because the path and station effects have been carefully corrected in their estimation of Lg-magnitude of the 2009 test; and, more importantly, the Lg-magnitude-yield relationship was calibrated and verified with several known chemical explosions using the Lg-magnitudes estimated based on their Q models and station corrections. We estimate the yield of the 2013 test in two steps: we first estimate the Lg-wave magnitude of the 2013 test using the amplitude ratios of the Lg waves observed between the 2009 and 2013 tests and the Lg-magnitude estimation of North Korea's 2009 nuclear test by Zhao et al. ; we then calculate the yield of the 2013 test based on a modified empirical Lg-magnitude-yield-depth relationship using the estimated Lg-magnitude and inferred burial depth of the test.
 Because the separation of the 2009 and 2013 tests is just about 570 m (Figure 3), the path effects and station corrections are the same for a same station between the two tests. The Lg-magnitude difference of the two tests is thus scaled with their Lg-wave amplitude ratio, i.e.,
where mb,2009 and mb,2013 are the Lg-magnitudes of North Korea's 2009 and 2013 tests, respectively, and R is the estimated Lg-wave amplitude ratio between the 2013 and 2009 nuclear tests. mb,2009 = 4.53 ± 0.12 [Zhao et al., 2012].
 We follow the same data processing procedures in Zhao et al.  and estimate the Lg-amplitude ratios between the two tests at eight (MDJ, CN2, SNY, BNX, DL2, HEH, BJT, and HIA) of the nine stations used in Zhao et al.  (Figure 4). We first deconvolve the instrument response from the observed broadband vertical component seismograms and then convolve the seismograms with the World-Wide Standardized Seismograph Network instrument response. We then pick Lg waves in a group velocity window between 3.6 and 3.0 km/s and measure their amplitudes through three different methods: integrated envelope [Salzberg and Marshall, 2007; Zhao et al., 2012], third-peak amplitude [Nuttli, 1973, 1986], and the root mean square (rms) amplitude [Ringdal et al., 1992; Zhao et al., 2012]. The rms amplitude is also corrected for the pre-P noise. Average Lg-wave amplitude ratios between the 2013 and 2009 tests estimated using these three methods are 2.29 ± 0.38, 2.34 ± 0.39, and 2.36 ± 0.41, respectively (Table 3). We take the average of the measurements by these three methods, R = 2.33 ± 0.39, as our estimate of Lg-amplitude ratios between the two tests. Lg-magnitude of North Korea's 2013 nuclear test is inferred to be mb(Lg) = 4.89 ± 0.14 based on equation (1), including the uncertainty of ±0.12 inherited from Zhao et al.  and an uncertainty of ±0.07 from the variation of estimation of relative Lg-amplitude ratios between the two tests.
Table 3. Lg-Wave Amplitude Ratio at Each Station (2013/2009)a
“Average” and “S.D.” are the average value and standard deviation, respectively.
 Empirical hard rock magnitude-yield relationships for fully coupled nuclear explosions were reported by many studies [e.g., Ringdal et al., 1992; Bowers et al., 2001]. Zhao et al. [2008, 2012] examined various empirical relationships and concluded that the empirical relationship provided by Bowers et al.  fit the North Korea's test site best:
for a standard minimum burial depth 120 m and a 1 kt explosion.
 For a nuclear test with an actual burial depth h and a yield Y, Patton and Taylor  proposed a correction term to equation (2) using the scaling relationship proposed by Denny and Johnson :
 This depth correction term was derived based on body wave magnitude. In the seismic data along the paths we study, Zhao et al.  showed that the magnitudes derived from the Lg waves are linear with those derived based on the body waves. We thus adopt this depth correction term for the relationship between the Lg-magnitude and yield for North Korea's nuclear tests. With the depth correction, the magnitude-yield relationship becomes
 According to equation (3) and the inferred depth of the 2013 test (430 m), we estimate the yield of the 2013 test to be 12.2 ± 3.8 kt from mb(Lg) = 4.89 ± 0.14. The yield of the 2009 test is reestimated to be 7.0 ± 1.9 kt based on a burial depth 610 m.
 We determine the location and yield of North Korea's 2013 nuclear test using the 2009 test as reference based on seismic data and satellite imagery. The location of North Korea's 2013 nuclear test site is obtained based on inferred relative location of North Korea's 2009 and 2013 nuclear tests and the previously determined location of the 2009 nuclear test, while its yield is estimated based on the Lg-magnitude difference between the two tests, the previously determined Lg magnitude of the 2009 nuclear test and the burial depth inferred from satellite imagery as presented on Google Earth. North Korea's 2013 nuclear test is determined to be located at (41°17′26.88″N, 129°4′34.68″E), about 345 m south and 453 m west of its 2009 nuclear test site, with a geographic precision of 94 m. The yield of the test is estimated to be 12.2 ± 3.8 kt. Our analyses indicate that the location and yield of a nuclear test can be quickly and accurately determined using seismic data, information of previous tests, and satellite imagery.
 We thank Frank V. Pabian and another anonymous reviewer for their comments, which greatly improved the paper. We thank the China Earthquake Networks Center, the Incorporated Research Institutions for Seismology, the New China Digital Seismograph Network, and the F-net in Japan for providing seismic data. This work is supported by the National Natural Science Foundation of China under grant NSFC41130311 and the Chinese Academy of Sciences and State Administration of Foreign Experts Affairs International Partnership Program for Creative Research Teams.
 The Editor thanks Frank V. Pabian and an anonymous reviewer for their assistance in evaluating this paper.