### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. GNSS TEC Mapping of Traveling Ionospheric Disturbances (TIDs)
- 3. North Korean UNE of 25 May 2009
- 4. Conclusions
- Acknowledgments
- References
- Supporting Information

[1] The total electron content (TEC) measurements of the Global Navigation Satellite System (GNSS) revealed traveling ionospheric disturbances (TID) that locate North Korea's underground nuclear explosion (UNE) of 25 May 2009 to within about 3.5 km of its seismically determined epicenter. The random chance for this pattern of TIDs to register across the eleven GNSS stations is roughly 1 in 19 billion. Monte Carlo analysis of nearly 1,300 TIDs from a 7-station subset of the 11 GNSS stations supports the statistical strength of the array's signature. The UNE was also detected by seismic stations and possibly a local infrasound network of the International Monitoring System (IMS) of the Comprehensive Nuclear Test Ban Treaty Organization (CTBTO), but no radionuclide evidence was found. Thus, global GNSS infrastructure enables mapping spatial and temporal variations of TEC that augment and complement other methods of detecting and locating clandestine UNEs.

### 1. Introduction

- Top of page
- Abstract
- 1. Introduction
- 2. GNSS TEC Mapping of Traveling Ionospheric Disturbances (TIDs)
- 3. North Korean UNE of 25 May 2009
- 4. Conclusions
- Acknowledgments
- References
- Supporting Information

[2] The International Monitoring System (IMS) established by the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO; www.ctbto.org) uses several global networks to monitor and detect nuclear explosions. They include a seismic network that monitors for terrestrial shock waves from nuclear explosions, a hydroacoustic network that scans the oceans for nuclear explosion generated sound waves, an infrasound network of acoustic pressure sensors to identify and locate atmospheric nuclear explosions, and a radionuclide network to detect radioactive particulate and gas (e.g., xenon) by-products of nuclear explosions [*Medalia*, 2010].

[3] The presence of radionuclides that provides ultimate clarity on the occurrence of a nuclear explosion is problematic when dealing with well-contained nuclear explosions detonated deeply underground. Indeed, the radionuclide network apparently did not find evidence of the 25 May 2009 underground nuclear explosion (UNE) carried out by North Korea (i.e., the Democratic People's Republic of Korea). Thus, independent scientific evidence for the several-kiloton estimated UNE was restricted primarily to its seismic signature and possibly epicentral infrasonic signals that may have been recorded at five of the seven operating seismo-acoustic arrays in South Korea [*Che et al.*, 2009].

[4] The behavior of the ionosphere to the North Korean UNE, however, may also contain clues to help augment the detection capabilities of the IMS. Atmospheric effects from mostly atmospheric nuclear explosions have been studied since the 1960s [e.g., *Rose et al.*, 1961; *Donn and Ewing*, 1962; *Saha et al.*, 1963; *Webb and Daniels*, 1964; *MacKinnon*, 1968]. Examples of underground testing include telemetry from the Russian INTERCOSMOS 24 satellite that recorded ELF and VLF electromagnetic disturbances of an UNE at Novaya Zemlya Island on 24 October 1990, which were attributed to an acoustic-gravity wave in the ionosphere's E layer [*Mikhailov et al.*, 2000]. Ionospheric disturbances can also be detected using the continuously tracking Global Navigation Satellite System (GNSS) of ground receivers established by the International GNSS Service (IGS) for geodetic and geophysical applications (http://www.igs.org). The network is capable of continuously monitoring global ionospheric behavior based on ionospheric delays in the GNSS signals. The GNSS signals are readily accessible anywhere on Earth at a temporal resolution ranging from about 30 seconds up to less than 1 second. The study presented here investigates the GNSS data for the effects of the recent North Korean UNE and their possible utility for augmenting IMS efforts to detect and locate clandestine UNEs.

### 2. GNSS TEC Mapping of Traveling Ionospheric Disturbances (TIDs)

- Top of page
- Abstract
- 1. Introduction
- 2. GNSS TEC Mapping of Traveling Ionospheric Disturbances (TIDs)
- 3. North Korean UNE of 25 May 2009
- 4. Conclusions
- Acknowledgments
- References
- Supporting Information

[5] The ionospheric delay in GNSS signals observed by the ground stations can be processed into total electron content (TEC), which is the total number of electrons along the GNSS signal's path between the satellite and the receiver on the ground [e.g., *Mannucci et al.*, 1998; *Hofmann-Wallenhof et al.*, 2001; *Grejner-Brzezinska et al.*, 2004; *Heki and Ping*, 2005; *Hong et al.*, 2008; *Morton et al.*, 2009]. The TEC derived from the slant signal path, called the slant TEC (STEC), was observed and analyzed in this study to identify disturbances associated with the UNE.

[6] It has been long recognized that there are numerous disturbances or irregularities on various temporal and spectral scales in the ionosphere [*Booker*, 1979]. These disturbances are frequently observed on TEC measurements. A powerful means to isolate and relate disturbances observed in TEC measurements from different receiver-satellite paths is to analyze the spectral coherence of the disturbances. For the UNE event discussed in this paper, *Garrison et al.* [2010] have presented spectral analysis of a large number of TEC measurements in the vicinity of the event source and demonstrated that acoustic-gravity waves were indeed generated by the event. In this paper, we take a different approach that emphasizes the spatial and temporal relationships among the TEC observations. Spatial and temporal fluctuations in TEC are indicative of the dynamics of the ionosphere, and thus help in mapping traveling ionospheric disturbances (TIDs) excited by acoustic-gravity waves from point sources [*Drobzheva and Krasnov*, 2003; *Karhunen et al.*, 2006], as well as by geomagnetic storms [*Nishioka et al.*, 2009], tropical storms [*Vadas and Crowley*, 2010], earthquakes [*Occhipinti et al.*, 2010], tsunamis [*Artru et al.*, 2005; *Occhipinti et al.*, 2006], volcanic explosions [*Kanamori et al.*, 1994], and other effects.

[7] The velocity of a TID provides an important constraint for inferring and locating its source. The first-order velocity can be calculated using the detected time of a TID and the slant distance from a point source event (e.g., a UNE) to the ionosphere's pierce point (IPP), where the ray connecting the receiver to the GNSS satellite intersects the peak of ionosphere at roughly 300 km altitude [*Che et al.*, 2009]. This simple assumption is reasonable given that the ionosphere effectively is a thin shell compared to the 20,000 km and greater altitudes of the GNSS satellites. Additional improvements to TID velocity can be made by adjusting the velocity estimates from multiple GNSS receivers for the drag effects of ionospheric winds [*Richmond and Matsushita*, 1975].

[8] As shown in Figure 1, the UNE-generated TID was modeled assuming a constant radial propagation velocity, *v*_{T}, using an apparent velocity *v*_{i} of the TID at the *i*th GNSS station. Velocity *v*_{i} was computed by dividing the slant distance, *s*_{i}, from the station's IPP to the UNE, by the TID's arrival time, *t*_{i}. To estimate the slant distance, an approximate location of the UNE's epicenter from seismic or other monitoring information is required. The TID's velocity is also strongly affected by the ionospheric wind velocity components *v*_{N} and *v*_{E} in the North and East directions, respectively. As described below, the unknown parameters, *v*_{T}, *v*_{N}, and *v*_{E}, can be estimated in terms of the TID velocities and IPP azimuths (*α*_{i}) relative to the UNE's hypocenter (Figure 1). In addition, the coordinates of the hypocenter may be estimated from the GNSS network solution of more than 6 stations.

[9] Specifically, the hypocenter coordinates of the UNE and the related TID velocity can be evaluated from the slant distance

where *t*_{i} is the arrival time of the TID at the IPP of the *i*th station. Equation (1) can be expanded as

where *N*_{i}, *E*_{i}, and *D*_{i} are the local coordinate components of the IPP for the *i*th GNSS station in the local coordinate system centered at the UNE's location, *α*_{i} is the azimuth of the line with length *s*_{i} connecting the UNE's hypocenter and the *i*th station, and ɛ_{i} is the *i*th station's IPP elevation angle measured from station's path (*d*_{i}) to the UNE's hypocenter. The local *N*, *E*, and *D* components in the UNE's geodetic latitude (ϕ), longitude (*λ*), and ellipsoidal height (*h*) coordinates may be expressed by

Here, [*x*_{i}, *y*_{i}, *z*_{i}] are the coordinates of the IPP of the *i*th station, and [*x*, *y*, *z*] are geocentric coordinates of the UNE given by

where *a* is the semi-major axis, and is the eccentricity of the WGS 84 reference ellipsoid [e.g., *Malys and Slater*, 1994; *Seeber*, 2003] used in this study. Thus, the unknown parameters *ξ* = [ϕ, *λ*, *h*, *v*_{T}, *v*_{N}, *v*_{E}]^{T} can be estimated by the Gauss-Helmert (GH) model [*Grafarend, and Schaffrin*, 1993]

where *W* is an *n* × 1 column vector with elements *w*_{i} = *s*_{i} − *v*_{i}*t*_{i}. The components in this difference equation are iteratively updated using equation (1) until the update parameter vector converged to the threshold value of 0.001. The elements of A are *a*_{ip} = with *i* = {1, …, *n*} for the number of GNSS stations *n*, and *p* = {1, …, *m*} for the *m* unknowns. The elements of B are *b*_{iq} = with *i* = {1, …, *n*}, and *q* = (*i* − 1) × *l* + *k* with *k* = {1, …, *l*} and *l* is the number of observables at the *i*th station (i.e., *l* = 4 for [*x*_{i}, *y*_{i}, *z*_{i}, *t*_{i}]), where *e*_{i,k} corresponds to the specific observation [*x*_{i}, *y*_{i}, *z*_{i}, *t*_{i}]; *e* is the observation error vector characterized by zero mean; *P* is the weight matrix of the observations that is based on the observation quality indicators described in Table S1 in Text S1 in the auxiliary material.

[10] Equation (4) is solved using the stochastic constraint, κ_{0} = *Kξ* + *e*_{0}, *e*_{0} ∼ (0, *σ*_{0}^{2}*Q*_{0}), where *K* is the identity matrix, and κ_{0} is the constraint vector for *ξ* with the error *e*_{0}. The dispersion matrix, *Q*_{0}, was tuned based on the uncertainty of prior information for each parameter. For example, the standard deviations of ϕ and *λ* are the differences of the maximum and minimum latitudes and longitudes, respectively, of the GNSS stations. The ellipsoidal height *h* was tightly constrained in the *Q*_{0} weight matrix because for this study, only a limited number of observed GNSS stations were available for determining the UNE's epicenter. For determining the velocities, 300 m/s was used for the standard deviations for *Q*_{0} matrix. The errors *e* and *e*_{0} were considered normal with zero mean and respective *σ*_{0}^{2}*P*^{−1} and *σ*_{0}^{2}*Q*_{0} variances.

[11] Thus, the constrained least squares solution, , of the system (4) becomes

with the unconstrained solution = [*A*^{T}(*BP*^{−1}*B*^{T})^{−1}*A*]^{−1}*A*^{T}(*BP*^{−1}*B*^{T})^{−1}*W*. The solution was obtained by iteratively driving the residual vector estimate

to the threshold ∣∣ = 0.001.

### 3. North Korean UNE of 25 May 2009

- Top of page
- Abstract
- 1. Introduction
- 2. GNSS TEC Mapping of Traveling Ionospheric Disturbances (TIDs)
- 3. North Korean UNE of 25 May 2009
- 4. Conclusions
- Acknowledgments
- References
- Supporting Information

[12] The Democratic People's Republic of Korea announced the successful completion of a second underground nuclear test in a program that conducted its first UNE on 9 October 2006. The seismically determined epicenter coordinates reported by the International Data Center (IDC) of the CTBTO and US Geological Survey (USGS) located the second UNE near P'unggye at 41.311°N latitude and 129.046°E longitude with the respective 90% confidence intervals of ±4.8 km and ±4.4 km. The reported depth at the estimated epicenter was 0.6 ± 0.4 km below the surface elevation of ∼2.0 km above sea level. The origin time was 00:54:42.8 ± 0.32 sec UTC of 25 May 2009. The event magnitude was estimated between 4.5–4.7 mb based on the seismic magnitude measurements [*Bennett*, 2010]. The explosion's yield was estimated to be about 2.2–4.8 kT from conventional mb/yield relationships [*Murphy*, 1996].

[13] The GPS data from five IGS stations and six stations in South Korea's local GNSS network (Figure 2) were examined for the STEC effects of the event. The relatively low geomagnetic activity index K_{p} ≈ 1 reported by the Space Weather Prediction Center (SWPC) indicated minimal geomagnetic storm activity at the time of the UNE.

[14] The records of the GNSS stations in Figure 2 were scanned for STEC disturbances. Figure 3 (left) shows an example of the results for the nearest South Korean station, INJE. The STEC record exhibits a broad minimum over the six-hour period that includes the time of the explosion, which is marked by the vertical dashed line. In Figure 3 (right), the numerical third order horizontal 3-point derivatives of the STEC, hereafter simply referred to as the STEC derivatives, were taken to see the fluctuations in greater detail and suppress the regional trend. The STEC derivatives clearly resolved a prominent event at 22.79 min after the explosion that is consistent with the propagation velocities of TIDs. This event was taken as the TID signature of the UNE at station INJE because it is part of a pattern of TID arrivals across the 11-station array that has an exceedingly low statistical probability of being a random event.

[15] For example, if the epicenter resolution of the TIDs was comparable to the 10 km resolution of the seismic data in each axis, then the probability of establishing the epicenter at any particular station is one in the number of 10-km segments on the circle centered on the station with radius equal to the epicentral distance r – i.e., 10 km: 2*π*r. Thus, the chances of the epicenter identified by the intersection of the circles from *n* stations being a random event is 10^{n} in [(2*π*)^{n} × r_{1} × r_{2} × … r_{n}]. In the case of the 11 GNSS stations of this study with an average distance from the UNE of 500 km, this probability works out to be smaller than 1:3 × 10^{27}.

[16] To test the possible UNE affiliation of the TID marked in Figure 3, the TIDs at the other 10 GNSS stations were screened to identify those with comparable propagation velocities. The search algorithm used the STEC derivative signature of the TID in Figure 3 within the 1.5-minute window centered on its initiation and cross-correlated it with the STEC derivatives of the other stations. The cross-correlation analysis identified TIDs at the other stations with velocities that made them plausible UNE events. The correlograms and STEC derivatives for the other 10 GNSS stations are given in the figures in Text S1 in the auxiliary material, whereas the travel-time attributes of the selected plausible events are shown in Figure 4.

[17] The raw travel-time data (i.e., without ionospheric wind correction [IWC]) for the selected TIDs were evaluated for the least squares estimates of the arrival times given by equation *T*1 in Figure 4. The parameter uncertainties of equation *T*1 are expressed in terms of their 95% confidence intervals. Using the result in equation (4) obtained the first-order epicenter estimate of (40.4886°N, 132.3884°E), which is about 3.3° (∼365 km) off of the seismically determined epicenter. However, despite the relatively crude epicenter constraint that the raw TID arrival times provide, the probability of this array pattern to occur randomly is still exceeding small at less than 1: (2*π* [500/365])^{11} ≈ 19 × 10^{9}.

[18] To test the strong apparent statistical significance of the array pattern, a Monte Carlo analysis was conducted of 1,272 TIDs at station DAEJ. This analysis considered only the seven IGS stations (i.e., BJFS, CHAN, STK2, DAEJ, SUWN, OSN1 USUD, YSSK) with open public records and excluded the South Korean stations with restricted-access records (e.g., CHLW, DOND, INJE, SOUL, YANP). The STEC derivatives for five days in the spring periods (May–June) of the years 2006 to 2010 were scanned by the cross-correlation of the STEC derivative waveform at INJE to identify 1,272 candidate events. The spring periods were chosen to simulate the climatic conditions of the 2009 UNE. For each candidate event with the derivative properties shown in Figure 3, the STEC derivatives at the other six stations were screened for matching events over time intervals centered on the delays indicated by equation *T*1 in Figure 4. The 95% confidence interval for equation *T*1 defined the time interval of each search. The TID pattern did not survive on more than five stations and thus the analysis does not reject the detected array signature's strong statistical improbability.

[19] The UNE connection of the TIDs can be further strengthened by adjusting their velocities for the ionospheric winds. The north and east components of ionospheric wind velocities along with the UNE's epicenter coordinates were estimated from the Gauss-Helmert model in equation (4) with stochastic constraints. After 5 iterations, convergence on the threshold parameter vector yielded a solution that pinpointed the UNE's epicenter at (41.2797°N, 129.0450°E) for the estimated TID velocity of 273 [m/s] of equation *T*2 in Figure 4. The coordinate differences from the seismically determined epicenter were roughly 3.5 km and 0.15 km in latitude and longitude, respectively. These epicenter coordinates for the UNE are greatly improved relative to the significantly degraded initial estimate that neglected the *v*_{N} and *v*_{E} ionospheric wind velocity components.

[20] The strong ionospheric wind effects are listed in Table S2 in Text S1. Adjusting the travel-time data in Figure 4 for the wind effects yields the linear model in equation *T*2 that is enhanced in its intercept, and slope or average TID velocity, as well as its correlation coefficient which corresponds to an improvement of roughly 44% in the signal-to-noise ratio [e.g., *Foster and Guinzy*, 1967]. Clearly, ionospheric wind velocity components are important to evaluate in analyzing TIDs for UNE effects. These estimates also may contribute to ionospheric wind studies by Doppler interferometry [e.g., *Wu et al.*, 2008], and for the effects of joule heating [e.g., *Fuller-Rowell et al.*, 2008].