Acoustic-Gravity Waves (AGWs) in the neutral atmosphere can induce disturbances in the ionosphere that are subsequently observable in trans-ionospheric Global Navigation Satellite System (GNSS) measurements. Disruptive events on the Earth's surface, such as earthquakes, tsunamis and large explosions are one source of these disturbances. In this study, we apply wavelet analysis to enhance a cross-correlation technique for detecting the presence of ionospheric disturbances in dual frequency GNSS time series collected from the GEONET (Japan) during the North Korean Underground Nuclear Tests (UGTs) conducted on 9 October 2006 and 25 May 2009. Through use of the wavelet coherence analysis, we are able to find significant wave trains in the Integrated Electron Content (IEC) data collected from the network. Low frequency disturbances, with periods between 3 and 12 min and horizontal propagation speeds between 75 and 453 m/s were found coincident with both the 2006 and 2009 events. High frequency disturbances, with periods between 2 and 5 min and horizontal speeds between 297 and 1322 m/s were found only after the 2009 event. The disturbances extracted from these signals showed propagation speeds, directions, and times of arrival coincident with the reported geographic location and times of the UGTs.
 In contrast to the Doppler radio sounding techniques, GPS senses the integrated electron content (IEC) along its signal propagation path. Ionospheric disturbances caused by earthquakes [Ducic et al., 2003], mine blasts [Calais et al., 1998], tsunamis [Artru et al., 2005] and many other natural and anthropogenic sources have been observed in GPS network data. Signal processing methods for detecting these disturbances in IEC time series include spectral tests [Afraimovich et al., 2003], the Statistical Angle-of-Arrival and Doppler Method (SADM-GPS) [Afraimovich et al., 2000] and cross-correlation [Garrison et al., 2007; Hernández-Pajares et al., 2006]. All of these approaches assume that a single perturbation is observable at a time and that the disturbance can be approximated as a quasi-monochromatic wave. However, multiple perturbations may be present within the same time and space, as prior studies have shown that the occurrence rate of natural disturbances is quite high.Šauli et al.  applied wavelet decomposition to ionosonde measurements of disturbances produced during a solar eclipse, demonstrating an improved ability to separate different wave structures.
 North Korea is known to have conducted two UGTs, the first on 9 October 2006 and the second on 25 May 2009. The reported magnitude of the UGT in 2009 was larger than that in 2006. The reported location for the first and second tests were 41°17′14″N, 129°06′30″E and 41°17′38″N, 129°04′54″E, respectively. A recent study on ionospheric responses from the 2009 UGT event has conclude that a UGT-generated ionospheric disturbances propagate radially from the event with the relatively constant velocity of roughly 273 m/s, estimated from GNSS measurements of 7 stations in South Korea [Park et al., 2011]. However, the method used by Park et al.  is not able to classify different types of disturbances that may be present in the same IEC time series, or to directly estimate the propagation speed and direction.
 In this study, we applied wavelet analysis to identify time-frequency regions of high coherence, identifying the presence of a propagating disturbance in the GEONET GPS data collected during the week of each of the two reported UGTs. We then used this information to select the bandwidth of filters that were applied to the IEC time series. The filtered time series were then cross-correlated following the approach ofGarrison et al.  to estimate the speed and direction of propagation for each disturbance. Geometric consistency between these measurements and the reported time and location of the UGT events suggest that AGWs produced from these explosions were the source of the observed ionospheric disturbances.
2. Data Processing
 The Integrated Electron Content (IEC) is defined as the integral of electron density along the path of radio frequency propagation from the transmitter to the receiver.
Time-variation arises both due to the relative motion of the transmitter and receiver and variations in the electron density. For a dual-frequency GNSS receiver, the IEC time series can be calculated using the method ofMannucci et al. .
Wn(a,b) is the continuous wavelet transform (CWT) [Mallat, 1999] of the IEC time series, IECn(t), observed by receiver n.
ψ is a wavelet function, a is the wavelet scale, and b is the localized time index. W2*(a,b) is the conjugate of W2(a,b). We chose the Morlet wavelet, defined as a complex exponential function (when p > 5) ψ(t) = where p (frequency parameter) adjusts the time and scale resolution. The Morlet wavelet has a special feature in that the wavelet scale is the inverse of frequency (i.e., f = 1/a). |Wn(a,b)| is the scalogram used by Šauli et al. . R1,22(a,b) can take values from 0 to 1, with larger values indicating the presence, at time index b, of coherent structure, at scale a, in both signals. Due to the finite IEC time series used to calculate the CWT, the cone of influence (COI) is analyzed to ensure the identified high coherence spectrums are not in the regions of edge effects. For the significance test of wavelet coherence, a Monte-Carlo approach is applied to test the null hypothesisH0 statistically by repeating many independent realizations of the IEC time series. A detection threshold λα at the significance level α with N multiple tests is defined as λα = 1 − α1/(N−1). For more details regarding the significance test refer to Maraun and Kurths . A threshold of 0.58 was set on R1,22(a,b) to identify strong coherence structures above significance at 5% level which implies 95% confidence interval in statistics (see Figure 1).
 A set of band-pass filters, tuned to the frequencies of highest coherence, were then applied to each time series, before masking only those time frames of high coherence (R1,22(a,b) > 0.58 in Figure 1). The cross-correlation method ofGarrison et al. was then applied to the filtered and masked time series to estimate propagation speeds and directions of the corresponding disturbances. This technique was based on the assumptions of planar wave propagation, a locally flat earth and thin shell ionosphere at the height of the maximum electron content. Through dividing the full network into smaller sub-areas, the variation of propagation direction and speed over a large area can be observed while maintaining the assumption of a planar wave over each small sub-area. We divided the full GEONET network (1235 GPS stations) into 32 sub-areas (on an approximately 1° × 1° grid as shown inFigure 2and ran the wavelet coherence analysis on small sets of GPS stations within each sub-area.
 In this section, we will summarize our discovery, through use of the methods described above, of ionospheric disturbances coincident with the first and second North Korean UGT. GEONET data were processed over a range of 5-day windows of data centered on the 2009 and the 2006 events. These 5-day windows were used to determine if any disturbances appeared multiple days, in order to confirm that the observed disturbances were not diurnal artifacts, appearing by chance at the time and place of the UGT. Other than the disturbances reported later, which we attribute to the UGTs, only two other disturbances were observed in either 5-day windows of data. Some ionospheric disturbances were observed on the east coast of Japan approximately 15 hours and 39 hours after the 2009 event. However, the geometry of their propagation vectors were not consistent with the disturbances attributed to the UGTs, described later. No disturbances, other than those attributed to the 9 Oct 2006 UGT, were observed in the 2006 data. We also checked for space and terrestrial weather events which could have occurred within hours of the observed disturbances, to reduce the likelihood of the coincident appearance of a disturbance from another source. The space weather records from Space Weather Prediction Center of the National Oceanographic and Atmospheric Administration (NOAA) (http://www.swpc.noaa.gov/SWN/) did not indicate any sudden and severe weather events during the time windows.
Figure 1shows wavelet coherency computed between stations 0433 and 1041 on each of the 5 days of data, centered on the 2009 test. This example shows observations of satellite PRN 24 collected in sub-area 31. A high wavelet coherency exists on the event date (May 25 2009) only. The region of high coherency lies within a frequency band between 0.0035–0.0078 Hz, centered at 1:03H UT (approximate 9 minutes after the reported time of the detonation). These findings were used to design a Butterworth band-pass filter that was applied to the IEC time series prior to the cross-correlation method ofGarrison et al. . Figure 3 presents an example of a filtered IEC waveform. The averaged signal to noise ratio (SNR) of these disturbance signals from the four stations in Figure 3 on the event day (Day 145) is 11.2 dB. The averaged SNR is 2.6 dB for the other four days.
 After filtering, the amplitude of the disturbances were found to range up to 0.17 TEC unit. This represents approximately a 2.6 percent change in the background level (6.5 TEC unit). This result is consistent with the calculations and experimental observations from Doppler radio sounding measurements presented by Krasnov and Drobzheva .
 We applied this approach to the IEC data from every satellite visible during a 5-day window centered on each event. For the 25 May 2009 event, we also observed long-period (3–12 min) disturbances in data from PRN 18 and 21 from 7 and 6 different sub-areas, respectively. The estimated horizontal speeds of these disturbances ranged from 61 to 174 m/s, consistent with gravity waves. Next, we tested the geometric consistency of these observed disturbances with a source at the reported UGT location. We plotted the apparent propagation time (difference between the mean time of the peak IEC and the reported explosion time) against the great-circle distance from the reported test location.Figure 4 shows these results, overlaid with the expected arrival times for a range of horizontal propagation speeds. A 15 min shift was included in the apparent propagation times to account for the propagation delay from the surface of the Earth to the ionosphere. This figure shows the the arrival times and propagation distances are consistent with a disturbance propagating with a mean horizontal speed within the range of those observed.
 We observed some short-period (2–5 min) disturbances in the signal from PRN 24 as reported above, within 3 subareas. Similar short-period disturbances were observed in the data from PRN 29 in 2 subareas. The horizontal speeds of these disturbances were also generally higher than the speed of the long-period disturbances (up to 1322 m/s) and appeared between 7 and 19 min. after the reported UGT time. This suggests that these disturbances were the result of acoustic waves produced at the source.Figure 5 shows ray traces (solid lines) of the acoustic field calculated by integrating
where xi = (x1, x3) represents the horizon distance and the altitude from the point source, s is the arc length of the ray path, and c is the sound speed dependent on altitude. Dashed lines represent the arrival times in 1 minute increments. The horizontal distances of these observed IPP locations for PRN 24 and 29(at the height 350 km of ionosphere) are 257 km and 756 km, respectively, from the reported UGT location, indicated on Figure 5 as the thick circles. This observed arrival times, reported earlier, are consistent with the ray trace calculations that predict: 7 and 15 mins vs. 9 and 18 mins, respectively. All of the disturbances coincident with the 2009 UGT are plotted as vectors on Figure 2. The length of each vector is scaled with the estimated horizontal speed. The satellite PRN and subarea number are indicated on each vector and the tail of each vector is placed at the location of maximum IEC variation.
 For the 9 Oct 2006 event, only long-period (3–12 min) disturbances were observed. These disturbances were detected in IEC measurements from satellites PRN 16 and 23, within 3 sub-areas each. Horizontal speeds for these disturbances were also within the gravity-wave regime, between 135 and 453 m/s.Figure 2 shows the location, horizontal speed, and direction of each of the disturbances found for the 9 Oct 2006 UGT.
 Traveling ionospheric disturbances were detected using measurements from a GNSS network at distances of more than 1000 km from the reported locations of the 2006 and 2009 North Korean UGT events. Observations of short period disturbances with a fast horizontal speed (up to 1322 m/s) were observed 7–18 minutes after the 2009 UGT. Other disturbances with long period (180–720 sec) and slower propagation speeds (75–453 m/s) were observed 1–2 hours after both the 2006 and 2009 explosions. Directions of these observed disturbances were consistent with a source at the reported UGT locations.
 Additionally, we have demonstrated that the cross-correlation method, enhanced with a wavelet analysis, can be applied to detect and identify different types of ionospheric disturbances, separated in time and frequency. Ionospheric sounding, using large networks of GNSS receivers already deployed, has the potential to be a new sensing technique for monitoring weapons development and verifying test treaty compliance, complementing the present use of seismic and infrasound methods.
 Yu-Ming Yang was supported by a NASA Earth and Space Science Fellowship, grant number NNX09AN52H. James Garrison was supported by the 2008 ASEE Summer Faculty Fellowship Program (SFFP) at Hansom Air Force Base.
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.