J Seismol (2013) 17:753–769DOI 10.1007/s10950-012-9352-1

ORIGINAL ARTICLE

Seismic discrimination of the 2009 North Korean nuclearexplosion based on regional source spectra

Tae-Kyung Hong

Received: 1 July 2012 / Accepted: 27 November 2012 / Published online: 29 December 2012© Springer Science+Business Media Dordrecht 2012

Abstract Seismic discrimination of an under-ground nuclear explosion (UNE) based on regionalwaveforms in continental margins is challengingdue to large variations among waveforms. The2009 North Korean UNE test was conducted inthe far eastern Eurasian plate. The UNE wasrecorded by densely-located regional seismic sta-tions, and regional waveforms exhibit highly path-dependent amplitude and arrival time featuresdue to complex crustal structures. Regional sourcespectra are calculated by correcting for the patheffects on the waveforms. A two-step approach isproposed for stable inversion of source-spectralparameters and path parameters. Characteristicovershoot features are observed in the sourcespectra, particularly strong in Pn. The path para-meter, Q, is determined uniquely regardless of thesource-spectral model implemented, which sug-gests stable separation of path effects from wave-form records. The estimated source spectra fitwell to a theoretical UNE source-spectral model.

T.-K. Hong (B)Department of Earth System Sciences,Yonsei University, 50 Yonsei-ro, Seodaemun-gu,Seoul 120-749, South Koreae-mail: tkhong@yonsei.ac.kr

The fitness between the estimated and theoreticalsource-spectral models allows us to discriminateUNEs from natural earthquakes. Also, the P/Ssource-spectral ratio is observed to be an effectivediscriminant of UNE.

Keywords Seismic discrimination ·Underground nuclear explosion · North Korea ·Continental margin

1 Introduction

Seismic analyses play an important role in themonitoring of underground nuclear explosions(UNEs). Various seismic methods have beenproposed for discriminating UNEs from naturalearthquakes, which include comparison betweenbody-wave magnitudes and surface-wave magni-tudes (e.g., Taylor et al. 1989; Bonner et al. 2008),comparison of P/S amplitude ratio (e.g., Xie andPatton 1999; Richards and Kim 2007), analy-sis of energy contents in surface waves (Bruneand Pomerory 1963), analysis of spectral energy(Weichert 1971), and analysis of moment-tensorcomponents (Ford et al. 2009).

Small and moderate-sized UNEs are observedonly up to regional distances in which seismic wavesare highly influenced by crustal structures (e.g.,Walter et al. 2007; Hong et al. 2008; Koper et al.2008; Zhao et al. 2008; Patton and Taylor 2008;

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Chun and Henderson 2009; Hong 2010b). Stablediscrimination of UNEs at regional distances isa long-standing issue, especially for regions withcomplex crustal structures such as continentalmargins. It is known that regional waves are highlyvariable in the continental margins depending onthe path (e.g., Kennett and Furumura 2001; Honget al. 2008; Hong 2012; Hong and Lee 2012). Also,seismologists often observe strong S wave trainsfrom UNEs in regional distances (e.g., Xie andPatton 1999; Patton 2001; Hong and Xie 2005;Kim and Richards 2007; Bonner et al. 2008; Zhaoet al. 2008; Hong 2010b). These features hinderstable discrimination of UNEs based on seismicwaveforms at regional distances in and around thecontinental margins.

The highly path-dependent seismic waveformscause difficulty in application of conventionalmethods for discrimination of UNEs. Thus, it isdesirable to use path-corrected source spectra ofthe UNEs for stable discrimination. There havebeen attempts to determine regional-wave sourcespectra by correcting the waveform spectra forseismic attenuation along paths (e.g., Mueller andMurphy 1971; Burdick et al. 1984; Fisk 2007).Here, various source-spectral models have beenconsidered (e.g., Mueller and Murphy 1971; Akiet al. 1974; Lay et al. 1984; Sereno et al. 1988;Denny and Johnson 1991). However, such seismicdiscrimination of UNEs based on the path-corrected source spectra has been rarely con-ducted in the continental margins, and its validityremains unclear.

North Korea conducted two moderate-sizedUNE tests in 2006 and 2009. The UNEs were det-onated at the far eastern margin of the Eurasianplate (Richards and Kim 2007; Hong et al. 2008;Ford et al. 2009; Shin et al. 2010). The events werewell recorded by densely-located regional seismicnetworks in Korea, Japan, and China. The UNEsprovide us with a unique opportunity to examinethe feasibility of the discrimination method usingcomplex high-frequency regional waveforms.

In this study, we investigate the characteristicsof regional waveforms from the UNEs. We de-termine the regional source spectrum of the 2009UNE from the regional waveforms. The invertedparameters are compared among different sourcemodels, and their validity is examined. The path

parameters for common stations are comparedbetween the UNEs to verify the inversion method.Also, seismic discrimination based on the sourcespectra is performed for the 2009 UNE.

2 Data and geology

The North Korean UNE tests were conducted onOctober 9, 2006 and May 25, 2009 at nearby loca-tions that are separated by about 8.9 km (Table 1).The magnitudes (mb ) of the UNEs are 4.2 and4.7. These UNEs were well observed by regionalseismic networks (Fig. 1). The scalar isotropicmoments are reported to be ∼ 3 × 1014 Nm forthe 2006 UNE (Walter et al. 2007; Hong and Rhie2009) and 1.8 × 1015 Nm for the 2009 UNE (Fordet al. 2009).

The Korean Peninsula is located in the far east-ern margin of the Eurasia plate and is composedof three precambrian massif blocks and two inter-vening fold belts (e.g., Chough et al. 2000). TheKorean Peninsula is underlain by a typical con-tinental crust with a mid-crustal seismic disconti-nuity (He and Hong 2010). Toward the east, thecontinental crust in the Korean Peninsula changesto transitional or oceanic crusts in the East Sea(Sea of Japan) (e.g., Hong et al. 2008; Hong2010a). It is reported that structural variations inthe crust cause high modulation in regional phases(e.g., Kennett and Furumura 2001; Hong et al.2008; Hong 2011).

We collect 801 regional seismograms for the2009 UNE from seismic stations in South Korea,Japan, and China (Fig 1). The epicentral dis-tances are 342–1884 km. The seismic stations areequipped with either broad-band or short-periodvelocity seismometers and accelerometers. Thesampling rates of records from the Korean sta-tions are 0.01 s, and those from the Chinese and

Table 1 Event information of the 2006 and 2009 NorthKorean UNEs and a nearby earthquake in 2002

Event Date Time Lat Lon mb

(◦N) (◦E)

UNE 2009 05/25/2009 00:54:43 41.30 129.03 4.7UNE 2006 10/09/2006 01:35:27 41.29 129.13 4.2EQ 2002 16/04/2002 22:52:38 40.66 128.65 4.1

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108˚ 112˚ 116˚ 120˚ 124˚ 128˚ 132˚ 136˚ 140˚ 144˚

32˚

36˚

40˚

44˚

48˚

-6000 -4000 -2000 0 2000 4000

m

108˚ 112˚ 116˚ 120˚ 124˚ 128˚ 132˚ 136˚ 140˚ 144˚

32˚

36˚

40˚

44˚

48˚

0 500

km

UNEs

EQ East Sea(Sea of Japan)

YellowSea

China

Russia

Japan

Fig. 1 The locations of events and stations on a topo-graphic map. The epicenter of the 2006 North KoreanUNE is marked with a green circle, that of the 2009 UNEwith a blue circle, and that of the 2002 earthquake (EQ)with an open star. The stations are marked with red trian-

gles. The great-circle paths from the 2009 UNE to stationsare presented with solid lines. A total of 801 seismic wave-forms are collected for an analysis of the 2009 UNE. Thetwo UNEs are separated by ∼82 km. The focal depth ofthe earthquake is 10 km

Japanese stations are 0.05 s. The raw waveformsare corrected for instrument responses and thenconverted to ground displacements (Fig. 2).

3 Regional waveforms

Some selected regional waveform records arepresented in Fig. 2. We find significant path-dependent variations in the amplitudes and ap-parent velocities of the phases. In particular, wefind strong attenuation of crustal-guided shearwaves (Lg) for paths across the East Sea in whichtransitional or oceanic crusts are present (Hong2010a). A similar feature is observed in the crustalP waves (Pg). We observe relatively prominentmantle-lid P waves (Pn) at most stations. On theother hand, the mantle-lid S waves (Sn) are weakat distances greater than about 1,000 km.

The strong attenuations of Pg and Lg along thepaths across the East Sea suggests the presence ofa laterally inhomogeneous crustal structure. Theprominent Pn phase suggests strong excitation ofP energy from the source. The signal-to-noise ra-

tios of Pn phase are as high as 2–5 in most records(Fig. 3). The strong Pn phase appears to be usefulfor inference of the source properties.

The vertical displacement waveforms for the2006 and 2009 UNEs at eight common stationsare compared to examine the similarity of wave-forms (Fig. 4). The stations are selected to covervarious raypaths and azimuths in the KoreanPeninsula. Paths to stations in the east coast ofthe Korean Peninsula (CHC, DAG) cross ma-jor oceanic crustal segments, while those to thewest coast (BRD, SES) largely (or, entirely) crosscontinental crust. Also, three pairs of stationswith similar azimuths (SEO-SES, CHC-KWJ, andDGY-DAG) are prepared to examine distance-dependent features. Stations at farther distanceshave longer continental paths than those at nearerdistances. A bandpass filter between 0.8 and 2 Hzis applied to the waveform records.

The phase compositions in wave trains ap-pear to vary significantly with azimuth and path.We find strong development of Lg phase alongthe continental paths, while weak or rare Lg isobserved along the suboceanic paths. We alsoobserve that the phase composition is different

756 J Seismol (2013) 17:753–769

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200

100 200 300 400 500

Dis

tanc

e (k

m)

Time (s)

2009 North Korean UNE

SEHBMDJ

DGY

HESGWLINCNYOJMGYSESGUM

GBIUSNHAC

BUSYSUTOY

MOKN.HINHHUKNRWN.SETHN.SGWH

SGPKNMMMASBTN.HSEHN.HMTHTMRKSKSGNBJTTSK

HIAZPn Pg Sn Lg

Fig. 2 Vertical displacement record sections for the 2009North Korean UNE from some selected paths that aremarked with blue lines in Fig. 1. Each record section isnormalized by its maximum amplitude. The arrival timesof major regional phases (Pn, Pg, Sn, Lg) are markedwith solid lines. The regional phases are observed to beinfluenced by discriminative path-dependent attenuation

between the stations with similar azimuths (SEO-SES, CHC-KWJ, and DGY-DAG). We findstrong Lg waves in stations with longer continen-tal paths. For instance, stations CHC and DGYdisplay weak Lg and strong Sn, while stationsKWJ and DAG present strong Lg and weak Sn.

The arrival times of major phases are observedto be similar between the UNEs, supportinghypocentral proximity between the UNEs. We,however, find large differences in wave train com-positions and relative phase amplitudes betweenthe UNEs. As a result, the P/S amplitude ratiosat common stations appear to be highly differentbetween the UNEs. For instance, at station DGY,the peak S amplitude is larger than the peak Pamplitude in the record for the 2006 UNE, while

0.0

0.4

0.8

1.2

nois

e / P

n

1 2 3 4 5 6 7 8

0.0 0.2 0.4

portion

f (Hz)

Fig. 3 Distribution of the inverse of Pn signal-to-noiseratios of collected waveforms that are strong enough at fre-quencies between 1 and 8 Hz for a source-spectral analysis.The ambient noise field is collected from 20-s-long recordsections before Pn arrivals

the peak P amplitude is larger than the peak S am-plitude in the record for the 2009 UNE (Fig. 4e).Similar observations are found in other UNEs(Hong 2010b).

The waveform variations between the UNEsmay be associated with changes in raypaths ordifferences in source-region geology (Rodgerset al. 2010). This observation suggests that directcomparison of peak amplitudes of waveforms maynot be suitable to constrain the relative strengthbetween the UNEs. Also, it is suggested thatstable seismic discrimination may be difficult toachieve with records from sparsely-located net-works.

4 Theory

The high variability of waveforms by path makesit difficult to use the simple P/S amplitude ratios ofsingle seismic records for discrimination of UNE.It is desirable to use the energy directly excitedfrom the source for stable discrimination. In thisstudy, we discriminate the UNE sources based onthe source spectra.

The displacement spectrum of seismic waves atstation i, Ai( f ), can be expressed as (Sereno et al.1988; Xie and Patton 1999)

Ai( f ) = S( f )G(di) exp

(− π f di

vg Qi( f )

)ei( f ), (1)

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124˚ 126˚ 128˚ 130˚34˚

36˚

38˚

40˚

42˚

44˚

124˚ 126˚ 128˚ 130˚34˚

36˚

38˚

40˚

42˚

44˚ 0 100 200

km

20092006

BRDCHC

DAG

DGY

KWJ

MDJ

SEOSES

40 60 80 100 120 140 160 180 200 220 240Time (s)

2006

2009

528.8 km

523.2 km

BRD Z

Pn Pg Sn Lg

40 60 80 100 120 140 160 180 200Time (s)

2006

2009

406.6 km

405.5 km

CHC Z

Pn Pg Sn Lg

60 90 120 150 180 210 240 270 300Time (s)

2006

2009

613.8 km

614.9 km

DAG Z

Pn Pg Sn Lg

40 60 80 100 120 140 160 180 200Time (s)

2006

2009

402.1 km

402.6 km

DGY Z

Pn Pg Sn Lg

90 120 150 180 210 240 270 300 330Time (s)

2006

2009

706.3 km

705.2 km

Z

Pn Pg Sn Lg

40 60 80 100 120 140 160 180 200Time (s)

2006

2009

371.1 km

370.8 km

MDJ Z

Pn Pg Sn Lg g

40 60 80 100 120 140 160 180 200Time (s)

2006

2009

463. km

461.2 km

Z

Pn Pg Sn Lg

60 80 100 120 140 160 180 200 220 240Time (s)

2006

2009

551.3 km

548.8 km

Z

Pn Pg Sn Lg

(a)

(b)

(c)

(d)

(e)

(f) (g)

(h) (i)

KWJ

SEO SES

Fig. 4 Comparisons of waveforms at common stationsbetween the 2006 and 2009 North Korean UNEs: (a) mapfor events and stations, and the vertical displacement wave-forms for stations (b) BRD, (c) CHC, (d) DAG, (e) DGY,(f) KWJ, (g) MDJ, (h) SEO, and (i) SES. The epicentersof the 2006 and 2009 North Korean UNEs are marked

with circles, and the locations of stations are with indicatedby triangles. The great-circle paths are presented by solidlines. The epicentral distance and major regional phasesare denoted in each record section. The record sections arebandpass-filtered between 0.8 and 2 Hz. The waveformsare observed to be different between the pairs of stations

758 J Seismol (2013) 17:753–769

where f is the frequency, S( f ) is the source spec-trum, di is the epicentral distance, G(di) is thegeometrical spreading term, Qi( f ) is the qualityfactor along the path to station i, vg is the groupvelocity, and ei( f ) is the cumulative effect of un-accounted factors along the path. The influence ofthe unaccounted factors is trivial compared to thatof the major source and path factors. The qualityfactor Qi( f ) can be written as

Qi( f ) = Q0,i f ηi , (2)

where Q0,i is the quality factor at 1 Hz, and ηi isthe power-law frequency dependence.

The geometrical spreading term, G(di), isgiven by

G(di) = (d0/di)γ d−1

0 , (3)

where γ is the decay rate of phase, and d0 is thereference distance. We set d0 = 100 km and γ =0.5 for Lg, and d0 = 1 km and γ = 1.1 for Pn, Pgand Sn (Zhu et al. 1991; Walter and Taylor 2002;Hong and Rhie 2009). The source spectrum, S( f ),is given by (Mueller and Murphy 1971; Xie andPatton 1999)

S( f ) = M0

4πρsv3s

√1 + (1 − 2ξ) f 2/ f 2

c + ξ 2 f 4/ f 4c

, (4)

where M0 is the moment, ξ is the overshoot para-meter, fc is the corner frequency, ρs is the densityin the source region, and vs is the phase velocity inthe source region.

Equation 1 can be recast to be a linear system as

a = Bm, (5)

where a is a column vector for observed spectralamplitudes, B is a matrix for linear operators, andm is the model vector. The column vector a isgiven by

a = [ln A1( f1), ln A1( f2), · · · , ln A1( fm),

ln A2( f1), ln A2( f2), · · · , ln An( fm)]T

, (6)

where m is the number of discrete frequencies,and n is the number of stations. The total numberof rows in vector a is m × n. The model vector mis given by

m = [M0, fc, ξ, Q0,1, η1, Q0,2, η2, · · · , Q0,n, ηn

]T,

(7)

where M0, fc, ξ , Q0,i and ηi are unknown parame-ters to be determined. Parameters M0, fc, and ξ

represent source properties, and parameters Q0,i,and ηi present path properties. Here, M0 is anapparent moment that varies with the size of timewindow and frequency band applied. On the otherhand, parameters fc, ξ and Q are determineduniquely for each phase.

For each regional phase, discrete sets of M0,fc, and ξ are prepared. The path parameters Q0,i

and ηi are determined using the LSQR inversionmethod (the sparse linear equations and sparseleast squares method; Paige and Saunders 1982)for given discrete sets of M0, fc, and ξ . A set ofsource parameters (M0, fc, and ξ) yielding theminimum misfit error between the observed andtheoretical source spectra is determined. The pathparameters (Q0,i, ηi) associated with the best-fitsource parameters are determined subsequently.It is noteworthy that parameters M0 and Q aredetermined nonuniquely in the inversion due totheir mutual trade-offs; a high M0 incorporates aset of low Q in the inversion, and vice versa.

To avoid the nonunique determination ofmodel parameters, we introduce a two-step inver-sion approach (Hong and Rhie 2009). In the firststep of inversion, we determine M0 that yieldsthe Q values consistent with previous studies(Kim et al. 1999; Chung and Sato 2001; Hongand Rhie 2009; Hong 2010a). Here, we apply agrid-searching scheme to determine an optimumM0 that yields the minimum residual betweeninverted and reported Q values. In the secondstep, we invert fc and ξ with implementation ofthe predetermined apparent moment (M0). A setof fc and ξ yielding the minimum misfit errorbetween the inverted and theoretical source spec-tra is searched. The path parameter Q is newlydetermined at every inversion of fc and ξ . TheQ parameters inverted with the best-fit source

J Seismol (2013) 17:753–769 759

0.6

0.8

1.0

1.2

1.4

3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0

error ratio

Pn M0 = 4x1014 Nm M0 = 6x1014 Nm

M0 = 4.5x1014 NmM0 = 2.5x1014 Nm

M0 = 1x1014 Nm M0 = 1.4x1014 Nm

M0 = 8x1013 NmM0 = 4x1013 Nm

ξ

0.6

0.8

1.0

1.2

1.4

3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0

error ratio

Pn

ξ

0.2

0.4

0.6

0.8

1.0

1.2

2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4

error ratio

ξ

0.2

0.4

0.6

0.8

1.0

1.2

2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4

error ratio

Pg

ξ

0.2

0.4

0.6

0.8

1.0

1.2

2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4

error ratio

ξ

0.2

0.4

0.6

0.8

1.0

1.2

2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4

error ratio

Sn

ξ

0.2

0.4

0.6

0.8

1.0

1.2

2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4

error ratio

ξ

0.2

0.4

0.6

0.8

1.0

1.2

2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4

1 2 3 1 2 3

1 2 3 1 2 3

1 2 3 1 2 3

1 2 3 1 2 3error ratio

ξ

(a)

(b)

(c)

(d)

LgLg

Sn

Pg

fc (Hz) fc (Hz)

fc (Hz) fc (Hz)

fc (Hz) fc (Hz)

fc (Hz) fc (Hz)

Fig. 5 Estimation of misfit errors as function of cornerfrequency ( fc) and overshoot parameter (ξ) for variousgiven apparent moments: a Pn, b Pg, c Sn, and d Lg. The

model parameters ( fc, ξ) are determined to be consistentfor changes of implemented moments at all phases

760 J Seismol (2013) 17:753–769

parameters are chosen as the representative pathparameters.

5 Process and analysis

The velocities vg in Eq. 1 are set to be 7,950 m/sfor Pn, 6,050 m/s for Pg, 4,550 m/s for Sn, and3,500 m/s for Lg (Hong and Kang 2009; Hongand Rhie 2009). The P and S wave velocities inthe source and receiver regions, vs and vr, areset to be 5,670 and 3,273 m/s, respectively. Thedensity in the source region (ρs) is assumed to be2,580 kg/m3.

The Pn phase is collected from wave trains in atravel-time range between d/7.95 + 5 and d/6.6 +0.8 s, where d is the epicentral distance in kilome-ter. The waveforms in a travel-time range betweend/6.05 + 0.8 and d/5.0 + 11.0 s are analyzed forPg, those between d/4.50 + 11.0 and d/3.7 + 0.5 sare for Sn, and those between d/3.57 + 0.5 andd/3.15 s are for Lg (Hong and Rhie 2009). A 4.5-slong moving time window with 0.2-s-long cosinetapers at both ends is used to collect waveforms ofregional phases.

The representative spectrum of a regionalphase is calculated by stacking the spectra ofwaveforms in moving time windows. The spectraare stacked in the frequency range of 1–8 Hzconsidering the frequency contents of regionalseismic waves and the size of time window. Here,the levels of stacked spectral amplitudes varywith the moving-time-window size and the pre-scribed travel-time ranges. Note that the lengthsof wave trains analyzed are determined by theprescribed travel-time ranges. Thus, the lengthsof wave trains analyzed increase with distance.It is noteworthy that only the apparent momentscan be determined based on the stacked spec-tral amplitude that changes with the moving-time-window size and the prescribed travel-time range.The frequency interval in the stacked spectra is0.01 Hz. The source spectra are inverted basedon the stacked spectra between 1 and 8 Hz. Thenumber of discrete frequencies (m in Eq. 6) is 701.

We determine the model parameters using thetwo-step inversion approach. In the first step of

inversion, we determine apparent moments yield-ing Q parameters that are consistent with previousstudies (Kim et al. 1999; Chung and Sato 2001;Hong and Rhie 2009; Hong 2010a). We then de-termine the corner frequency ( fc) and overshootparameter (ξ) with implementation of the appar-ent moments determined in the first step of in-version. The source-spectral parameters are grid-searched in every 0.1 Hz for fc and every 0.1 forξ . The best-fit set of fc and ξ is determined by av-eraging the discrete parameters satisfying a givenlevel of misfit error that is set to be the 1.1 timesthe minimum misfit error. This procedure allowsus to stably determine the model parameters inthe inversion based on grid-searching scheme.

In the inversion of model parameters, thereare trade-offs between the apparent moment andquality factors. Thus, when attenuation is over-estimated, the apparent moment is determinedto be larger than the true value. Similarly, theapparent moment is determined to be lower thanthe true value when the attenuation is under-estimated. On the other hand, the corner fre-quency ( fc) and overshoot parameter (ξ) are esti-mated to be nearly constant for change of moment(Fig. 5, Table 2). The consistent determination offc and ξ for different M0 verifies the two-stepapproach.

Table 2 Variation of source-spectral parameters of re-gional phases for changes of apparent moments (M0)

Phase M0 (N·m) fc (Hz) ξ

Pn 4.0 × 1014 4.45 1.055.0 × 1014 4.44 1.056.0 × 1014 4.44 1.06

Pg 2.5 × 1014 3.71 0.743.5 × 1014 3.75 0.754.5 × 1014 3.79 0.76

Sn 1.0 × 1014 3.74 0.621.2 × 1014 3.76 0.641.4 × 1014 3.78 0.64

Lg 4.0 × 1013 3.72 0.636.0 × 1013 3.71 0.658.0 × 1013 3.70 0.65

The corner frequencies ( fc) and overshoot parameters (ξ)are determined to be nearly constant for changes of M0

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In this study, the source-spectral inversions arebased on a large number of waveforms (801 wave-forms) from stations on various paths, in order tostably determine the source parameters. We findthat the source parameters rarely vary with in-clusion or exclusion of particular data when largenumbers of data are analyzed in the inversion.This is because the source spectra are determinedbased on the full data set, and inclusion or exclu-sion of particular records hardly causes significantvariation in the inverted source parameters.

Similarly, the inverted source-spectral parame-ters are hardly influenced by inclusion of wave-form records with low signal-to-noise ratios in theanalysis. This is because such waveforms with lowsignal-to-noise ratios are determined to have lowQ values along the paths in the inversion. It is alsonoteworthy that the path parameters (Q0, j, η j) aredetermined by path, and they are determined tobe constant for given M0, fc, and ξ regardless ofaddition or removal of data from other stations.This is because the path parameters for a certainpath are determined based only on the corre-sponding waveform. Thus, the path parametersfor a certain path are determined independentlyfrom those for other paths.

6 Regional source spectra

The corner frequencies ( fc) are determined to be4.44 Hz for Pn, 3.75 Hz for Pg, 3.76 Hz for Sn, and3.71 Hz for Lg (Table 3). The Pn phase displaysa slightly higher corner frequency than the otherphases that present comparable corner frequen-cies. This Pn corner frequency is smaller than that

Table 3 Inverted source-spectral parameters of regionalphases from the 2009 North Korean UNE

Phase M0 (N·m) fc (Hz) ξ

Pn 5.0 × 1014 4.44 1.05Pg 3.5 × 1014 3.75 0.75Sn 1.2 × 1014 3.76 0.64Lg 6.0 × 1013 3.71 0.65

The apparent moments (M0), corner frequencies ( fc), andovershoot parameters (ξ) are presented

of the 2006 UNE (Hong and Rhie 2009). Theobservation agrees with the general relationshipbetween the corner frequency and event size (e.g.,Atkinson 1993; Xie and Patton 1999).

The overshoot parameter (ξ) is estimated tobe 1.05 for Pn, 0.75 for Pg, 0.64 for Sn, and0.65 for Lg. The Pn phase displays the largestovershoot parameter. Such a large overshoot fea-ture is consistent with the 2006 UNE (Hong andRhie 2009), suggesting that the source may beassociated with a strong explosive source such asan underground nuclear explosion. We, however,observe relatively weak overshoot features in theother phases (Pg, Sn, and Lg). The observationsuggests that the Pn phase may be more suitablefor investigation of UNE source properties thanother phases.

The inverted source spectra from single recordsare observed to be similar, and their standarddeviations are found to be small (Fig. 6). Theaverage source spectra match well with the the-oretical models that are calculated based on theinverted source-spectral parameters, particularlyat frequencies of 1.5 Hz or higher. The fractionaldifferences between the observed and theoreticalsource spectra based on the UNE model presentthe maximum fractional differences of 2.0–2.6 %and the average fractional differences of 0.9–1.0 % at frequencies of 1.5–7.5 Hz for all regionalphases. The high similarity among the source spec-tra estimated at individual stations supports thestability of the inversion. This observation alsosuggests that records with low signal-to-noise ra-tios can be applied without degrading the stabilityof source-spectral inversion.

7 Seismic discrimination based on source-spectralfitness

The UNE source is discriminated by compar-ing the estimated source spectra with theoreticalmodels. We find that the source spectra invertedbased on a UNE source-spectral model matcheswell with the theoretical model (Fig. 6). Weadditionally perform a source-spectral inversion

762 J Seismol (2013) 17:753–769

0.01

0.1

1

87654321

Am

plitu

de (

m·s

)

Frequency (Hz)

Pn, Z UNE

observedaverage

theoretical

0.01

0.1

1

87654321Frequency (Hz)

Pg, Z UNE

observedaverage

theoretical

0.01

0.1

1

87654321

Am

plitu

de (

m·s

)

Am

plitu

de (

m·s

)A

mpl

itude

(m

·s)

Frequency (Hz)

Sn, Z UNE

observedaverage

theoretical

0.01

0.1

1

87654321Frequency (Hz)

Lg, Z UNE

observedaverage

theoretical

(a)

(c)

(b)

(d)

Fig. 6 Source spectra of regional phases from the 2009UNE: a Pn, b Pg, c Sn and d Lg. The source spectrainverted from single records are presented by red lines, andtheir mean variations along with standard deviations are

marked with blue lines. The theoretical source spectra arepresented by green lines. The inverted source spectra matchwell with the theoretical source spectra for all regionalphases

based on an earthquake source-spectral modelto evaluate the model-dependent source-spectralfitness.

We apply the Brune’s earthquake source-spectralmodel that is given by (Brune 1970; Stevens andDay 1985)

S( f ) = M0 Rθφ

4π√

ρsρrv5s vr

(1 + f 2/ f 2

c

) , (8)

where Rθφ is an amplitude scaling factor forsource radiation pattern, and ρr and vr are thedensity and seismic velocity in the receiver region,respectively. The radiation pattern Rθφ is set to be0.63 for P phases (Pn, Pg) and 0.43 for S phases(Sn, Lg) (Hong and Rhie 2009).

We first compare the Q factors with thosefrom inversion based on the UNE source-spectralmodel and examine the model dependence onthe inverted Q factors. We measure the fractionalQ−1 differences between the two results (Fig. 7).The fractional differences are calculated by

γ = Q−1EQ − Q−1

UNE

Q−1UNE

, (9)

where QEQ is the Q parameter from analysisbased on an earthquake source-spectral model,and QUNE is the Q parameter from analysis basedon the UNE source-spectral model. We find thatthe fractional Q−1 differences are close to zerofor all phases, suggesting high similarity of the

J Seismol (2013) 17:753–769 763

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 6 7 8

frac

tiona

l Q-1

dif

fere

nce

frac

tiona

l Q-1

dif

fere

nce

frac

tiona

l Q-1

dif

fere

nce

frac

tiona

l Q-1

dif

fere

nce

frequency (Hz)

Pn, Z

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 6 7 8

frequency (Hz)

Pg, Z

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 6 7 8

frequency (Hz)

Sn, Z

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 6 7 8

frequency (Hz)

Lg, Z

(a)

(c)

(b)

(d)

Fig. 7 Fractional Q−1 differences between the inversionsbased on a UNE source-spectral model and those based onan earthquake source-spectral model: a Pn, b Pg, c Sn, andd Lg. The fractional Q−1 differences are observed to be

close to zero for all frequencies, suggesting that the pathproperties are determined to be consistent for changes ofsource-spectral models

Q values between the results. The observationsuggests that path parameters (Q) are determinedto be consistent regardless of the source-spectralmodel implemented, suggesting stable separationof path properties from waveform records. Theobservation also supports the stability of the in-version scheme.

We find changes in apparent moments and cor-ner frequencies due to implementation of a differ-ent source-spectral model. The apparent moments(M0) are determined to be 1.3 × 1015 Nm forPn, 6.6 × 1014 Nm for Pg, 3.5 × 1014 Nm for Sn,and 1.8 × 1014 Nm for Lg. The corner frequenciesare determined to be similar between the phases,which are 4.8 Hz for Pn, 4.9 Hz for Pg, 5.0 Hz forSn, and 4.8 Hz for Lg.

The inverted source spectra display the char-acteristic overshoot feature in all phases, partic-ularly strong in Pn (Fig. 8). The stacked sourcespectra of regional phases are compared with thetheoretical Brune source spectra. The invertedsource spectra are found to match poorly withthe theoretical Brune source spectra, particularlyaround the corner frequencies where characteris-tic spectral overshooting is observed (Fig. 8).

The fractional differences between the ob-served and theoretical source spectra based onthe Brune source-spectral model present maxi-mum fractional differences of 9.7 % and averagefractional differences of 5.3 % for Pn at frequen-cies of 1.5–7.5 Hz. Also, the maximum fractionaldifferences are determined to be 4.7–5.2 %, and

764 J Seismol (2013) 17:753–769

0.01

0.1

1

87654321

Am

plitu

de (

m·s

)A

mpl

itude

(m

·s)

Am

plitu

de (

m·s

)A

mpl

itude

(m

·s)

Frequency (Hz)

Pn, Z Brune model

observedaverage

theoretical

0.01

0.1

1

87654321Frequency (Hz)

Pg, Z Brune model

observedaverage

theoretical

0.01

0.1

1

87654321Frequency (Hz)

Sn, Z Brune model

observedaverage

theoretical

0.01

0.1

1

87654321Frequency (Hz)

Lg, Z Brune model

observedaverage

theoretical

(a)

(c)

(b)

(d)

Fig. 8 Source spectra of regional phases that are invertedwith an earthquake source-spectral model: a Pn, b Pg, c Sn,and d Lg. The source spectra inverted from single recordsare presented by red lines, and their mean variations along

with standard deviations are marked with blue lines.Thetheoretical source spectra are presented by green lines. Theinverted source spectra of P phases (Pn, Pg) match poorlywith the theoretical source spectra

the average fractional differences are estimated tobe 2.8–3.2 % for the other phases. These fractionaldifferences are higher than those from inversionsbased on the UNE source-spectral model. The ob-servation suggests that comparisons between ob-served and theoretical source spectra may allow usto discriminate between UNEs and earthquakes.

8 Seismic discrimination based on P/Ssource-spectral ratios

In principle, S energy is rarely radiated fromexplosion sources. However, it is known thatthe S waves are developed by various secondarysources such as rock cracking (Massé 1981), tec-

tonic release (Toksöz and Kehrer 1972; Ekströmand Richards 1994), spalling (Stump 1985; Dayand McLaughlin 1991), S* (Gutowski et al. 1984;Vogfjörd 1997), P-to-S scattering (Rodgers et al.2010), and Rg-to-S scattering (Gupta et al. 1992;Myers et al. 1999). Also, the amplitudes of seismicwaves are highly influenced by medium propertiesalong raypaths (Fig. 4). Thus, it is often found thatsimple P/S amplitude ratios of single time recordsmay not be useful for discrimination of sourcetypes.

Source spectra of phases present the phasestrengths in the source, in which the path effectsare not included. Here, we use the P/S source-spectral ratios instead of simple P/S amplitude ra-tios. The P/S source-spectral ratios are calculated

J Seismol (2013) 17:753–769 765

using the inverted source spectra based on theUNE source model. We calculate four pairs ofP/S source-spectral ratios: Pn/Sn, Pn/Lg, Pg/Sn,and Pg/Lg source-spectral ratios (Fig. 9). The P/Ssource-spectral ratios are determined to be nearlyconstant at frequencies of 1–8 Hz. The P/S source-spectral ratios are compared with the theoreticalsource-spectral ratios. We find that the stackedP/S source-spectral ratios match well with the the-oretical source-spectral ratios.

We additionally calculate the P/S source-spectral ratios using the source spectra invertedwith an earthquake source-spectral model (Brune’smodel). It is intriguing to note that the P/S source-spectral ratios based on the Brune’s model are

observed to be close to those based on the UNEmodel (Fig. 10). This feature may be associ-ated with the fact that the path parameters (Q)are inverted uniquely regardless of the type ofsource model applied. Thus, the source spectraare inverted to be consistent for different sourcemodels.

The P/S source-spectral ratios of the 2009 UNEare compared with those of a nearby mb 4.1 earth-quake. The earthquake occurred in a locationabout 82 km southwest from the UNE (Fig. 1,Table 1). The source-spectral parameters of theearthquake are collected from Hong and Rhie(2009). We find large differences in P/S source-spectral ratios between the 2009 UNE and the

0.1

1

10

87654321

Am

plitu

de R

atio

Frequency (Hz)

UNE Pn/Sn Z observedaverage

theoretical

0.1

1

10

87654321

Am

plitu

de R

atio

Frequency (Hz)

UNE Pn/Lg Z observedaverage

theoretical

0.1

1

10

87654321

Am

plitu

de R

atio

Frequency (Hz)

UNE Pg/Sn Z observed

averagetheoretical

0.1

1

10

87654321

Am

plitu

de R

atio

Frequency (Hz)

UNE Pg/Lg Z observed

averagetheoretical

(a)

(c)

(b)

(d)

Fig. 9 P/S source-spectral amplitude ratios for the 2009UNE: a Pn/Sn, b Pn/Lg, c Pg/Sn, and d Pg/Lg. The P/Ssource-spectral amplitude ratios for every station are pre-sented by red lines. The mean P/S ratios and the standarddeviations are presented by blue lines. The theoretical P/S

source-spectral amplitude ratios are displayed by greenlines. The mean P/S ratios match well with the theoreticalP/S ratios. The mean P/S ratios are determined to be nearlyconstant at frequencies of 1–8 Hz

766 J Seismol (2013) 17:753–769

0.1

1

10

87654321

Am

plitu

de R

atio

Frequency (Hz)

Pn/Sn Z

UNE model, observed UNE model, theoreticalBrune model, observed

Brune model, theoreticalEQ 2002, observed

EQ 2002, theoretical

0.1

1

10

87654321

Am

plitu

de R

atio

Frequency (Hz)

Pn/Lg Z

UNE model, observed UNE model, theoreticalBrune model, observed

Brune model, theoreticalEQ 2002, observed

EQ 2002, theoretical

0.1

1

10

87654321

Am

plitu

de R

atio

Frequency (Hz)

Pg/Sn Z UNE model, observed UNE model, theoreticalBrune model, observed

Brune model, theoreticalEQ 2002, observed

EQ 2002, theoretical

0.1

1

10

87654321

Am

plitu

de R

atio

Frequency (Hz)

Pg/Lg Z

UNE model, observed UNE model, theoreticalBrune model, observed

Brune model, theoreticalEQ 2002, observed

EQ 2002, theoretical

(a)

(c)

(b)

(d)

Fig. 10 Comparisons between P/S source-spectral ampli-tude ratios from analyses based on the UNE source modeland those from analyses based on an earthquake source

model: a Pn/Sn, b Pn/Lg, c Pg/Sn, and d Pg/Lg. TheP/S ratios are determined to be consistent for changes ofimplemented source-spectral models

earthquake in the frequency range of 1–5 Hz.This observation suggests that P/S source-spectralratios are effective for discrimination of UNE.

9 Discussion and conclusions

Discrimination of UNE is a crucial task in nuclear-monitoring seismology. Seismic discrimination isoften based on the comparison of waveform prop-erties between an unidentified source and knownnatural earthquakes of comparable magnitudes.Thus, when such comparable earthquakes arenot available, it is difficult to discriminate theUNEs. This is particularly challenging for small ormoderate-sized UNEs that are typically observed

up to regional distances. This is because the re-gional waveforms are highly influenced by crustalstructures.

The regional waveforms for the North KoreanUNEs are observed to be highly path-dependentdue to complex crustal structures around theKorean Peninsula that is located in the north-eastern Eurasian plate margin. The relative am-plitudes of major phases at common stations areobserved to be highly varying between the UNEs,suggesting difficulty of direct analysis of singlerecords for discrimination of source type in re-gions with complex crustal structures. Thus, it ishighly desired in source discrimination to ana-lyze the source properties with correction of patheffects.

J Seismol (2013) 17:753–769 767

In this study, the source-spectral parametersand path parameters are inverted from denserecords. A two-step inversion approach was foundto be stable and effective for the inversion. It isobserved that the corner frequencies of regionalsource spectra appear to be comparable amongdifferent phases. The P overshoot parameters aredetermined to be slightly larger than the S over-shoot parameters, which is consistent with pre-vious studies (e.g., Xie and Patton 1999). Thepath parameter (Q) is determined to be consistentfor change of source-spectral models, suggestingstable determination of the Q parameter. This fea-ture supports the validity of the two-step inversionapproach.

The inverted source spectra based on a UNEmodel match well with the theoretical source spec-tra. The average fractional differences betweenthe observed and theoretical source spectra arefound to be 0.9–1.0 % at frequencies of 1.5–7.5 Hzfor all phases. On the other hand, the invertedsource spectra based on an earthquake modelare found to match poorly with the theoreticalsource spectra. The average fractional differencesbetween the observed and theoretical source spec-tra are found to be 5.3 % for Pn and 2.8–3.2 %for the other phases. The misfit errors of theobserved source spectra with respect to the the-oretical source spectra based on an earthquakemodel are three to six times larger than those withrespect to the theoretical source spectra based ona UNE model. The observation suggests that thefitness degree between the inverted and theoreti-cal source spectra can be used as an effective UNEdiscriminant. The source discrimination based onthe source-spectral fitness may be particularly use-ful for regions with rare natural earthquakes withmagnitudes comparable to those of UNEs.

We also compare the P/S source-spectral ratiosof the 2009 UNE with those of a nearby nat-ural earthquake. We find large differences in theP/S source-spectral ratios between the UNE andthe nearby earthquake in the frequency range of1–5 Hz. This observation suggests that the P/Ssource-spectral ratios are applicable for regionswith complex crustal structures. It is also foundthat the P/S source-spectral ratios are similar be-tween the results based on a UNE source-spectralmodel and those based on an earthquake source-

spectral model. The observation suggests that thesource-spectral ratios can be estimated uniquelyregardless of the source-spectral model imple-mented.

Acknowledgements I am grateful to the Korea Meteo-rological Administration, the Korea Institute of NuclearSafety, the National Research Institute for Earth Scienceand Disaster Prevention in Japan, and the IncorporatedResearch Institutions for Seismology, for making seismicdata available. I thank two anonymous reviewers and theassociate editor, Dr. Thomas Braun, for valuable reviewcomments and suggestions that improved the presentationof paper. This work was supported by the Korea Me-teorological Administration Research and DevelopmentProgram under Grant CATER 2012-8050.

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