○E

Moment Tensor Source-Type Analysis for theDemocratic People’s Republic of Korea–Declared Nuclear Explosions (2006–2017)and 3 September 2017 Collapse Eventby Andrea Chiang, Gene A. Ichinose, Doug S. Dreger, Sean R. Ford,Eric M. Matzel, Steve C. Myers, and W. R. Walter

ABSTRACT

The Democratic People’s Republic of Korea (DPRK) conductedits sixth announced nuclear test on 3 September 2017 03:30UTC (mb 6.1). There was an aftershock 8.5 min later (mb 4.1).Such aftershocks were noteworthy and often associated withpost–nuclear explosion collapses. We performed moment tensor(MT) and network sensitivity solution (NSS) analysis usingregional long-period surface-wave and first-motion (FM) polar-ities. We also extended this analysis to the previous five DPRKnuclear tests. The NSS results, which includeMTsolution uncer-tainties, show large isotropic components for the events and arewithin the population of otherU.S. nuclear and collapse events onthe fundamental lune. The FM data improved the NNS source-type resolution. The agreement between MT seismic momentsand independent coda-envelope amplitudes indicated no biaseswith theEarthmodel error or poorly constrained seismicmomentfor shallow seismic sources. TheMTfor the collapse is not a pureimplosion and consistent with an equivalent tensional closingcrack mechanism and two-sided vertical point force.The DPRK aftershock has similar circumstances to the collapse21 min after the 5 August 1982 Atrisco nuclear test. We calcu-lated a range of volume reduction of 1:06 × 105–4:23 × 105 m3

due to 2:68 × 1015–1:07 × 1016 N ·m seismic moment rangebased on diorite rock properties and a closing tensile crackmodel. In comparison, the cavity radius-yield scaling relation re-sulted in 2:84 × 105–1:14 × 106 m3 volume range. The overlapin the volume range suggests that the aftershock can be explainedby collapse of the explosion cavity. A less likely tunnel-collapsescenario requires a 3- to 13-km-long tunnel to match an equiv-alent volume change (assuming a 30 m2 cross-sectional area)and would possibly resulted in secondary sources and mecha-nism asymmetries detectable by MTmethods.

Electronic Supplement: Waveform fits for the moment tensor(MT) inversion results of the five Democratic People’s Republic

of Korea (DPRK) events previous to 2017 and associatednetwork sensitivity solution (NSS) for both MT-only andMT + FM (first-motion) datasets.

INTRODUCTION

Democratic People’s Republic of Korea (DPRK) conducted sixannounced underground nuclear explosions at the Punggye-ritest site between 2006 and 2017. The DPRK announced thatit had conducted a sixth test of a thermonuclear weapon shortlyafter 3 September 2017 03:30 UTC. The ComprehensiveNuclear-Test-Ban Treaty Organization (CTBTO) reported anevent near that time with a body-wave magnitude (mb) of 6.1located near the previous five announced DPRK nuclear tests(Fig. 1). This event was followed 8.5 min later by a large after-shock with mb of 4.1 (CTBTO). The aftershock was initially amysterious event to researchers with speculation it was a secon-dary explosion, a natural earthquake, or a tunnel collapse(Cyranoski, 2017). Large aftershocks greater than magnitude4 were noteworthy in the history of U.S. underground nuclearexplosion testing at the Nevada National Security Site (NNSS),formerly known as the NevadaTest Site (e.g., Ford and Walter,2010). The best historical example is theMw 4.5 collapse (Fordet al., 2009b) approximately 21 min after the 5 August 1982mb 5.7 Atrisco underground nuclear test (Springer et al., 2002).

Moment tensor (MT) and source-type analysis provide anew physics-based event discrimination tool for nuclear explo-sion monitoring (e.g., Dreger and Woods, 2002; Ford et al.,2009b) in augmenting the traditional empirical methods such asmb=M s (e.g., Bonner et al., 2008) and regional P/S phaseamplitude ratios (e.g., Walter et al., 2008). One benefit of MTanalysis is the ability to distinguish between explosion andcollapse events. Additionally, a combination of regional MTandfirst-motion (FM) polarities can still provide some discrimina-

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tion power between earthquakes and explosions (e.g., Chianget al., 2014) despite observations of large Love-wave and Ray-leigh-wave reversals from historical underground nuclear tests(e.g., Ekström and Richards, 1994). These observations indicatedeviations from purely isotropic explosion by tectonic release orfree-surface spall processes.

Performing the MT uncertainty analysis for all 2006–2017DPRK events in a consistent manner is necessary for a compre-hensive examination of the nonisotropic components. Previousstudies examined only one or two DPRK events at a time (e.g.,Ford et al., 2009a, 2010, 2012; Shin et al., 2010; Barth, 2014;Vavryčuk and Kim, 2014; Cesca et al., 2017; Ichinose et al.,2017; Liu et al., 2018; Tian et al., 2018; Wang et al., 2018).We repeat the MT analysis for the six previous DPRK eventsusing more regional waveform data from any available open seis-mic networks. We will also be adding regional and teleseismicP-wave FM to constrain the MT source-type uncertainties.Additionally, an MT analysis of the two recent 3 September2017 DPRK events will be beneficial to the scientific commu-nity. Unprecedented high-resolution images of ground deforma-tion of Mount Mantap were collected from the Earth orbitingsatellites (e.g., Dreger et al., 2017; Wang et al., 2018) for therecent 3 September 2017 DPRK explosion and the subsequentaftershock. Including the MTsource type for both the explosionand aftershock is necessary for modeling the combined deforma-tion observed between the two satellite scenes.

Precise relative and absolute locations ofshallow depth seismic events are important forunderstanding effects of topography and geologyon source mechanisms. Wen and Long (2010)and Zhang and Wen (2013) previously analyzedthe relative location of the 2006, 2009, and 2013DPRK events using regional body waves. Myerset al. (2018) estimated the precise relative andabsolute locations for all of the DPRK eventsbased on differential and absolute travel timesmeasured from regional and teleseismic body-wave phases using Bayesloc, a Bayesian hierarchi-cal seismic event locator (e.g., Myers et al., 2007,2018). They constrained the relative locationsby modeling geodetic surface deformation onMount Mantap by the 6 January 2016 DPRKevent observed from Interferometric SyntheticAperture Radar. The depth of burial (DoB)for the DPRK nuclear tests should be shallowerthan 760 m given the difference in elevation be-tween the tunnel-adit entrance at ∼1400 m andthe peak elevation of Mount Mantap at 2205 m(e.g., Coblentz and Pabian, 2015). The DoBsare between 300 and 600 m given their preciselocations beneath the mountain surface and tun-nels are typically mined with a slight slope up-ward for drainage (e.g., Pasyanos and Myers,2018). The geology of the Mount Mantap areais composed of a Jurassic-aged granite or Tokur-eido diorite and quartz diorite intrusions into

sedimentary rocks, with mountain peaks capped with stratifiedShintokuri volcanic tuff and basalt flows (e.g., Coblentz and Pa-bian, 2015). The absolute locations suggest the emplacement iswithin the granite or quartz diorite intrusions.

The focus of this study is to identify the source type forboth the 3 September 2017 seismic event, the aftershock, andthe five previous DPRK events using MT analysis of long-period regional waves based on the time-domain methods (e.g.,Ford et al., 2009b). We provide uncertainty analysis using thenetwork sensitivity solutions (NSS) method including FMpolarities (e.g., Ford et al., 2010). We compare the seismic mo-ment estimates with independent estimates of regional S-wavecoda-derived moment magnitudes (e.g., Gök et al., 2016). Wefinally use magnitude–yield scaling relations to compute theexpected cavity volume of the explosion and compare themwith the estimated collapse volume from the seismic momentusing a closing tensile crack model (Müller, 2001) and discuss aprobable collapse mechanism for the aftershock.

DATA

For the MTanalysis, we assembled data from three-componentbroadband regional waveforms and metadata from variousseismic networks (Fig. 2) archived at Incorporated ResearchInstitutions for Seismology (IRIS). We used the New ChinaDigital Seismic Network data from stations Mudanjiang

▴ Figure 1. Google Earth image of the location and timeline of the six announcednuclear explosions at the Punggyre-ri test site, Democratic People’s Republic ofKorea (DPRK). IDC, International Data Centre at the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO). The color version of this figure is available onlyin the electronic edition.

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(MDJ), Baijiatuan (BJT), Hailar (HIA), and Shanghai (SSE).We also used Global Seismic Network data from stations inInchon, Republic of Korea (INCN), and Matsushiro, Japan(MAJO). The Korean Seismic Network station Taejon,Republic of Korea (TJN), is operated by Korean Institute ofGeoscience and Mineral Resources. We used SSE data only forthe 2013 DPRK event because INCN was not available. Weused the Geoscope station INU in Inuyama, Japan, for the2013 DPRK event. TJN was not available for the 2006 DPRKevent and was not used for the 2017 DPRK aftershock becauseof high noise. MAJO and HIA were not used for the 2006DPRK event also because of high noise. The 2006 DPRKevent also included four stations (MJD, LJPZ, XDIAN,and WTANG) from the XG network a 2002–2008 Programfor Array Seismic Studies of the Continental Lithosphere(PASSCAL) temporary deployment (Stump, 2002).

We assembled data from vertical-component broadbandregional and teleseismic distance stations for the FM polaritymeasurements (Fig. 2). We used all available data from IRIS forany seismic networks, which we can measure a regional or tele-seismic P-wave including temporary PASSCAL deploymentslocated within arc distance less than 100°. We also includedmeasurements from the Full Range Seismograph Network ofJapan (F-NET), a 73-station seismic network across Japan. TheP-wave polarities were measured from uncorrected data thatwere demeaned and high-pass filtered to remove long-periodnoise.

METHOD: MOMENT TENSOR INVERSION

The nine force couples of a generalized symmetric MT candescribe a seismic point source as three force couples and threevector dipoles. This form is ideal for characterizing seismicsources including mine collapses, volcanic earthquakes, andexplosions (e.g., Ford et al., 2009b). The data are modeled asa linear combination of the MT elements with 10 Green’sfunctions based on the three fundamental faults and isotropicsource (e.g., Jost and Herrmann, 1989). We performed a linear

inversion to solve for the MT with a time-domain method using long-period regional dis-tance surface waves. The inversion techniqueincludes the formulation of Minson and Dreger(2008) allowing for the calculation of isotropiccomponents.

The Green’s functions were computed usingf �k reflectivity method (e.g., Herrmann, 2013)from the MDJ2 1D-layered Earth model (e.g.,Ford et al., 2009a), which is a modification of thesurface-wave dispersion derived MDJ model byNguyen (1994). The MDJ2 model was tested byFord et al. (2010) using the 16 December 2004earthquake near the Punggye-ri test site, resultingin a well-resolved full MTsolution and NSS witha high-fitting double-couple (DC) mechanismand a poorly fitting isotropic mechanism usinga similar station geometry in this study. We used

a source depth of 600 m for all the events based on estimatedDoB from the absolute locations except for 9 October 2006DPRK event, which is more uncertain. There we used a defaultsource depth of 1 km.

We obtained the best-fit full MT by inverting the three-component, complete waveform data using a time-domain gen-eralized least-squares inversion and goodness of fit between dataand synthetics as measured by the variance reduction (VRreg)

EQ-TARGET;temp:intralink-;df1;323;433VRreg ��1 −

Pi�d i − si�2P

id2i

�× 100; �1�

in which d is the data vector and s is the synthetic waveformvector for the ith station.

METHOD: REGIONAL AND TELESEISMIC FIRSTMOTIONS

We included regional and teleseismic P-wave polarities in theanalysis to better constrain the MTsolution (e.g., Chiang et al.,2014; Guilhem et al., 2014; Nayak and Dreger, 2015; Chianget al., 2016). The observed vertical-component P-wave polar-ities were labeled −1 for downward tensional motion and�1 for upward compressional motion and compared withsynthetic FMs for a given MT mechanism. The VR for theFMs (VRfm) is calculated as

EQ-TARGET;temp:intralink-;df2;323;213VRfm ��1 −

Pwi�Polobs − Polsynth�2P

wiPol2obs

�; �2�

and the combined regional waveform MT and FM VR iscomputed as

EQ-TARGET;temp:intralink-;df3;323;147VR � �sVRreg × sVRfm� × 100; �3�in which the sVRreg and sVRfm are the normalized regionalMT and FM polarity VRs. Each station can be assigned aweight wi and downweighted when the polarity is poorlyobserved because of emergent waveforms and when there

▴ Figure 2. (a) P-wave first-motion (FM) polarities and (b) broadband waveformswere used to estimate the moment tensors (MTs) and network sensitivity solutions(NSSs). The color version of this figure is available only in the electronic edition.

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was high prephase noise levels. The take-off angles for the sta-tion polarities were calculated using TauP (Crotwell et al.,1999) from the IASP91 Earth model.

METHOD: LUNE EIGENVALUES ON SPHERE ANDSOURCE TYPES

Tape and Tape (2012a,b) worked out the geometry and param-eterization of MT eigenvalues on a unit sphere. From an MT3 × 3 symmetric matrix, there are three eigenvalues (λ1, λ2, λ3)and three eigenvectors, representing the principal stress axes ofan associated focal mechanism. The eigenvalues define the patternand size of the focal mechanism, and the eigenvectors describe theorientation. When there is no specific order for the three eigen-values, an MT focal mechanism will appear in six different pointson the unit sphere because of the six possible permutations of thethree eigenvalues. We use an arbitrarily selected ordered set ofeigenvalues (λ1 ≥ λ2 ≥ λ3) to define a single fundamental lune,which is one-sixth of the sphere containing the point withone specific set of eigenvalues. Tape and Tape (2012a) define thefundamental lune longitude γ and latitude δ, which serves thesame purpose as the Hudson et al. (1989) T�k space, as

EQ-TARGET;temp:intralink-;df4;40;481

tan γ � −λ1 � 2λ2 � λ3���������������������3�λ1 − λ3�

pcos β � λ1 � λ2 � λ3��������������������������������

3�λ21 � λ22 � λ23�p

δ � π

2− β; �4�

in which β is the colatitude on the unit sphere. Orientation in-formation is lost on the fundamental lune because only eigenval-ues are considered in the parameterization. The three-coordinateaxes of the lune or unit sphere are rotated so that the location ofthe north and south poles of the sphere are��1; 1; 1� rather than�0; 0;�1�. The fundamental lune spans the unit sphere in lati-tude δ from the equator to the north pole ��π=2� and to thesouth pole �−π=2�. The lune also spans in longitude γ from anarbitrary origin point along the equator to�π=6. The latitude δis zero for deviatoric focal mechanism patterns and at the origin inwhich δ and γ are both zero contains all the pure DC focalmechanism patterns.

METHOD: NETWORK SENSITIVITY SOLUTIONS

The NSS method developed by Ford et al. (2010) is a grid searchof the full MTsolution space in which the maximum goodness-of-fit values (equations 1–3) between data and synthetics ismapped into source-type space. The source-type space is chosenas two parameters, either T�k or δ�γ (e.g., Hudson et al., 1989;Tape and Tape, 2012a). The NSS characterizes a full MT inver-sion confidence region and solution uniqueness in source-typespace taking into account a unique station distribution, fre-quency band, and signal-to-noise ratio for a single real or hypo-thetical event.

Ford et al. (2010) used the NSS to demonstrate the regionalsurface-wave trade-offs between positive isotropic andnegative vertical compensated linear vector dipole (CLVD)sources for near-surface explosions. This is due to the similarradiation patterns for horizontally traveling surface waves forthese two source radiation patterns. The NSS was then modified(e.g., Ford et al., 2012; Chiang et al., 2014) to include teleseismicP-wave polarities that reduced these trade-offs by decreasing thesize of the confidence region. This is due to improved samplingof the radiation pattern from near-vertical ray paths where theisotropic and vertical CLVD radiation patterns differ most.

The NSS compares thousands to millions synthetic data ina forward calculation with a distribution of all possible sourcetypes beyond the well-known points of optimally fitting pureDC, pure isotropic, deviatoric, and full MTs. The grid-searchmethod for the NSS is limited by the need for the random searchthrough a discrete space of source types including DC compo-nents leading to increased computational time and sampling ac-curacy issues. Nayak and Dreger (2015) developed an iterativedamped least-squares inversion scheme to invert waveforms andP-wave FMs for best-fitting MTsolutions for any specific sourcetype. They reformulate the forward calculation of syntheticsfrom MT parameterization to one based on three eigenvalues,a scalar seismic moment factor, and five variables for the eigen-vectors. The FM polarity Green functions are calculated fromthe formula for the far-field P-wave radiation (Aki and Richards,2002) as a function of the MT eigenvalues, source-to-receiverazimuth, and take-off angle. Nayak and Dreger (2015) droppedthe scalar moment scale factor and modified the FM function tobe continuous and differentiable so that it could be included inthe iterative damped least-squares inversion. This method sig-nificantly reduced the computation time and recovers the truemaximum goodness-of-fit surface in the source-type space. Wefavor the fundamental lune (δ, γ) source-type space from Tapeand Tape (2012a) over the T�k source-type space of Hudsonet al. (1989) in the parameterization of the NSS because of thesimple and natural representation of the MT eigenvalues on asphere rather than on a cube.

RESULTS

The best-fitting MT solutions are listed in Table 1, includingthe source-type parameters for the fundamental lune based ononly the regional MT inversion results. The waveform fits forthe 3 September 2017 explosion and aftershock are shown inFigures 3 and 4 between data and synthetics. The waveform fitsfor the prior DPRK events are shown in Ⓔ Figures S1–S5(available in the electronic supplement to this article). In theanalysis of the 2006 and 2013 DPRK events and 2017 after-shock, there were a few stations that we did not use in the MTinversion because of higher noise levels. We provided syntheticpredictions for comparison with the unused noisy data in casesin which data were still available. The plots also show the fullMT as a focal mechanism with the fault planes from thedeviatoric component. All the explosion MTs have isotropiccomponents greater than 50% (Table 1), so all FM polarities

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are expected to be compressional and (δ, γ) points above thearc line above the equator in Figure 5a. The FM polarities areshown on the focal mechanism in Figure 3 andⒺ Figures S1–S5. There were a few measured dilatational FMs, but they weredownweighted because of emergent and noisy P waves. Thefundamental lune parameters for the best-fitting full MT sol-utions are shown on the eigenvalue unit sphere in Figure 5,which best illustrates in three-dimensions the relation of thethree eigenvalue axes with the fundamental lune as one-sixthof the unit sphere. There is also still good separation betweenthe explosion population and earthquakes as well as good sep-aration between the collapse and earthquake population.

The NSS shows the maximum VR as a function of thesource-type parameters on the fundamental lune using theHammer projection. The NSS for the 3 September 2017 DPRKexplosion and aftershock are shown in Figures 6–7 and priorDPRK events inⒺ Figures S6–S10. NSS is shown as a contourmap on which each contour represents the population of best-fitting MTsolution that has percent VR (%VR) equal and abovecertain thresholds. In descending order, the contour maps of thesolution that have VR of 98%, 95%, 90%, 80%, 70%, 60%, and50% of the maximum VR in the NSS population. The P-wavepolarity counts by event are 9 October 2006, 18 polarities; 25May 2009, 107 polarities; 2 February 2013, 182 polarities; 6January 2016, 197 polarities; 9 September 2016, 355 polarities;and 3 September 2017, 664 polarities. The 2006 DPRK eventMT NSS has a very large confidence region defined by the 98%VR contour (98% of the maximum and above) spanning fromthe +crack component, to the +isotropic component, down tothe −LVD between the DC and negative CLVD points on thefundamental lune (Ⓔ Fig. S6). The NSS with MT + FM polar-ities decreased the 98% VR confidence region (γ between 38°and 45°; δ between −10° and �20°). The other DPRK eventsshow more common MT + FM 98% VR confidence regionsthat cover the +isotropic region γ > �50°. The NSS VR atthe DC and negative CLVD points on the fundamental luneare reduced from 70% to 90% of the maximum VR to about60% VRwith the addition of the FM data to the MT only NSS.The collapse NSS shown in Figure 7 does not have FM polar-ities; however, the MT only NSS shows about 90% of the VRregion spanning from closing crack to positive CLVD points onthe lune.

The analysis of stable coda-envelope amplitudes comparedwith regional long-period MT results provides an independentcheck on scalar seismic moment biases. Coda envelopes are notsensitive to 3D propagation path effects because of the scatteringnature of coda envelope, which averages path and source varia-tions (e.g., Mayeda and Malagnini, 2010; Gök et al., 2016). Wemeasured coda-envelope amplitudes for station MDJ fromnarrowband-filtered waveforms between 0.03 and 8 Hz. Thedetails of the method are described by Gök et al. (2016). Theabsolute scaling of these spectra was calculated from a 1D trans-fer function. To avoid circularity, transfer functions are typicallyderived from a smaller subset of regional earthquakes fromwhere moment magnitudes are estimated using independentwaveform modeling and MT analysis.

Table1

Best-FittingRe

gion

alLong

-PeriodRe

gion

alMom

entTe

nsor

(RMT)

Solutio

ns,S

eism

icMom

ent(M

0),M

omen

tMag

nitude

s(M

w),an

dCo

da-M

omen

tMag

nitude

s(M

wCo

da)

Even

t(yyyy/

mm/dd)

Mw

RMT

Mw

Coda

CTBT

Om

b

Depth

(km)

Mxx

×10

15

(N·m

)M

yy×10

15

(N·m

)M

zz×10

15

(N·m

)M

xy×10

15

(N·m

)M

xz×10

15

(N·m

)M

yz×10

15

(N·m

)M

0×10

15

(N·m

)% VR

%ISO/%

CLVD

/%DC

δγ

2006/10/09

3.78

3.69

4.1

1.0

0.341

0.457

0.461

−0.027

0.022

−0.121

0.585

62.6

72/27/01

74.4

−28.3

2009/05/25

4.11

4.14

4.5

0.6

1.67

1.57

1.16

−0.21

0.05

0.03

1.83

85.0

80/05/15

79.1

−6.7

2013/02/12

4.39

4.43

4.9

0.6

3.13

3.64

4.05

−0.82

0.32

0.49

4.86

73.6

74/18/08

75.9

19.6

2016/01/06

4.39

4.32

4.8

0.6

4.36

4.33

3.61

−0.44

0.26

−0.04

4.82

90.4

85/06/09

82.4

−10.2

2016/09/09

4.49

4.48

5.1

0.6

5.69

6.09

3.08

−0.71

0.20

−0.05

6.84

89.5

72/06/22

73.5

5.6

2017/09/03

5.21

5.20

6.1

0.6

66.3

65.3

70.3

−10.3

2.0

5.0

80.6

87.7

84/09/07

81.8

16.0

2017/09/03*

4.42

—4.1

0.6

−4.15

−4.21

−5.15

−0.01

0.47

0.10

5.35

68.5

84/11/05

−82.4

20.5

%VR

,perce

ntvaria

nceredu

ction;

%ISO/%CLVD

/%DC

,perce

ntisotropic,

compe

nsated

linea

rvector

dipo

le,a

nddo

uble

coup

le;δ

andγ,fund

amen

tallun

elatitud

ean

dlong

itude

;CTB

TO,C

ompreh

ensive

Nuc

lear-Test-B

anTrea

tyOrga

nization.

*Collapseeven

t.

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The MDJ coda-envelope amplitude spectra are shown inFigure 8a. The spectra have low-frequency ramps below thecorner frequencies predicted by the static term of the Saikia(2017) explosion time-domain source function. The spectralamplitudes above the corner frequency fall off approximatelyas 1 over frequency squared (f −2). Figure 8b shows the com-parison between regional MTmoment magnitudes (Mw) andcoda magnitude Mw listed in Table 1. The average differencebetween the MTmagnitudes and coda magnitudes is 0.02 with

a standard deviation of 0.05 over the six DPRK events. Com-monly, these types of comparisons are expected to within�0:1magnitude units from moment magnitude catalogs.

DISCUSSIONS: MT RESULTS

The DPRK collapse event was observed byTian et al. (2018) tohave reversed long-period surface waves (0.02–0.05 Hz) and in-phase 1–2 Hz P waves relative to the 3 September 2017 DPRK

▴ Figure 3. MT solution for DPRK-6 (3 September 2017) event. Black waveforms are data, and red waveforms were used in the inversion.The focal mechanism shown is from the deviatoric component of the full MT. Compressional FMs are black circles and dilatational FMsare white circles. The color version of this figure is available only in the electronic edition.

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explosion event. They fit these P waves and surface waves using anear-vertical single downward force located offset from the explo-sion by 440 m to the northwest. We compute synthetics using avertical point force (VF), an idealized tensional closing crackmechanism, and our MT solution and compare the 1–2 HzP-wave and surface-wave synthetics tomake quantitative compar-isons (Figs. 9 and 10). Including both theMTandVFsources in apoint-source linear inversion will lead to a singular inverse prob-lem according to Day and McLaughlin (1991) because the twosources are equivalent (e.g., Stump, 1990; Dahlen, 1993).

Day et al. (1983) derives an idealized seismic source forcollapse consisting of three terms in their equation (10), whichcorrectly conserves momentum. The first term is a vertical sep-aration and downward force of an Earth layer, which goes intofree fall. The second term is a relaxation of the continuumpreviously exerted by the collapse mass. The third term isanother downward force applied to the continuum by the col-lapse mass upon closure. Kawakatsu (1989) describes an effec-tive force as the difference between the force initially extendedto the Earth by the sliding object and the force exerted during

▴ Figure 4. MT solution for DPRK-6 collapse (3 September 2017) aftershock. Black waveforms are data, red waveforms were used in theinversion, and blue waveforms are predicted from the best full-MT solution. The color version of this figure is available only in theelectronic edition.

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the sliding motion. The positive part of the effective force cor-responds to the acceleration stage and negative part the decel-eration stage, hence referred to as the two-sided force. A surveyof previous studies by Kanamori and Given (1982), Kanamoriet al. (1984), Hasegawa and Kanamori (1987), Kawakatsu(1989), Chouet et al. (2003), and Ekström et al. (2003) using

single force sources in their analyses all use an effective forcethat is two sided and have net zero sum. Takei and Kumazawa(1994) suggest that the net zero sum of the forces acting withinthe source volume is not an explicit requirement from the con-servation of momentum but rather a consequence from theformulation of the equivalent forces; however, their argument

of using a single force may be more appropriatefor deep Earth mass advection sources includingnonlinear higher order moments and not forlinear point-source models.

We construct synthetics using frequency–wavenumber method (Herrmann, 2013) withthe MDJ2 velocity model for distances between370 and 1100 km. The closing crack syntheticwas constructed using an idealized MT model(Mxx � Myy � −1 and Mzz � −3) scaled tothe total seismic moment determined fromthe collapse MT (Table 1). We used a forceof −6:0 × 1011 N for theVF synthetic. The firsttime derivative of the VF converts the step re-sponse to impulse. The second time derivativeof the VF synthetic generates a two-sided force.This second time derivative of the VF is iden-tical to the closing crack synthetic (Figs. 9 and10). This result simply confirms Day andMcLaughlin’s (1991) derivation and Taylor’s(1994) analysis that the tensional closing crackmodel was equivalent to a vertically orientedpoint force with the force time history propor-tional to the crack separation acceleration his-tory. We also compute synthetics from the MTinversion result for the 3 September 2017

▴ Figure 5. (a) The upper-hemisphere of the eigenvalue unit sphere and (b) the lower hemisphere. The fundamental lune parameters (δ,γ) for the DPRK explosions and collapse are compared with Ford et al. (2009b) Nevada National Security Site (NNSS) explosions, westernU.S. (WUS) earthquakes, and mining collapses. The blue arc is the crack plus double-couple MTs (assuming Poisson ratio 0.25), and focalmechanisms above the red arc are completely shaded focal mechanism plots. The color version of this figure is available only in theelectronic edition.

▴ Figure 6. (a) MT NSS and (b) MT + FM NSS for the 3 September 2017 DPRKevent. The cross denotes the point with the maximum variance reduction (VR).The color version of this figure is available only in the electronic edition.

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DPRK collapse and explosion event (Table 1and Ⓔ Table S1). The second derivative VFmodel and closing crack MT model syntheticsagree with synthetics computed using our MTsolution for both vertical-component surfacewaves (0.01–0.1 Hz) and 1–2 Hz P waves. Wecompared synthetics for a distance of 380 km(e.g., MDJ) to distances of 1100 km (e.g., BJTand HIA) with the same results. It is interestingto note that the P waves from the VF withouttime differentiation fit with explosion MTsynthetics, but the surface waves do not fit theclosing crack or collapse MT synthetics. Thefirst derivative of the VF does not fit either theexplosion P waves or collapse surface waves.Our DPRK collapse MT is not a pure implo-sion mechanism and is consistent with a two-sided VF mechanism proposed by Tian et al.(2018). There may be other complex mecha-

▴ Figure 7. MT NSS for the DPRK aftershock at 3 September2017 00:38 UTC. The color version of this figure is available onlyin the electronic edition.

▴ Figure 8. (a) Station MDJ coda-envelope amplitude spectra measured for thesix DPRK events. (b) Coda moment magnitude (coda Mw) versus regional momenttensor moment magnitude (RMT Mw).

▴ Figure 9. Synthetic P waves computed at a distance of 474 kmusing vertical point force (VF), tensional closing crack MT mecha-nism (Mxx � Myy � 1,Mzz � 3), collapse MT (Table 1), and explo-sion MT (Ⓔ Table S1, available in the electronic supplement to thisarticle). The vertical-component displacements were bandpassfiltered between 1 and 2 Hz. The closing crack and second derivativeof the VF are equivalent sources (see the Discussions: MT Resultssection) and consistent with the DPRK collapse MT. The colorversion of this figure is available only in the electronic edition.

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nisms that can cause reversed P waves. One possibility is offsetsources similar to offset of the collapse and explosion proposed byTian et al. (2018) and other scenarios involving simultaneousdouble events. The differences between high- and low-frequencyradiation are an interesting observation byTian et al. (2018) andidentify a limitation of the point-source long-period MT inver-sion methodology. Unfortunately, high-resolution 3D Earth mod-els needed to compute higher frequency Green’s functions are notrealistic enough to invert for both low- and high-frequency pointforce and MTmechanism sources. Investigating this further is be-yond the scope of this short note but is worthy of further study.

A comparison between our DPRK explosion MT solu-tions and those of Ford et al. (2009a), Cesca et al. (2017),and Ichinose et al. (2017) show good agreement. Their MTsolutions plot within the MT-only NSS region bounded byhighest VR contours and the trade-offs between isotropicand negative CLVD (Ⓔ Figs. S6–S10) for each respectiveevent. The 6 January 2016 and 9 September 2016 DPRKMT-only NSS uncertainty regions also agrees with the Cesca

et al. (2017) uncertainty region for the 2016 events. OurMT +FM NSS results also agree with the Cesca et al.’s (2017) resultsin that FM helps reduce the MT uncertainty and is able toreject some of the uncertainty region in the source-type space.A comparison with ourMTsolutions for the 3 September 2017DPRK explosion and collapse are consistent with results by Liuet al. (2018) in the sense that the explosion was an openingtensile crack, and the collapse was a closing crack. Our MTresults were used by Wang et al. (2018) and produce goodagreement with geodetic Synthetic Aperture Radar measure-ments of the explosion and collapse mechanisms.

The independently derived coda magnitude estimates forthe six DPRK events are less than �0:1 magnitude units of theestimated MTmoments (Fig. 8b). The close agreement betweenthe independently derived coda magnitudes and MT validatesthe scalar seismic moment estimates for the DPRK events,indicating that they are not biased because of the Earth modeluncertainty. There is a condition that can lead to an overesti-mate of seismic moment in MT inversions of shallow sources,in which the Mxz, Myz, and Mzz components of the MT arepoorly resolved. As the source depth approaches the free surface,the Green’s functions for these components go to zero (e.g.,Chiang et al., 2016). The close agreement between the inde-pendently derived coda magnitudes and MT indicates that thiscondition is not an issue with the DPRK MT solutions.

DISCUSSION: CAVITY VOLUME

Collapse events in mining areas could be modeled as a fallingblock model (Taylor, 1994) or as a tabular excavation collapsethat is mathematically equivalent to a closing tensile crack(Walter et al., 1997, 2018). They also note that the 5 August1982 Atrisco underground nuclear explosion (mb 5.7) at theNNSS was followed 21 min later by a cavity collapse thatwas large enough to generate regional surface waves (Springeret al., 2002). Waveform modeling byWalter et al. (1997) of thesurface waves resulted in MTmodel that fits well with closinghorizontal crack model (Mzz > Mxx � Myy) more than a pureimplosion (Mxx � Myy � Mzz), which was confirmed byFord et al. (2009b) in an MT inversion for the Atrisco collapse.

Müller (2001) noted a change in volume caused by a ten-sile crack based on an isotropic seismic moment is significantlylarger than a volume change from the same moment using aspherical model, and this discrepancy should bound the pos-sible range of volume change for seismic sources that have non-DC components. Richards and Kim (2005) reviewed thederivations of both models. Although both models were foundto be correct, Richards and Kim (2005) preferred the sphericalmodel for underground explosions because it related thekinematic volume change caused by an isotropic source to thefar-field P wave. Until now, neither model has yet to be provenor disproven.

We compare the estimates of the cavity created by theexplosion with the collapse volume estimated from the MT.Because the 3 September 2017 03:38 DPRK collapse MTexhibits an implosion plus tensile closing crack components

▴ Figure 10. Synthetic surface waves computed at a distanceof 474 km using VF, tensional closing crack MT mechanism(Mxx � Myy � 1,Mzz � 3), collapse MT (Table 1), and explosionMT (Ⓔ Table S1). The vertical-component displacements werebandpass filtered between 0.01 and 0.1 Hz. The closing crackand second derivative of the VF are equivalent sources (see theDiscussions: MT Results section) and consistent with the DPRKcollapse MT. The color version of this figure is available only inthe electronic edition.

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in source-type space (Figs. 4 and 7) we decided to use theMüller (2001) tensile crack model. Following Müller (2001),we compute the volume change (∂V ) for a tensile crack as theseismic moment (M0) divided by the bulk modulus

EQ-TARGET;temp:intralink-;df5;52;436∂V crack �M0

λ� 2μ3

; �5�

in which λ is the elastic Lame constant and μ is the shear modu-lus. We used quartz diorite rock properties (Simmons, 1964)under a pressure of around 10–500 bars (VP � 5100 m=s,VS � 3600 m=s, and density � 2900 kg=m3) to calculate theelastic constants. The collapse volume and approximate radiusare listed in Table 2 with an assumed factor 2 uncertainty in theestimation of seismic moment resulting in a range of volumesbetween 1:06 × 105 and 4:23 × 105 m3, or as large as one thirdof the size of the Houston Astrodome (∼1:2 × 106 m3). Forcomparison, a 2:0 × 105 m3 size cavity is approximately createdfrom a 100-kT explosion in granite based on Denny and John-son (1991). Using the Müller (2001) spherical model, P-wavemodulus rather than the bulk modulus in equation (5) resultedin volumes that were a factor of 3 smaller.

We used Denny and Johnson’s (1991) cavity radius–yieldrelationship to estimate the cavity volume of the explosion inquartz diorite granitic type rock. The same rock properties usedin the previous collapse volume change calculation are used tocalculate the explosion cavity volume. The range of explosion cav-ity volumes is based on explosion yield for two body-wave mag-nitude and yield (mb–W ) relationships. Ringdal et al. (1992)published an mb–W relationship for Semipalatinsk test site inKazakhstan for hard rock and low attenuation path similar tothe geology at Mount Mantap (mb � 4:5� 0:75 × log10 W ).We also use the Murphy (1981)mb–W relationship for southernNevada (mb � 3:91� 0:8 × log10W ) known as a high attenu-ation path. Themb–W relations above include both site-emplace-

ment and path attenuation effects, and because the true pathattenuation is uncertain, we then use both relations to capturethe variability in W . We assume a DoB of 600 m and set thegas porosity to 0 in the cavity radius calculation. The explosioncavity volume ranges between 2:84 × 105 and 1:14 × 106 m3.These volumes listed in Table 3 overlap those estimated for thecollapse using the seismic moment (Table 2).

From the history of containment practices for U.S.nuclear tests (U.S. Congress, Office of Technology Assessment[USC-OTA], 1989), the following is a summary of whattypically happens after a large underground nuclear explosion.A cavity is created by the shock wave and vaporization of rock.The resulting cavity is filled with high-pressure steam and gasover a puddle of molten rock. As the shock wave continues, itcrushes and fractures the surrounding rock outside of the cavity.The explosion is contained when the material rebounds and cre-ates a large compressive hoop stress field, closing any fracturessurrounding the cavity. Minutes to days after the nuclear explo-sion, the gas temperature and pressure in the cavity decrease tothe point at which they cannot support the overlying rock. Thecollapse occurs as rock breaks into the overlying rubble and fallsinto the cavity void. The process continues until the cavity voidis full or when the collapse of the overlying rubble (called thechimney) reaches the surface, and a crater is formed.

The range of volume reduction of the collapse is withinthe range of volumes estimated for a cavity created for nuclearexplosions in quartz diorite. Using granite rock properties gaveslightly less overlap in the volume range. This suggests that it isplausible for the collapse event to be caused by the complete orpartial collapse of the explosion cavity as described earlier.

A tunnel collapse scenario seems unlikely because of thelarge size of the volume reduction from to the seismic momentestimate. A volume reduction from the seismic moment of thissize would result in a collapse of approximately 3–13 km length

Table 2Volume Reduction Estimates from Seismic Moment M 0 � 5:35 × 1015 N · m (Mw 4.42) Including a Factor of 2 Uncertainty in

Moment

Seismic Moment M 0 (N · m) Collapse Volume (m3) Crack Radius (m)12 ×M0 2:68 × 1015 1:06 × 105 29M0 5:35 × 1015 2:11 × 105 37

2 ×M0 1:07 × 1016 4:23 × 105 47

We used the Müller (2001) formula for tensile crack to compute the volume and radius (see equation 5).

Table 3Volume Estimates for an Explosion Cavity from Yield–Cavity Radius Scaling Relation of Denny and Johnson (1991)

mb–W Relations Yield–W (kt) DoB (m) Gas Porosity (%) Volume (m3) Cavity Radius (m)Low attenuation 136 600 0 2:84 × 105 41High attenuation 546 600 0 1:14 × 106 65

We used the same rock properties as those for the collapse volume change estimates. DoB, depth of burial.

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tunnel with 30 m cross-sectional area. Such a scenario would bemore similar to a trap-door tunnel collapse likely creating asecondary source with stronger shear waves and source mecha-nism asymmetries that should have been detectable usingregional MT analysis (e.g., Dreger et al., 2008).

CONCLUSIONS

We performed an MT inversion and source-type analysis of theDPRK announced nuclear explosions using complete long-period regional surface waves and regional and teleseismicP-wave polarities. The 3 September 2017 DPRK explosion wasMw 5.2 and had a strong positive isotropic component. Thiswas followed 8.5 min later by anMw 4.42 aftershock with col-lapse MT. It is plausible that the aftershock was generated by acollapse of the explosion cavity based on the volume changeestimated from the seismic moment. Overall interpretationwith this study and Tian et al. (2018) agree that the aftershockwas a collapse and the surface waves fit a two-sided verticaldownward point force. Their observations of P waves withpolarities reversed from the collapse mechanism are interestingand deserve further study. The differences between low- andhigh-frequency radiation points out a limitation in thelong-period regional MTmethod. Such mechanisms that canproduce such observations, for example, double events or offsetsources such as those proposed byTian et al. (2018), cannot bemodeled using simple point-source MT mechanisms and re-quire further study.

We also estimated the MT solutions of the previous fiveDPRK events. All of the DPRK events plot along with otherNNSS explosions and western U.S. collapse events from Fordet al. (2009b). The NSS for each event exhibited a trade-offbetween positive isotropic and negative CLVD as expected be-cause of the inability to resolve the isotropic and verticalCLVD radiation patterns from surface waves. The additionof the FM polarities from body waves resulted in a reductionof the 10% highest best-fit solutions in source-type space to anarea of the fundamental lune above +LVD and along the�50°latitude grid line generally considered for highly explosivesource mechanism where the FM of the focal sphere is expectedto be all compressional motions. That is what we observe withthe FM polarities with the exception of a few cases with emer-gent and noisy arrivals. Estimated coda magnitudes for the sixDPRK events from broadband coda measurements of S wavesprovided independent validation of the scalar seismic momentestimates with no indication of model bias or seismic momenterror due to poor resolution of some MT elements sensitive tothe free-surface traction condition.

DATA AND RESOURCES

Seismograms and metadata used in this study are archived atIncorporated Research Institutions for Seismology (IRIS; www.iris.edu, last accessed March 2018). The Full Range Seismo-graph Network of Japan (F-NET) is operated by the NationalResearch Institute for Earth Science and Disaster Resilience

(NIED) and data were provided with registered access throughhttp://www.fnet.bosai.go.jp (last accessed April 2018). GenericMapping Tools v.5.2.1 was used to create the plots (http://gmt.soest.hawaii.edu, last accessed April 2018).

ACKNOWLEDGMENTS

Lawrence Livermore National Laboratory (LLNL) is operatedby Lawrence Livermore National Security, LLC, for the U.S.Department of Energy, National Nuclear Security Administra-tion under Contract DE-AC52-07NA27344. Doug Dregerwas supported by the Air Force Research Laboratory ContractFA9453-16-C-0024. This is LLNL contribution LLNL-JRNL-750307. The authors acknowledge Guest Editor LianxingWenfor his thoughtful review. The facilities of IRIS Data Services,specifically the IRIS Data Management Center, were used foraccess to waveforms, related metadata, and derived productsused in this study. IRIS Data Services are funded through theSeismological Facilities for the Advancement of Geoscienceand EarthScope (SAGE) Proposal of the National ScienceFoundation under Cooperative Agreement EAR-1261681.

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Andrea ChiangGene A. Ichinose

Sean R. FordEric M. MatzelSteve C. MyersW. R. Walter

Lawrence Livermore National Laboratory7000 East Avenue, MC-043, MC-046Livermore, California 94550 U.S.A.

chiang4@llnl.govford17@llnl.gov

ichinose1@llnl.govmatzel1@llnl.govmyers30@llnl.govwalter5@llnl.gov

Doug S. DregerBerkeley Seismological Laboratory

307 McCone HallBerkeley, California 94720 U.S.A.

ddreger@berkeley.edu

Published Online 19 September 2018

14 Seismological Research Letters Volume XX, Number XX – 2018

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