Depth Calculation for the January 06, 2016, the September 09, 2016 and the September 03, 2017 Nuclear Tests of North Korea from Detailed Depth Phases Using Regional and Teleseismic Arrays SO GU KIM, 1 YEFIM GITTERMAN, 2,3 and SEOUNG-KYU LEE 1,4 Abstract—North Korea has conducted six underground nuclear explosions so far. In this study, we determined source depth and characterization for the 2016J, 2016S and 2017S tests which were conducted on January 6, 2016 (2016J), September 9, 2016 (2016S) and September 3, 2017 (2017S), respectively. It has been difficult to ascertain the accurate depth of North Korean nuclear explosions due to paucity of data and information. We explore the depth calculation for the North Korean nuclear tests based on the detailed depth phases using teleseismic and regional arrays. We present the coherent spectral nulls from the average spectra of pP ? P/sP ? P and pPn ? Pn/sPn ? Pn which correlate with the depth phases showing 180° phase reversals with the P-wave arrivals. We estimated the burial depths at 2.12, 2.10, 1.98 km for the 2016J, 2016S and 2017S nuclear tests, respectively, We anticipate our absolute findings to be significant since in the past depth estimates for North Korean nuclear tests have been inconclusive and unclear owing to not only paucity of data but also trade-offs of the relative assessment based on the satellite images between the true source location and the tunnel entrance for the 2006 nuclear test used as a reference event. Key words: CTBTO, spectral null, take-off angle, Fermat principle, Mantapsan (Mt. Mantap). 1. Introduction North Korea conducted its fourth nuclear test (m b 5.1) on January 6, 2016, fifth (m b 5.3) on September 9, 2016 and sixth (m b 6.3) on September 3, 2017 near Mt. Mantap in the Punggye-ri region of northeastern North Korea. Many researchers have studied source mechanisms (e.g., Bonner et al. 2008; Patton and Taylor 2008; Ford et al. 2009; Vavrycuk and Kim 2014; Dreger 2017) and source depth estimations (Zhang and Wen 2013; Murphy et al. 2013; Gitter- man et al. 2015; Kim et al. 2015; Zhao et al. 2017) with uncertainty due to the paucity of data and rela- tive assessment of trade-offs between the surface- looking interpretation from satellite images and true depth base on the reference event of the 2006 test. In this paper, we stress the point that the accurate depths for last three North Korean nuclear tests (2016J, 2016S and 2017S) were determined comparing them with previous North Korean nuclear tests utilizing the teleseismic arrays and regional arrays. We estimated the source depth using depth phases pP and sP as well as pPn and sPn taking into account take-off angles for further corroboration and improvement. The detona- tion source depths are pertinent vis-a `-vis enforcement of CTBTO as nuclear explosions are unlikely to be fired at depths of more than a few kilometers (Dou- glas et al. 1972; Bakun and Johnson 1973; Bowers et al. 2001; Heyburn et al. 2013). However, absolute depth determinations are presently based on the delay times of pP-P which often present the problem of free surface reflection, pP from the direct signal P waves in shallow nuclear explosions. The usual way to estimate the depth of an event using teleseismic waves is to measure the time difference between the arrival time of the direct P wave and the onset of the surface reflection phase of pP (180° phase reversal). The pP phases are signals that travel upward from the focus as P waves from the explosions (Cohen 1970; Kulhanek 1971) and then travel steeply downwards following a path to the same receiving stations as the 1 Korea Seismological Institute, Goyang, Gyeonggi-do 10332, Republic of Korea. E-mail: sogukim@hanmail.net 2 Seismology Division, Geophysical Institute of Israel, P.O.B. 182, 71100 Lod, Israel. 3 Present Address: Department of Structural Engineering, Protective Technologies R&D Center, Ben-Gurion University of the Negev, Beer-sheba, Israel. 4 Department of Physics, Hanyang University, Seoul, Republic of Korea. Pure Appl. Geophys. Ó 2018 Springer Nature Switzerland AG https://doi.org/10.1007/s00024-018-1958-y Pure and Applied Geophysics