Forensic seismologiy for an underwater explosion vis- à-vis the ROKS Cheonan Sinking

Forensic seismologiy for an underwater explosion vis- à-vis the ROKS Cheonan Sinking | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Forensic seismologiy for an underwater explosion vis- à-vis the ROKS Cheonan Sinking So Gu Kim This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2053199/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract For a very shallow underwater explosion, spectral analysis is preferable to cepstral analysis to find characteristics of a bubble pulse and reverberation effects. Time-domain analyses show bubble pulses and bubble jets as well as positive polarities of the first P-wave arrivals on the vertical component, and spectral analyses also clearly reveal the bubble pulse and reverberation effects. The ROKS Cheonan sinking was a shallow underwater explosion that occurred near the surface showing a bubble jet characteristic resulting in splitting the ship into two pieces including a bubble pulse. The findings of a bubble jet and a toroidal bubble deformation including a bubble pulse are highlighted in this study. The ROKS Cheonan sinking took place off the Baengnyeong Island in the Yellow Sea of the Korean Peninsula at a depth of about 8 m in the sea depth of 44 m on March 26, 2010. The explosive charge weight was estimated at 136 kg TNT using the seismological analyses and boundary element method. The 136 kg TNT is equivalent to one of the abandoned land control mines (LCM) that were deployed near the Northern Limited Lines (NLL) in the Yellow Sea by the South Korean Navy in the late 1970s. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Introduction The underwater explosion (UWE) incident vis-à-vis the ROKS Cheonan took place off the coast of Baengnyeong Island in the Yellow Sea of the Korean peninsula on March 26, 2010 (see Fig. 1). Considerable efforts have been devoted estimating the net explosive weight of this UWE using spectral analysis 1-3 and analytical approaches including the boundary element method (BEM) 4 . It is also attempted to estimate and interpret the source depth and a net explosive weight using underwater acoustics (hydroacoustics) as well as infrasound records. This study presents new findings of a bubble pulse, a bubble jet, and a toroidal bubble deformation from the high-resolution spectra as well as in the detailed time domain for an underwater explosion. The source depth and explosive charge weight estimated are verified using a ray-trace model in the shallow channel. It was possible to determine the direction of a back azimuth (BAZ) of the incident site by measuring the positive polarity on the vertical component and the first arrival amplitudes on the horizontal components (HHE and HHN) in the time domain of the seismograms shown in Fig. 2. The above seismograms and accelerograms are the most important evidence that the ROKS Cheonan sinking was due to an underwater explosion, i.e. the seismological record could be the “smoking gun” in investigating the cause of the ROKS Cheonan Sinking. P, S, BP, BJ, PP, LR, SW, LQ and T-phase indicate the first of P- and S-wave arrivals, gas bubble pulse, bubble jet, peak pressure, Rayleigh waves, probably Stoneley waves at sea bottom - seabed interface which follows Rayleigh waves on the vertical (HHZ) and E-W (HHE) components. T waves (T-phase of the tertiary wave) following Love waves (LQ) are observed on the N-S (HHN) component (tangential), which propagate in the channel waves with the group velocity of the sound velocity (1500 m/sec) with periods less than 1 sec in the ocean. . Stoneley waves 5. travel along a solid-fluid interface as a tube wave on the vertical component, originally along the walls of a fluid-filled borehole with a low-frequency and lower velocity than T-phase 6 . Love waves may be due to the shearing force of the bubble jet at 5 m portside splitting the ship into two parts in the north-south direction so that the tangential motion can be recorded on the N-S component (HHN). It should be noted that a back azimuth of the site location can be calculated by measuring the first arrival amplitudes (μm/sec) of the vertical component and two horizontal components of N-S (HHN) and E-W (HHE) components (Fig. 2). Taking into account the vector resultant of the first arrival amplitudes of N-S and E-W components it is possible to estimate the angle between two vector components by measuring atan[AE(HHE)/AN(HHN)] in the inlet figure of Fig. 2. The compressional motions of the first P-wave arrivals on the vertical component indicate that the source is in the opposite pushing towards the station. As a result, the back azimuth (BAZ) and location of the incident site can be determined using only the 3-component single station 1-3,7 . . The finding of BAZ at 224° from the station is in good agreement with the incident site. The higher amplitude of the first P-wave arrival on the vertical component than that on the horizontal components shows that the upward compressional motion by an explosion occurred in the water. A shallow underwater explosion beneath a ship results in very complicated phenomena-associated with buoyancy and Bjerknes forces 2,3,8-10 , including the Archimedes principle, conservation of angular momentum, and the counter-clockwise vortex due to Coriolis force in physics 3 . The larger amplitudes of Love waves may be also due to the splitting of the ship into two pieces. The maximum acceleration and velocity of 0.084 gals and 8.4 µm/sec are recorded on the Z-components about 13 km away from the epicenter. Furthermore, it is also verified that the event may be an underwater explosion by observing the rarefaction motion (downward) of a bubble pulse phase (BP) and a bubble jet (BJ) peak in the time domain (Figs. 2 and 6). Figs. 2 and 5 highlight the proofs of an underwater explosion for the ROKS Cheonan Sinking showing the characteristic motions of an underwater explosion in seismograms and spectra showing a bubble pulse on the vertical component, bubble jets on the horizontal components (N-S and E-W) and a toroidal bubble deformation on the N-S component. It is also noticeable to find a series of clear modulations of bubble pulse at 1.012 Hz and at 1.723 Hz in Fig. 5. Fig. 3 shows that the sound waves arrived at the seismic station about 31 seconds later indicating that the signals of sound waves from an underwater explosion reached the station much slower than P-wave arrivals. However, in the beginning, Korean mass communication media such as broadcast, SNS (social networking service), and websites mentioned the collision of the stern against the sea bottom 31 seconds later owing to the misinterpretation of the 31 second-signal. Nonetheless, the actual sinking times of the stern and bow for the ROKS Cheonan were found to be about 6 minutes and 16 hours, respectively 3,7 . A high-frequency monotonic acoustic wave with an apparent group velocity of 340 m/s is observed in the time domain (Fig. 4). The acoustic-wave amplitudes in horizontal components (N-S component) are stronger than those in the vertical component, which is consistent with the splitting direction of the ship as shown in the toroidal bubble deformation 11 of high-resolution spectra in Fig. 5. The travel time of the acoustic wave additionally constrains the event location. The observation of the highest amplitude with the compressional first motion (up, + ) on the vertical component (≥10^3 nm/sec) and high P/S amplitude ratios may also suggest an underwater explosion (Figs. 4 and 8). It seems that the 1.1 s is not interval due to supersonic N-wave effects, not to s bubble pulse. However, it is very possible to determine the definite bubble pulse of 1.012 Hz (0.988 s) in terms of the high-resolution spectra in Fig. 5. The infrasound records detect the infrasound signals (<20 Hz) and cannot detect the bubble pulse of an underwater explosion in this case.. The first peak is a burst of an underwater explosion and the second one is a sonic boom (N-wave) 2 - 3,7 in Fig. 4. N-waves are made by shock waves or sonic booms which are faster than sound waves. The fundamental concept of N-wave is described as a shock wave which is made up of two cones high-pressure cone with the apex at the bow of the supersonic aircraft and a low-pressure cone with - the apex at the tail resulting in the shape of the letter N 13 . The time interval of 1.1 s is a time difference between the first burst of an underwater explosion and a sonic boom of shock waves and it is not a bubble pulse period. Therefore, it may be not correct for MCMJIG 14 to apply this time interval from the infrasound signals for the Willis formula to estimate the detonation charge weight. Two marine sentries on the ground heard two impactful sounds: the first, a relatively weak sounding ‘Kung’, and around 1 second later, a thundering and wrecking sound ‘Kwang’. The first sound is the burst of an underwater explosion whereas the second one is a sonic boom (Fig. 4). Two marine sentries also saw a flash prior to "Kwang" at a maximum height of around 103 m, .3.1 5 from 2.5 km away at around 21:22 (origin time, 21:21:57) on March 26, 2010 1 4 . It is noticeable to have observed a sonic boom as well as a blast of an underwater explosion in the seismic and infrasound records (Figs. 3 and 4). It should be noted that an interval of 1.1 s in Fig. 4 is almost the same as the bubble pulse period (0.988 s), but it is not the bubble pulse period for an underwater explosion of the ROKS Cheonan Sinking. Results To verify the source of the ROKS Cheonsinking, the high- resolution spectral analysis using the 3-component seismograms recored at the seismic station (BAR) in the Baengyeong-do island of the Yellow Sea. Spectral analyses Love waves strongly appear on the N-S (tangential) component in the time domain because the ship headed for 327º with 6.7 knots when it was split into two parts in the direction of the NS and Love waves are detected on the tangential component. The first bubble pulse (BP) appears on the vertical component (HHZ) showing the rarefaction motion (downward collapse) whereas bubble jets (BJ) are present on the horizontal components (N-S and E-W) due to the vortex motion 11 in the time-domain and frequency-domain, but the initial toroidal bubble deformation (a large peak TB) and last toroidal bubble deformation (a small peak TB) on the N-S component (HHN) on the high-resolution spectra due to the splitting direction in the north-south direction. The maxima amplitudes on the spectra start with the first toroidal bubble deformation (TB) 8 - 9,11 and are followed by a bubble jet (Fig. 6) and a bubble collapse (pulse). In the spectral analyses (Fig. 6) the fundamental bubble pulse frequency f b and its spectral harmonic series are clearly explained in the right spectra with a long time window. The characteristic phenomena of an underwater explosion are revealed as a bubble pulse (BP) and reverberation effects (green downward arrows and a strong downward brown arrow) including reflection frequencies from the hull of the ship (upward red arrows) which appear on the vertical and radial (E-W) components due to the property of P-wave propagation. The left spectra with a1.9 s time window do not include every spectral characteristic like the right spectra with a 10.0 s time window due to the lack of higher multiple frequencies.. The first bubble pulse (black arrow, 1.012 Hz) is clearly revealed at the high resolution spectra in Fig. 5, reverberation frequencies (upward red arrows, 8.5 Hz, 25 Hz, and 42.5 Hz; f H ), reflected P-wave arrivals from the hull bottom (downward green arrows, ≈ 17-18 Hz and ≈ 34-35 Hz) which are multiple frequencies of a series of the first and the second harmonic series with spectral nulls, and a shallow guide wave (downward brown arrow, 47. 5 Hz; f d ) which is also revealed in the ray-tracing modeling in Fig. 10. The cutoff frequency associated with the detonation depth (47.5 Hz) can be also used to estimate the detonation depth (7.89 m). The finding of a very low frequency at around 2 Hz for the T-phase is noticeable on the N-S component in the time domain in Fig. 2. Using the surface cutoff frequency, the detonation depth is estimated at 7.89 m. It is very clear to find reverberation frequencies from the sea floor and reflected frequencies from the hull of the ship in the spectra of 15 s time window in Fig. 7. The spectral maxima at 8.5 Hz and ≈ 25 Hz are reverberation frequencies ( the first and third harmonic), whereas the maxima of the red arrows at ≈ 17-18 Hz (first harmonic) and at ≈ 34-35 Hz (second harmonic) indicate reflection spectral amplitudes which are formed by reflection from the hull bottom with small spectral nulls which are made by the superposition of destructive interference of direct P-wave arrivals and the reflected P-wave arrivals from the hull. The reflected amplitude maxima distinctly appear on the vertical and radial (E-W) components due to the characteristics of P-wave propagation. It is also evident that spectral nulls at 17.5 Hz and 34.5 Hz are due to the time difference between the onsets of P-wave arrivals and those of the downswing depth phases pP in the time domain, which in the frequency domain delay times for depth phase produce sharp holes as spectral nulls at 17.5 Hz and 34.5 Hz. The observed P-wave spectra are analyzed at frequencies of 8.5 Hz and its multiples (17.7, 34.6 Hz) including modulation of spectral amplitudes at frequencies around 26 Hz 16 . However, it may be confused that 8.5 Hz, 17.7 Hz, 26 Hz, and 34.6Hz may be considered a series of modulations of reverberation 16 . It is of significance to observe small spectral nulls (17.5 Hz and 34.5 Hz) on the vertical and E-W components. Those spectral nulls may be due to destructive interference by reflected P- wave amplitudes under the ship hull and the direct P- wave arrivals at the same station (Fig. 7). The findings of spectral nulls at around 17.5 Hz and 34.5 Hz may suggest that the detonation depth can be estimated using the spectral nulls 3,7 . Taking into account the previous depth estimates, the medium velocity inside the gas bubble may turn out to be around 280 m/sec which may be much less than the normal sound velocity in air, creating a gaseous void of lower pressure than the surrounding water by pushing all of the materials such as smoke (vapor), dirt, debris and explosive chemicals from the central point, but the void is instantaneously mixed with them in the cold seawater. It should be noticeable that 8.5 Hz, 17-18 Hz, 25 Hz, and 34-35 Hz are not natural frequencies from the collision between a ship and a submarine. However, Submarine collision asserters 17 used those frequencies as natural frequencies from the collision. As a result, they must have made some mistakes resulting in a collision of the ROKS Cheonan with a submarine. However, frequencies of a vibration source for a submarine cannot be detected at seismic stations because the vibration source is a low energy and little impact force for viscous dynamic force in impulse (little force over a long time by force x time interval in physics ). Sang-Gab Lee 18 hydrodynamically denied the collision story of the ROKS Cheonan Sinking with a submarine because of the low energy and resistance of the water. Damage Phenomena and hydrodynamic modeling by BEM The first figure shows how the bubble jet struck the hull of the ship when the ship was split into two parts. The red equilateral triangle-type damage at the portside may indicate that the ship must have been stricken by the strong and elaborate physical force with symmetry at a centroid. The force may be due to the bubble jet resulting in the counter-clockwise vortex immediately before the gas bubble pulse. The tangled fishing net wires (white arrows) on the propeller axis indicate the running aground before the explosion and the black charred hull surface (soot) may be due to the flame at the moment of the blast for an underwater explosion (black arrows). Also, it cannot be ruled out that the strong ICCP current might flow on the hull surface when it ran aground before the underwater explosion 3,7 . The equilateral triangle damage mark also reveals the material evidence that the damage and split of the ship were not due to arbitrary and asymmetrical forces such as a collision of a ship with a submarine or a running aground. The more severe damage on the stern part (b in Fig. 8b) may be due to the counter-clockwise vortex from the bubble jet resulting in sinking the stern part much earlier than the bow part. It took about 6 minutes for the stern to sink while it took about 16 hours for the bow to sink 3 . It is the start of the running aground that the last recorded time of the CCTV image was recorded at 21:17:03, indicating that electricity was lost by cutting off inside the ship 3 . Fishing nets were found entangled around the right screw axle of the damaged ship in Fig. 8b. This contradicts the MCMJIG 14 claim that there were no fishing zones in the area of the ship’s voyage. The running aground site was also reported at a depth of 6.4 m and about 4 m in case of a low ebb which caused a running aground of the ROKS Cheonan because of a draft of 2.87 m for the ship 3 . The tangled fishing net wires (white arrows) on the propeller axis indicate that there must have been running aground before the explosion. Before the sinking, the bottom of the Cheonan ship touched the shallow ocean floor. The fore side deformation of the starboard propeller (screw) and off-set shaft axis is due to a collision with the seabed, The aft view of the starboard propeller blades bent opposite of its rotation (clockwise) may be formed during the collision with the seabed 2 . The entangled fishing net wires are found around the right screw axle of the damaged ship. The black charred hull surface (smoke soot) in Fig. 8b may be due to the flame at the moment of a blast for an underwater explosion (black arrows). However, the strong ICCP (Impressed Current Cathodic Protection) current might flow on the hull surface and cannot be ruled out during running aground before the underwater explosion 3,4,,7 . Source possibility of 136 kg TNT (LCM) 1-4,14 versus 250 kg TNT (torpedo 2-4,14 ) using BEM (Boundary Element Method). 3D bubble shape simulation with source parameters such as detonation depth, yield, and position including a bubble pulse period. Through the bubble pulse period of 0.988 s obtained via spectral analysis, the approximate net explosive weight and explosion depth are estimated by narrowing down the possible parameters along with supplementary estimations of the bubble pulse periods of 0.967 s via Rayleigh–Willis equation, 0.976 s via BEM (Boundary Element Method) and 1.030 s via 3D bubble shape simulation derived for the case of a 136 kg TNT net explosive weight detonation. The more detailed studies about hydrodynamics are well presented in the previous work 2-,4,7 . From Fig. 9, The 3D modeling produces a maximum bubble, (BP Max), a toroidal bubble deformation (TB), a bubble jet (BJ), and a bubble pulse (BP) as follows: 0.5 s = BP Max, 0.791 s = TB, 1.007 s = BJ, 1.030 s = BP (0.988 s from Fig. 5) The bubble pulse of 1.030 s is slightly larger than 0.988 s on the vertical component of spectra. The bubble jet at 1.007 s is earlier than the bubble pulse, which is consistent with the horizontal components (N-S and E-W) of time and frequency domains (Figs. 2 and 5). Relative errors are estimated from the observed bubble pulse period vis-à-vis 3D simulation with detonation occurring at 3 m and 5 m portside (PS) of the hull from the centerline in the case of 136 kg TNT and 250 kg TNT as follows : 4.04 % 136 kg TNT at 8 m (depth), PS (portside) 5 m; 6.87 % 136 kg TNT at 8 m, PS 3 m, 18.38 % 250 kg TNT at 9 m, PS 5 m; 20.10 % 250 kg TNT at 9 m, PS 3 m After a bubble pulse starts contracting, a toroidal bubble formation 8,19 at TB (0.791 s), just before a bubble pulse (BP) at 1.030 s and a bubble jet (BJ) occurs at around t=1.007 s and the bubble gets a minimum at 1.030 s (BP ) 1-4,,7 . By the Bjerknes Effect 3,8 - 10 , the rigid boundary can attract the explosion bubble while the free surface repels it. Since the buoyancy force and Bjerknes attraction of the rigid hull are comparable, the bubble pulse from the experiment may be longer than that of the ROKS Cheonan Sinking underwater explosion (Figs. 6 and 9). If the oscillation gas bubble is close enough to a rigid body then the pressure differential created as the bubble decreases in volume will result in the bubble collapsing onto the hull and producing high speed (130-170 m/s range) 1,3 water jet (bubble jet) which may be capable of holing the hull of the ship (Fig. 8a). The bubble shape immediately before and immediately after jet impact has been investigated by various researchers 1 - 2,8 - ,11 . As a result. The analyses show that, by parametric study, a 136 kg charge yields a bubble pulse consistent with the observed seismic data. Discussion A source size of an explosion in water is not the same as inland due to a high Q factor with little attenuation, salinity, and pressure including the optimum depth in which an experiment is conducted using depth–charge relations. In this study, the ROKS Cheonan sinking was found to be an underwater explosion that occurred at a depth of around 8 m, approximately 5 m port side of the hull centerline with 136 kg TNT net explosive weight equivalent to 2.04 of a seismic magnitude. The misuse 17 of 8.5, 25, 18, and 35 Hz as harmonic frequencies from a previous researcher 16 who stated that P energy was dominant at around 8.5 Hz, with multiple frequencies of 17.7 and 34.6 Hz missing 25 Hz. 8.5 Hz and 25 Hz are odd frequency series for reverberation, while 17.7 Hz and 34.6 Hz could be the fundamental and its harmonics by the reflection of P waves from the broad hull just under the ship 3 . Consequently, it may be most unlikely that the ROKS Cheonan sank by a collision with a large submarine. It was proved that the collision with a submarine was incorrect in the light of detailed scientific aspcts of seismology, hydroacoustics, and hydrodynamic (fluid mechanics) 3 . The fabrication of the collected torpedo was also asserted by not only some academic people 20 , but also many other laymen. Conclusions This study concludes that the ROKS Cheonan sinking was due to an underwater explosion by 136 kg TNT yield at a depth around 8 m and 5 m portside from one of the abandoned land control mines (LCM) which were deployed near NLL (Northern Limited Lines) by the South Korean Navy in the late 1970s neither a collision with a submarine nor a running aground against a reef according to the scientific data 1 – 4 . Methods The cause of the ROKS Cheon sinking was already verified using spectral and hydrodynamic analyses in the front. It is inductively proved using the underwater wave propagation of a ray-tracing model with a detonation at a depth of 8 m (Fig. 10). It is possible to calculate the hydroacoustic wave propagation using the BELLHOP Gaussian beam ray-tracing program 21 from an underwater explosion in the early spring cold water of the Yellow Sea, assuming that a seismic source is detonated at a depth of about 8 m in the water depth of around 44 m 1--4 . Declarations Data availability The raw data (seismic and infrasound) that were used in this study can be downloaded from Korea Meteorological Administration (KMA) (see https://necis.kma.go.kr) and Korea Institute of Geoscience and Mineral Resources (KIGAM) (see https://www.kigam.re.kr/english/) Acknowledgments First of all, I am much obliged to Yefim Gitterman, my long collaborator for the spectral analyses of the ROKS Cheonan Sinking data. I also wish to thank Aman Zhang (Harbin Engineering University, China) for hydrodynamic analysis using the boundary element method and Orlando Camargo Rodriguez (University of Algarve, Portugal) for the ray tracing for a shallow underwater explosion. Khoo Boo Cheong (National University of Singapore) and Anne Trehu (Oregon State University, USA) provided valuable discussions and constructive criticisms about fluid mechanics and underwater explosion phenomena which would be appreciated. I acknowledge KMA (Korea Meteorological Administration) and KIGAM (Korea Institute of Geoscience and Mineral Resources) for providing waveform data for this study. Author contributions S.G.K. wrote the manuscript text and processed the data and produced the base of the figures with collaborators. No permission is required to reuse all figures in this paper because the copyright of the figures belongs to the author (So Gu Kim) in Multiple Studies of Underwater Explosions vis- à-vis the ROKS Cheonan Sinking. Publisher: Independently published (September 18, 2021) by self-publishing Amazon Kindle direct publishing https://kdp.amazon.com/en_US/. Competing interests The author declares no competing interests. Additional information Supplementary information Raw data (seismic) can be obtained from https://necis.kma.go.kr Modeling figures for “Boundary Element Method (BEM) for the ROKS Cheonan Sinking” are available for this paper in the attached file as “Supplementary information to the manuscript”. Correspondence and requests for materials should be addressed to S.G.K References Kim, S. G. & Gitterman, Y. (2013). Underwater Explosion (UWE) Analysis of the ROKS Cheonan Incident, Pure, and Appl. Geophys , 170 , 547-560 (2013). Kim, S. G. Estimating Depth and Explosive Charge Weight for an Extremely Shallow Underwater Explosion for the ROKS Cheonan Sinking in Forensic Explosion Seismology: Technologies and Applications (eds. Kim S. G. Gitterman Y.), 359-375 (Publisher Cambridge Scholars Publishing, New Castle upon Tyne, UK, 523pp. 2020). Kim S. G. Seismic Characteristics of an Underwater Explosion for the ROKS Cheonan Sinking as Compared with Kursk and ARA San Juan Submarine Explosions in Multiple Studies of Underwater Explosions vis- à -vis the ROKS Cheonan Sinking (ed. Kim S. G.) 83-96 (Publisher: Independently published (September 18, 2021) by self-publishing Amazon Kindle direct publishing https://kdp.amazon.com/en_US/Amazon, 2021). Kim, S. G.. Forensic seismology and boundary elementary method application vis-à-vis ROKS Cheonan underwater explosion , J. Marine Sci. Appl . 12 , 422-433 (2013). Biot, M. A. The Interaction of Rayleigh and Stoneley Waves in the Ocean Bottom, Bull.Seism. Soc. Am ., 42 (1), 81-93 (1952). Ewing, W. M., Jardetzky, W. S. & Press, F. Elastic Waves in Layered Media , McGraw-Hill Book Company, USA, 380pp. (1957). Kim, S. G. Overview and Review for Hydroacoustic Studies in Underwater Explosions in Forensic Seismology vis- à -vis DPRK Nuke tests and the ROKS Cheonan Sinking, (ed. Kim S. G.) 279-282 (Publisher Kindle Book, Amazon, USA 466pp. 2021b). Wang, Q. X., Yeo, K. S., Khoo, B. C. & Lam, K. Y. (1996a). Strong interaction between a buoyancy bubble and a free surface, Theroret. Comput. Fluid Dynamics , 8 , 3-88 (1996a). Wang, Q. X., Yeo, K. S., Khoo, B. C. & Lam, K. Y. (1996b). Nonlinear interaction between a gas bubble and free surface, Computers & Fluids , 25 (7) , 607-628 (1996b). Waghmare, Y. G., Knopf, F. C. & Rice, R. G. The Bjerknes effect: explaining pulsed-flow behavor in bubble columns, AIChE Journal , 53 (7) , 1678-1686 (2007). Zhang, A. M., Yao, X. L. & J. Li (2008 ). Interaction of underwater explosion bubble with complex elastic-plastic structure. Applied , Ocean Research , 30 , 159-171 (2008). Sorrells, G., Bonner, J. & Herrin, E. Seismic precursors to space shuttle shock fronts, Pure & Appl. Geophys ., 159 , 1153-1181 (2002). Hewitt, P. G. Conceptual Physics , 10 th edition, Pearson, Addition-Wesley, Pearson International Edition, 788pp, (see page 375), USA (2006). MCMJIG (Multinational Civilian-Military Joint Investigation Group) Joint Investigation Report: On the Attack against ROKS Cheona n , Ministry of National Defense, Republic of Korea, 313 pp. (2010). Swisdak, M. M. Explosion effects and properties: part II — explosion effects in water , NSWC/WOL TR 76-116, 22 Feb 1978 (1978). Hong, T. Seismic Investigation of the 26 March 2010 Sinking of the South Korean naval vessel Cheonanham, Bull. Seism. Soc. Am. , 101 , 1554-1562 (2011). Kim, H. S. & Caresta, M. What really caused the ROKS Cheonan warship sinking? Hindawi Publishing Corporation, Egypt , Advances in Acoustics and Vibration , Volume 2014 , Article ID 514346, 10 pages, http://dx.doi.org/10.1155/2014/514346 (2014). This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. However, this article and journal no longer exist. Lee, S. G. Personal communication with Prof. Sang-Gab Lee on April 28, 2020 , Division of Naval Architecture and Ocean Systems Engineering, Maritime and Ocean University, CEO, Marine Safety Technolog y, Busan, Korea, (2020). Wang, Q. X., Yeo, K. S., Khoo, B. C. & Lam, K. Y. Vortex ring modelling of toroidal bubbles, Theor. Comput. Fluid Dynamics, 19 (5), 303-317 (2005). Lee, S. H. & Suh, J. J. South Korean government’s failure to link the Cheonan’s Sinking to North Korea: in correct inference and fabrication of scientific data, The Internatioal Journal of Science in Society , Common Ground, 4 (1), 15-24 (2012). Porter, M. B. & Bucker, H. P. Gaussian beam tracing for computing acoustic fields , J. Acoust.Soc. Am., 82, 1349-1359 (1987). Additional Declarations No competing interests reported. Supplementary Files ScientificReportssupplementarySGKim0910202215h29h.pdf Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2053199","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":136258606,"identity":"294a9d99-46b7-4a40-b294-16d1f54fe026","order_by":0,"name":"So Gu Kim","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3ElEQVRIiWNgGAWjYJACxgYDBjkDMNPAgngtxlAtEkCCmRgtDAyJGyBsIrTIt7dfk5xRsC19O/vZoxt+FEgwmLP3H8CrxeDMmTLJDQa3c3f25KXd7AE6zLLnMH5bDCRy0iQfALVsOJBjdoMHqMXgRjIBh82AaEk3OP/G7OYfkJb7j/FrYbiRfgzksASDGzlmtyG2EPA+0C/MljMMbhtuuPHG7LaMgQSPwZlkA/wOa29/eLPnz215g/M5Zjff/LGRMzh+8AEBl/GgmslDQDkIsBMycxSMglEwCkY8AACLX0pM8J5pMAAAAABJRU5ErkJggg==","orcid":"","institution":"Korea Seismological Institute","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"So","middleName":"Gu","lastName":"Kim","suffix":""}],"badges":[],"createdAt":"2022-09-11 08:14:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2053199/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2053199/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":26834768,"identity":"0064e1f7-3c24-45ea-b62c-c4bcf70c366c","added_by":"auto","created_at":"2022-09-22 16:47:27","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":44439,"visible":true,"origin":"","legend":"\u003cp\u003eMap of the UWE site and seismic stations in and near Baengyeong-do in the Yellow Sea of the Korean Peninsula. The red star and black triangles indicate the UWE site and seismic stations including an infrasound array. \u0026nbsp;1 and 2 represent seismic stations in Baengnyeong-do for KIGAM (Korea Institute of Geoscience and Mineral Resources) with BRDAR infrasound array and KMA (Korea Metrological Administration). 3 and 4 represent seismic stations run by KMA and station 5 is INCN run by IRIS.\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-2053199/v1/9b4dfff814d416d1f43e9c5f.jpeg"},{"id":26834979,"identity":"cb3fc736-17fc-4cfd-bf7b-d9c058563012","added_by":"auto","created_at":"2022-09-22 16:52:27","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":97487,"visible":true,"origin":"","legend":"\u003cp\u003eVelocity (µm/sec) and acceleration (g) record wiondth 20 and 100 SPS (samples per second) by the underwater explosion of ROKS Cheonan at the Baenyeong Island station (BAR, KMA) in the Yellow Sea of the Korean Peninsula. The polarities (+), bubble pulses (BP), bubble jets (BJ), P- (P). S- (S), Love (LQ), Rayleigh (LR), Stoneley (SW)5, T (T-phase)6waves, and a back azimuth (BAZ) are presented. The figure in the inlet shows how to estimate the direction of a site of the underwater explosion using the vector resultant of the first-arrival amplitudes (AN and AE) from two horizontal components of N-S and E-W and the positive motion of the first arrival on the vertical component.\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-2053199/v1/8cdfcd83f0a6f6d37520c8f1.jpeg"},{"id":26835172,"identity":"1071ab6d-d813-4e8a-a8b1-f1f40d9a4994","added_by":"auto","created_at":"2022-09-22 16:57:27","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":80360,"visible":true,"origin":"","legend":"\u003cp\u003eAir waves (\u0026gt;30 Hz) with a blast and a sonic boom are detected 31s later at Baengnyeongdo station after the ROKS Cheonan underwater explosion. The high amplitudes of air waves on the N-S component may indicate that the ship was split into two parts in the north-south direction.\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-2053199/v1/6b5977d76e81b638c5f4d687.jpeg"},{"id":26835173,"identity":"654d7fde-5892-4e39-90b9-65995f919e55","added_by":"auto","created_at":"2022-09-22 16:57:27","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":381575,"visible":true,"origin":"","legend":"\u003cp\u003eThe infrasound records for the ROKS Cheonan Sinking on March 26, 2010. The inlet figure shows seismic precursors to space shuttle fronts from the sound pressure N-wave recorded on 21 February 1997 as the STS-82 shuttle mission passed over the TXAR array \u003cstrong\u003e12\u003c/strong\u003e(Sorrells et al., 2002).\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-2053199/v1/1a12de9d00b4bcb88c3582e4.png"},{"id":26835654,"identity":"211de19d-42b4-4fd7-bc2c-216806e44262","added_by":"auto","created_at":"2022-09-22 17:02:27","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":181363,"visible":true,"origin":"","legend":"\u003cp\u003e3-component seismograms and high-resolution spectra for the ROKS Cheonan Sinking underwater explosion at BAR station. The characteristic motions of an underwater explosion (BP, BJ, and TB) are clearly shown on the 3-component (N-S, E-W, and Z) spectra. It is very remarkable to observe a toroidal bubble (TB) deformation which is followed by a bubble jet (BJ) immediately before a bubble pulse (BP) in the time domain as well as in the frequency domain. It is also possible to observe a series of clear modulations of bubble pulse at 1.012 Hz (first bubble pulse) and 1.723 Hz (second bubble pulse) in the spectra.\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-2053199/v1/ca0216b87fdd573ee90dfe55.jpeg"},{"id":26834775,"identity":"8fd3ad4b-1ef0-454e-b188-5a821ad10e90","added_by":"auto","created_at":"2022-09-22 16:47:27","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":261178,"visible":true,"origin":"","legend":"\u003cp\u003eThe positive (+) first motion of P-wave arrivals and the clear advent of a bubble pulse (BP) and a bubble jet (BJ) as well as Rayleigh (LR) and Love (LQ) waves in the time domain (upper) and spectral characteristic frequencies of 3-component \u0026nbsp;spectra in the frequency domain (lower) at the BAR station comparing a short time window (1.9 s) with a long time window (10 s). The black arrows, red upward arrows, green downward arrows, and a brown downward arrow indicate a bubble pulse frequency, reverberation frequencies from the bottom and reflection from the hull, and the reverberation frequency from the free surface, respectively.\u003c/p\u003e","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-2053199/v1/33a829eb6f415cf462e66b50.jpeg"},{"id":26834976,"identity":"10e0c8dc-dc1f-40b2-bb13-8f935b1bb3a1","added_by":"auto","created_at":"2022-09-22 16:52:27","extension":"jpeg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":75184,"visible":true,"origin":"","legend":"\u003cp\u003eSmoothed normalized spectra of a seismic signal of time window 15 sec. The downward green arrows at 8.5 Hz and 25 Hz show reverberation frequencies from the seabed while the downward red arrows at 17-18 Hz and 34-35 Hz reveal the reflected P-waves from the hull of the ship showing spectral nulls at 17.5 Hz and 34.5 Hz on the vertical and E-W (radial) components.\u003c/p\u003e","description":"","filename":"floatimage7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-2053199/v1/a298b4bfbcb9e1d71ec088f2.jpeg"},{"id":26835175,"identity":"8ae4695d-4f0d-41bb-808a-8edbe174f954","added_by":"auto","created_at":"2022-09-22 16:57:27","extension":"jpeg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":859845,"visible":true,"origin":"","legend":"\u003cp\u003ea) The split forms indicate that the split forms for starboard and portside fractures show an equilateral triangle-split form due to an explosion at the portside15.. \u0026nbsp;b) The black charred hull of the ship with a tangled fishing net.\u003c/p\u003e","description":"","filename":"floatimage8.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-2053199/v1/f9a7ec62a15547693242359c.jpeg"},{"id":26834771,"identity":"47b5abd8-c3ae-4130-b9b1-6644e1b6bef9","added_by":"auto","created_at":"2022-09-22 16:47:27","extension":"jpeg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":122944,"visible":true,"origin":"","legend":"\u003cp\u003eThe behavior of 3D bubble shape simulation takes into account the interaction between the bubble and the ship’s hull based on the boundary element method (BEM). The color contour represents the magnitude of the velocity potential11. \u0026nbsp;(a) (1) bottom view (\u003cem\u003eL \u003c/em\u003e= 88 m) (2) side view (\u003cem\u003eD \u003c/em\u003e= 2.9 m) (3) front view (\u003cem\u003eW \u003c/em\u003e= 10 m). \u0026nbsp;(b). Bubble shape formation near ship’s hull: \u003cem\u003et \u003c/em\u003e= 0.000, 0.089, 0.500, 0.791, 0.932, 0.947, 1.007, 1.030, 1.122 s with 136-kg net explosive weight detonation at a depth of 8 and 5 m port side of the hull centerline (cf. Supplementary information to the manuscript).\u003c/p\u003e","description":"","filename":"floatimage9.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-2053199/v1/a0a449a185afc0cdf852a9a2.jpeg"},{"id":26835176,"identity":"22dd01c0-2207-48c3-b3a1-019dfb01914e","added_by":"auto","created_at":"2022-09-22 16:57:27","extension":"jpeg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":59702,"visible":true,"origin":"","legend":"\u003cp\u003eRay-tracing based on hydroacoustic wave speed in the early spring season with a UWE source detonated at about 8 m offshore the Baengnyeong Island in the Yellow Sea. It exhibits shallow guided waves produced by total reflection of hydroacoustic waves from the free surface in the low-velocity layer at subsurface and deep guided waves which are trapped by total reflection of hydroacoustic waves from the sea bottom2,3.\u003c/p\u003e","description":"","filename":"floatimage10.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-2053199/v1/3e510e384902959a77332cf5.jpeg"},{"id":31374017,"identity":"d83b68a0-b6af-4a7c-a37b-6ca7efad75c6","added_by":"auto","created_at":"2023-01-10 16:14:20","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1423956,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2053199/v1/329d41e8-7519-4995-8f1b-9afa65ff76c5.pdf"},{"id":26834974,"identity":"4b3bbeb6-a866-4af4-aaff-8606189394e6","added_by":"auto","created_at":"2022-09-22 16:52:27","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":171269,"visible":true,"origin":"","legend":"","description":"","filename":"ScientificReportssupplementarySGKim0910202215h29h.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2053199/v1/c7a90553602541f84c30f3e6.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Forensic seismologiy for an underwater explosion vis- à-vis the ROKS Cheonan Sinking","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe underwater explosion (UWE) incident vis-\u0026agrave;-vis the ROKS Cheonan took place off the coast of Baengnyeong Island in the Yellow Sea of the Korean peninsula on March 26, 2010 (see Fig. 1). \u0026nbsp;Considerable efforts have been devoted estimating the net explosive weight of this UWE using spectral analysis\u003cstrong\u003e\u003csup\u003e1-3\u003c/sup\u003e\u003c/strong\u003e and analytical approaches including the boundary element method (BEM)\u003csup\u003e4\u003c/sup\u003e. \u0026nbsp;It is also attempted to estimate and interpret the source depth and a net explosive weight using underwater acoustics (hydroacoustics) as well as infrasound records. This study presents new \u003cem\u003efindings of a bubble pulse, a bubble jet, and a toroidal bubble deformation from the high-resolution spectra as well as in the detailed time domain for an underwater\u003c/em\u003e explosion. \u0026nbsp;The source depth and explosive charge weight estimated are verified using a ray-trace model in the shallow channel.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIt was possible to determine the direction of a back azimuth (BAZ) of the incident site by measuring the positive polarity on the vertical component and the first arrival amplitudes on the horizontal components (HHE and HHN) in the time domain of the seismograms shown in Fig. 2. \u0026nbsp; The above seismograms and accelerograms are the most important evidence that the ROKS Cheonan sinking was due to an underwater explosion, i.e. the seismological record could be the \u0026ldquo;smoking gun\u0026rdquo; in investigating the cause of the ROKS Cheonan Sinking. \u0026nbsp; P, S, BP, BJ, PP, LR, SW, LQ and T-phase indicate the first of P- and S-wave arrivals, gas bubble pulse, bubble jet, peak pressure, Rayleigh waves, probably Stoneley waves at sea bottom - seabed interface which follows Rayleigh waves on the vertical (HHZ) and E-W (HHE) components. \u0026nbsp; T waves (T-phase of the tertiary wave) following Love waves (LQ) are observed on the N-S (HHN) component (tangential), which propagate in the channel waves with the group velocity of the sound velocity (1500 m/sec) with periods less than 1 sec in the ocean.\u003csup\u003e.\u0026nbsp;\u003c/sup\u003e Stoneley waves\u003csup\u003e5.\u003c/sup\u003e travel along a solid-fluid interface as a tube wave on the vertical component, originally along the walls of a fluid-filled borehole with a low-frequency and lower velocity than T-phase\u003csup\u003e6\u003c/sup\u003e. \u0026nbsp;Love waves may be due to\u0026nbsp;the\u0026nbsp;shearing force\u0026nbsp;of the bubble jet at 5 m portside splitting the ship into two parts in the north-south direction so that the tangential motion can be recorded on the N-S component (HHN).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIt should be noted that a back azimuth of the site location can be calculated by measuring the first arrival amplitudes (\u0026mu;m/sec) of the vertical component and two horizontal components of N-S (HHN) and E-W (HHE) components (Fig. 2). Taking into account the vector resultant of the first arrival amplitudes of N-S and E-W components it is possible to estimate the angle between two vector components by measuring atan[AE(HHE)/AN(HHN)] in the inlet figure of Fig. 2. The compressional motions of the first P-wave arrivals on the vertical component indicate that the source is in the opposite pushing towards the station. \u0026nbsp;As a result, the back azimuth (BAZ) and location of the incident site can be determined using only the 3-component single station\u003csup\u003e1-3,7\u003c/sup\u003e.\u003csup\u003e\u0026nbsp;\u003c/sup\u003e .\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eThe finding of BAZ at 224\u0026deg; from the station is in good agreement with the incident site. \u0026nbsp;The higher amplitude of the first P-wave arrival on the vertical component than that on the horizontal components shows that the upward compressional motion by an explosion occurred in the water. \u0026nbsp;A shallow underwater explosion beneath a ship results in very complicated phenomena-associated with buoyancy and Bjerknes forces\u003csup\u003e2,3,8-10\u003c/sup\u003e\u003c/em\u003e,\u0026nbsp;\u003cem\u003e\u0026nbsp;including the Archimedes principle, conservation of angular momentum, and the counter-clockwise vortex due to Coriolis force in physics\u003csup\u003e3\u003c/sup\u003e. \u0026nbsp;The larger amplitudes of Love waves may be also due to the splitting of the ship into two pieces. \u0026nbsp;The maximum acceleration and velocity of 0.084 gals and 8.4 \u0026micro;m/sec are recorded on the Z-components about 13 km away from the epicenter. \u0026nbsp; Furthermore, \u0026nbsp;it is also verified that the event may be an underwater explosion by observing the rarefaction motion (downward) of a bubble pulse phase (BP) and a bubble jet (BJ) peak in the time domain (Figs. 2 and 6).\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eFigs. 2 and 5 highlight the proofs of an underwater explosion for the ROKS Cheonan Sinking showing the characteristic motions of an underwater explosion in seismograms and spectra showing a bubble pulse on the vertical component, \u0026nbsp;bubble jets on the horizontal components (N-S and E-W) and a toroidal bubble deformation on the N-S component. It is also noticeable to find a series of clear modulations of bubble pulse at 1.012 Hz and at 1.723 Hz in Fig. 5.\u003c/p\u003e\n\u003cp\u003eFig. 3 shows that the sound waves arrived at the seismic station about 31 seconds later indicating that the signals of sound waves from an underwater explosion reached the station much slower than P-wave arrivals. However, in the beginning, \u0026nbsp;Korean mass communication media such as broadcast, SNS (social networking service), and websites mentioned the collision of the stern against the sea bottom 31 seconds later owing to the misinterpretation of the 31 second-signal. \u0026nbsp; Nonetheless, the actual sinking times of the stern and bow for the ROKS Cheonan were found to be about 6 minutes and 16 hours, respectively\u003csup\u003e3,7\u003c/sup\u003e. \u0026nbsp;\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eA high-frequency monotonic acoustic wave with an\u0026nbsp;apparent group velocity of 340 m/s is observed in the time domain (Fig. 4). The\u0026nbsp;acoustic-wave amplitudes in horizontal components (N-S component) are stronger\u0026nbsp;than\u0026nbsp;those\u0026nbsp;in\u0026nbsp;the\u0026nbsp;vertical\u0026nbsp;component,\u0026nbsp;which\u0026nbsp;is\u0026nbsp;consistent\u0026nbsp;with\u0026nbsp;the splitting direction of the ship as shown in the toroidal bubble deformation \u003csup\u003e11\u003c/sup\u003e of high-resolution spectra in Fig. 5.\u0026nbsp; The travel time of the acoustic\u0026nbsp;wave\u0026nbsp;additionally\u0026nbsp;constrains\u0026nbsp;the\u0026nbsp;event\u0026nbsp;location.\u0026nbsp;The\u0026nbsp;observation of the highest amplitude with the compressional first motion (up, \u003cstrong\u003e+\u003c/strong\u003e) on the vertical component \u0026nbsp; (\u0026ge;10^3 nm/sec) and high \u003cem\u003eP/S\u0026nbsp;\u003c/em\u003eamplitude \u0026nbsp;ratios may also suggest an underwater\u0026nbsp;explosion (Figs. 4 and 8).\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eIt seems that the 1.1 s is not interval due to supersonic N-wave effects, not to s bubble pulse. \u0026nbsp; However, it is very possible to determine the definite bubble pulse of 1.012 Hz (0.988 s) in terms of the high-resolution spectra in Fig. 5. \u0026nbsp;The infrasound records detect the infrasound signals (\u0026lt;20 Hz) and cannot detect the bubble pulse of an underwater explosion in this case..\u0026nbsp;\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eThe first peak is a burst of an underwater explosion and the second one is a sonic boom (N-wave)\u003csup\u003e2\u003c/sup\u003e\u003csup\u003e-\u003c/sup\u003e\u003csup\u003e3,7\u003c/sup\u003e in Fig. \u0026nbsp;4. N-waves are made by shock waves or sonic booms which are faster than sound waves. \u0026nbsp;The fundamental concept of N-wave is described as a shock wave which is made up of two cones high-pressure cone with the apex at the bow of the supersonic aircraft and a low-pressure cone with - the apex at the tail resulting in the shape of the letter N\u003csup\u003e13\u003c/sup\u003e. The time interval of 1.1 s is a time difference between the first burst of an underwater explosion and a sonic boom of shock waves and it is not a bubble pulse period. \u0026nbsp;Therefore, it may be not correct for MCMJIG\u003csup\u003e14\u003c/sup\u003e to apply this time interval from the infrasound signals for the Willis formula to estimate the detonation charge weight.\u003c/p\u003e\n\u003cp\u003eTwo marine sentries\u0026nbsp;on the ground heard two\u0026nbsp;impactful\u0026nbsp;sounds: the first,\u0026nbsp;a relatively\u0026nbsp;weak sounding\u0026nbsp;\u0026lsquo;Kung\u0026rsquo;, and around 1 second later,\u0026nbsp;a\u0026nbsp;thundering and wrecking sound \u0026lsquo;Kwang\u0026rsquo;. The first sound is the burst of an underwater explosion whereas the second one is a sonic boom (Fig. 4).\u0026nbsp;Two marine sentries\u0026nbsp;also saw a flash prior to \u0026quot;Kwang\u0026quot; at a maximum height of around 103 m,\u003csup\u003e.3.1\u003c/sup\u003e\u003csup\u003e5\u003c/sup\u003e from 2.5 km away at around 21:22 (origin time,\u0026nbsp;21:21:57) on March 26, 2010\u003csup\u003e1\u003c/sup\u003e\u003csup\u003e4\u003c/sup\u003e. It is noticeable to have observed a sonic boom as well as a blast of an underwater explosion in the seismic and infrasound records (Figs. 3 and 4). It should be noted that an interval of 1.1 s in Fig. 4 is almost the same as the bubble pulse period (0.988 s), but it is not the bubble pulse period for an underwater explosion of the ROKS Cheonan Sinking.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003e\u003cem\u003eTo verify the source of the ROKS Cheonsinking, the high- resolution spectral analysis using the 3-component seismograms recored at the seismic station \u0026nbsp;(BAR) in the Baengyeong-do island of the Yellow Sea.\u0026nbsp;\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e\u003cstrong\u003eSpectral analyses\u003c/strong\u003e\u003c/em\u003e\u003cem\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eLove waves strongly appear on the N-S (tangential) component in the time domain because the ship headed for 327\u0026ordm; with 6.7 knots when it was split into two parts in the direction of the NS and Love waves are detected on the tangential component. The first bubble pulse (BP) appears on the vertical component (HHZ) showing the rarefaction motion (downward collapse) whereas bubble jets (BJ) are present on the horizontal components (N-S and E-W) due to the vortex motion \u003csup\u003e11\u003c/sup\u003e in the time-domain and frequency-domain, but the initial toroidal bubble deformation (a large peak \u0026nbsp;TB) and last toroidal bubble deformation (a small peak TB) on the N-S component (HHN) on the high-resolution spectra due to the splitting direction in the north-south direction. The maxima amplitudes on the spectra start with the first toroidal bubble deformation (TB)\u003csup\u003e8\u003c/sup\u003e\u003csup\u003e-\u003c/sup\u003e\u003csup\u003e9,11\u003c/sup\u003e\u0026nbsp; and are followed by a bubble jet (Fig. 6) and a bubble collapse (pulse).\u003c/p\u003e\n\u003cp\u003eIn the spectral analyses (Fig. 6) the fundamental bubble pulse frequency f\u003csub\u003eb\u003c/sub\u003e and its spectral harmonic series are clearly explained in the right spectra with a long time window. \u003cem\u003e\u0026nbsp;\u003c/em\u003eThe characteristic phenomena of an underwater explosion are revealed as a bubble pulse (BP) and reverberation effects (green downward arrows and a strong downward brown arrow) including reflection frequencies from the hull of the ship (upward red arrows) which appear on the vertical and radial (E-W) components due to the property of P-wave propagation. The left spectra with a1.9 s time window do not include every spectral characteristic like the right spectra with a 10.0 s time window due to the lack of higher multiple frequencies..\u003c/p\u003e\n\u003cp\u003eThe first bubble pulse (black arrow, 1.012 Hz) is clearly revealed at the high resolution spectra in Fig. 5, reverberation frequencies (upward red arrows, 8.5 Hz, 25 Hz, and 42.5 Hz; f\u003csub\u003eH\u003c/sub\u003e), \u0026nbsp;reflected P-wave arrivals from the hull bottom (downward green arrows,\u0026nbsp;\u0026asymp;\u0026nbsp;17-18 Hz and\u0026nbsp;\u0026asymp;\u0026nbsp;34-35 Hz) which are multiple frequencies of a series of the first and the second harmonic series with spectral nulls, and a shallow guide\u003cem\u003e\u0026nbsp;\u003c/em\u003ewave\u003cem\u003e\u0026nbsp;\u003c/em\u003e(downward brown arrow, 47. 5 Hz; f\u003csub\u003ed\u003c/sub\u003e ) which is also revealed in the ray-tracing modeling in Fig. 10. \u0026nbsp;The cutoff frequency associated with the detonation depth (47.5 Hz) can be also used to estimate the detonation depth (7.89 m). The finding of a very low frequency at around 2 Hz for the T-phase is noticeable on the N-S component in the time domain in Fig. 2. \u0026nbsp;Using the surface cutoff frequency, \u0026nbsp;the detonation depth is estimated at 7.89 m.\u003c/p\u003e\n\u003cp\u003eIt is very clear to find reverberation frequencies from the sea floor and reflected frequencies from the hull of the ship in the spectra of \u0026nbsp;15 s time window in Fig. 7. \u0026nbsp;The spectral maxima at 8.5 Hz and \u0026asymp; 25 Hz are reverberation frequencies ( the first and third harmonic), whereas the maxima of the red arrows at \u0026asymp; 17-18 Hz (first harmonic) and at \u0026asymp; 34-35 Hz (second harmonic) indicate reflection spectral amplitudes which are formed by reflection from the hull bottom with small spectral nulls which are made by the superposition of destructive interference of direct P-wave arrivals and the reflected P-wave arrivals from the hull.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe reflected amplitude maxima distinctly appear on the vertical and radial (E-W) components due to the characteristics of P-wave propagation. \u0026nbsp;It is also evident that spectral nulls at 17.5 Hz and 34.5 Hz are due to the time difference between the onsets of P-wave arrivals and those of the downswing depth phases pP in the time domain, which in the frequency domain delay times for depth phase produce sharp holes as spectral nulls at 17.5 Hz and 34.5 Hz.\u003c/p\u003e\n\u003cp\u003eThe observed P-wave spectra are analyzed at frequencies of 8.5 Hz and its multiples (17.7, 34.6 Hz) \u0026nbsp;including modulation of spectral amplitudes at frequencies around 26 Hz \u003csup\u003e16\u003c/sup\u003e. However, it may be confused that 8.5 Hz, 17.7 Hz, 26 Hz, and 34.6Hz may be considered a series of modulations of reverberation \u003csup\u003e16\u003c/sup\u003e.\u0026nbsp;It is of significance to observe small spectral nulls (17.5 Hz and 34.5 Hz) on the vertical and E-W components.\u0026nbsp;Those spectral nulls may be due to destructive interference by reflected P- wave amplitudes under the ship hull and the direct P- wave arrivals at the same station (Fig. 7).\u0026nbsp;The findings of spectral nulls at around 17.5 Hz and 34.5 Hz may suggest that the detonation depth can be estimated using the spectral nulls\u003csup\u003e3,7\u003c/sup\u003e. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTaking into account the previous depth estimates, the medium velocity inside the gas bubble may turn out to be around 280 m/sec which may be much less than the normal sound velocity in air, creating a gaseous void of lower pressure than the surrounding water by pushing all of the materials such as smoke (vapor), dirt, debris and explosive chemicals from the central \u0026nbsp;point, but the void is instantaneously mixed with them in the cold seawater.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIt should be noticeable that 8.5 Hz, 17-18 Hz, 25 Hz, and 34-35 Hz are not natural frequencies from the collision between a ship and a submarine. However, \u0026nbsp;Submarine collision asserters \u003csup\u003e17\u003c/sup\u003e used those frequencies as natural frequencies from the collision. As a result, they must \u0026nbsp;have \u0026nbsp;made \u0026nbsp;some\u0026nbsp;\u003c/p\u003e\n\u003cp\u003emistakes resulting in a collision of the ROKS Cheonan with a submarine. \u0026nbsp;However, frequencies of a vibration source for a submarine cannot be detected at seismic stations because the vibration source is a low energy and little impact force for viscous dynamic force in impulse (little force over a long time by force x time interval in physics\u003cem\u003e).\u0026nbsp;\u003c/em\u003eSang-Gab Lee \u003csup\u003e18\u003c/sup\u003e\u003cem\u003e\u0026nbsp;hydrodynamically denied the collision story of the ROKS Cheonan Sinking with a submarine because of the low energy and resistance of the water.\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eDamage Phenomena and hydrodynamic modeling by BEM\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe first figure shows how the bubble jet struck the hull of the ship when the ship was split into two parts.\u0026nbsp;The red equilateral triangle-type damage at the portside may indicate that the ship must have been stricken by the strong and elaborate physical force with\u0026nbsp;symmetry at a centroid. The force may be due to\u0026nbsp;the bubble jet resulting in\u0026nbsp;the counter-clockwise vortex immediately before the gas bubble pulse.\u003cem\u003e\u0026nbsp;\u003c/em\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe tangled fishing net wires (white arrows) on the propeller axis\u0026nbsp;indicate the running aground before the explosion and the black charred hull\u0026nbsp;surface (soot) may be due to the flame at the moment of the blast for an\u0026nbsp;underwater explosion (black arrows).\u0026nbsp;Also, it cannot be ruled out that the\u0026nbsp;strong ICCP current might flow on the hull surface when it ran aground before the\u0026nbsp;underwater\u0026nbsp;explosion\u003csup\u003e3,7\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe equilateral triangle damage mark also reveals the material evidence that the damage and split of the ship were not due to arbitrary and asymmetrical forces such as a collision of a ship with a submarine or a running aground. The more severe damage on the stern part (b in Fig. 8b) may be due to the counter-clockwise vortex from the bubble jet resulting in sinking the stern part much earlier than the bow part.\u0026nbsp;It took about 6 minutes for the stern to sink while it took about 16 hours for the bow to sink\u003csup\u003e3\u003c/sup\u003e. \u0026nbsp;It is the start of the running aground that the last recorded time of the CCTV image was recorded at 21:17:03, indicating that electricity was lost by cutting off inside the ship\u003csup\u003e3\u003c/sup\u003e. \u0026nbsp; Fishing nets were found entangled around the right screw axle of the damaged ship in Fig. 8b.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThis contradicts the MCMJIG\u003csup\u003e14\u003c/sup\u003e claim that there were no fishing zones in the area of the ship\u0026rsquo;s voyage. The running aground site was also reported at a depth of 6.4 m and about 4 m in case of a low ebb which caused a running aground of the ROKS Cheonan because of a draft of 2.87 m for the ship\u003csup\u003e3\u003c/sup\u003e.\u0026nbsp;The tangled fishing net wires (white arrows) on the propeller axis\u0026nbsp;indicate that there must have been\u0026nbsp;running aground before the explosion. Before the sinking, the bottom of the Cheonan ship touched the shallow ocean floor. The fore side deformation of the starboard propeller (screw) and off-set shaft axis is due to a collision with the seabed, The aft view of the starboard propeller blades bent opposite of its rotation (clockwise) may be formed during the collision with the seabed\u003csup\u003e2\u003c/sup\u003e. \u0026nbsp; The entangled fishing net wires are found around the right screw axle of the damaged ship. The black charred hull surface (smoke soot) in Fig. 8b may be due to the flame at the moment of a blast for an underwater explosion (black arrows). However, the strong ICCP (Impressed Current Cathodic Protection) current might flow on the hull surface and cannot be ruled out during running aground before the underwater explosion\u003csup\u003e3,4,,7\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e\u003cstrong\u003eSource possibility of 136 kg TNT (LCM)\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e\u003csup\u003e\u0026nbsp;1-4,14\u003c/sup\u003e\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003cem\u003e\u0026nbsp;versus 250 kg TNT (torpedo\u003c/em\u003e\u003csup\u003e2-4,14\u003c/sup\u003e\u003cem\u003e) using BEM (Boundary Element Method). \u0026nbsp;3D bubble shape simulation \u0026nbsp;with source parameters such as detonation depth, yield, and position including a bubble pulse period.\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThrough the bubble pulse period of 0.988 s obtained via spectral analysis, the approximate net explosive weight and explosion depth are estimated by narrowing down the possible parameters along with supplementary estimations of the bubble pulse periods of 0.967 s via Rayleigh\u0026ndash;Willis equation, 0.976 s via BEM (Boundary Element Method) and 1.030 s via 3D bubble shape simulation derived for the case of a 136 kg TNT net explosive weight detonation. The more detailed studies about hydrodynamics are well presented in the previous work \u003csup\u003e2-,4,7\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eFrom Fig. 9, The 3D modeling produces a maximum bubble, (BP Max), a toroidal bubble deformation (TB), a bubble jet (BJ), and a bubble pulse (BP) as follows:\u003c/p\u003e\n\u003cp\u003e0.5 s = BP Max, 0.791 s = TB, 1.007 s = BJ, 1.030 s = BP (0.988 s from Fig. 5)\u003c/p\u003e\n\u003cp\u003eThe bubble pulse of 1.030 s is slightly larger than 0.988 s on the vertical component of spectra. \u0026nbsp;The\u0026nbsp;\u003c/p\u003e\n\u003cp\u003ebubble jet at 1.007 s is earlier than the bubble pulse, which is consistent with the horizontal components (N-S and E-W) of time and frequency domains (Figs. 2 and 5).\u003c/p\u003e\n\u003cp\u003eRelative errors are estimated from the observed bubble pulse period vis-\u0026agrave;-vis 3D simulation with detonation occurring at 3 m and 5 m portside (PS) of the hull from the centerline in the case of 136 kg TNT and 250 kg TNT as follows :\u003c/p\u003e\n\u003cp\u003e4.04 % 136 kg TNT\u0026nbsp;at 8 m (depth), PS (portside) 5 m;\u0026nbsp;6.87 % 136 kg TNT at 8 m, PS 3 m,\u003c/p\u003e\n\u003cp\u003e18.38 % 250 kg TNT at 9 m, PS 5 m; 20.10 % 250 kg TNT at 9 m, PS 3 m\u003c/p\u003e\n\u003cp\u003eAfter a bubble pulse starts contracting, a toroidal bubble formation\u003csup\u003e8,19\u0026nbsp;\u003c/sup\u003eat TB (0.791 s), just before a bubble pulse (BP) at 1.030 s and a bubble jet (BJ) occurs at around t=1.007 s and the bubble gets a minimum at 1.030 s (BP\u003cstrong\u003e)\u003csup\u003e1-4,,7\u003c/sup\u003e\u003c/strong\u003e. \u0026nbsp;By the Bjerknes Effect\u003csup\u003e3,8\u003c/sup\u003e\u003csup\u003e-\u003c/sup\u003e\u003csup\u003e10\u003c/sup\u003e, the rigid boundary can attract the explosion bubble while the free surface repels it.\u0026nbsp;Since the buoyancy force and Bjerknes attraction of the rigid hull are comparable, the bubble pulse from the experiment may be longer than that of the ROKS Cheonan Sinking underwater explosion (Figs. 6 and 9). If the oscillation gas bubble is close enough to a rigid body then the pressure differential created as the bubble decreases in volume will result in the bubble collapsing onto the hull and producing high speed (130-170 m/s range)\u003csup\u003e1,3\u003c/sup\u003e\u0026nbsp; water jet (bubble jet) which may be capable of holing the hull of the ship (Fig. 8a). The bubble shape immediately before and immediately after jet impact has been investigated by various researchers\u003csup\u003e1\u003c/sup\u003e\u003csup\u003e-\u003c/sup\u003e\u003csup\u003e2,8\u003c/sup\u003e\u003csup\u003e-\u003c/sup\u003e\u003csup\u003e,11\u003c/sup\u003e. As a result. The analyses show that, by parametric study, a 136 kg charge yields a bubble pulse consistent with the observed seismic data.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eA source size of an explosion in water is not the same as inland due to a high Q factor with little attenuation, salinity, and pressure including the optimum depth in which an experiment is conducted using depth\u0026ndash;charge relations. In this study, the ROKS Cheonan sinking was found to be an underwater explosion that occurred at a depth of around 8 m, approximately 5 m port side of the hull centerline with 136 kg TNT net explosive weight equivalent to 2.04 of a seismic magnitude.\u003c/p\u003e \u003cp\u003eThe misuse\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e of 8.5, 25, 18, and 35 Hz as harmonic frequencies from a previous researcher\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e who stated that P energy was dominant at around 8.5 Hz, with multiple frequencies of 17.7 and 34.6 Hz missing 25 Hz. 8.5 Hz and 25 Hz are odd frequency series for reverberation, while 17.7 Hz and 34.6 Hz could be the fundamental and its harmonics by the reflection of P waves from the broad hull just under the ship\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. Consequently, it may be most unlikely that the ROKS Cheonan sank by a collision with a large submarine. It was proved that the collision with a submarine was incorrect in the light of detailed scientific aspcts of seismology, hydroacoustics, and hydrodynamic (fluid mechanics)\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. The fabrication of the collected torpedo was also asserted by not only some academic people\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e, but also many other laymen.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eThis study concludes that the ROKS Cheonan sinking was due to an underwater explosion by 136 kg TNT yield at a depth around 8 m and 5 m portside from one of the abandoned land control mines (LCM) which were deployed near NLL (Northern Limited Lines) by the South Korean Navy in the late 1970s neither a collision with a submarine nor a running aground against a reef according to the scientific data\u003csup\u003e\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003eThe cause of the ROKS Cheon sinking was already verified using spectral and hydrodynamic analyses in the front. \u0026nbsp;It is inductively proved using the underwater wave propagation of a ray-tracing model with a detonation at a depth of 8 m (Fig. 10). \u0026nbsp;It is possible to calculate the hydroacoustic wave propagation using the BELLHOP Gaussian beam ray-tracing program\u003csup\u003e21\u003c/sup\u003e from an underwater explosion in the early spring cold water of the Yellow Sea, assuming that a seismic source is detonated at a depth of about 8 m in the water depth of around 44 m\u003csup\u003e1--4\u003c/sup\u003e.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe raw data (seismic and infrasound) that were used in this study can be downloaded from Korea Meteorological Administration (KMA) (see https://necis.kma.go.kr) and Korea Institute of Geoscience and Mineral Resources (KIGAM) (see https://www.kigam.re.kr/english/)\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFirst of all, I am much obliged to Yefim Gitterman, my long collaborator for the spectral analyses of the ROKS Cheonan Sinking data. I also wish to thank Aman Zhang (Harbin Engineering University, China) for hydrodynamic analysis using the boundary element method and Orlando Camargo Rodriguez (University of Algarve, Portugal) for the ray tracing for a shallow underwater explosion. Khoo Boo Cheong (National University of Singapore) and Anne Trehu (Oregon State University, USA) provided valuable discussions and constructive criticisms about fluid mechanics and underwater explosion phenomena which would be appreciated. I acknowledge KMA (Korea Meteorological Administration) and KIGAM (Korea Institute of Geoscience and Mineral Resources) for providing waveform data for this study.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eS.G.K. wrote the manuscript text and processed the data and produced the base of the figures with collaborators. No permission is required to reuse all figures in this paper because the copyright of the figures belongs to the author (So Gu Kim) in \u003cem\u003e Multiple Studies of Underwater Explosions vis- \u0026agrave;-vis the ROKS Cheonan Sinking.\u003c/em\u003e Publisher: Independently published (September 18, 2021) by self-publishing Amazon Kindle direct publishing https://kdp.amazon.com/en_US/. \u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe author declares no competing interests. \u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAdditional information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupplementary information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eRaw data (seismic) can be obtained from https://necis.kma.go.kr\u003c/p\u003e\n\u003cp\u003eModeling figures for \u0026ldquo;Boundary Element Method (BEM) for the ROKS Cheonan Sinking\u0026rdquo; are available for this paper in the attached file as \u0026ldquo;Supplementary information to the manuscript\u0026rdquo;.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCorrespondence \u003c/strong\u003eand requests for materials should be addressed to S.G.K\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eKim, S. G. \u0026amp; Gitterman, Y. (2013). Underwater Explosion (UWE) Analysis of the ROKS Cheonan Incident, \u003cem\u003ePure, and Appl. Geophys\u003c/em\u003e, \u003cstrong\u003e170\u003c/strong\u003e, 547-560 (2013).\u003c/li\u003e\n\u003cli\u003eKim, S. G. Estimating Depth and Explosive Charge Weight for an Extremely Shallow Underwater Explosion for the ROKS Cheonan Sinking in \u003cem\u003eForensic Explosion Seismology: Technologies and Applications \u003c/em\u003e(eds. Kim S. G. Gitterman Y.), 359-375 (Publisher Cambridge Scholars Publishing, New Castle upon Tyne, UK, 523pp. 2020).\u003c/li\u003e\n\u003cli\u003eKim S. G. Seismic Characteristics of an Underwater Explosion for the ROKS Cheonan Sinking as Compared with Kursk and ARA San Juan Submarine Explosions in \u003cem\u003eMultiple Studies of Underwater Explosions vis- \u003c/em\u003e\u003cem\u003e\u0026agrave;\u003c/em\u003e\u003cem\u003e-vis the ROKS Cheonan Sinking \u003c/em\u003e (ed. Kim S. G.) 83-96 (Publisher: Independently published (September 18, 2021) by self-publishing Amazon Kindle direct publishing https://kdp.amazon.com/en_US/Amazon, 2021).\u003c/li\u003e\n\u003cli\u003eKim, S. G.. Forensic seismology and boundary elementary method application vis-\u0026agrave;-vis ROKS Cheonan underwater explosion\u003cem\u003e, J. Marine Sci. Appl\u003c/em\u003e. \u003cstrong\u003e12\u003c/strong\u003e, 422-433 (2013).\u003c/li\u003e\n\u003cli\u003eBiot, M. A. The Interaction of Rayleigh and Stoneley Waves in the Ocean Bottom, \u003cem\u003eBull.Seism. Soc. Am\u003c/em\u003e., \u003cstrong\u003e42 (1),\u003c/strong\u003e 81-93 (1952).\u003c/li\u003e\n\u003cli\u003eEwing, W. M., Jardetzky, W. S. \u0026amp; Press, F. \u003cem\u003eElastic Waves in Layered Media\u003c/em\u003e, McGraw-Hill Book Company, USA, 380pp. (1957).\u003c/li\u003e\n\u003cli\u003eKim, S. G. Overview and Review for Hydroacoustic Studies in Underwater Explosions in \u003cem\u003eForensic Seismology vis-\u003c/em\u003e\u003cem\u003e\u0026agrave;\u003c/em\u003e\u003cem\u003e-vis DPRK Nuke tests and the ROKS Cheonan Sinking, \u003c/em\u003e(ed. Kim S. G.) 279-282 (Publisher Kindle Book, Amazon, USA 466pp. 2021b).\u003c/li\u003e\n\u003cli\u003eWang, Q. X., Yeo, K. S., Khoo, B. C. \u0026amp; Lam, K. Y. (1996a). Strong interaction between a buoyancy bubble and a free surface, \u003cem\u003eTheroret. Comput. Fluid Dynamics\u003c/em\u003e, \u003cstrong\u003e8\u003c/strong\u003e, 3-88 (1996a).\u003c/li\u003e\n\u003cli\u003eWang, Q. X., Yeo, K. S., Khoo, B. C. \u0026amp; Lam, K. Y. (1996b). Nonlinear interaction between a gas bubble and free surface, \u003cem\u003eComputers \u0026amp; Fluids\u003c/em\u003e, \u003cstrong\u003e25 (7)\u003c/strong\u003e, 607-628 (1996b).\u003c/li\u003e\n\u003cli\u003eWaghmare, Y. G., Knopf, F. C. \u0026amp; Rice, R. G. The Bjerknes effect: explaining pulsed-flow behavor in bubble columns, \u003cem\u003eAIChE Journal\u003c/em\u003e, \u003cstrong\u003e53 (7)\u003c/strong\u003e, 1678-1686 (2007).\u003c/li\u003e\n\u003cli\u003eZhang, A. M., Yao, X. L. \u0026amp; J. Li (2008\u003cem\u003e). \u003c/em\u003eInteraction of underwater explosion bubble with complex elastic-plastic structure.\u003cem\u003e Applied\u003c/em\u003e , \u003cem\u003eOcean Research\u003c/em\u003e, \u003cstrong\u003e30\u003c/strong\u003e, 159-171 (2008).\u003c/li\u003e\n\u003cli\u003eSorrells, G., Bonner, J. \u0026amp; Herrin, E. Seismic precursors to space shuttle shock fronts, \u003cem\u003ePure \u0026amp; Appl. Geophys\u003c/em\u003e.,\u003cstrong\u003e159\u003c/strong\u003e, 1153-1181 (2002).\u003c/li\u003e\n\u003cli\u003eHewitt, P. G. \u003cem\u003eConceptual Physics\u003c/em\u003e, 10\u003csup\u003eth\u003c/sup\u003e edition, Pearson, Addition-Wesley, Pearson International Edition, 788pp, (see page 375), USA (2006).\u003c/li\u003e\n\u003cli\u003eMCMJIG (Multinational Civilian-Military Joint Investigation Group) \u003cem\u003eJoint Investigation Report: On the Attack against ROKS Cheona\u003c/em\u003e\u003cem\u003en\u003c/em\u003e, Ministry of National Defense, Republic of Korea, 313 pp. (2010).\u003c/li\u003e\n\u003cli\u003eSwisdak, M. M. \u003cem\u003eExplosion effects and properties: part II\u003c/em\u003e\u0026mdash; \u003cem\u003eexplosion effects in water\u003c/em\u003e, NSWC/WOL TR 76-116, 22 Feb 1978 (1978).\u003c/li\u003e\n\u003cli\u003eHong, T. Seismic Investigation of the 26 March 2010 Sinking of the South Korean naval vessel Cheonanham,\u003cem\u003e \u003c/em\u003e\u003cem\u003eBull. Seism. Soc. Am.\u003c/em\u003e, \u003cstrong\u003e\u003cem\u003e101\u003c/em\u003e,\u003c/strong\u003e 1554-1562 (2011).\u003c/li\u003e\n\u003cli\u003eKim, H. S. \u0026amp; Caresta, M. What really caused the ROKS Cheonan warship sinking? Hindawi Publishing Corporation, Egypt\u003cem\u003e, Advances in Acoustics and Vibration\u003c/em\u003e, \u003cstrong\u003eVolume 2014\u003c/strong\u003e, Article ID 514346, 10 pages, http://dx.doi.org/10.1155/2014/514346 (2014). This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. However, this article and journal no longer exist.\u003c/li\u003e\n\u003cli\u003eLee, S. G. \u003cem\u003ePersonal communication with Prof. Sang-Gab Lee on April 28, 2020\u003c/em\u003e, Division of Naval Architecture and Ocean Systems Engineering, Maritime and Ocean University, CEO, Marine Safety Technolog\u003cem\u003ey, \u003c/em\u003eBusan, Korea, (2020).\u003c/li\u003e\n\u003cli\u003eWang, Q. X., Yeo, K. S., Khoo, B. C. \u0026amp; Lam, K. Y. Vortex ring modelling of toroidal bubbles, \u003cem\u003eTheor. Comput. Fluid Dynamics,\u003c/em\u003e \u003cstrong\u003e19 (5),\u003c/strong\u003e 303-317 (2005).\u003c/li\u003e\n\u003cli\u003eLee, S. H. \u0026amp; Suh, J. J. South Korean government\u0026rsquo;s failure to link the Cheonan\u0026rsquo;s Sinking to North Korea: in correct inference and fabrication of scientific data, \u003cem\u003eThe Internatioal Journal of Science in Society\u003c/em\u003e, Common Ground, \u003cstrong\u003e4 (1),\u003c/strong\u003e 15-24 (2012).\u003c/li\u003e\n\u003cli\u003ePorter, M. B. \u0026amp; Bucker, H. P. Gaussian beam tracing for computing acoustic fields\u003cem\u003e, J. Acoust.Soc. Am.,\u003c/em\u003e \u003cstrong\u003e82,\u003c/strong\u003e 1349-1359 (1987).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-2053199/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2053199/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"For a very shallow underwater explosion, spectral analysis is preferable to cepstral analysis to find characteristics of a bubble pulse and reverberation effects. Time-domain analyses show bubble pulses and bubble jets as well as positive polarities of the first P-wave arrivals on the vertical component, and spectral analyses also clearly reveal the bubble pulse and reverberation effects. The ROKS Cheonan sinking was a shallow underwater explosion that occurred near the surface showing a bubble jet characteristic resulting in splitting the ship into two pieces including a bubble pulse. The findings of a bubble jet and a toroidal bubble deformation including a bubble pulse are highlighted in this study. The ROKS Cheonan sinking took place off the Baengnyeong Island in the Yellow Sea of the Korean Peninsula at a depth of about 8 m in the sea depth of 44 m on March 26, 2010. The explosive charge weight was estimated at 136 kg TNT using the seismological analyses and boundary element method. The 136 kg TNT is equivalent to one of the abandoned land control mines (LCM) that were deployed near the Northern Limited Lines (NLL) in the Yellow Sea by the South Korean Navy in the late 1970s.\n","manuscriptTitle":"Forensic seismologiy for an underwater explosion vis- à-vis the ROKS Cheonan Sinking","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-09-22 16:47:25","doi":"10.21203/rs.3.rs-2053199/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"2be900e4-1ced-4227-9f5a-aa12f770ea20","owner":[],"postedDate":"September 22nd, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2023-01-10T16:14:13+00:00","versionOfRecord":[],"versionCreatedAt":"2022-09-22 16:47:25","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-2053199","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2053199","identity":"rs-2053199","version":["v1"]},"buildId":"7rjqhiLT3MXkJMwkYKINL","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}