Underwater Explosion (UWE) Analysis of the ROKS Cheonan Incident

Estimation of Depth and Charge Weight for a Shallow Underwater Explosion Using cut off Frequencies and Ray-Trace Modeling

“…Cutoff frequencies are 8.5, 25, 43 Hz from the bottom reflection and 45 Hz from the surface reflection. The bubble pulse (1.01 Hz) which was determined from the previous study [1] is not displayed on the left figure in Figure 4 but it appears on the right figure in Figure 4 because the bubble pulse period is 0.990s after P-wave arrival at 12:21:59.24. On the other hand in Figure 5, we can observe all spectral anomalies at 17.5 Hz and 35 Hz as well as 8.5 Hz, 25 Hz, and 43 Hz (cutoff frequencies of reflection off the bottom) and 45 Hz (cutoff frequency of reflection off the free surface) as well as 1.01 Hz (bubble pulse).…”

“…The previous study [1][2] determined bubble and reverberation effects of hydroacoustic waves as well as the seismic yield through seismic and acoustic waves, including the bubble pulse period of 0.990s (1.01Hz) which was essential to estimate a net explosive weight using Rayleigh-Willis equation without information of a source depth. Here we estimate the source depth first and then we simply determine a NEW with known bubble pulse period and the detonation depth.…”

“…Provided the attenuation is not too large and dispersion is little, we estimated a horizontal cycle distance (D C ) at about 325 m with group velocity of 1460 m/s at a bottoming depth (Z C ) of about 8 m [1][2]. The horizontal cycle distance is clearly visible (Figure 3) and is strongly associated with the group velocity carrying energy along a ray or beam shift [9][10].…”

“…Considerable efforts have been devoted to estimate the net explosive weight of this UWE using spectral analysis and analytical approach including simulation of boundary element method [1][2]. These attempts have typically used ad hoc models of the relationship between bubble pulse period and net explosive weight or have been based on 3D shape simulation by BEM [1][2]. This paper presents the relationship between the cutoff frequencies and the detonation depth resulting in obtaining the net explosive weight, including application of ray-trace modeling for confirmation of estimation.…”

“…We also verified whether our estimated source depth fitted the observed one using ray-trace modeling in the shallow channel. The compelling reason of this study is to estimate the net explosive weight (NEW) for a very shallow underwater explosion (< 50m) using only cutoff frequencies and Rayleigh-Willis equation [1][2]. The NEW estimation is possible using a cutoff frequency and the bubble pulse period from spectral analysis relating to the Rayleigh-Willis equation since it is a function of detonation depth and NEW.…”