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Brief Note

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Document on November 3, 2021​

1 　Overview:  Nuclear tests in the past

  Since researches and developments of nuclear weapons got active around the 1940’s, many countries have conducted nuclear weapons tests as listed below.[1-9]


       Table 1.  History of nuclear tests   
 

  • United States: about 1945-1992

  • Soviet Union: about 1945-1972

  • Unite Kingdom: about 1952-1991

  • France: about 1960-1996

  • India: 1974 and 1998   

  • Pakistan: 1998

  • China:  about 1964-1996                  

  • North Korea: about 2006-2017

    
 

   It has been a while since a global society started worrying about other new nations having bran-new nuclear weapons.  However, the so-called “subcritical nuclear tests” are continuously conducted by many countries including the United States.  A subcritical nuclear test is the experiment in which nuclear materials are designed not to reach critical conditions.[1]  

  So far, nuclear weapons tests have been monitored in various international efforts.  One of them, the Comprehensive Nuclear Test Ban Treaty (CTBT) was adopted in 1996, as the treaty to prohibit nuclear explosions anywhere including underground, underwater, atmosphere, and spaces.  As of 2019, 184 countries signed the treaty, and 168 countries ratified it.  Among the 44 countries that were required to ratify for the treaty to be effective, eight countries (the United States, China, North Korea, Egypt, India, Iran, Israel, and Pakistan) had not ratified yet as of 2018. [10]    Furthermore, Treaty on the Prohibition of Nuclear Weapons (TPNW) was adopted in 2017, and entered into force in January, 2021.  TPNW is the international treaty to prohibit nuclear weapons as a law.[11, 12]     
  In recent years, there were a series of nuclear tests conducted in North Korea[6] and there are many past researches about the nuclear tests in North Korea.[13-32]  

 This study analyzes numerical data of nuclear explosions and natural earthquakes and discusses some of features for them.  This study is based on open information.

2    Data Analysis of nuclear explosions and natural earthquakes　　　　

2-1   Dataset　　　

Nuclear explosion 

 

 Figure 1 shows the distribution of artificial earthquakes resulting from nuclear explosions.

 

  • North Korea, Nuclear Test, 2016/09/09, Magnitude 5.3, Focal depth=0.0km, Station Mudanjiang (China)

  • North Korea, Nuclear Test, 2016/01/06, Magnitude 5.1, Focal depth=0.0km, Station Mudanjiang (China)

  • North Korea, Nuclear Test, 2013/02/12, Magnitude 5.3, Focal depth=0.0km, Station Mudanjiang (China)

fig1.jpg

Natural earthquake 


  In comparison to nuclear explosions, the data of natural earthquakes are also evaluated.  Figure 2 shows the distribution of natural earthquakes in Asian regions. 

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  • North Korea, Natural earthquake, 2002/04/16, Magnitude 4.6, Focal depth=10.0km, Station Mudanjiang (China)

  • China,            Natural earthquake, 2012/05/03, Magnitude 5.2, Focal depth=15.8km, Station Urumqi (China)

  • Pakistan,       Natural earthquake, 2016/03/21, Magnitude 5.6, Focal depth=10.0km, Station Kabul (Afghanistan)

fig2.jpg

Criteria for selecting the data

 

  Next, general criteria for selecting the data (nuclear explosions and natural earthquakes) are shown below.

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  1. Epicentral distance range between seismic source and station:  about 3~16 degrees (Angular distance of 1 degree is assumed to be roughly equivalent to 111 km)

  2. Magnitude range:  about 4.0~5.9

  3. Among three components of seismogram (one vertical component, two lateral components), this study uses the initial P-wave of vertical component.

  4.  Evaluating the initial phase of vertical component intends to capture P-wave in similar fashion for all computations of any particular distance in the analysis (the epicentral distance range is relatively large in this study).  P-wave is a longitudinal wave which is radiated compressionally from a seismic source, and its propagation velocity is larger than that of S-wave (transverse wave).  Therefore, P-wave generally tends to reach the seismic stations in the earliest order.      

 

**

 The data are selected based upon preprocessing and noise check.  Information for earthquakes (seismic stations, observational data) are obtained from IRIS (Incorporated Research Instituted for Seismology).[33]

 

**　

  The North Korea nuclear test of September 2017 (Magnitude 6.3, reported as a hydrogen bomb) is not included in the analysis.  In this study, the nuclear explosion-type seismic data showing the high complexity of earthquake source physics (such as “Tectonic release [34, 35]”) are not used.  Evaluation of those kinds of data will be left as future assignments.

2-2    Features of Signals:  Seismic data due to seismic fault motion and nuclear explosion


     Features of seismic data are discussed in time domain and frequency domain for natural earthquakes and nuclear explosions.  We have a closer look on the waveform data and spectral data (after getting the Fourier Transform) in detail.  
  Here first in figure 3, some of general features of seismic data are shown for a natural earthquake and a nuclear explosion.



General features of natural earthquake data, due to a fault motion [shown in (a) and (b) in Fig. 3]

  At the seismic source, relatively large-scale destruction is generally dominant and directive energy radiation due to fault motion is characteristic.
  At the seismic stations, low frequency signals (large wavelength) depending on a fault size generally become dominant.  And on the other hand, high frequency signals generally decay with the frequency as 1/ ω**n (ω is frequency, and n is about 2~3).[35, 36, 37, 38]   This frequency-dependent tendency (such as ω**2 and ω**3) is generally noticeable for a spectrum.  
  Since a natural earthquake is originated from a fault motion which is rich in shear component (more deviatoric), the amplitude of first arrival (mainly compressional component) in time domain series data tends to be relatively small.  


General features of artificial earthquake data, due to an explosion [shown in (c) and (d) in Fig. 3]

  At the seismic source, relatively small-scale destruction is generally dominant and energy is radiated in more isotropic fashion due to explosion phenomena.  
  At the seismic stations, on the contrary to the case of natural earthquakes, high frequency signals (small wavelength) due to relatively small-scale destruction become dominant.  This tendency is generally noticeable for a spectrum.   
Since the artificial earthquake being originated from an explosion is generally rich in compressional component, the amplitude of first arrival (mainly compressional component) in time domain series data tends to be relatively large. 
 

fig3_new.jpg

   Next, a series of plots of natural earthquakes and nuclear explosions are shown in figure 4.  
  The three seismic events in the left-hand side of figure show the features of natural earthquakes.  Since a natural earthquake is originated from a fault motion which is rich in shear component (more deviatoric), the amplitude of first arrival (mainly compressional component) in time domain series data tends to be relatively small.  The spectral data show the typical ω**2 like frequency-dependent tendency of natural earthquakes.  Low frequency (large wavelength) signals due to a fault size generally become dominant and high frequency signals decay with the frequency.  
   The three seismic events in the right-hand side of figure show the features of nuclear explosions.  Since the artificial earthquake being originated from an explosion is generally rich in compressional component, the amplitude of first arrival (mainly compressional component) in time domain series data tends to be relatively large.  The spectral data show the typical frequency-dependent tendency of nuclear explosions.  High frequency signals due to relatively small-scale destruction become dominant.  That tendency generally indicates that energy is radiated in more isotropic fashion at the seismic source due to explosion phenomena.
  The data information for the events in figure 4 were introduced in the section 2-2.  Some of typical features of seismic data were already shown in figure 3.
 

fig4_new.jpg

3   Estimating magnitudes of nuclear explosions
 

  This chapter shows the explosion magnitudes of nuclear explosions.  Here, based on “TNT equivalent,” the magnitude of nuclear explosion is estimated from information of earthquake magnitude. [1, 6, 33]

  TNT equivalent is one of the methods for expressing an energy.[39, 40]  It is typically used to describe the energy released in an explosion, by converting the energy released in an explosion to the equivalent amount of TNT mass.  The unit of TNT equivalent is kiloton (1 kiloton is equivalent to 4.184×1012 J [joules]).  TNT stands for Trinitrotoluene (one of chemical compounds).    
 

       
   Here, the TNT equivalent is estimated by the following equation.

mb = A + B log Y
　　　Y：TNT Equivalent（kiloton）
　　　mb：Body wave magnitude (Body wave magnitude is the magnitude estimated from the amplitude 
                              value of body wave, which is one of seismic waves) 
　　　A and B are constants.   For A and B, this study refers to [A=4.45, B=0.75] of Ringdal. et al (1992).[34]

   A and B are the constants which can be various values, depending on the reference model.  Therefore, the output value of TNT Equivalent is essentially model-dependent estimate.  However, since this study only focuses on “relative difference” of explosion magnitudes among several nuclear tests, minor problems (such as the variance of constants A and B among the empirical models and the model dependency of a TNT Equivalent value) are assumed not to be problematic in this study.   Furthermore, the TNT Equivalent is generally to compute the value of explosion magnitude, although it does not consider chemical aspects of a nuclear explosion.


[The estimated values of magnitude for nuclear explosions]  

   Shown below are the estimated values of magnitude for nuclear explosions.    
In addition to the nuclear tests conducted in North Korea from 2006 to 2016, another artificial earthquake data of the 2017 event in North Korea (Magnitude 6.3, reported as a hydrogen bomb) is included in the analysis.   

  • North Korea,  Nuclear Test (2017/09/03),  mb=6.3,  TNT Equivalent = 292.9 kiloton

  • North Korea,  Nuclear Test (2016/09/09),  mb=5.3,  TNT Equivalent = 13.6 kiloton

  • North Korea,  Nuclear Test (2016/01/06),  mb=5.1,  TNT Equivalent = 7.4 kiloton

  • North Korea,  Nuclear Test (2013/02/12),  mb=5.1,  TNT Equivalent = 7.4 kiloton

  • North Korea,  Nuclear Test (2009/05/25),  mb=4.7,  TNT Equivalent = 2.2 kiloton

  • North Korea,  Nuclear Test (2006/10/09),  mb=4.3,  TNT Equivalent = 0.6 kiloton


   Figure 5~7 show the results.

fig5.jpg
fig6.jpg
fig7.jpg

Summary
   This study analyzed numerical data of nuclear explosions and natural earthquakes and discussed some of features.  For more detailed and comprehensive information, it is good to go through other information.



Acknowledgments　
   We are grateful for all the support we received.  Seismic data were distributed by the IRIS Data Center. 

 This study is based on open information. 

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AUTHOR

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SOJI SHIKA

Work history-words in HPC: Numerical data optimization, Numerical simulation, Parallel computing, Research activities in applied science field.

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BRIEF NOTES    

Analysis for Numerical Data of Nuclear Explosions, Soji Shika, November 3, 2021.

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**  This is not a peer-reviewed article.

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