1. Supported by RFBR, project No. 08-05-00445
Effects of atmospheric turbulence on azimuths and grazing angles estimation at the long distances from explosions
Sergey Kulichkov
Igor Chunchuzov
Gregory Bush
Vladimir Asming
Elena Kremenetskaya
Anatoly Barishnokov
Yurii Vinogradov
Supported by RFBR, project No

2. ___________________________________________________________
OUTLINE
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 INTRODUCTION
 EXPERIMENTAL RESULTS
 THEORY
 high – frequency approximation of normal-mode code
(fine-layered structure of the atmosphere
 theory of anisotropic turbulence
 CONCLUSIONS

3. INTRODUCTION phase velocity Cphase = C0 / cos 0 ; 0 – grazing angle
Cphase = C0 / cos 0  C0 (sound velocity at the
earth surface)
sufficient variations of azimuths of infrasonic
arrivals and grazing angles are observed in
the experiments
effects of fine atmospheric structure
theory of anisotropic turbulence; normal
mode code

4. (tropospheric arrivals)
EXPERIMENTAL RESULTS
(tropospheric arrivals)

5. Finnish military explosions (31) during August 16 – September16, 2007
Finnish military explosions (31) during August 16 – September16, R=303 km. ‏

6. Signals spectrum

7. Effective sound velocity 18.08.2007 (rocket data)

8. Acoustic field calculated by TDPE code

9. Infrasonic signals (theory- TDPE code; experiment)

10. TROPOSPHERIC ARRIVALS (azimutes and trace velocity)

11. Corr>0.8

12. Corr>0.9

13. STRATOSPHERIC ARRIVALS (azimutes and trace velocity)

14. (stratospheric arrivals)
EXPERIMENTAL RESULTS
(stratospheric arrivals)

15. EXPERIMENTAL RESULTS

16. AZIMUTHS

17. TRACE VELOCITY

18. Averaged azimuths of stratospheric arrivals (33 explosions, different time)

19. normal mode code high-frequency approximation
THEORY
normal mode code high-frequency approximation
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coefficient of reflection
V = exp i{2 (z = h )+ /2 +  (h)}  exp {i};
phase of the coefficient of reflection
 (z = h) =
kcos (z) dz =
(wl - wl-1) = k f;
phase shift due to fine atmospheric structure
 =
(-1)l { 1/(6wl) cos(2kl) (ql - ql+1)/ql+1 } ;
l =
( cos3 s +1- cos3 s )/qs+1;
 =900 – 0 ; ql  n2(z)/z ;
wi  (2/3) t 3/2 = cos3( i ) >1
(high- frequency approximation)

20. THEORY С phase = (Co / cos 0 ) =
normal mode code high-frequency approximation
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С phase = (Co / cos 0 ) =
(Co / cos o)[1+r (/ sin2) /( k  r/ sin2 ) ]
The value of phase velocity depends from the value of additional parameter
r (/ sin2) / ( k   r/ sin2 )
It`s possible that
С phase = (Сo / cos 0 ) < Co

21. normal mode code high-frequency approximation
THEORY
normal mode code high-frequency approximation
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22. THEORY anisotropic turbulence
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tg= x1 t2/(y2t1)–x2/y2; (0,0), (x1,0) and (x2,y2) – positions of different microphones 1, 2 and 3
t1= t2–t1 и t2= t3–t1
The errors of azimuths calculation depends from the fluctuations of t2 and t1 ,
t2=t2 -<t2 >= (t3–t1) – (<t3 > - <t1 >)  3–1
 (tg)/ <tg>=t2/<t2 >+t1/<t1> 2 t2/<t2 >
{< [ (tg)]2>)/(<tg>)2 }1/22 [<(t2) 2>/<t2 >2]1/2
for tg  
[<( )2>]1/2/<> 2 [<(t2) 2>]1/2/ <t2 >
[<(t2) 2>]= < (3–1) 2>= D(z0=0, y0, T=0)

23. THEORY anisotropic turbulence [<( )2>]S1/2  8 0 Stratosphere
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Stratosphere
m* = N/(21/2) = 0.02 rad/s/ (21/2 5 m/s) = rad/m
L = 2/ m* ~ 1800 m – external scale;
N – Brent-Vaisala frequency
e0 = 0.026
e0m*2ym2<<1)
D(0, y0) 6<12> (e0 m*2ym2)
 = <vх2>)1/2 = 5m/s
< 2>s = [sec2] (  0.1).
D(0, y0)  6<12> (e0 m*2ym2)  3.3510 -3 s2
(D)s1/2  s
<t2 > ~ 0.9 s
[<(t2)2>]1/2/<t2>= 0.06
[<( )2>]S1/2  8 0

24. THEORY anisotropic turbulence
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cos()={(c0t1/x1)2+[c0t2/y2- (c0t1x2)/(y2 x1)] 2]} 1/2
t22<<t12
cos()  c0t1/x1, sin()    [1-(c0t1/x1)2] 1/2.
  (c0/x1)2 t1 t1/[1- (c0t1/x1)2] 1/2  (c0/x1) t1/sin(),
(<2>)1/2 (c0/x1) (<t12>)1/2/<sin()>
[<(t2) 2>]= D(0, y0) 3.3510-3 s2
R= 300 km
(<2>)1/2(c0/x1)(<t12>)1/2/<sin()> =
(2.27) (0.057)/(0.57) ~ 0.227
 = 350
S ~ 130

25. EXPERIMENT
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26. due to effects of anisotropic turbulence
CONCLUSIONS
The effect of the atmospheric fine structure on the azimuth and grazing angle of
infrasonic signals recorded at long distances from surface explosions is studied
both theoretically and experimentally.
The data on infrasonic signals corresponded to tropospheric and stratospheric
infrasound propagation from explosions are analyzed.
The experiments were carried out during different seasons.
Variations in the azimuths and grazing angles of infrasonic signals are revealed for
both the experiments carried out within one series and carried out during different
seasons.
It is shown that, due to the presence of atmospheric fine-layered inhomogeneities,
fluctuations in the phase of infrasonic waves mainly affect the errors in
determining the azimuths and grazing angles of infrasonic signals.
 ~ 50 ;  ~ 100
due to effects of anisotropic turbulence

27. THANK YOU
FOR ATTENTION