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Sergey Kulichkov 1 , Konstantin Avilov 1 , Oleg Popov 1 ,

ON EXPERIENCE IN USING THE PSEUDODIFFERENTIAL PARABOLIC EQUATION METHOD TO STUDY THE PROBLEMS OF LONG-RANGE INFRASOUND PROPAGATION IN THE ATMOSPHERE. Sergey Kulichkov 1 , Konstantin Avilov 1 , Oleg Popov 1 , Vitaly Perepelkin 1 , Anatoly Baryshnikov 2

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Sergey Kulichkov 1 , Konstantin Avilov 1 , Oleg Popov 1 ,

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  1. ON EXPERIENCE IN USING THE PSEUDODIFFERENTIAL PARABOLIC EQUATION METHOD TO STUDY THE PROBLEMS OF LONG-RANGE INFRASOUND PROPAGATION IN THE ATMOSPHERE Sergey Kulichkov1, Konstantin Avilov1, Oleg Popov1, Vitaly Perepelkin1, Anatoly Baryshnikov2 1 Oboukhov Institute of Atmospheric Physics RAS, Pyzhevsky 3, Moscow,119017, Russia. 2 Federal State Unitary Enterprise “Research Institute of Pulse Technique” 9, Luganskaya St., Moscow, 115304, Russia. ______________________________________________________________________ SUPPORTED by ISTC, Project 1341 and RFBR, Project 02-05-65112

  2. OUTLINE • INTRODUCTION • METHODS TO STUDY LONG-RANGE SOUND PROPAGARION IN THE ATMOSPHERE • BASIC EQUATIONS • RESULTS • CONCLUSION

  3. INTRODUCTION • Infrasonic signals from explosions at the long distances have an inhomogeneous structure formed due to the properties of the profile of the effective sound velocity (adiabatic sound velocity plus wind velocity in the direction of sound wave propagation). • The mean profile of the effective sound velocity determines the refraction of sound rays and forms the zone of audibility and geometric shadow, on the earth surface. • A fine structure of the sound velocity profiles provide an “illumination” of the geometric-shadow zones and result in significant changes in the structure of the signals recorded in the audibility zone. • Different methods are used to explain features of the infrasonic signals at the long distances from explosions (amplitude; duration; different phases; etc.)

  4. METHODS TO STUDY LONG-RANGE SOUNDPROPAGARION IN THE ATMOSPHERE • RAY THEORY (basic properties of formation of infrasonic signals: different phases - tropospheric, stratospheric, mesospheric, or thermospheric; propagation speed, and maximum amplitude within the refractive audibility zone) • PARABOLIC CODE (Tappert 1970;Gilbert, White, 1989; Lingevitch, Collins and Westnood 1991; Ostashev 1997; Collins, and Siegmann 1999; Collins et. al.,2002; Avilov 1985 -2003) • NORMAL MODE CODE (Pierce, Posey and Kinney 1976) • OTHER METHODS (ReVelle 1998; Talmage and Gilbert 2000; etc.)

  5. BASIC EQUATIONS (1) p – acoustic pressure; k=2 / ;  - wave length (2) (3) T - cross differential operator

  6. BASIC EQUATIONS (4) (5) (6) (7) (8)

  7. RESULTS(infrasonic field from air explosion)

  8. Comparison PE vs. experiment (signal shape)

  9. FAST INFRASONIC ARRIVALS Profiles of the effective sound velocity and ray tracings. Samples of the infrasonic arrivals at the distance about 635 km from surface explosions with yields of 500 t (June27,1985-a;June26,1987-b)

  10. PE code vs experiment (signal shape)

  11. ON USING OF NORMAL MODE CODE TO FORECAST INFRASONIC SIGNALS AT THE LONG DISTANCES FROM SURFACE EXPLOSIONS Sergey Kulichkov1, Konstantin Avilov1, Oleg Popov1, Vitaly Perepelkin1, Anatoly Baryshnikov2 1 Oboukhov Institute of Atmospheric Physics RAS, Pyzhevsky 3, Moscow,119017, Russia. 2 Federal State Unitary Enterprise “Research Institute of Pulse Technique” 9, Luganskaya St., Moscow, 115304, Russia. ______________________________________________________________________ SUPPORTED by ISTC, Project 1341 and RFBR, Project 02-05-65112

  12. BASIC EQUATIONS By using of р = рr(r)p(z) one can obtain (1) (2) n2(z) –acoustic refractive index,  = ksin, /2 - ;  - grazing angle. (3)

  13. BASIC EQUATIONS V1 – coefficient of sound reflection from level z=0, V11. V() – coefficient of sound reflection fromhalf-space z0. (4) where (5) p0 p(r = r0);f(t)= (6) -- profile of the initial pulse.

  14. MODEL Piece-wise linear profile of the acoustic refractive index (7)

  15. RESULTS (8) u(t) ; v(t) – Airy functions ti = -(k/qi)2/3[cos2 +ql(z-hl)]. (9)

  16. RESULTS(high frequency approximation of Airy functions) u(t);v(t)~ wi-1/6[A + B awi-1 + o(wi-1)]; (10) where A(B) = sin(wi + /4) or cos(wi + /4);a= 5/72 , or a = 7/72.

  17. COMPARISON NM code vs experiment (signal shape – p(t))

  18. COMPARISON NM code vs experiment (signal shape – p(t))

  19. COMPARISON NM code vs experiment (signal shape – p(t))

  20. COMPARISON NM code vs experiment (the amplitude squared – p2(t))

  21. CONCLUSION • Parabolic equation code and Normal mode code produce good results by forecasting different features of the infrasonic signals at the long distances from explosions both in the zones of audibility and shadow (amplitude; duration; different phases; etc.) • The propagation velocity and spatial variations of ray azimuths not forecasted correctly by using of Parabolic equation code and Normal mode code. ( ceff (z) = c (z) + v(z)cos (D(z) – 1800 -  ); D(z) – wind direction;  - azimuth of the receivers (from the North))

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