ON EXPERIENCE IN USING THE ON EXPERIENCE IN USING THE PSEUDODIFFERENTIAL PARABOLIC EQUATION PSEUDODIFFERENTIAL PARABOLIC EQUATION

METHOD METHOD TO STUDY THE PROBLEMS OF TO STUDY THE PROBLEMS OF

LONG-RANGE INFRASOUND PROPAGATION LONG-RANGE INFRASOUND PROPAGATION IN THE ATMOSPHEREIN THE ATMOSPHERE

Sergey KulichkovSergey Kulichkov11, Konstantin Avilov, Konstantin Avilov11, Oleg Popov, Oleg Popov11, , Vitaly PerepelkinVitaly Perepelkin11, Anatoly Baryshnikov, Anatoly Baryshnikov22

11 Oboukhov Institute of Atmospheric Physics RAS, Oboukhov Institute of Atmospheric Physics RAS, Pyzhevsky 3, Moscow,119017, Russia. Pyzhevsky 3, Moscow,119017, Russia.

2 2 Federal State Unitary Enterprise “Research Institute of Pulse Technique”Federal State Unitary Enterprise “Research Institute of Pulse Technique” 9, Luganskaya St.9, Luganskaya St., Moscow, , Moscow, 115304115304, Russia., Russia.____________________________________________________________________________________________________________________________________________SUPPORTED by ISTC, Project 1341 and RFBR, Project 02-05-65112SUPPORTED by ISTC, Project 1341 and RFBR, Project 02-05-65112

OUTLINEOUTLINE

• INTRODUCTIONINTRODUCTION

• METHODS TO STUDY LONG-RANGE METHODS TO STUDY LONG-RANGE SOUND PROPAGARION IN THE SOUND PROPAGARION IN THE ATMOSPHERE ATMOSPHERE

• BASIC EQUATIONSBASIC EQUATIONS

• RESULTSRESULTS

• CONCLUSIONCONCLUSION

INTRODUCTIONINTRODUCTION• Infrasonic signals from explosions at the long distances have Infrasonic signals from explosions at the long distances have

an inhomogeneous structure formed due to the properties of an inhomogeneous structure formed due to the properties of the profile of the effective sound velocity (adiabatic sound the profile of the effective sound velocity (adiabatic sound velocity plus wind velocity in the direction of sound wave velocity plus wind velocity in the direction of sound wave propagation). propagation).

• The mean profile of the effective sound velocity determines The mean profile of the effective sound velocity determines the refraction of sound rays and forms the zone of audibility the refraction of sound rays and forms the zone of audibility and geometric shadow, on the earth surface. and geometric shadow, on the earth surface.

• A fine structure of the sound velocity profiles provide an A fine structure of the sound velocity profiles provide an “illumination” of the geometric-shadow zones and result in “illumination” of the geometric-shadow zones and result in significant changes in the structure of the signals recorded in significant changes in the structure of the signals recorded in the audibility zone.the audibility zone.

• Different methods are used to explain features of the Different methods are used to explain features of the infrasonic signals at the long distances from explosions infrasonic signals at the long distances from explosions (amplitude; duration; different phases; etc.) (amplitude; duration; different phases; etc.)

METHODS TO STUDY LONG-RANGE SOUNDPROPAGARION IN THE ATMOSPHERE

• RAY THEORYRAY THEORY (basic properties of formation of infrasonic (basic properties of formation of infrasonic signals: different phases - tropospheric, stratospheric, signals: different phases - tropospheric, stratospheric, mesospheric, or thermospheric; propagation speed, and mesospheric, or thermospheric; propagation speed, and maximum amplitude within the refractive audibility zone) maximum amplitude within the refractive audibility zone)

• PARABOLIC CODEPARABOLIC CODE (Tappert 1970;Gilbert, White, 1989; (Tappert 1970;Gilbert, White, 1989; Lingevitch, Collins and Westnood 1991; Ostashev 1997; Lingevitch, Collins and Westnood 1991; Ostashev 1997; Collins, and Siegmann 1999; Collins et. al.,2002; Avilov 1985 Collins, and Siegmann 1999; Collins et. al.,2002; Avilov 1985 -2003)-2003)

• NORMAL MODE CODENORMAL MODE CODE (Pierce, Posey and Kinney 1976) (Pierce, Posey and Kinney 1976)

• OTHER METHODSOTHER METHODS (ReVelle 1998; Talmage and Gilbert (ReVelle 1998; Talmage and Gilbert 2000; etc.)2000; etc.)

BASIC EQUATIONSBASIC EQUATIONS

s2

2

2zz

rr2zrpzk

zrzrpr

rr1

),( )(, (1)

p – acoustic pressure; k=2 / ; - wave length

szzrTizrp (0)1

H),( (2)

)(zkz

T 22

2

(3)

T - cross differential operator

BASIC EQUATIONSBASIC EQUATIONS

(4)

(6)

(8)

rTirTi

2rT expH(0)1

zrpzkz

ir

zrp 22

2,)(,

szzTi

2z0p

,

)(

)(exp

hT

hTПTih

l

lL

1

),)(exp, zrpzkz

ihzhrp 22

2

(5)

(7)

RESULTSRESULTS(infrasonic field from air explosion)(infrasonic field from air explosion)

Comparison PE vs. experiment (signal shape)Comparison PE vs. experiment (signal shape)

FAST INFRASONIC ARRIVALSFAST INFRASONIC ARRIVALS

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

PE code vs experiment (signal shape)PE code vs experiment (signal shape)

ON USING OF NORMAL MODE CODE TO ON USING OF NORMAL MODE CODE TO FORECAST INFRASONIC SIGNALS FORECAST INFRASONIC SIGNALS

AT THE LONG DISTANCES AT THE LONG DISTANCES FROM SURFACE EXPLOSIONSFROM SURFACE EXPLOSIONS

Sergey KulichkovSergey Kulichkov11, Konstantin Avilov, Konstantin Avilov11, Oleg Popov, Oleg Popov11, , Vitaly PerepelkinVitaly Perepelkin11, Anatoly Baryshnikov, Anatoly Baryshnikov22

11 Oboukhov Institute of Atmospheric Physics RAS, Oboukhov Institute of Atmospheric Physics RAS, Pyzhevsky 3, Moscow,119017, Russia. Pyzhevsky 3, Moscow,119017, Russia.

2 2 Federal State Unitary Enterprise “Research Institute of Pulse Technique”Federal State Unitary Enterprise “Research Institute of Pulse Technique” 9, Luganskaya St.9, Luganskaya St., Moscow, , Moscow, 115304115304, Russia., Russia.____________________________________________________________________________________________________________________________________________

SUPPORTED by ISTC, Project 1341 and RFBR, Project 02-05-65112SUPPORTED by ISTC, Project 1341 and RFBR, Project 02-05-65112

BASIC EQUATIONSBASIC EQUATIONS

By using of By using of р = рр = рrr((rr))pp((zz) ) one can obtainone can obtain

0 1 2 rprrpr

rr rr

0 )( 2222

2

zpznkzpz

nn22 ((zz)) – – acoustic refractive indexacoustic refractive index, , = = kk sinsin , , /2 - /2 - ; ; - grazing angle.- grazing angle.

00 zzp

(1)(1)

(2)(2)

((33))

BASIC EQUATIONSBASIC EQUATIONS

V1 – coefficient of sound reflection from level z=0, V1 1. V() – coefficient of sound reflection from half-space z0.

(4)

where (5)

p0 p( r = r0); f(t)= (6)

-- profile of the initial pulse.

dkrHeVeVVVikkzrp zikzik sinsin

11

2,, 1

0coscos

1

1

0/0

zzp

dkkcgkrHeVkriptrp nn

otikc

n

n n0

)1(

0 0'00 sinsin2Re, 0

1nV

dge ti1

MODELMODELPiece-wise linear profile of the acoustic refractive index

z h),h-(zq)h-(hq1

..........................

hz h),h-(zq)h-(hq1

..........................hz h),h-(zqhq1

hz 0z,q1

(z)n

m

m

1lii1-lll

1ii

i

1lii1-lll

211201

11

2(7)

RESULTSRESULTS

z h)(t vB..........................

hz h)(t vB)(t u A..........................

hz h)(t vB)(t u Ahz 0)(t vB)(t u A

0zcosθ ikz -exp V(θ(cosθ z ikexp

θ)p(z,

mmm

1iiiiii

212222

11111

(8)

u(t) ; v(t) – Airy functions

ti = -(k/qi)2/3[cos2 +ql(z-hl)]. (9)

RESULTSRESULTS(high frequency approximation of Airy functions)

u(t);v(t) ~ wi-1/6 [A + B a wi

-1 + o(wi-1)]; (10)

where

i

1lll

2i

2i

3

i323/2

32

i )h-(zq θcosθcos , 1 ) (θcos qkt w

A(B) = sin(wi + /4) or cos(wi + /4); a = 5/72 , or a = 7/72.

R E S U L T SV = e x p i { 2 ( z = h ) + / 2 + ( h ) } e x p { i } ; ( t o t a l R e f l e c t i o n ) ( 1 1 )

( z = h ) = )( h

0k c o s ( z ) d z =

m

1l( w l - w l - 1 ) = k f

m

1i 131

1i1

ii3 qqq32f }/cos)({cos)/( ( 1 2 )

=

m

0l( - 1 ) l { 1 / ( 6 w l ) c o s ( 2 k

l ) ( q l - q l + 1 ) / q l + 1 } ( 1 3 )

l =

32

1l

0s( c o s 3 s + 1 - c o s 3 s ) / q s + 1 ; ( 1 4 )

θ22n sin)]( h[ ( 1 5 )

ii

1iie

w121

w121V

)(

( p a r t i a l r e f l e c t i o n f r o m l a y e r i ) ( 1 6 )

COMPARISON NM code vs experiment (signal shape – COMPARISON NM code vs experiment (signal shape – pp((tt))))

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

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

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

• 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))

CONCLUSIONCONCLUSION