OCAFig. 1. (a) An eruption of Mount Pinatubo (Courtesy of Dr. J. Mori). (b) Dispersion relation of acoustic-gravity waves in an isothermal atmosphere (modi!ed from Gill (1982)). The

!!"#$%&&'()#*+,%'-./01234#5#6"#!%7(%((,#*86+60694#

!"#$%&'()*+,-$)#./,#$0(%,$1,"'(,2.)"',!

"#$%&'!()*!%+,$&-(.%),!

JOVIAL Kick-Off meeting– April 19, 2016

2 JOVIAL Kick-Off meeting– April 19, 2016

"/0!*(1(!231$&$*!4&%5!6!1%!67!589!

:;!

<%=)!

7

$%&&'()#:;#'&"#*<=>>4#

>%&5(3!5%*$,!$?@A1$*!+'!(!-$&'!3(&B$!$(&1#CD(E$!F!G+,$&-(.%),!!

H"%#%ED!I766J!K=LMNIO!

JOVIAL Kick-Off meeting– April 19, 2016JOVIAL Kick-Off meeting– April 19, 2016

•! 0%5;D1$!1#$!5%*$,!%4!(!4D33!/(&1#!5%*$3!!F!P)1$&A%&J!A)@3D*A)B!5()13$!()*!@%&$!!F!G@$()!!F!Q15%,;#$&$!()*!P%)%,;#$&$!

•! 0%5;D1$!=(-$,!+'!@%5;D.)B!1#$!$?@A1(.%)!%4!1#$,$!5%*$,!()*!,D55A)B!1#$!5%*$,!

•! 0%5;(&$!1%!%+,$&-(.%),!

3$/*0,2.)"',4,-(5")./,."#$%&'()(,+$5&/*-67,,-$)#./,#$0(%,#$0(/*-6,


Q)$3(,.@A1'!$CD(.%)!

•! 0%5;D1$!1#$!5%*$,!%4!(!4D33!/(&1#!5%*$3!!F!P)1$&A%&J!A)@3D*A)B!5()13$!()*!@%&$!!F!G@$()!!F!Q15%,;#$&$!()*!P%)%,;#$&$!

•! 0%5;D1$!=(-$,!+'!@%5;D.)B!1#$!$?@A1(.%)!%4!1#$,$!5%*$,!()*!,D55A)B!1#$!5%*$,!

•! 0%5;(&$!1%!%+,$&-(.%),!

!R;#$&A@(3!,'55$1&'!

R%3A*!/(&1#!8,."#$%&'()(!!

6<!/(&1#!5%*$3!

Q)$3(,.@A1'!$CD(.%)!

ST/K!U!Q-$&(B$!,$A,5A@!5%*$3!%4!1#$!,%3A*!/(&1#!H*$),A1'J!V;!JV,O!

!

3$/*0,2.)"',4,-(5")./,."#$%&'()(,+$5&/*-67,,-$)#./,#$0(%,#$0(/*-6,



R%3A*!5%*$,!

Q15%,;#$&A@!5%*$,!

T('3$AB#!

*!%7(%((,#5#2&,?,),@>AAB4#W!).0*.9:(,+$-0*9$-!

!:*%+$%*";,

*3/;/.#5#!%7(%((,@#<==>4#

"#$!>%&5(3!5%*$,!(&$!$AB$)F,%3D.%),!!F!%4!1#$!$3(,1%*')(5A@!=(-$!$CD(.%)!

$-$&'=#$&$!F!-$&A4'A)B!(33!+%D)*(&'!@%)*A.%),!(1!

*A,@%).)DA.$,!!

!

"2! u =! A (! u )

3$/*0,2.)"',4,-(5")./,."#$%&'()(,+$5&/*-67,,-$)#./,#$0(%,#$0(/*-6,


Q3.1D*$!HE5O!

Frequency (mHz)<%5-.#*%, =.;/(*6',>.:(%,

Q@%D,.@!@D1F%X!!4&$CD$)@'!

Y&D)1FV(A,(3(!4&$CD$)@'!

R%3A*!5%*$,!

Q15%,;#$&A@!5%*$,!

T('3$AB#!

*!%7(%((,#5#2&,?,),@>AAB4#W!).0*.9:(,+$-0*9$-!

!:*%+$%*";,

*3/;/.#5#!%7(%((,@#<==>4#

"#$!>%&5(3!5%*$,!(&$!$AB$)F,%3D.%),!!F!%4!1#$!$3(,1%*')(5A@!=(-$!$CD(.%)!

$-$&'=#$&$!F!-$&A4'A)B!(33!+%D)*(&'!@%)*A.%),!(1!

*A,@%).)DA.$,!!

!

"2! u =! A (! u )

3$/*0,2.)"',4,-(5")./,."#$%&'()(,+$5&/*-67,,-$)#./,#$0(%,#$0(/*-6,

Frequency mHz0 1 2 3 4 5 6 7 8 9 10

Ener

gy fr

actio

n in

atm

osph

ere

10-7

10-6

10-5

10-4

10-3

10-2 Rayleigh modes coupling with atmosphere: Chelyabinsk continental model

Rayleigh fundamental1st overtone

=.;/(*6',>.:(%,

0 1 2 3 4 5 6 7 8 9 10

Ener

gy fr

actio

n in

atm

osph

ere

10-7

10-6

10-5

10-4

10-3

10-2

100 101 102

100

101

Angular order l

Freq

uenc

y (m

Hz)

(0)

(1)

(2)

(2)

(1)

(0)

(0)

(1)

(2)


=.;/(*6',>.:(%,,1$)+(0,?;,"'(,@AA@,B*-."5?$,(C&/$%*$-!

JOVIAL Kick-Off meeting– April 19, 2016!%7(%((,#:;#'&"@#C(#/:?CDC%(#

(0) (1) (2)

2 H. Kanamori / Fluid Dynamics Research 34 (2004) 1 { 19

2. Excitation of atmospheric waves by volcanic eruptions

The thermal energy emitted by a volcanic eruption excites atmospheric waves and oscillations(Fig. 1). A comprehensive review on this subject is found in Blanc (1985). The most notable isthe air wave excited by the 1883 Krakatoa eruption in Indonesia (Harkrider and Press, 1967), andthe most recent is that excited by the 1991 Pinatubo eruption in the Philippines. In general, threetypes of waves can be excited as illustrated by Fig. 1b which shows the dispersion relation foracoustic-gravity waves for an isothermal atmosphere on the frequency-wave number space (e.g.,Gill, 1982; Hines, 1960). We summarize the basic concept in the following, taken mainly fromHoughton (1986).

2.1. Basic equations and dispersion relation

We take a Cartesian co-ordinate system (x; y; z), with the z-axis taken upward vertical in anisothermal atmosphere, and write the x, y, and z components of the velocity !eld measured fromthe stationary state by u, v, and w, respectively. The pressure and density are written as p+p0, and!+ !0 where p0 and !0 represent the background states and p and !, the perturbations from them.Then the equations of state and hydrostatic equilibrium are given by

p0 = !0RT0;@p0@z

=−g!0; (1)

Fig. 1. (a) An eruption of Mount Pinatubo (Courtesy of Dr. J. Mori). (b) Dispersion relation of acoustic-gravity wavesin an isothermal atmosphere (modi!ed from Gill (1982)). The vertical axis is the angular frequency, !, and k and m arethe horizontal and vertical wave numbers, respectively, and H is the vertical scale height. (c) Schematic diagram showingthe excitation mechanism of atmospheric oscillations by a volcanic eruption. The eruption can be modeled as injectionof mass, "!, injection of energy, "e, and perturbation of pressure "p. The thermal energy emitted by an eruption excitesacoustic and gravity modes of atmospheric oscillations. The energy of the atmospheric acoustic mode is coupled to theground and excites seismic Rayleigh waves.

D$)(,=.;/(*6',>.:(%,*-,."#$%&'()(,


EF:;GHI#1GGHCJC(K#:;#'&"#*<=>=4#

10 JOVIAL Kick-Off meeting– April 19, 2016

>%&5(3!5%*$,!$?@A1$*!+'!(!-$&'!3(&B$!$(&1#CD(E$!F!G+,$&-(.%),!!

H"%#%ED!I766J!K=LMNIO!

"/0!*(1(!231$&$*!4&%5!6!1%!67!589!

:;!

<%=)!

7

>%&5(3!5%*$,!

$%&&'()#:;#'&"#*<=>>4#

D5/9E#$0(,%*6-./,F,+/.%%*G+.9$-,$1,<HI%,

Z%&@A)B!,%D&@$!T('3$AB#!=(-$,!R$A,5A@!&D;1D&$!",D)(5A!

!!

@,J#4%,KLM,J#4%,

@N@,#4%,OOM,#4%,

!+$5%9+,,>.:(%,

P).:*";,>.:(%,

$%&&'()#:;#'&"@#<=>>L#

KLM,J#4%,

[GVPQ\!]A@EFGX!5$$.)B^!Q;&A3!6MJ!I76_!

D5/9E#$0(,%*6-./,F,+/.%%*G+.9$-,$1,<HI%,

@,J#4%,KLM,J#4%,

@N@,#4%,OOM,#4%,

!+$5%9+,,>.:(%,

P).:*";,>.:(%,

$%&&'()#:;#'&"@#<=>>L#

KLM,J#4%,

[GVPQ\!]A@EFGX!5$$.)B^!Q;&A3!6MJ!I76_!M:)&C(#5#N'&F:/#*<=><4#

Q!4D33!5%*$3!4%&!`SR!*$&A-$*!A%)%,;#$&A@!;$&1D&+(.%)!A)*D@$*!+'!()!$(&1#CD(E$U!T('3$AB#!=(-$,!4%&@A)B!

© L

ogno

nné

and

Clév

édé

(200

2)

3$/*0,K%*$,!F!!"#$%&'()*+,

Q?%():.9$-%,D$0(/,

a<!5%*$3!%4!)$D1&(3!-$3%@A1'!H-&O!M77,!(b$&!1#$!"%E(@#AFGEA!$(&1#CD(E$!I77aJ!K=cNaO!!

a<!5%*$3!%4!;$&1D&+$*!A%)%,;#$&A@!*$),A1'!H*>$O!

13

T('3$AB#!6<!R%3A*!K%*$,!,D55(.%)!

K8<!@%D;3A)B!

P)1$B&(.%)!!`SR!,(1$33A1$F,1(.%)!

P)1$B&(.%)!!`SR!,(1$33A1$F,1(.%)!

T%33()*!$1!(3NJ!I766(!


!+$5%9+,#$0(%,

<%5-.#*E*-05+(0,."#$%&'()*+,>.:(%,#$0(/*-6,

© L

ogno

nné

and

Clév

édé

(200

2)

2%ODD%(#:;#'&"#*<=>P4#


8(A*(!`=(AA!1,D)(5A!

`&(=$!d!K(E$3(!HI76eO!

T%33()*!$1!(3NJ!I76f!

I76Ig67gIcJ!K=!hNc!

H7aU7f!:"O!

D$-*"$)*-6,"'(,*$-$%&'()(,1)$#,,%&.+(,

`SR!

`SR!

P%)%,;#$&A@!!"%5%B&(;#'!

P)FRA1D!,(1$33A1$!

<%;;3$&!R%D)*$&!

G@@D31(.%)!

:V!

QA&B3%=!

\/G!

`SR!

0%D&1$,'!%4!SN!\%B)%))i! JOVIAL Kick-Off meeting– April 19, 2016

3$/.),.-0,R$:*.-,3(*%#$/$6;,


E%./G:I#N"#!:CL'GH:/#

!%7(%((,#:;#'&"#*>AAQ4#

S%*-6,2.)"',T$)#./,#$0(,%$U>.)(,1$),R5&*"(),

•! /(&1#!)%&5(3!5%*$,!,%b=(&$!@()!+$!D,$*!1%!@%5;D1$!+%1#!(@%D,.@!()*!B&(-A1'![%-A()!>%&5(3!5%*$,J!A)@3D*A)B!1#%,$!=$(E3'!%&!)%1!1&(;;$*!+'!1#$!1&%;%,;#$&$!

•! R$$!!%7(%((,#5#R%H(D%(@#<=>S#4%&!$?(5;3$!

0 50 100 150 200 250 3001

1.5

2

2.5

3

Log Q

3.5

4

Angular order

Freq

uenc

y

1

1.5

2

2.5

3

3.5

4

4.5

5

! "! #! $! %! &!!

#!

%!

'!

(!

)*+,-./*0123+*/.40567-

8)9/,-

0:6

!0 "! #! $!!

#!

%!

'!

(!

92;-/.40<7*6$

8)9/,-

0:6

" # $−%!!

−$!!

−#!!

−"!!

!

"!!

#!!

)*+,-./*0123+*/.4

)3./.,9

20=56>

!?!!!" !?!" "?−%!!

−$!!

−#!!

−"!!

!

"!!

#!!

@2;-/.405<76$

)3./.,9

20=56>

! " # $ % &−%!!

−$!!

−#!!

−"!!

!

"!!

#!!

A,.+BB0B82C,2;*40=06DE>

)3./.,9

20=56>

!%7(%((,#5#R%H(D%(#*<=>P4# R$A,5A@!;&%;$&.$,!%4![D;A1$&!4%&!*AX$&$)1!5%*$3,!!HT%DD:/#>AAUO!

B$%%*?/(,+$-%").*-"%,$-,"'(,(C+*".9$-,0(&"',

•! Z&%5!1#$!/@#$3%)!4&$CD$)@'!;&%;%,$*!+'!+'.&V:#:;#'&"@#<=>>J!=$!@()!1#$)!,DBB$,1!1#()!1#$!$?@A1(.%)!A,!;&$4$&$).(33'!1#%,$!%4!#(&5%)A@,!)L_FcJ!,%!3AE$3'!(1!*$;1#!%4!677!+(&,!

! !"# $ $"# % %"# & &"# '$$!

$%!

$&!

$'!

$#!

$(!

$)!

$*!

$+!

%!!

%$!

,-./0.1234567

8.9:;4,-./0

.12345<2-=−6

7

>2?.9=14@-./0.1234A4ν1B$−ν1C4D.-E0E4@-./0.1234A4ν1C

FGE.-D;:<=1EHI$HI%HI&

−!"# −! −$"# $ $"# ! !"#%&!$#

!$−'

!$$

!$'

!$(

!$)

!$*

+,-./0&1%,23-3245&-67.2380/

9:/;

;8:/

<&=-:

>?@>?(>?#>?)>?A>?*>?B>?!$>?!!

!%7(%((,#5#R%H(D%(#*<=>P4#

•! >QRQ!8R"J!jZ0!A)!%;.@(3!5%*$!•! [D3'!IIJ!6MMf!R#%$5(E$&F\$-'!M!

A5;(@1!•! kD(E$!$CDA-(3$)1!5(B)A1D*$!KLM!•! V$&.@(3!*A,;3(@$5$)1!6775!+D1!=A1#!

@3%D*,F(3+$*%!5%*A2@(.%)!•! >%!,$A,5A@!=(-$,!%+,$&-$*!%)!B&%D)*!

()*!,;(@$!%+,$&-(.%),!•! `&(-A1'!=(-$,!%+,$&-$*!

3'$#.J()EV(:;,A,*#&.+",

130,000 km H. Hammel et al, MIT


T$)#./,#$0(%,W#$0(/*-6X,LLL,

•! Y%1#!B&(-A1'!5%*$,!()*!(@%D,.@!5%*$,!


!%7(%((,#:;#'&"#*>AAQ4#

!P5;(@1!%4!1#$!R#%$5(E$&!\$-'FMU !!!`&(-A1'!=(-$,!*$1$@1$*!+'!8R"!

`&(-A1'!=(-$,!

Slow wave front

8%*%@#&%)$,!(&$!,.33!1%%!4(,1!4%&!1#$!;&$,$)1!5%*$3,!%4![D;A1$&!

M'VV:&#:;#'&"@#>AAP#

Fast wave front

P).:*";,>.:(%,%(-%*-6,$-,R5&*"(),


H. Kanamori / Fluid Dynamics Research 34 (2004) 1 { 19 9

Fig. 5. Left: Hubble Space Telescope image of the impact site of the G fragment of the Shoemaker-Levy 9 comet. Theimage was taken at 109 min after the impact. The radius of the prominent dark ring is 3700 km (from the cover pageof Nature, 374, No. 6524, 1995). Right: Synthetic ring pattern computed for the 10 × solar case. Note the approximateagreement of the positions of the outer and inner rings between the observed and synthetic patterns.

Fig. 6. Time{di stance curve for the circular rings shown in Fig. 5. The shape of the symbols identi!es the fragments A,E, G, Q1, and R. \ Acoustic" refers to the speed of sound at the temperature minimum in Jupiter' s atmosphere. \ solar"and \ 10×solar" refer to the speed of a gravity wave in the water cloud with solar and 10×solar abundance of water. Thedata points around the line with v= 210 m=s are for the inner rings. Redrawn from Hammel et al. (1995), and Ingersolland Kanamori (1995b).

W'('V%/C#*<==Q4#

JOVIAL Kick-Off meeting– April 19, 2016JOVIAL Kick-Off meeting– April 19, 2016

<'.-J,;$5,Y,

H. Kanamori / Fluid Dynamics Research 34 (2004) 1–19 11

Fig. 7. Left: Temperature pro!les for the no-water (adiabatic), solar, 5 × solar (not labeled), and 10 × solar cases usedby Ingersoll and Kanamori (1995a). Right: The pro!les of the Brunt-V"ais"al"a frequency corresponding to the temperaturepro!les shown on the left.

leads to

@@t

!"

@2!@t2

+ f2!#

ddp

"

1"d#dp

#

+1r@@r

"

r@!@r

#

#$

=−"

@2$(t)@t2

+ f2$(t)#

ddp

"

%&(p)"p

#

$(r): (34)

Then, the vertical normal mode #(p) satis!es

ddp

"

1"d#dp

#

=− 1c2#(p); (35)

where c2 is the separation constant (unit of velocity).Let ci and #i(p) be the ith eigen-value and eigen-function and we expand the heating source,

using #i(p), as

ddp

"

%&(p)"p

#

=∞%

i=0

ai#i(p); (36)

where

ai =

& ddp(

%&(p)"p )#i(p) dp

&

#2i (p) dp: (37)

Kanamori (2004)

Z.)*.?*/*";,$1,"'(,2.)"'[%,."#$%&'()(,

Seasonal Local time Solar flux Latitude

R%D)*!,;$$*!H5g,O!

3;V%DJH:/:#V%):&#X$!TE8EYZ==#


74 CHAPITRE 3. ONDES ET COUPLAGES

3.2.3 Variabilité du couplage

En analysant le bruit sismique enregistré par un réseau global de sismomètres Nishidaet al. (2000) ont observé la variation annuelle de l’énergie des modes propres de la Terreet démontré l’excitation continue des modes 0S29 et 0S37. Ces auteurs soulignent aussi quela variation observée peut atteindre 40% pour les modes 0S29 et 0S37 tandis que pour lesautres modes, elle est de 10% maximum.

Rappelons que les modes solides sont e�cacement couplés avec l’atmosphère lorsqueleurs fréquences propres sont proches des modes atmosphériques. Les modes atmosphé-riques les plus énergétiques sont piégés dans le guide d’onde de la basse atmosphère à3.7 mHz et 4.3 mHz (Lognonné et al., 1998). En fonction des conditions atmosphériques,les modes solides 0S28 ou 0S29 sont alternativement résonants à environ 3.7 mHz. Le mode

0S37 est résonant à 4.4 mHz. Lognonné (2009) a ainsi montré que la proportion d’énergieinjectée par couplage dans l’atmosphère est dépendante de l’heure solaire locale2. La fi-gure 3.10 illustre cette variation au niveau de l’amplitude des modes 0S28 ou 0S29 pour unprofil d’atmosphère modélisée pour le cas du séisme de Tokachi-Oki survenu à 19 : 50 GMTà une longitude de 144�, soit 5 : 25 heure solaire locale.

0

6

12

18

24

!0.100.10.20.30.40.50.60

50

100

150

200

Local Time (h)

Amplitude Ur

Altit

ude

(km

)

Fig. 3.10 – Variation de l’amplitude des modes 0S28 et 0S29 dans la basseatmosphère en fonction de l’heure solaire locale à gauche et à droite respective-ment. L’atmosphère est modélisée en lieu et date du séisme de Tokachi-Oki par le modèleNRLMSISE-00.

2l’heure solaire locale hLT peut se calculer en fonction de l’heure GMT hGMT et de la longitude estlon (en degrés) via la relation : hLT=hGMT+lon/15

\%@(3!.5$!!#&/*"50(,$1,#$0(,\3OA,

*-,."#$%&'()(,

B.)",$1,(-()6;,").-%1())(0,1)$#,%$/*0,"$,"'(,."#$%&'()(,

>%&5(3!5%*$,!5%*$3!R%3A*!/(&1#!W!Q15%,;#$&$!HKP>Q"!@%*$O!

Z.)*.?*/*";,$1,"'(,2.)"'[%,."#$%&'()(,

Latitude (°)

Ener

gy p

art in

atm

osph

ere

Tokachi−Oki

F107En

ergy

par

t in a

tmos

pher

e

Tokachi−Oki

50 100 150 200 25010−4

10−3

10−2

0S280S291S18

0 6 12 18 2410−4

10−3

10−2

Local Time (h)

Ener

gy p

art in

atm

osph

ere

Tokachi−Oki

0S280S291S18

50 100 150 200 250 300 35010−4

10−3

10−2

Day of year

Ener

gy p

art in

atm

osph

ere

Tokachi−Oki

0S280S291S18

90 S 45 S 0 45 N 90 N10−4

10−3

10−2

0S280S291S18

Sound Speed (m/s)270 280 290 300 310 320 330 340 350

Local Time (h)JOVIAL Kick-Off meeting– April 19, 2016

!"# #$%&#''()* +)& !"# #,-'!)./*-0(1 *)&0-, 0).#' (* !"#1)0%,#$ +&#23#*1/ .)0-(* (* )%#&-!)& +)&04

!!5!"!# $ !"!"!# $ #"!#!"!# % 6 "78#

9"#&# !"# :)&(),(' )%#&-!)& " -*. !"# #,-'!)./*-0(1;)%#&-!)&# -&# #$%&#''#. </

"!"!# % 5!!! !

#"!#!"!# % 7

"6&!" ! "$ ! "!! ! !"%6# $ .(=""6!# &'6

$ "6""7"!#( "7>#

?)9 !"# )*,/ .(++#&#*1# <#!9##* !"# #,-'!(1 -*. *)*;#,-'!(11-'# (' !"# %)''(<,# +&#23#*1/ .#%#*.#*1# )+ !"# '!(++*#''!#*')& $@ A),,)9(*B C-,#!!# D7EF8GH !"# )%#&-!)& #H !)B#!"#&9(!" !"# <)3*.-&/ 1)*.(!()*'H 1-* <# &#9&(!!#* (* !"# "/.&);'!-!(1 1-'# -*. +)& - +&## '3&+-1# -'

)'*#!+ %!

"# ' !#! %!

"# "!$%&'%(&'!)$ ! (%'!)$'%*!$6

"

$ .(=""6!#&'6 ! '$ "6' !""7

#"7F#

9"#&#

"!$%& % +!$%& $ ,6-!$-%& ! ,6-!%- $& ! ,6- $%-!& "7E#

9(!" ,6 <#(*B !"# (*(!(-, %&#''3&# -*. 9"#&# 9# "-=# .#I*#. !"#<&-1J#! <(,(*#-& +)&0

)'*!+ %!

#" "# !"(# ! '"(# "56#

K!"#& #$%&#''()*' +)& !"# )%#&-!)& 1-* <# +)3*.H '31" -'

)'*#!+ %!

"# "!$%&'%(&'!)$ $ ". "! ! & .(="'#$

! ' !""! ! &##( !!

"""!# !"""'#L#!

!!

#.&! ! )"'# ! "# ,6( "# "57#

9"#&# .D / D!H 'GG (' !"# '/00#!&(1 +)&0 . % 75 " / "!H '#$

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

!" #$%&'()$*+, $- ' ./0+%12'(#$34$5'51367(',512 8,$5%$/127'%50)$*+(

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

N"# 0).#&* !"#)&/ +)& - P?RMS 0).#, 9-' .#'1&(<#. </N-J#31"( -*. P-(!) D7E>5G -*. T"(**#/ -*. U3&&(.B# D7E>VG@W#! 3' &#1-,, +&)0 !"#'# 9)&J' !"# '),3!()* )+ !"# P?RMS#23-!()*

!5! % #6"!# "55#

9"#&# !"# )%#&-!)& #6 (' .#I*#. +)& - '%"#&(1-,,/ '/00#!&(10).#, '31" -' TRMX DYZ(#9)*'J( -*. [*.#&')*H 7EF7G@ [' -1)*'#23#*1# )+ !"# '/00#!&/H </ 3'(*B B&)3% !"#)&/ -&B3;0#*!'H )& </ - '#%-&-!()* )+ =-&(-<,#'H (! 1-* <# '")9* !"-! !"#

%#"*+ , P300-&/ )+ !"# <)3*.-&/ 1)*.(!()*' +)& .(++#&#*! !/%#' )+ '3&+-1#' -*..('1)*!(*3(!(#'@ N"# +3*1!()* 0D$G (' B(=#* </ W)B*)**#\ 12 3&@ D7EEFG -*. ('-'')1(-!#. 9(!" !"# &-.(-!(*B '3&+-1#

N/%# )+ P3&+-1# P!&#'' Y('%,-1#0#*!

P),(.]'),(. &!,6)6"# ! !$ ,6"#!")6# $ %%#,-'!(1 !)6($! &!($!P),(.],(23(. &!,6)6"# ! !$ ,6"#!")6# $ %%#,-'!(1 !)6($! &! !)6 )6($!W(23(.],(23(. &!,6)6"# ! !$ ,6"#!")6# $ %%#,-'!(1 !)6($! &! !)6 )6($!A&## '),(. '3&+-1# %%#,-'!(1

! )6% 6 -*. ,6% 6

A&## -!0)'%"#&(1 '3&+-1# %,%&" ! !% 6

R-.(-!(*B -!0)'%"#&(1 '3&+-1# %,%0D$G "D&6!)6GD! !)6G

!"# !"#$"$$%& '$( )*%&+%&(%&

Practically: • Rayleigh and Acoustic waves are modelled with Radiative BL at low altitude

or FS at high altitude (600-400 km e.g. where waves are damped by attenuation) • Tsunami and gravity waves are modelled with FS at high altitude (600-400

km range e.g. where waves are damped by attenuation)


T(5")./,."#$%&'()(,4,*$-$%&'()(,+$5&/*-6,

>$D1&(3!!(15%,;#$&$!

A%)%,;#$&$!

K%5$)1D5!@%),$&-(.%)!$CD(.%)!

lR5(33m!nD@1D(.%),!(&%D)*!1#$!$CDA3A+&AD5!

P)!(!B$%5(B)$.@!2$3*!Y!

>$D1&(3!*&(B!%)!A%),!

0%).)DA1'!$CD(.%)!ZA)A1$!*AX$&$)@$!,@#$5$!a<!,;#$&A@(3!B&A*!

\%&$)19!4%&@$!


Documents

OCAFig. 1. (a) An eruption of Mount Pinatubo (Courtesy of Dr. J. Mori). (b) Dispersion relation of acoustic-gravity waves in an isothermal atmosphere (modi!ed from Gill (1982)). The