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# Method of analysis

ドキュメント内 Barometer Coefficients of High Latitude Neutron Monitors (ページ 34-44)

## ５５０    ‥  ６００ Atmospheric

### The counting rate of the neutron monitor at time ￡is expressed by

NCR｡， ｐ， t)ﾆｴﾌＹ(とＲ， Ｐ)i(ｙﾒ)ぷ･ (7.1)

### Substituting eqト(7.1) into ｅqバ6.2)にwe have the barometer ｃｏｅ:fficientβin place of 況 c as

(7.2)

From eq. (7.2) it is clear that the barometer coefficienトis dependent on the primary cosmic ray spectrum.       ＼

Let the primary spectrum be      ‥‥‥‥‥‥‥‥‥  ‥‥‥ ‥‥‥‥       ‥‥

Barometer Coefficients of High Latitude Neutron Monitors (Kusunose)

ﾊﾞ私･O=j｡(Ｒ)十SiiR, t)

43

(7.3)

jｖ(拓、ｐ、ｔ)＝ 工:

YCR, p)几{R)dR十

### 石

＝凰(Ｒ･，．ｐﾐ)＋6N(Ｒ｡， ｐ， t)

where Ｎ.。and ∂Ｎ are defined respectively by

and

### 石

Y{R, p)6j(R, t)dR

ｙ(Ｒ， Ｐ)i。(R) dR,

β｡(凡，μ)＝

NoiRc, P) dp

(7.4)

(7.5)

(7.6)

(7.7)

### 1 and the primary variation spectrum ５ｊ／i。is expressed by using eq. (7.6) and eq. (7.8) as follows:

β、(Ｒ｡、ｐ、ｔ)＝

￡ﾌ∂ｙ(ぶ'‑^Sj(R, OdR ｴﾌｙ(私夕)司(私t)dl?

### By using the response function F{R, p) = YiＲ, Ｐ)ﾉ。CR),we rewrite eq. (7.9) as

･･∂Ｆ(Ｒ， Ｐ)3j(R, t)

うj

ﾌﾞ

ｽﾞ土佐]ぎ

### Ｆ(凡ｐ)＝−∂呪諮'ρ)。

(7.9)

(7.10)

(7.13)

(7.14)

7｡2. Computation       ▽

Now let us begin to calculate the variation rate a r of the barometer coefficientβby using eq. (7.14). It can be computed from the rigidityトdependence of the sea level barometer coefficient β。iR, p) and the cosmic ray neutron intensity N, iR, p)。

### ‑ 1966 survey data. Further extrapolation must be made for the computation of higher rigidity rangeレThe ｅχtrapolatedcurve is shown in Fig√20.＼

The rigidity dependence of neutron intensity in 1965 is shown in Fig. 18, where dots represent the values given by Carmichel and Bercovitch (1969)……:＼Ａsmoothed curve fitted to

44 Res. Rep. Kochi Univ. Vol. 46j(1997) Nat.

### Substituting into eq. (7.10), we obtain

β、(Ｒｃ、ｐ、ｔ)＝ (7.11)

lfβ｡(‑R, p)= const, with respect to R, then it follows from むq. (7.11) that β， ＝ β。.

Furthermore, in this case it can be concluded from eq. (6.6) that a,=0. Therefore, the difference between the barometer coefficients ＼β。(尽｡∧,p)and〕βニベ凡, p) can be attributed to the dependence of β｡CRc ,p) on the rigidity R.十  二   ∧   ｊ

Let us assume the primary variation spectrum as

づ         ○(瓦乙)／ル(召)cｘ: 良一≒  ………7= r (￡)｡万レ   十…………    (7.12) Substituting into eq.(7.11), we obtain, by partiaしntegration,

β人Ｒｃ、ｐ、約＝

?,夕)呪(Ｒ, Ｐ)Ｒフ￣ljR−β。(Re, P)K。(瓦，

：｡Ｎｏ(タリ)ｙ∇｡即一愉町功２ﾅ＼

β。(私夕)呪(Ｒ, Ｐ)Ｒフ￣ljR−β。(Ｒ≪ Ｐ)べ(Ｒ．， 1>)R‑'

From eq. (6.7) and eq. (7.13) we can obtain

a, (Re,｡p, ￡)=β，(Ｒｅ，Ｐ， tＶβ｡(.Re, p) ＼   ノ

ア工≒β。(私戸)−β。(Ｒ．, Ｐ)]呪(Ｒｃ，ｐ)Ｒ￣７￣｀ｄＲ

rJ^

^

KiR, p)R‑'‑'di?不皿(罵･/砂タフ

Barometer Coefficients of High Latitude Neutron Monitors (Kusunose)

１００

### ‑９０

ｇ︶ Ａ４ＩＳＵ８４ＵＩ   ＵＯＪｊｎＳＺ

８０

〇  〇  〇７  ６  ５

４０

45

２ ▽４  ６  ８

Vertical Ｃｕ↑off

10∇ 12 Riqidi↑V

14 16 18 (ＧＶ)

Fig.18. Rigidity dependence of cosmic ray neutron monitor〉intensity at sea level in 1965. The     values of filled points are cited from the table given by Carmichael and Bercovitch     (1969e)トCurve shows the approximated value used in the numerical calculation.

０     ５     ０ Ｏ     ０︶ｑ

１︵｀エＥＥ＼￠︶↑ｃの一Ｑｉのｏり ﹄の↑ＱＥＯ

k。

ａ］ ．８５

８  １０  １２  １４  １６  １８

### the numerical calculation.      ＼       上

46

Fig.20レRiがdity∧dependence of baro㎡eter

### The quantity 6j／j。represen臨ヶthe intensi Weﾚ印ecify its precise depeねdence on the

1ﾄlhﾄthe num･eｒl:dalトcalculation μ淮=ﾚ珀ﾚthe丿卸ｒｅ√………ニ＼二………

where R。is the lower cuto廿rigidity.

〉Theﾀﾞcalculations 6f α＼√have been上p邸f Thus obtained values areﾌﾞpJo緋色d in Fig∠21，

assumed. In practice, the computatio前回ha佃………beeね｡万一j･･j･=d (7.14)△independently, and the･ resu叫:6fﾄbφ伍臨

of丿omputation、Ｃｕ:toffﾚrigidity凡七∧are taken

Figure 22 repre卵nts th:e rigid:i片白dependeねφ……=jj｡･==｡･

expone聯∧７ ダノ凡芦刈GV∧i万s･

"■■■ ■‑･･ ・  ・ ････

I

with∧the

### period

ﾆactivity of the

︵ＦＥＥ＼︶

1･

４ ３  ２

￨(5?

４ ３

(5４

Barometer Coefficients of

２    ５  ４ ｒ  石工ＥＥ／ｃＰ

○ ３

Re IGV

### Latitude Neutron Monitors (Kusunose)

47

Fig.21. Results of numerical calculation ｏｆ叫に(7,14). Wher白白primaryﾀﾞ皿riation spectrum i5 aｓｓｕｍｅｄ＼ａｓ∂J／Jo oc R77 (Ｒ

＜40GV)ａｎｄ ∂J／J｡＝O(Ｒ＞40Gｖy Cutoff rigidity Re's sre taken as 1,ト1.5, 2, 3ト５ and 7 GV.        犬上

３  ．４  ５ ６

二  万      ト    ＼ＲｃニCｕ↑off Rigidi↑y （ＧＶ）＼   ･･ .･. ・ . .･ . .･･.

Fig.22 Distribution c丿α7 are plotted in absolute value. The abscissa is the cutoff rigidity    ＝  where the neutron monitor is located, or the mean rigidity at several stations√ The      ･curved line・represents the distribution of a r , which iｓしthe result of numerical      calculation of eq. (7.14)レwhere フョ1.7GV is assumed………j       ＼      Ａトand Ａ２ (Average of eight ｈ汝ｈ latitude statio心）.:Kusunose (1984).    ト ＼十     11 and l2 （lnｕｖik）:Kusunose (1985)・ ･･. . ・ダ‥‥‥‥‥‥‥‥‥‥  ‥ ＼＼    .･ ･..･ :.･.･

Bi, B2 and Ｂ３ (Average of several stations):Ｂａぐhelet et･･ ｢･.(1972).犬上  上 ＼      （ン(Deep River): Carmichael and Peterson (1971)よ       ユ    ． ＼

48 Ｒ叩レRep. Kochi Un征………Vol.ｿﾞ嫉(1997)………:ﾄﾔ愉比し……ﾑ]…………万………1:しこ万.=ly        " ■ ■■■■  ■

### old ones∧are discussed.     十： ダ

!n Section 6,ぺｗe.ｹdiscuss∇a possible solar cycle二varia that is〉the second objective of theダpresent㈲ork. The coefficient has been clarified by analyzing the c

### the sam口method as app!ied in the previous

/b面ｏ面面ｒ=ﾄむoefficients,

### ﾔvariationﾚof barometer

〔==姉畑作耐ﾉ柏れﾄt軸I難:海面s二by means c〕f 裕二Tれ（仰向rved datsレ･are shown in Fig.

ﾉ礼::面緋如尚トcorrelatedに＼j加ith the cｑ自治ic 14. The absolute value of the barometer: coefficie皿∧鋤:=面組拍灯し頑=!rrelatedにﾚwith･ the cQg･垣･･１ｃ ｍｙ入姐tensity ； the fractio皿1 variation of the………わ壮φ面面で二面efficient二如/f面面ﾚ]如be in……the rangeニof 0.1％心0.4%, when the､cosmic ray ｎ叩竹卵白………1･ｎ=:t.j･6=れsi:..tﾑ=y万I..=･vari:･atio･h:･.16･==4･slarge as 1 %.

The year‑to‑year variation rate (jf the baroir period than that in theトsolar active period. Tl attributed to the primary spectΓum variationイ

IれSection 7, aれ〉analysis is perforポed onしt佃土

coefficient and the cosmic十ねy primary部如trum･=･……j………:リ･siねg･.･.万.･･t皿j barometer coefficient and the･ sea level neutron i牡ｅ心社元十七㈲………j.･40 coefficient on the spectrum of primaかcosmic………ﾔ･巨y｡s is一万:c6:ポ.皿j･･t=･Q｡d that the year‑to‑year variation rate of……ths

coefficient on the spectrum of primary cosmiと………jr･4y｡§･･is･万:丿皿 that the year‑to‑year variation rate ｏＬ:t㈲……hi

(ホanges of bothトthe cutoff ｒ･igidity犬and the pr助命ダ==……師弟毎々町くspectrum.………ｙｊ･  １…………

……

…Ｉ．･．･．・・．･･

・．･．･･  ．・Acknow[edge巾ents･=………ﾚ……ﾉ………:.=宍く･:………ﾚj万…

……ﾄ＼ｹﾞ……ｿﾞ……jﾉ1=j･=:.j･j･I/……＼……＼○………:

Ｌ曲ａれk Drs. N. Ogita√SレｙO shida and helpful suぱestions throuぱhout the present and Y.ﾄInoue………ヶ:l j  :  ＼‥‥‥ ‥‥‥

Barometer Coefficients of High Latitude :Neutron Monitors (Kusunose) 49

### for their valuable suggestions and careful readings ･of the manuscript. l am indebted to the members of the Department of Physics and Department of Information Science, Faculty od Science, Kochi University. Computer works were performed by using FACOM computers at the Computation Center of the Institute of Physical and Chemical Research, and the Data Processing Center of Kochi University.        上 丿   犬   ＞ ･■■■■   ・

References

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nth Int. Ｃｏｎｆにon Cosmic Rays√Budapest 1969,Ａ ｅtａ Ｐｈ,＾iｓｉｃａＡｃａｄｅｍｉａｅ Ｓｃｉｅｎtiaｒｕｍ.

Ｈｕｎｇａｒｉｃａｅ,29, Suppl. 2, 597 − 600 (1970). ダ      十   ＼   ＼  …………

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Bachelet, F., P. Balata, EレDyring, and N. Iucci : Attenuation coefficients of the cosmic‑ray   nucleonic component in the lower atmosphere√Ｎｕｏｕｏ Ｃｉ?ｎｅｎtｏ,35, 23 − 35 (1965).

Bchelet, F･，Ｎ. Iucci, G. Villoresi, and Ｎ. Zangrilli:The cosmi己寸ay spectral modulation above   ２ GV, IV. The influence on the attenuation coefficient ofﾚthe nucleo°nic component, Ｎｕｏｕｏ   Cimento, 11B, 1ブ12 (1972).  二       六十

Belov, A. V.√and L. T. Dorman : Dependence of cosmic ray barometer effect on primary   variation spectrum, Ｐｒｏｃ. 16th. Int. Ｃｏｓｍｉｃ Ray Cと)可･, Kyoto, 4, 310 − 314 (1979).十

Bercovitch, M.:Atmospheric effects on むosmic ray monitoＴｓ, Ｐｒｏｃ. Int. Ｃｏｎｆ. ｏｎ.Ｃｏｓｍｉｃ Ｒａｙｓ,   Ｃａｌｇａｒ＾l,Part Ａ， 269 − 344 (1967),       ＝      .・.･..  ・I ‥

BlorQster, K. A., and Ｐ. J. Tanskanen : The influence of snow and water on the different   multiplicities as observed in neutron monitor NM‑64 1n Oulu, Proc. 11th Int. Conf. on   Cosmic Rays, Budapest 1969, Ａｃtａ Ｐｈｙｓｉｃａ ＡｃａｄｅｒｒtｉａｅＳｃｉｅｒｉＵａｒｕｍ,Ｈｕｎｓａｒｉｃａｅ, 29,Suppl.

ご 2, 627二630 (1970)レ       ニ   レ ..  ・・･: ..   .･.･・ . .･

:・

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CarmichaeljH‑:Cosmic Rays, ＩＱＳＹ Ｉｎｓtｒｕｃtｉｏｎｍａｎｕal,No. 7レIQSY SecretariatにLondon    (1964); Cosmic Rays (Instruments), J‑.Ｖｎｎａｌｓof tｈｅ ＩＱＳＹ√1, MIT Press, Cambridge, 178一 犬197 (1968).

Carmichael, H., M. Bercovitch, M. A. Shea, M. Magidin, and R. W. Peterson : Attenuation of   neutron monitorしradiation in the atmosphere, Proc. 10th Int. Conf. on Cosmic Rays,   Calgary 1967, Ｃａｎ. Ｊ， Ｐ九ｙＳし46, S1006 ‑ S1013 (1968).     十

Carmichael, H., and Ｍ. Bercovitch : Ｖ. Analysis ６ｆ IQSY cosmic‑ray survey measurements,   Can. J. Phys｡47, 2073ニ2093 (1969).      犬   ＞ ＼      Ｉ

Carmichael･Ｈ･レ尽nd R. Ｗ． ダPeterson : Dependence of the ｎ叩tron monitor attenuation   coefficient on atmospheric depth and on geomagnetic cutoff in 1966 and in 1970, Proc.招請 尚  Int. Ｃｏｓｍｉｃ ＴｉａｙＣ'ｏｎｆ｡Ｈｏｂａｒt， 3, 887 − 892 (1971).  ニレ  ：   ．  ．   ・ ． ．Ｉ    Ｉ

Compton, A. H., E. O. WoUan, and Ｒ． D. Bennet ： 八precision･recording cosmic‑ray meter,   Rev. Sci. Insび., 5, 415 − 422 (1934).    ：     十 十      十      し

Dorman, L. Ｉ．： ＣｏｓmiりＲａｙ Ｖａｒiatｉｏｎｓ, Transl. Teen. Ｄｏｃ√Liaison Office, Wright‑Patterson   Air Force Base in USA (1958).      ト    ▽   十     ダ

Dyring, E., and Ｂ. Sporre:The latitude effect Ｑｆ∧the neutrc multiplicity as detected by a   shipborne neutron monitor, 力演. Geoかs., 5, 67 ‑ 77 (1966a)∧       ＼

Dyring, E., and Ｂ. Sporre : Multiplicity measurements on the Uppsala IGY‑neutron monitor,    Ark. Geofys., 5, 79 ‑ 85 (1966b).       犬      ニ

5 0

Ｆｏrｍ叫,こＭｊＡ．=÷Ｎ叫trｏｎｍ呻itorニｍ４ss∧aｂSor面φ垣………=.ニ4

ノt肋面拉ｒｃy巾１9ノ(1り54)レよ＼Ｇむ0加片刃卵……,ノ却√雄叫ド‥……肘符………申郎仁＼ノ………＼………フ=ノニ＼……=j……

＼士。エ1………j……

Ｆ９加lｅｒ√しＬン：Ｖ昨ｙｊＩａ呟ｅ ｂ０ｒｏれｔｒ岨ｕｏｒｉｄｅ＼ｐ叫ｐ付牡卵冊ケφ面柿加ノ,＝沢雨＞叙八‥仙縦ｒl/,＞３４,万Ｉ７３Ｉ=1二ア３９

ＭａねｎｅtiｓｃｈｅｎへＶｅｒｅｉｎｓ▽im ＪａＫｒｅ』卵8、

Weidmann､∧Leipzigト1レ57 (1839)………∧

Griffiths, WトK., G. ＶレHarm an√Ｃ……J. Hatt(

j………coefficients:of=ＩＧＹﾚand ＮＭ･64 neutron 血Ｏ

……475 − 477 (1965).: ＼    ‥

Griffiths, W, K.,∧C. J. Hatton, P. Ryder, and C.

･coefficientof the Leeds neutron‑皿onitor during

＼,レフ1,1895ニ1898ヶ(1966).  ∧ 十六 ………=･･

:

Griffiths√ＷレＫよG. V. Harman, C. JレHatton, P…………,.=･.Ｌ･l j∧variations Ｏ一仁selectedニmultiplicities in the Ｌ･eeds卜

, S1044しS1047 C1968). ト  つj  ……∧………:/･=･……

レレ玖Gausかﾚ屈d上WL……Weber),･

■ｻ11 1……Studies of………the ba･rometric

………:ぐφ好くjﾉﾄＣｏｓｍｉｃ 尽（りｓ､ Ｌｏれｄｏれ、

of the barometer ﾚ=び……Ｇｅｏｐｈ.７ｓ二月叩

ﾉｿﾞp.Ryder : Theﾄintensity

∧ｙariations ofニs(向ctedレｍultipIicitiesゾiｎｔhりＬ叫面ノＮＭぞ財ケ向面サ面∴ブ―Jj加に)j

,S1o44こS1o47てI968)j レ  つj ………＼………:/I=I………フ∧…………jy………＜∧ダ―く…………>ニj…………レレ<レ………呂…………

Ｈａrｍ尽ｎ Ｃ・Ｖ ,……ａｎd Ｃ― Ｊ………Ｈａttｏn : Ｃｏｎtriｂｕti面（佞=/対加＼φ面単址∧叫坤＼ａ面1=ノj……t1}x9ニ=t面1ｐetａtｕヤe   白ｄe畑面卵cｅ司づ心ｕtroｎｍｏnitorS，Ｃ卯にげレ戸砂牡う……邨=ンノ:斟姉恥≒レ班o5ニ6………貝祁8)レL…………万………j………=万……

…エ…………:

Ｈ４ttｏｎ,＼ＣレＪ・仙ｎｄ卜江（7ａrｍicｈ=叫:＼ＥｘｐetiｍeｎぱI………:珀面叫縦牡i叶……=y涯………=1tｈje

エj万JＮＭｊ湊==叫ｕtroびノｍｏｎitｏr,

### Inoue, A., M. Wada, andﾚＬ Kondo ： As    DataCenter C2しfor Cosmic Rays,

……(1983).      ∧    ﾚﾚヶ‥

‥‥プj…………ト………:=……I Ishii, C.トNish･in巨!chigata Uchusenkei noトSho袖如6ﾔﾚ(如二

(1944).：………J ＝ ‥‥‥     ‥ ‥‥‥‥‥‥‥万ﾚｹ==j………j11JI:::II:ll Jory,･･ Ｆ. ･S,･･:･Selected cosmic‑ray orbitsﾚin･.･the･函    1075 (1956). っ   十 ＼ ▽   十  …………

Kaminer,∧N. S., S. F. Ilgch, TニS√Khadakhai

### √Tokyo

☆Ｒｉｆｅｅｎ……疏０，千23, 535 545'

field,:=Ｐｈｙｓﾌﾞｹμ印之∧!03,1068

the cosmicいra･ｙ

∧れeｕtron cQｍｐｏｈent，朽刃c．面￡2＝Ｃ0ゼ．(コ向叫泌……=.お妙心ゾ石面面戻浅に486ケ1乙=レ4I86I.j(。μ

Ｋ尽ｍｐｈｏｕ卵，よＬ,：Ｃ６rreIａtiｏｎ oｆｎ回伴ｏn ｍ９μlニニtJφtエjエ1Ijや:エo万4sjj牡戸回エ万宍=jぐエφりff'iニぐ゜iQi

### Kawasaki, S.:Free air pressure reduced from

barometer effect, Proc.16tfi:Iれ:tレＣｏｓｍｉｃ:Ray 4√263 ‑ 265 (1979)･.   ･･･    ………ﾚ

j ﾉ … … … : . . ･ ・ . = … … … I . 一 一 l . 1 . ･ . ･ . L ･ . ･ ･   ト ‥ ‥ ‥   ‥ ‥ ‥ ‥

ｹ 皿 （ 叫 瞎 畔 i 9 = 皿 万 o f C O S 毎 畑 r a y

Barometer Coefficients of High Latitude Neutron Monitors (Kusunose) 51

Kawasaki, S., K. Imai, and Ｍ. Wada : The cosmic ray intensities observed by Mt. Norikura  ∧neutron monitor, 1968 − 1980, ＩＣＲ‑Ｒｅｐｏｒt‑109‑83‑03,Inst. Cosmic Ray. Res., Univ. Tokyo   (1983).      ニ      ト 犬  △ ニ      ＜   ト

Kawasaki, S･, and Ｍ. Wada : Estimation of f恥e airﾊﾟpressure from radio如nde data for the   correction of cosmic ray barometer effect,:Ｐｒｏｃ.18tK Int.Ｃｏｓｍｉｃ Ｒａｙ Ｃｏｒが.,Ｂａｎｇａｌｏｒｅ, S   , 473 ‑ 475 (1983).      ...･.・・ ･.･･. ・. ･･..･・. ・・.・   ･･･

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