Katsumi Hattori and Daishi Kaida Graduate School of Science, Chiba University, Japan

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1 Sngular spectral analyss and prncpal component analyss of UF geomagnetc data; reducton of global noses and possble changes assocate wth the 000 Izu Islands Earthquake swarm n Japan Katsum Hattor and Dash Kada Graduate School of Scence, Chba Unversty, Japan

2 -. Background UF Geomagnetc data nclude. geomagnetc pulsatons (orgnated from solar-terrestral ntereacton) global varaton wth spatal resoluton several hundreds km. artfcal noses DC-drven tran noses etc. a few tens km 3. Varaton from crustal actvtes such as earthquakes and volcanc actvtes In order to montor or dentfy crustal actvty-related sgnals from UF magnetc data, t s mportant how to dscrmnate. Geomagnetc pulsatons. Artfcal noses

3 -. Prevous study of Prncpal Component analyss for the 000 Izu Islands swarm Hattor et. al. (PCE 004) 3 staton data wth ntersensor dstance of 5 km samplng rate.5 Hz narrow band pass flter wth center frequency at 0.0 Hz st Prncpal Component geomagnetc pulsatons nd Prncpal Component artfcal noses are domnant 3 rd Prncpal Component earthquake-related sgnals Problem The contrbuton of 3 rd prncpal component s less than 6 %.

4 -3. Present study In order to overcome the dffcultes n prevous analyss () Reduce the most ntense varaton n UF geomagnetc pulsatons wth usng the sngular spectral analyss. () Perform prncpal component analyss for the 000 Izu Islands swarm n Japan.

5 -. Staton map and EQs Reference ste JA Kakoka Observatory (kak) Hz samplng Izu network staton Kamo (kam), Sekosh (sks), and ochkosh (mck) Hz samplng data staton lat. long. kak kam sks mck EQs (>6) durng the 00 Izu Islands EQ swarm)

6 Kak (Reference) -. Observed data -kak Kam (nt) Sks Smlar global varaton has been observed. -kam -sks ck Reduce the global varaton usng Sngular Spectral Analyss (SSA) -mck December, 000 (UT)

7 3-. Sngular Spectral Analyss (SSA) SSA s a knd of tme seres analyss. Etract perodctes from the tme seres data wth use of sngular value decomposton wthout any models. SSA has an advantage aganst wavelet analyss and fourer analyss n pulse detecton and so on Procedure of SSA

8 j N, } { = N k k k X O = st Step Tme seres data -. Created the atr (kx) from tme seres data -. Compute covarance matr S of X = = N k k k N k k k T X X S O O : Wndow ength 3-. Sngular Spectral Analyss (SSA)

9 = U U S = O ( ) = = u u u u u u u u u u u u U O Egenvalue Λ Egenvector U -. Sngular Decomposton (Egen valus decomposton) of S matr -. Compute V matr = = k k k T v v v v v v v v v v v v U X V O T V U X = nd Step

10 = k k k k X O T V U X = T T T v u v u v u λ λ λ = X X X = 3-. Reconstructon of atr X usng prncpal components th matr X 3 rd Step reconstructon 4 th Step dagonal averagng 4-. Reconstructon of th prncpal Component of G ~G n from X K N K K N G G G G G = + = + + = + = = / ) ( 3 / ) ( / ) (,, { } N j G G G G, =

11 4-. Global nose reducton wth usng SSA 00:0 00: 5 Aprl 7, 000 UT -Kak (reference) (nt) -Kam (nt) UT Apply SSA

12 Result of SSA kam Reconstructed - 0th prncpal components by SSA (=00) kak (reference) Etract common varatons Investgate the correlaton among components

13 Global nose reducton wth SSA Use correlaton > 0.7 weak Number of prncpal component (kam) Correaton Reconstruct wth,,3,4,0,4,5,8 th Components strong Number of prncpal component (kak)

14 Result of global nose reducton wth SSA -kak (reference) (nt) -Reconstructed Kam global varaton wth SSA -kam (orgnal) -resduals (blue - green) 00:0 00:5 Aprl 7, 000 UT

15 Result of global nose reducton wth SSA (In the case of local varaton estence at Kam data) -kak(reference) -kam (orgnal) ocal varaton at kam (nt) -reconstructed global Kam data wth SSA Perform SSA global nose reducton from Feb. Dec. 000 for Kam, Sks and ck wth reference of Kak. -resdual varaton at Kam (Blue - Green) Data length 5 mn (300 ponts) Keep the local varaton 5:0 5:5 Aprl 7, 000 UT

16 orgnal data kak SSA flter SSA flter can kam Perods remove of 45-50s global varaton (Pc4) (nt) varaton (Pc4) sks Narrow bandpass fler at 0.0 Hz Estmated global varaton at Kam by SSA kam UT mck kak kam (nt) sks (nt) sks Comparson between results of SSA flterng and narrow mck bandpass flterng at 0.0 Hz UT UT mck

17 Orgnal data kak Varaton caused by EQ(4.8,4.3) kam Narrow band pass flter at 0.0 Hz can remove shakng effect. (nt) SSA flter can remove the global varaton and enhance the small shakng varatons. sks SSA flterng Narrow band pass flterng at 0.0 Hz mck June 9, 000 UT kak Estmated global varaton at kam usng SSA kam sks mck June 9, 000, UT June 9, 000 UT

18 5-. Prncpal Component Analyss (PCA) after flterng narrow band pass flter centered at 0.0Hz remove shakng effects SSA flter Reducton of global varaton SSAflter narrow band 0.0Hz flter Perform PCA dnght data (UT5-9) (less artfcal nose perod)

19 () Result of narrow bandpass flter at 0.0 Hz (egenvalue varaton) ---:EQ wth >6 λ λ λ 3 ap λ λ λ 3 :egenvalue Effect of of geomagnetc st prncpal actvtes component :egenvalue of nd prncpal component :egenvalue of 3 rd prncpal component ap:ap nde (magnetc dsturbance) Es:Regonal EQ energy (wthn 50 km from ck staton for 30 mn ntervals) Es January December, 000

20 () Results of narrow bandpass flter at 0.0 Hz (egenvalue) (nghttme data) EQ wth >6 λ λ ncrease nd and 3 rd comp. before the EQ wth >6 (same results Hattor et. al.( PCE 004)). λ 3 ap 3 3 Es st prncpal comp. st Prncpal comp. InactveEQ perod Jan. Dec., 000 Actve EQ perod

21 D/N: rato between daytme and nghttme W/H: rato between weekdays and weekend/ holdays () Result of narrow bandpass flter at 0.0Hz (artfcal nose effect) (a) (b) Varaton of prncpal components ntensty n Aprl 000. (a) Weekdays (b) Weekend and holdays λ λ λ 3 nd prncpal comp. : nfluence by artfcal noses s large. Nghttme data : contamnaton s less. D/N D/N(weekdays) D/N(weeekend) W/H W/H(daytme) W/H(nghttme) st comp nd comp rd comp UT weekend UT

22 () Result of SSA flter (varaton of nghttme egenvalues) λ --- EQ wth >6 Appearence of varaton caused by shakng effect λ λ 3 No correlaton betweem st prncpal comp. and ap nde ap Confrmaton of SSA flter performances Es reducton of global geomagnetc varaton January December 000

23 () Results of SSA flter (artfcal nose effect) (a) (b) λ Varaton of ntensty of prncpal components n Aprl 000. (a) weekdays (b) weekend and holdays λ λ st Comp. : nfluence 3 of artfcal noses s large. Nghttme data : nfluence of artfcal UT nose s less. UT D/N D/N(weekdays) D/N(weeekend) W/H W/H(daytme) W/H(nghttme) st comp nd comp rd comp D/N: rato between daytme and nghttme W/H: rato between weekdays and weekend/holdays

24 (3) Results of SSA flter + narrow bandpass flter at 0.0Hz (varaton of egenvalues at nghttme) EQ wth >6 λ λ λ 3 ap 3 3 Es st prncpal comp. st prncpal comp. Inactve perod January December, 000 Actve perod

25 D/N: rato between daytme and nghttme W/H: rato between weekdays and weekend/holdays (3) Results of SSA flter + narrow bandpass flter at 0.0Hz nfluence of artfcal effect) λ (a) (b) Varaton of ntensty of prncpal components n Aprl 000. (a) weekdays (b) weekend and holdays λ λ 3 st comp. :??????? (maybe artfcal nose ) UT UT Nghttme data : nfluence of artfcal nose s small D/N D/N(weekdays) D/N(weeekend) W/H W/H(daytme) W/H(nghttme) st comp nd comp rd comp

26 6. Summary Inactve perod Actve perod Narrow bandpass flter 3 st Prncpal comp. 3 st Prncpal comp. Increase of nd and 3 rd Increase of nd comp. and 3 rd after comp. usng at SSA the swarm perod flter SSA +Narrow 3 3 Bandpass flter st Prncpal comp. st Prncpal comp.

27 6. Summary st comp. nd comp. 3rd comp Narrow bandpass flter at 0.0Hz SSA flter SSA+ narrow bandpass flter at 0.0Hz actve geomagnetc pulsatons shakng effects? nactve geomagnetc pulsatons daytme: artfcal noses? actve EQ- related varaton shakng effects EQ- related varaton nactve daytme: artfcal noses?? actve EQ- related varaton shakng effects EQ- related varaton nactve???

28 6. Concluson. Realze a global nose reducton wth SSA approach usng an adequate reference data.. Success to mprove the PCA performance usng SSA flter and narrow bandpass flter wth centered frequency of 0.0 Hz. 3. Confrm the performance of PCA wth two staton data after reduce the global varatons.

29 Thank you for attenton.

30 mckkam kamsks Varaton of nd prncpal comp. wth staton data usng SSA flter and narrow bandpass flter at 0.0 Hz (nghttme data) EQ wth >6 sksmck ap Es January December, 000

31 Eample of SSA (monthly average temperature at Chba from 967 to Observed data 007) Etract perodc varaton year perod varaton 4 month perod varaton 6 month perod varaton years varaton (Solar actvty dependence) Increase of Ave. Temp Resdual varaton

32 7. 観測点のデータを用いた PCA Serta et. al.(005) PCA SSA SSA PCA

33 第主成分の固有値の変動 ~ 夜間のみ ~ mckkam kamsks 6 sksmck ap Es 000

34 8. まとめ 3 SSA mck-kam, kam-sks, sks-mck 3 3 PCA

35 kam sks 000

36 相関 H D (kam,sks,mck) (kak) ( ) Z kam H H D D Z Z sks mck

37 固有ベクトルの変動 V : kam V : sks V3 : mck Z = VX kam + V X sks + V3 = V + V + V X mck 3 V V V3 SSA V V SSA+ V V V3 V

38 7. 今後の課題 Hz.5Hz SSA

39 6. まとめ 0.0Hz SSA PCA( ) 5% 0% SSA

40 0.0Hz フィルタのみ ~ ~6,7 月夜間の固有値の変動 6 λ λ λ 3 ap Es = λ + λ λ 3 + λ %

41 固有値の変動 λ λ λ ap Es

42 動 ~ SSA フィルタのみ ~6,7 月夜間の固有値の変 λ λ λ 3 ap Es

43 主成分解析 (PCA) の手順 30 分ごとのデータマトリクス X k, N = ( j ), j = = k k N=800(Hz 60 秒 30 分 ) K=3(kam,sks,mck) 共分散行列 3 3 k 3 O N N kn R N T = X X R = VΛV

44 固有値 Λ 固有ベクトル V Λ = λ k λ λ O = kk k k k k V V V V V V V V V V O 主成分の波形は以下の式で再現される mck sks kam X V X V X V Z =

45 主成分解析概念図 ( 次元 ) X = X = = =

46 常磐線 ( 取手駅以北 ) と水戸線は観測に悪影響の少ない交流電化と既存の直流電化区間を相互に走れる交直流電車の技術ができるまでは長らく非電化で運転されていたまた首都圏新都市鉄道つくばエクスプレス線の守谷駅以北は開業当初から交流電化でありさらに関東鉄道常総線と関東鉄道竜ヶ崎線はコストの問題もありいまだに非電化のまま運行している

47 f=0.hz s=7 信号強度比震央からの距離 (km) Pc 型周期 ( 秒 ) 波形型周期 ( 秒 ) 波形 Pc 0.~5 P ~40 不規則な Pc 5~0 P P 40~50 減衰波形 Pc3 0~45 規則的な P3 50~ (rregular) Pc4 45~50 連続波形 Pc5 50~600 (contnuous) Pc6 600~ 地磁気脈動の国際的分類

U N I T. 1. What are Maxine and Debbie talking about? They are talking about. 2. What doesn t Maxine like? She doesn t like. 3. What is a shame?

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