Singular spectral analysis and principal component analysis of ULF - PowerPoint PPT Presentation

Singular spectral analysis and principal component analysis of ULF geomagnetic data; reduction of global noises and possible changes associate with the 2000 Izu Islands Earthquake swarm in Japan Katsumi Hattori and Daishi Kaida Graduate School of Science, Chiba University, Japan

1-1. Background chiba-u geophysics ULF Geomagnetic data include 1. geomagnetic pulsations (originated from solar-terrestrial intereaction) global variation with spatial resolution several hundreds km 2. artificial noises （ DC-driven train noises etc. ） a few tens km 3. Variation from crustal activities such as earthquakes and volcanic activities In order to monitor or identify crustal activity-related signals from ULF magnetic data , it is important how to discriminate 1. Geomagnetic pulsations 2. Artificial noises

⇒ ⇒ ⇒ 1-2. Previous study of Principal Component chiba-u geophysics analysis for the 2000 Izu Islands swarm Hattori et. al. (PCE 2004) 3 station data with inter- sensor distance of 5 km sampling rate 12.5 Hz narrow band pass filter with center frequency at 0.01 Hz 1 st Principal Component geomagnetic pulsations 2 nd Principal Component artificial noises are dominant 3 rd Principal Component earthquake-related signals Problem The contribution of 3 rd principal component is less than 6 %.

1-3. Present study chiba-u geophysics In order to overcome the difficulties in previous analysis (1) Reduce the most intense variation in ULF geomagnetic pulsations with using the singular spectral analysis. (2) Perform principal component analysis for the 2000 Izu Islands swarm in Japan.

2-1. Station map and EQs chiba-u geophysics Reference site JMA Kakioka Observatory ( kak ) 1 Hz sampling Izu network station Kamo ( kam ), Seikoshi ( sks ), and Mochikoshi ( mck ) 1 Hz sampling data EQs (M>6) during the 200 Izu Islands EQ swarm) station lat. long. kak 36.23° 140.19° kam 34.86° 138.83° sks 34.90° 138.82° mck 34.89° 138.87°

2-2. Observed data chiba-u geophysics Kak (Reference) － kak Kam － kam (nT) Sks Similar global variation has been － sks observed. Mck Reduce the global variation using Singular Spectral Analysis (SSA) － mck December 21, 2000 (UT)

3-1. Singular Spectral Analysis (SSA) chiba-u geophysics SSA is a kind of time series analysis. Extract periodicities from the time series data with use of singular value decomposition without any models. SSA has an advantage against wavelet analysis and fourier analysis in pulse detection and so on Procedure of SSA

3-1. Singular Spectral Analysis (SSA) 1 st Step chiba-u geophysics = L { x } x 1 , x x Time series data j 2 N 1-1. Created the Matrix (kXL) from time series data L x x x x 1 2 3 L L x x x x + = 2 3 4 L 1 X L : Window Length M M M O M L x x x x + + k k 1 k 2 N 1-2. Compute covariance matrix S of X ⎛ ⎞ L x x x ⎜ ⎟ 1 2 k ⎛ ⎞ L x x x x ⎜ ⎟ 1 2 3 L ⎜ ⎟ L x x x + 2 3 k 1 ⎜ ⎟ L x x x x ⎜ ⎟ + = = 2 3 4 L 1 T L S X X x x x ⎜ ⎟ ⎜ ⎟ + 3 4 k 2 M M M O M ⎜ ⎟ ⎜ ⎟ M M O M ⎜ ⎟ ⎜ ⎟ L ⎝ ⎠ x x x x + + k k 1 k 2 N ⎝ L ⎠ x x x + L L 1 N

Λ Λ Λ Λ λ λ λ 2 nd Step chiba-u geophysics 2-2. Singular Decomposition (Eigen valus decomposition) of S matrix = − 1 S U U Eigenvalue Λ Eigenvector Ｕ ⎛ ⎞ ⎛ ⎞ L L 0 0 u u u ⎜ ⎟ ⎜ ⎟ 1 11 21 L 1 ⎜ ⎟ ⎜ ⎟ L L 0 0 u u u ( ) = = = 2 12 22 L 2 L U u u u ⎜ ⎟ ⎜ ⎟ 1 2 L M M O M M M O M ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ L L ⎝ ⎠ ⎝ ⎠ 0 0 u u u L 1 L 2 L LL 2-2. Compute V matrix ⎛ ⎞ L v v v ⎜ ⎟ 11 21 L 1 ⎜ ⎟ L v v v 12 22 L 2 T ⎜ ⎟ X U = T = = X U V L V v v v ⎜ ⎟ 13 23 L 3 ⎜ ⎟ M M O M ⎜ ⎟ L ⎝ ⎠ v v v 1 k 2 k Lk

Λ 3 rd Step reconstruction chiba-u geophysics 3-1. Reconstruction of Matrix X using principal components i th matrix X i = T X U V ⎛ ⎞ i i i i L x x x x = λ + λ + + λ ⎜ ⎟ T T T L 11 21 31 L 1 u v u v u v 1 1 1 2 2 2 L L L ⎜ ⎟ i i i i L x x x x = i 12 22 32 L 2 X ⎜ ⎟ = + + + 1 2 L M M M O M L X X X ⎜ ⎟ ⎜ ⎟ i i i i L ⎝ ⎠ x x x x 1 k 2 k 3 k Lk 4 th Step diagonal averaging 4-1. Reconstruction of ith principal Component of G 1i ～ G ni from X i = i i G x 1 11 = + i i i G ( x x ) / 2 2 12 21 = + + i i i i G ( x x x ) / 3 { } 3 13 22 31 = i i i i L 1 , G G G G M j 2 N = + i i i G ( x x ) / 2 − − − N 1 L 1 , K L , K 1 = i i G x N LK

4-1. Global noise reduction with using SSA chiba-u geophysics 00:10 – 00: 15 April 27, 2000 UT － Kak （ reference ） (nT) － Kam (nT) UT Apply SSA

⑰ ⑦ ⑱ ⑲ ⑳ ⑬ ⑭ ⑮ ⑯ ⑫ ⑪ ⑩ ⑨ ⑤ ⑥ ⑧ ④ ③ ② ① Result of SSA kam chiba-u geophysics Reconstructed 1 - 20th principal components by SSA (L=100) kak (reference) Extract common variations Investigate the correlation among components

Global noise reduction with SSA chiba-u geophysics weak Use correlation > 0.7 Number of principal Correation component (kam) Reconstruct with 1,2,3,4,10,14,15,18 th strong Components Number of principal component (kak)

Result of global noise reduction with SSA chiba-u geophysics － ka ｋ （ reference ） － Reconstructed Kam global variation with SSA － kam (original) (nT) － residuals (blue - green) 00:10 – 00:15 April 27, 2000 UT

Result of global noise reduction with SSA (In the case of local variation existence at Kam data) chiba-u geophysics － ka ｋ（ reference ） Local variation at － kam (original) kam (nT) － reconstructed global Kam data with SSA Perform SSA global noise reduction from Feb. – Dec. 2000 for Kam, Sks and Mck with reference of Kak. － residual variation at Kam (Blue - Green) Data length 5 min (300 points) Keep the local variation 15:10 – 15:15 April 27, 2000 UT

時 時 original data kak chiba-u geophysics kam SSA filter can remove global variation (Pc4) Periods of 45-150s (nT) variation (Pc4) sks SSA filter Narrow bandpass filer at 0.01 Hz mck UT kak Estimated global variation at Kam by SSA kam kam (nT) (nT) sks sks Comparison between results of SSA filtering and narrow mck mck bandpass filtering at 0.01 Hz UT UT

Original data kak Variation caused by EQ(M4.8,M4.3) chiba-u geophysics kam Narrow band pass filter at 0.01 Hz can remove shaking effect. (nT) SSA filter can remove the global variation and enhance the small shaking variations. sks SSA filtering Narrow band pass filtering at 0.01 Hz mck June 29, 2000 UT kak Estimated global variation at kam kam using SSA sks mck June 29, 2000, UT June 29, 2000 UT

5-1. Principal Component Analysis (PCA) after filtering chiba-u geophysics ① narrow band pass filter centered at 0.01Hz （ remove shaking effects ） ② SSA filter （ Reduction of global variation ） ③ SSAfilter ＋ narrow band 0.01Hz filter Midnight data (UT15-19) (less artificial noise period) Perform PCA

(1) Result of narrow bandpass filter at 0.01 Hz ( eigenvalue variation) chiba-u geophysics ---:EQ with M>6 λ 1 λ :eigenvalue of 1 st principal component Effect of geomagnetic activities 1 λ 2 :eigenvalue of 2 nd principal component λ 2 :eigenvalue of 3 rd principal component λ λ 3 3 ap ： ap index (magnetic disturbance) ap 地磁気の擾乱度 Es ： Regional EQ energy (within 150 km from ap Mck station for 30 min intervals) Es January – December, 2000

(1) Results of narrow bandpass filter at 0.01 Hz (eigenvalue) (nighttime data) ＊ EQ with M>6 chiba-u geophysics λ 1 λ 2 increase 2 nd and 3 rd comp. before the EQ with M>6 (same results Hattori et. al.( PCE 2004)) . λ 3 ap 3 3 2 2 1 st principal 1 st Principal Es comp . comp . Active EQ period InactiveEQ period Jan. – Dec., 2000

(1) Result of narrow bandpass filter at 0.01Hz (artificial noise effect) chiba-u geophysics (a) (b) λ 1 Variation of principal components intensity in April 2000. λ (a) Weekdays 2 (b) Weekend and holidays λ 3 2 nd principal comp. : influence by artificial noises is large. UT UT weekend Nighttime data : contamination is less. D/N D/N(weekdays) D/N(weeekend) W/H W/H(daytime) W/H(nighttime) 1st comp. 5.6 4.4 2.8 1.6 1.9 1.2 2nd comp. 34.9 36.4 10.9 3.5 3.4 1 3rd comp. 14.4 9.6 10.5 1.3 1.1 1.2 D/N: ratio between daytime and nighttime W/H: ratio between weekdays and weekend/ holidays

(2) Result of SSA filter (variation of nighttime eigenvalues) chiba-u geophysics --- EQ with M>6 Appearence of variation λ caused by shaking effect 1 λ 2 No correlation betweem 1 st principal λ comp. and ap index 3 ap Confirmation of SSA filter performances reduction of global geomagnetic variation Es January – December 2000