Taiwan Chi-Chi Earthquake Precursor Detection Using Nonlinear Principal Component Analysis to Multi-Channel Total Electron Content Records

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1 Journal of Earth Science, Vol. 24, No. 2, p , April 2013 ISSN X Printed in China DOI: /s Taiwan Chi-Chi Earthquake Precursor Detection Using Nonlinear Principal Component Analysis to Multi-Channel Total Electron Content Records Jyh-Woei Lin* Department of Earth Science & Institute of Geoscience, National Cheng Kung University, No. 1 University Road, Tainan ABSTRACT: This research uses eigenvalue characteristics of nonlinear principal component analysis (NLPCA) and principal component analysis (PCA) to investigate total electron content (TEC) anomalies associated with Taiwan s Chi-Chi earthquake of 21 September 1999 (LT) (M w =7.6). The transforms are used for ionospheric TEC from 01 August to 20 September 1999 (local time) using data from 13 GPS receivers. The data were collected at 22 N 26 N Lat. and 120 E 122 E Long.. Applying the NLPCA to the multi-channel total electron content records of GPS receivers, the earthquake-associated TEC anomalies were represented by large principal eigenvalues of NLPCA (>0.5 in a normalized set) on 14 August and 17, 18, and 20 September, with allowance given for the Dst index, which was quiet for the study period. Comparisons were then made with other researchers who also found TEC anomalies on September 17, 18, and 19 associated with the Chi-Chi earthquake, which cannot be detected by PCA. Consideration is also given for reported ground level geomagnetic field activity that occurred between mid-august and late October, leading up to and including the Chi-Chi and Chia-Yi earthquakes, which are associated with the same series of faults. It is possible that Aug. 14 is representative of an earthquake-associated TEC anomaly. This is an interesting result given how much earlier than the earthquake it occurred. KEY WORDS: nonlinear principal component analysis, principal component analysis, multi-channel total electron content records, Taiwan s Chi-Chi earthquake. INTRODUCTION In recent years, ionospheric total electron content (TEC) anomalies and their potential association with earthquakes have led some researchers to think that *Corresponding author: pgjw11966@gmail.com China University of Geosciences and Springer-Verlag Berlin Heidelberg 2013 Manuscript received December 10, Manuscript accepted March 15, such anomalies could be used in earthquake prediction (Hsiao et al., 2010; Lin, 2010a, b; Hayakawa, 2007; Hegai et al., 2006; Heki et al., 2006; Liperovskaya et al., 2006; Liu et al., 2006; Liu and Gao, 2004; Pulinets, 2004) instead of some anomalous detections related to the earthquakes (Li and Shen, 2011; Shen et al., 2011). This is partly because the examination of solid-earth and ionospheric coupling has been greatly improved by GPS satellite coverage where by TEC anomalies are detectable due to signal delay between ground-based receivers and GPS satellites.

2 Taiwan Chi-Chi Earthquake Precursor Detection Using Nonlinear Principal Component Analysis (NLPCA) 245 During earthquake preparation, there are many processes that could create TEC depletions and enhancements. The possibilities include radon ionization producing strong electric fields in the lower atmosphere (Pulinets and Boyarchuk, 2004); local electric fields caused by charge separation in stressed rock, whereby positive holes (pholes) flow out of the stressed rock portion to areas of less stress causing charge separation. These pholes can travel long distances from the earthquake preparation zone deep in the crust to the earth s surface. They concentrate at the ground-to-air interface creating electric field ionization of air molecules (Freund et al., 2009). The turbulence from rapid CO 2 gas release might also create lower atmosphere electric fields (Voitov and Dobrovolsky, 1994). Such lower atmosphere electric fields could travel along geomagnetic field lines into the ionosphere. The potential causes of earthquake-related TEC anomalies differ essentially from an earlier model for the generation of precursory electric field variations observed in Greece (termed Seismic Electric Signals, SES). This could be summarized as follows (Varotsos et al., 1998; Varotsos and Alexopoulos, 1984b). In the earthquake preparation zone, there are electric dipoles consisting of aliovalent impurities and point defects. The relaxation time of these dipoles may gradually decrease when the stress gradually increases in the future focal area. When the stress reaches a critical value, the relaxation time becomes too short; thus, the electric dipoles exhibit a cooperative orientation (the cooperativity is a typical behavior of critical phenomena), resulting in an emission of a transient electric signal that constitutes the SES. The SES enable the determination of the epicenter, the magnitude (Varotsos and Lazaridou, 1991; Varotsos and Alexopoulos, 1984a), and the time window of the impending earthquake when employing natural time analysis both in Greece (Varotsos et al., 2006a, b, 2005, 2002) and Japan (Uyeda et al., 2009). A final coseismic aspect that has been closely examined are fine vibrations in the earth s surface creating subaudible pressure waves that are amplified by density contrast in the atmosphere to produce large amplitude pressure waves, which are called atmospheric gravity waves in the ionosphere (Garcia et al., 2005). Other related studies include research into changes in the geomagnetic field in the preparation zone of earthquakes. For example, prior to the M=7.3 Sept. 21, 1999 Chi-Chi earthquake until after the M=6.2 October 22, 1999 Chia-Yi earthquake on Taiwan anomalous amplitudes in geomagnetic intensity as high as 200 nts existed for 6 weeks, leading up to the Chi-Chi earthquake and lasting until after the Chia-Yi earthquake sequence (Yen et al., 2004). The Chi-Chi earthquake occurred due to bedding slip along the Chelungpu fault, and the Chia-Yi earthquake occurred just at the south of this fault on the Meishan fault, considering the southern boundary of the Chi-Chi earthquake (Yue et al., 2005). Yen et al. (2004) consider the possibility of changes in the geomagnetic field being related to crustal stress during these earthquakes and cite earlier work by Freund (2000) and Bolt (1999) on rapidly moving streaming potentials and electrical charge transfers due to changes in electrical and hydraulic connectivity patterns by Lorne et al. (1999). Pulinets et al. (2004) showed that by using the daily cross-correlation coefficient for ionospheric TEC between two ionosondes (one covering the epicenter of the earthquake and the other hundreds of kilometers away), it was possible to identify statistically TEC anomalies occurring up to 7 days before mainshock nucleation. Liu and Gao (2004) used a 15-day running median of TEC, and the associated interquartile range applied to ground-based GPS-receiver data to measure ionospheric TEC anomalies for 20 (M 6) earthquakes (September 1999 to December 2002) in Taiwan. In their study, TEC anomalies occurred in 80% of cases and were prevalent within 5 days prior to the mainshock. Pulinets et al. s (2004) use of ionosondes was based on the cross-correlation coefficient for TEC anomalies between two ionosondes being high (~0.9). This is significant because the impact of geomagnetic activity on TEC could be measured simultaneously at both ionosondes, which means that a sharp drop in the correlation would be indicative of a localized TEC anomaly, furthering the case for earthquake association. Liu and Gao (2004) established earthquake association for TEC anomalies by using statistical analysis. First, they showed that sparse TEC anomalies

3 246 occurred on 25% of the days in the study period, giving a 1 in 4 chance of observing a sparse TEC anomaly on any given day. However, their data showed that the chance of an anomaly occurring in the 5 days before a major earthquake was 44%, which was almost twice the rate for any other 5-day period (23%). The use of ionosondes to measure TEC is well established; however, spatial and temporal coverage is limited making earthquake-related TEC anomaly correlations difficult (Liu and Gao, 2004). Plus TEC maps generated from ionosondes are subject to short-wave fadeout leading to data gaps (Liu and Gao, 2004; Davies, 1990). On the other hand, the number of ground-based GPS receivers is large and growing, giving good coverage, except over oceans. The validity of using principal component analysis (PCA) applied to one-dimensional TEC data gathered near the epicenters of 12 (M 5.0) earthquakes that occurred on Taiwan between January 2002 and December 2003 was examined (Lin, 2010a). These earthquakes were previously confirmed statistically by Liu et al. (2006) to have earthquake-related anomalies. The results of Lin (2010a) confirmed the findings of Liu et al. (2006) that TEC anomalies existed on the days they claimed; however, unlike the running median method used in Liu et al. (2006), the PCA method determines the existence of TEC anomalies on the basis of a mathematical index. The PCA method was able to give independent confirmation of Liu et al. s results. Like the running median method applied by Liu et al. (2006) and other researchers, PCA still requires elimination of other potential causes, such as solar flare and geomagnetic storm activity. However, Lin (2010a) showed that the technique is independent of long-term variance in TEC due to internal ionospheric features. Lin (2010a) helped establish criteria for using PCA to discover earthquake-related TEC anomalies. The criteria established allows PCA to detect earthquake-associated TEC anomalies when earthquakes are larger than M 5.0, detection is within the earthquake preparation zone, and no alternative explanation, such as X-ray flux or geomagnetic activity, is available to explain the TEC anomalies. This paper gives consideration to the research by Yen et al. (2004), who measured geomagnetic field anomalies between August and October 1999 close by the o Jyh-Woei Lin Chi-Chi and Chia-Yi earthquakes and to the research by Liu et al. (2001), who found statistically relevant TEC anomalies on 17, 19, and 20 September 1999 pertaining to the Chi-Chi earthquake. The goal of this paper is to use nonlinear principal component analysis (NLPCA) instead of PCA, which is based on nonlinear analysis for nonlinear ionospheric plasma, to look for and examine the spatial disturbance of any during earthquake ionospheric TEC anomaly, because the behavior of nonlinear ionospheric plasma should be complicated. NLPCA will be more suitable and sensitive than PCA for TEC analysis. For comparison, the NLPCA and PCA are applied to local GPS network (Fig. 1) ionospheric TEC records from 1 August to 20 September (local time) before the M=7.6 Chi-Chi earthquake in 21 September 1999 (01:47:159 local time), N and E at a depth of ~8 km. Data are based on GPS network data collected from 13 GPS receivers (15 min intervals) at 22 N 26 N and 120 E 122 E (Fig. 1). The results of the transforms are then compared with those of Liu et al. (2001), and the geomagnetic field disturbance that occurred at the earth s surface is attributed to the Chi-Chi earthquake by Yen et al. (2004). Latitude ( N) China main land Chi-Chi o Longitude ( E) Taiwan Island Figure 1. This figure shows the location of 13 GPS receivers (filled circle) and the epicenter of Chi-Chi earthquake (triangle). METHOD PCA into NLPCA PCA is a widely used technique in data analysis. It is a simple method that allows the extraction of relevant data from multivariate datasets. PCA is used

4 Taiwan Chi-Chi Earthquake Precursor Detection Using Nonlinear Principal Component Analysis (NLPCA) 247 to identify and remove correlations among problem variables so as to reduce dimensional space and uncover linear correlations between variables in a given dataset. NLPCA, on the other hand, can uncover both linear and nonlinear correlations, for example, the dynamics of ionospheric plasma. Mathematically, for PCA, the input data matrix is X, which has the dimensions n m; S is called the scores matrix and has dimensions n r, where r is the given number of factors; R is called the loading matrix, and it has dimensions m r (m>r); and the matrix of residuals is called E with dimensions n m (Kramer, 1991). The scores matrix is given by the following relation X=SP T +E (1) Taking P T P=I as the unit matrix for mapping a gaseous form, we have S=XR (2) where S is a row of S (a single data vector), and X is the corresponding row of X or the coordinates of S in the feature space. R is the matrix for linear transformation. By reversing the projection, we get X =SR T (3) where X =X E is the reconstructed measurement vector, and the Euclidean norm is E, which must be minimized for the given number of factors. To satisfy this criterion, then the columns of R must be the eigenvector corresponding to the r eigenvalues of the covariance matrix of X when computed. For NLPCA, by analogy to Eq. 2, mapping is in the form S=H(X) (4) where H is a nonlinear vector function with r individual nonlinear functions: H={H 1,H 2, H r } By analogy to Eq. 3 X =G(S) (5) where G is the second nonlinear vector function, which is composed of r individual nonlinear functions: G={G 1,G 2, G m }, the loss of information is again measured by E=X X to minimize E, as with PCA, when H and G are selected. To generate H and G, a basis function approach is used (Cybenko, 1989). Similar to PCA, the largest eigenvalues λ 1 of the covariance matrix X can then be computed. The largest eigenvalue is called the principal eigenvalue (λ 1 ), which represents the principal characteristics of input signals X. TEC Processing The NLPCA is applied to data from 1 August to 20 September The daily data were collected from 13 GPS receivers (15 min intervals) at 22 N 26 N and 120 E 122 E (Fig. 1). The 15 min intervals mentioned suggest that the GPS data were obtained from certain GPS satellites that appear over the horizon every 15 minutes. The Chi-Chi earthquake (M w =7.6) occurred at 01:47:159 (LT) on 21 September 1999 at N and E at a depth of ~8 km. In order for TEC characteristics to be described on a day-to-day basis, the TEC records for a day form matrices of dimensions 13 rows (receivers) (m) and 96 columns (a day) (n), and these are used as inputs in to Eqs. 2 and 3, whereas Eqs. 4 and 5 to output a principal eigenvalue of PCA and NLPCA for this day. The principle eigenvalues generated are representative of daily TEC. Figure 2a shows the principal eigenvalues of PCA from 1 August to 31 August and 15 to 20 September for the TEC records that are mentioned above. Figure 2b shows the principal eigenvalues of NLPCA for dame time interval as in Fig. 2a. All of the principal eigenvalues are normalized by dividing by the maximal value. Principal Eigenvalues of NLPCA are considered large when they are >0.5 in a normalized set (Lin, 2010a). The magnitudes of principal eigenvalues of NLPCA are large on 14 August and 17, 18, and 20 September, which may indicate the precursors of the earthquake. However, the Principal Eigenvalues of PCA are not large (<0.5). RESULTS AND DISCUSSION Figures 2a and 2b give the results of the PCA and NLPCA conducted for 1 August to 20 September Large principal eigenvalues of PCA are not found in Fig. 2a. Four large principal eigenvalues of NLPCA are found to represent earthquake-associated TEC anomalies for the time period: 14 August, 17, 18, and 20 September. Figures 3a, 3b, 3c, and 3d shows the latitude-time-tec plots obtained from the Taiwan GPS network (Liu et al., 2001) on 14 August and 17, 18, and 20 September before the Chi-Chi earthquake.

5 248 Jyh-Woei Lin 1 (a) Eigenvalues (August 1999) 1 (b) Eigenvalues (August 1999) Eigenvalues Eigenvalues Eigenvalues Date, August 1 Principal Eigenvalues from Sep.15 to Sep Date, September Eigenvalues Date, August Principal Eigenvalues from Sep.15 to Sep Date, September Figure 2. (a) The figure showing the magnitudes of the principal eigenvalues of PCA assigned to ionospheric TEC from 01 for the time periods from 1 August to 31 August and 15 to 20 September 1999; (b) the figure showing the magnitudes of the principal eigenvalues of NLPCA assigned to ionospheric TEC from 01 for the time periods from 1 August to 31 August and 15 to 20 September Figure 3e is a normal day. Note depletions are evident at the approximate latitude of the Chi-Chi earthquake according to these Figs. 3a, 3b, 3c, and 3d. The results of NLPCA for 17, 18, and 20 September are similar to those by Liu et al. (2001), who also found TEC anomalies for these dates. In another study, Liu et al. (2006) combined data from 13 GPS receiver stations with time and spatial variations in TEC prior to the Chi-Chi earthquake and found statistically significant decreases in TEC 1, 3, and 4 days before the earthquake based on a 15-day running median for TEC. Taiwan lies under the northern boundary of the equatorial ionospheric anomaly (EIA), and Liu et al. s paper describes an equatorialward shift of the EIA for the afternoon periods of 17, 18, and 20 September. Similarly, Tsai et al. (2006) utilizing a 15-day median, and the assumption of a normal distribution found with 80% to 85% confidence level TEC anomalies on 17 and 18 September for the time period 10:00 to 20:00 (LT). In a later study, Nishihashi et al. (2009) examining the spatial extent of GPS-TEC-related TEC anomalies found that it was possible the 17 September anomaly could have been influenced by geomagnetic storm activity; however, the study confirmed 18 and 20 September as potentially earthquake-related TEC anomaly days. As mentioned in the introduction, Yen et al. (2004) measured geomagnetic activity associated with the 1999 Chi-Chi and Chia-Yi earthquakes. These two earthquakes are closely related to a series of faults that include the Chelungpu, Tachiashan, Meishan, Luliao, and Chushiang faults, all of which are thought to have been active during the Chi-Chi and Chia-Yi earthquake sequence. Geomagnetic fluctuations for southern Taiwan were measured by a series of seven magnetometers distributed across seismic zones throughout southern and eastern Taiwan with an additional reference station in seismically quiet northern Taiwan.

6 Taiwan Chi-Chi Earthquake Precursor Detection Using Nonlinear Principal Component Analysis (NLPCA) 249 Figure 3. The latitude-time-tec plots obtained from the Taiwan GPS network on 14 August and 17, 18, and 20 September before the Chi-Chi earthquake, Fig. 3e is a normal TEC day. The line is the latitude of epicenter for the Chi-Chi earthquake; (a) 14 August 1999, (b) 17 September 1999, (c) 18 September 1999, (d) 20 September 1999, and (e) 19 September The study conducted from mid-august to November 1999 found frequent fluctuations in geomagnetic intensity caused by earthquake preparation processes for 6 weeks, leading up to the Chi-Chi earthquake until right after 22 October Chia-Yi earthquake after which time geomagnetic activity became quiet very abruptly (Fig. 2; Yen et al., 2004). The causes of geomagnetic fluctuations are not completely understood. Yen et al. (2004) consider the possibility of intense electric fields created by charge separation developing in stressed rocks when pholes move away from the stressed rock areas (Freund, 2000) as described in the introduction and also streaming potentials caused by changes in the hydraulics of crustal rocks and sediments (Lorne et al., 1999). Considering these results in association with those given in Fig. 2b for the NLPCA, a large principal eigenvalue was

7 Jyh-Woei Lin 250 found on 14 August and for the days close to the Chi-Chi earthquake. The date 14 August is earlier than the collection date for geomagnetic activity given by Yen et al. (2004), whereas their paper and a consequent paper by Tsai et al. (2006) do not mention why mid-august was chosen as the commencement date for observing geomagnetic activity associated with these two earthquakes, so one can assume that this is probably because this is when they first noted anomalous activity. This would mean that the 14 August anomaly perhaps occurred when earthquake-related geomagnetic activity was in a quiet period. However, this would need to be confirmed. The 14 August result, however, is interesting in another way. It occurred well before the Chi-Chi earthquake on a geomagnetic quiet day according to the Dst Index (Fig. 4). The result is similar for that 17, 18, and 20 September (also quiet days by the Dst Index), where NLPCA confirmed the results of TEC anomalies associated with the Chi-Chi earthquake by Liu et al. (2001), Tsai et al. (2006), and Nishihashi et al. (2009). It is possible that the TEC anomaly of 14 August is earthquake related, and it occurred well before the dates discovered above by these other researchers, all of which used 15-day running medians before the Chi-Chi earthquake. The reason why this is done is because the past research by Chen et al. (2004) showed that the observation of earthquake-associated TEC anomalies in Taiwan for M 5 earthquakes in the 1 to 5 days before an earthquake (1994 to 1999) was not due to statistical chance. This they proved with a simple coin-toss comparative study. However, if NLPCA has the ability to determine earthquakeassociated anomalies based on a firmer mathematical footing, then 14 August could possibly be an earthquake-associated anomaly. Two recent studies of the China 12 May 2008 Wenchuan earthquake (Jhuang et al., 2010; Kakinami et al., 2010) using empirical studies with normalized TEC data found possible earthquake-related TEC anomalies on days 6 and 13 before that earthquake. Their results are important in that they help support the result given in this work. Figure 4. Dst index from 1 August 1999 to 30 September There are many potential causes of ionospheric TEC anomalies resulting from lower atmospheric forcings. These include internal ionospheric features, radio waves from the lower atmosphere, cosmic rays, and geomagnetic storms (Lin, 2010a). In addition, long-term variance in TEC must also be considered when applying PCA. Previous studies using PCA have shown that the results are not affected by long-term variance (Lin, 2010a). Lin (2012) used NLPCA to examine both ionospheric TEC anomalies before the 12 May 2008 Wenchuan earthquake in China, and those of an earthquake-free day when a known geomagnetic storm was taking place. The magnitude of large principal eigenvalues returned (>0.5 in a nor-

8 Taiwan Chi-Chi Earthquake Precursor Detection Using Nonlinear Principal Component Analysis (NLPCA) 251 malized set) (Lin, 2010a) were relatively small for the geomagnetic storm day compared with those given for the earthquake. CONCLUSION The NLPCA can be applied to data from 13 GPS receivers to detect TEC anomalies related to the Taiwan s Chi-Chi earthquake of 21 September 1999 (LT) (M w =7.6) instead of PCA. The transforms are conducted for ionospheric TEC from 1 August to 30 September 1999 (local time). Data collection was for the region 22 N 26 N Lat. and 120 E 122 E Long.. TEC anomalies were given by large principal eigenvalues of NLPCA for 17, 18, and 20 September and 14 August with consideration given for the Dst Index, which was quiet for the study period. Comparisons are made with the work of other researchers, such as Liu et al. (2001), who also identified TEC anomalies for these days through deviations from a 15-day running median and Yen et al. (2004) who reported intense geomagnetic field activity at a ground level, leading up to the Chi-Chi earthquake until after 22 October 1999 Chia-Yi earthquake. Both these earthquakes are associated with the same series of faults. The comparative results for NLPCA with ground-level geomagnetic activity are inconclusive. The possibility, however, exists that 14 August had an earthquake-associated TEC anomaly earlier than 1 to 5 days period currently used to find these anomalies. ACKNOWLEDGMENTS The author is grateful to Dr. J Y Liu from the Institute of Space Science for the useful references. REFERENCES CITED Bolt, B. A., Seiamology: Resources for Teachers. Earthquake (4th Edition). W. H. Freeman and Company, New York. 366 Chen, Y. I., Liu, J. Y., Tsai, Y. B., et al., 2004, Statistical Tests for Pre-Earthquake Ionospheric Anomaly. TAO, 15(3): Cybenko, G., Approximation by Superpositions of a Sigmoidal Function. Math. Control Signal & Sys., 2: Davies, K., Ionospheric Radio. Peter Peregrinus Ltd., London. 580 Freund, F. T., Time-Resolved Study of Charge Generation and Propagation in Igneous Rocks. J. Geophys. Res., 105: Freund, F. T., Kulahci, I. C., Gyr, G., et al., Air Ionization at Rock Surfaces and Pre-Earthquake Signals. J. Atmos. Sol. Terr. Phys., 71(17 18): , doi: /j. jastp Garcia, R., Crespon, F., Ducic, V., et al., Three-Dimensional Ionospheric Tomography of Post- Seismic Perturbations Produced by the Denali Earthquake from GPS Data. Geophys. J. Int., 163: , doi:0.1111/j x x Hayakawa, M., VLF/LF Radio Sounding of Ionospheric Perturbations Associated with Earthquakes. Sensors, 7(7): , doi: /s Hegai, V. V., Kim, V. P., Liu, J. Y., The Ionospheric Effect of Atmospheric Gravity Waves Excited Prior to Strong Earthquake. Advance in Space Research, 37: Heki, K., Otsuka, Y., Choosakul, N., et al., Detection of Ruptures of Andaman Fault Segments in the 2004 Great Sumatra Earthquake with Coseismic Ionospheric Disturbances. J. Geophys. Res., 111(B09313): 11, doi: /2005JB004202, 2006 Hsiao, C. C., Liu, J. Y., Oyama, K. I., et al., Seismo- Ionospheric Precursor of the 2008 M w 7.9 Wenchuan Earthquake Observed by FORMOSAT-3/COSMIC. GPS Solutions, 14(1): 83 89, doi: /s Jhuang, H. K., Ho, Y. Y., Kakinami, Y., et al., Seismo- Ionospheric Anomalies of the GPS-TEC Appear before the 12 May 2008 Magnitude 8.0 Wenchuan Earthquake. Int. J. Remote Sens., 31(13): , doi: / Kakinami, Y., Liu, J. Y., Tsai, L. C., et al., Ionospheric Electron Content Anomalies Detected by a FORMOSAT- 3/COSMIC Empirical Model before and after the Wenchuan Earthquake. Int. J. Remote Sens., 31(13): , doi: / Kramer, M. A., Nonlinear Principal Component Analysis Using Autoassociative Neural Networks. AIChE Journal, 37(2): Li, J., Shen, W., Investigation of the Co-Seismic Gravity Field Variations Caused by the 2004 Sumatra-Andaman Earthquake Using Monthly GRACE Data. Journal of Earth Science, 22(2): , doi: /s x

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