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Detecting Ionospheric Precursor of a deep Earthquake on 7 July 2013,
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M w =7.2 Papua New Guinea under Geomagnetic Storm applying
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Two-Dimensional Principal Component Analysis to Two-Dimensional
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Total Electron Content:
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Abstract
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Two-dimensional ionospheric total electron content (TEC) data during the time period
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from 00:00 on 2 July to 12:00 UT on 08 July, 2013, which was 5 days before to 1 days
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after a deep earthquake at 18:35:30 on 7 July, 2013 UT ( M w =7.2) with a depth of
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378.8km in Papua New Guinea, were examined by two-dimensional principal component
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analysis (2DPCA) to detect TEC precursor related to the earthquake because TEC
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precursors usually have shown up in earlier time periods (Liu et al. 2006). A TEC
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precursor was highly localized around the epicenter from 06:00 to 06:05 on 6 July, where
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its duration time was at least 5 minutes. Radon gas release should be a possible reason to
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cause the anomalous TEC fluctuations e.g. a density variance. Other TEC anomalies
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caused by the geomagnetic storm, small earthquakes and non-earthquake activities e.g.
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equatorial ionization anomaly (EIA) resulted in the small principal eigenvalues, therefore
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the detection of TEC precursor was regardless of these anomalies.
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(Keywords: Ionospheric Two-dimensional Total Electron Content, Papua
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New Guinea, TEC anomaly, Two-Dimensional Principal Component
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Analysis, Anomalous TEC fluctuations; Equatorial Ionization Anomaly
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(EIA)).
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1. Introduction
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Recent studies have shown that using principal component analysis (PCA), which is a
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technique for mapping multidimensional data into lower dimensions with less loss of
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information (Kramer, 1991), the earthquake-related TEC anomalies can be
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distinguished from other possible causes of TEC disturbance such as TEC long term
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variance, solar flare and geomagnetic storm activity (Lin 2010; 2011). PCA applied to
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earthquake-related TEC anomalies has been able to detect and even described the
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spatial pattern or physical shape of earthquake-related TEC anomaly (Lin 2011). TEC
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is an important descriptive quantity for the ionosphere of the Earth. Lin’s work (2010)
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used the one-dimensional TEC data at the ground-based received stations near the
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epicenters of the earthquakes to detect the earthquake-related TEC anomalies in
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Taiwan. The global ionospheric maps (GIMs) were decoded by the image processing
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and then the earthquake-related TEC anomalies were found by PCA in Lin’s work
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(2011). In this study, two-dimensional principal component analysis (2DPCA) is used
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to detect ionospheric TEC precursor related to an earthquake at 18: 35:30 on 7 July,
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2013 (UT) ( M w =7.2) with the epicenter of 3.939° S, 153.882 ° E in Papua New
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Guinea. The interesting aspect about this earthquake is its depth at 378.8km. The time
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period of the investigated global ionospheric two-dimensional TEC data is during the
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time period from 2 July to 12:00 UT on 08 July, 2013, which starts 5 days before this
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earthquake, giving time for any TEC precursor to develop because the TEC precursors
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usually revealed in the mentioned time period (Liu et al. 2006). TEC data are
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examined to detect TEC precursor and GIMs are only used to observe TEC situation
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in this study.
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GPS users with single-frequency receivers need ionospheric electron content
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information in order to achieve positioning accuracy similar to dual-frequency receivers.
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The GDGPS System provides a global real-time map of ionospheric electron content
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(currently producing a map each 5 minutes). These maps are also of value in monitoring
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the effect of the ionosphere on radio signals, power grids, and on space weather. The
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maps are derived using data from the ~100 real-time GDGPS tracking sites. The
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integrated electron density data along each receiver-GPS satellite link is processed
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through a Kalman filter to produce the global maps of TEC each 5 minutes. The maps are
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available redundantly from multiple GDGPS Operations Centers (GOCs) as images, as
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text files containing the gridded TEC values, or as a binary data stream containing the
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gridded TEC values (two-dimension) (http://www.gdgps.net/products/tec-maps.html).
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The Kalman filter is performed to the estimate the differential orbit between the two
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satellites as well as a reference orbit, together with their associating dynamics parameters.
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The primary concept of performing Kalman filter is based on assuming that the two
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satellites are separated by a moderately long baseline (hundreds of km or less), and that
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they are of roughly similar shape. The differential dynamics, therefore, can be tightly
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constrained, strengthening the orbit determination. Without explicit differencing of GPS
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data, double-differenced phase biases are formed by a special transformation matrix.
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Integervalued fixing of these biases is then performed, greatly improving the orbit
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estimation (Wu and Bar-Sever, 2005; Kechine et al 2004; Muellerschoen et al 2004;
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Ouyang et al 2008). The TEC data need to be corrected because some biases or delays
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during measurements of dual-frequency (L1 = 1575.42 MHz and L2 = 1227.60 MHz)
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delays of GPS signals e.g. carrier phase biases, satellite state (orbit) corrections,
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Ionospheric delay corrections and troposphere, which need to be removed using
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ground-based post-processing software (Raman and Garin., 2005; Wu and Bar-Sever,
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2005).
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2. Method
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2. 1 2DPCA
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2DPCA is a procedure which can detect anomalies for two-dimensional data. Let the data
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be represented by a matrix B with the dimension of m x n, where m, n>1 (for a map with
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m x n pixels’ gray intensity). The linear projection of the matrix B is considered as
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follows (Sanguansat 2012),
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y  Bx
(1)
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Here
x is
projection axis with the dimension of n x 1 and
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dimension of m x 1 of this data on
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average of the elements of a vector. The covariance matrix for 2DPCA is defined as
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follows;
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W  ( y  Ey )( y  Ey )T
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The trace of
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tr(W )  tr{xT Sx} ,
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The vector
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and the largest eigenvalue is the most dominant component of the data, therefore largest
W
x called
y is
the projected feature with
principal component vector. E is ensemble
(2)
is defined;
where
S  ( B  EB)( B  EB)T
x maximizing
Eq.3 corresponds to the largest (principal) eigenvalue of
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(3)
W
,
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eigenvalue is represented the principal characteristics of the data (Kong et al 2005;
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Sanguansat 2012, Jeong et al. 2009). 2DPCA can be removed small sample signal size
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(SSS) problem for two dimensional TEC data (Fukunnaga, 1991). The PCA converts the
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measurements into one-dimensional data before covariance matrix calculation (Yang et al.
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2004). The covariance matrix of PCA is based on an input matrix with the dimension of
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m x n, which is reshaped from one-dimensional data (length of m multiplying n).
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Reshaping data will cause computing error because PCA is a tool to deal with
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one-dimensional data. Therefore the spatial structure information can not be well
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preserved with some original information loss when inverting to original dimension
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under the condition of the reshaped matrix being small sample size (SSS) using PCA
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(Kramer, 1991). Such information loss is called SSS problem. However, the covariance
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matrix in 2DPCA is full rank for a matrix (two-dimensional data) without reshaping the
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data. Therefore the curse of dimensionality and SSS problem can be avoided (Kong et al
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2005; Sanguansat 2012).
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2.2 Data Processing using 2DPCA
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The TEC data for the mentioned time period is examined by 2DPCA. However after the
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data processing, only a TEC precursor related to this earthquake is detectable during the
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time period from 06:00 to 06:05 UT on 6 July 2012, which is about 1 day before the
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earthquake. Therefore the procedure of TEC data processing in this time period is
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represented in the study. The TEC data in other examined time period are done with the
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same data analysis but not shown because earthquake-related anomalies are not
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detectable. Figure 1 (a) shows the GIM at the time 06:00 UT. Red spot indicates the
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epicenter of this earthquake. This global region is divided into 600 smaller areas, 12° in
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longitude and 9° in latitude to detect more detailed TEC situation. The spatial resolution
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of the TEC data for GDGPS system is 5 and 2.5 degrees in longitude and latitude,
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respectively (Hernández-Pajares et al. 2009; Chen and Gao 2005; Gao and Chen 2006)
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(http://www.gdgps.net/system-desc/references.html)
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(two-dimensional data) are taken in each area because the size of each small area is 12° in
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longitude and 9° in latitude. The 4 TEC data form the matrix B (it belongs to SSS data) of
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dimensions 2 x 2 for Eq. (1) to detect a TEC precursor related to the earthquake. This
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allows for principal eigenvalues to be computed for each of the 600 smaller areas.
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3. Results
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and
therefore
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TEC
data
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Figure 1(b) gives a color-coded scale of the magnitudes of principal eigenvalues
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corresponding to Figure 1 (a). Color intensity denotes magnitude. From this figure it can
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be seen that 600 principal eigenvalues are assigned. Each principal eigenvalue represents
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the TEC characteristic for each area. Figure 2 (a) and (b) show the similar results at the
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time 06:05 UT. High intensity, representative of large principal eigenvalues in this,
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shows the existence of a TEC precursor with a large principal eigenvalue given over the
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region of epicenter for this large earthquake during the time period from 06:00 to 06:05
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UT with the duration time of at least 5 minutes. TEC anomalies from other small
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earthquakes and non-earthquake activities e.g. equatorial ionization anomaly (EIA) in the
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same time period are also not detectable. A large geomagnetic storm activity occurred
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during the examined time period according to the Dst indices in Figure 3. TEC anomaly
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caused by the storm activity results in the small magnitude principal eigenvalues.
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Therefore, the factor of the geomagnetic storm activity can be eliminated when detecting
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the TEC precursor of the earthquake.
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4. Discussion
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2DPCA was able to detect a TEC precursor around the epicenter of this earthquake. The
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precursor was detected from 06:00 to 06:05 UT with the duration time of at least 5
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minutes. Another earthquake-associated TEC anomaly after China’s Wenchuan
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earthquake of 12 May, 2008 (UT) ( M w =7.9) has been identified using PCA and image
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processing (Lin 2011). However, unlike this earthquake, the Wenchuan earthquake was
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not a deep earthquake. However, 2DPCA has detected and located a TEC precursor
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apparently related to such deep earthquake. The physical reason of this relation will now
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be considered. Accordingly, studies of TEC disturbance suggest three possible
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explanations for earthquake associated anomalies. One is shock waves (Jin et al., 2010).
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Since the earthquake was very deep, it is not likely those acoustic shock waves from
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topside vibrations would be responsible for the TEC anomaly. The other possibility is the
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presence of an electric field creating large scale ionospheric density irregularities e.g.
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P-type semiconductor effects due to stress variance in rocks near the focus of the
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earthquake (Pulinets and Legen’ka, 2003; Pulinets, 2004; Freund, 2003; Bošková et al.
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1994; Rothkaehl et al. 2006). A possibility being generated by radon release in the lower
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atmosphere rather than P-type semiconductor effects would seem to be more likely.
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P-type semiconductor effects would not be able to travel through the heterogeneous rocks
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that exist between the surface and 378.8km down, while P and S type waves would have
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attenuated so greatly as to not create adequate rock compression at the surface to generate
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the P-type semiconductor effect. Radon gas release, on the other hand, could occur
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through micro-cracks formed in the crust and the Earth surface. Radon gas can lead to
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lower-atmosphere electric fields, and these can travel unimpeded into the ionosphere
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along geomagnetic lines (Pulinets, 2004). This seems like the most reasonable
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explanation for the TEC precursor. It implies that Radon gas release might cause the TEC
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anomalous TEC fluctuation e.g. a density variance. This fluctuation time is very short,
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the reason might be: Radon gas release caused such TEC fluctuation, however it was
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quickly tranquil because the plasma at that time had the large damping.
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5. Conclusion
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2DPCA has been used to detect a highly localized TEC precursor in the time period from
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06:00 to 06:05 UT on 6 2013 that occurred about 1 day before the mainshock of the July
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7, 2013 Papua New Guinea earthquake, where its duration time of the TEC precursor was
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at least 5 minutes. Radon gas release was a possible reason to cause the TEC anomalous
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TEC fluctuations e.g. a density variance. If it is true, then this technique could be useful
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for understanding of the physical coupling between the ionosphere and processes on the
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ground and at lower altitudes due to Radon gas release, and the large principal eigenvalue
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had a physical meaning and is not a mathematical index.
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Acknowledgements
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The author is grateful to: NASA Global Differential GPS system (GDGPS) for his useful
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references TEC Data and in memory of my German Life. I was Germany student
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(1996-2000).
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Figure Caption
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Figure 1 (a) shows the GIM at the time 06:00 on 06 July 2013. The red spots indicate the
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epicenter of this earthquake.
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Figure 1 (b) shows a color-coded scale of the magnitudes of principal eigenvalues
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corresponding to Figure 1(a).
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Figure 2 (a) shows the GIM at the time 06:05 on 06 July 2013. The red spots indicate the
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epicenter of this earthquake.
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Figure 2 (b) shows a color-coded scale of the magnitudes of principal eigenvalues
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corresponding to Figure 2(a).
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Figure 3 shows the Dst indices during the time period from 01, July to 12:00 UT, 08 July
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2013 (WDC for Geomagnetism, Kyoto).
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