The ICA of Gravity Earth Tide Based on Genetic Algorithm and Extraction of Seismic Precursor Information

2016 Joint International Conference on Artificial Intelligence and Computer Engineering (AICE 2016) and International Conference on Network and Communication Security (NCS 2016)

ISBN: 978-1-60595-362-5

The ICA of Gravity Earth Tide Based on Genetic Algorithm and

Extraction of Seismic Precursor Information

Xiao-Liang TANG

_{, Hai-Yan QUAN}

1_{Faculty of Information and Automation, Kunming University of Science and Technology,}

Kunming, Yunnan, China

a_{[email protected],} b_{[email protected]}

*Corresponding author

Keywords:  The Gravity Earth Tide, ICA, GA, Singular Waveform, Earthquake Precursors

Information. 

Abstract: In the analysis of the Gravity Earth Tide signal, using a three－dimensional orthogonal

decomposition model to decompose the harmonic information of the tidal signal into 3 orthogonal components. And this paper uses the traditional ICA and real coded genetic algorithm (GA) combined method, which has been proved is feasible and effective by the experiments .By the way we used the combination of the measured signal and the theoretical signal to extract the harmonic information of the tidal signal. This paper found some singular waveform in the long period waves before the indefinite earthquake point, which reflects the change of the earthquake energy before the earthquake point.

Introduction

Under the common action of the gravitational force of the sun and the moon, the regular tides generated by the solid earth are called the solid tide [1]. It can be divided into long period wave, daily wave, semidiurnal wave and 1\3 daily wave.

In order to extract the harmonic component effectively, the three-dimensional orthogonal decomposition model will be used. Based on this model, and used the method that combines the independent component analysis (ICA) method with the real coded genetic algorithm (GA), extracting the long period wave, daily wave, semidiurnal wave. And analyzed the 3 characteristic harmonics, in order to captured the seismic precursor information.

Decomposition Model of the Gravity Earth Tidal

As shown in Figure1, it is the three-dimensional orthogonal decomposition model. Take the observation point A on the earth as an example, to analyze the Fm that represents the gravity Earth tide which is caused by the moon's tidal force to the earth [2].

According to the model, we can put forward the hypothesis, that FR parallels to the Earth's rotation axis, so that the component is not affected by the earth's rotation. Therefore, this component does not contain harmonics caused by the earth's rotation, and it mainly consists of long-period harmonic component caused by the sun, the moon's tidal force. The FE parallels to the equatorial plane, and affected by the earth's rotation, so this harmonic component contains mainly short-period harmonics. In summary, according to the mechanism of the gravity earth tidal, we can decompose the different factors into different harmonic lines vector to form a three-dimensional orthogonal decomposition model.

Independent Component Analysis (ICA) Based on Real Code Genetic Algorithm

ICA is a method for processing the blind signal which can separate an unknown source signal from the linear mixing of unknown source [3]; Because ICA can fully describe the essential properties of signal, so it can be applied in extracting seismic signal and denoising of seismic signal; we can use ICA to extract the attribute data, eliminate the interference of the original property of seismic signal to get the independent seismic attributes [4], in the hypothesis that it is effectively independent between seismic signals and random noise signal. The signal can be expressed in the form of the following matrix:

  .  (1) 

Y=W*X, Where the Y is the output signal, W is the separation matrix, X is the observation signal. The problem of ICA is to find out the optimal separation matrix W. There are always some assumptions about the mean and variance of the signal before processing it. We need to do some centered processing (de-mean) and whitening processing [5] to satisfy assumptions.

ICA constituted by the objective function and learning methods with the estimation and optimization of the target. Due to defects of the normal learning methods, this paper uses the genetic algorithm as the optimization algorithm to optimize the objective function .Experiments show that the method can search the optimal answers quickly and stably. The basic flow chart of the algorithm is shown in Figure 2.

Figure 2. Flow chart of the algorithm.

In this paper, we use the genetic algorithm (GA) to search for the maximum value of the negentropy[6]-the objective function, so as to update the separation matrix W continuously. When the W gets the best, the output signal Y also reaches the global optimal value.

the traditional ICA algorithm, this paper adopts GA as an optimization algorithm to optimize the objective function and tries different objective functions to separate the tidal signal, finally chooses the best one as the final objective function. The main steps of the algorithm to process the gravity earth tide signal are as follows:

(1) Get the input signal.

(2) Preprocessing. The purpose of the de-mean is to ensure that the source signal’s mean is zero. The whitening processing can eliminate the linear correlation between the individual signals, so that the signals can be independent of the two order.

(3) Using the GA to search the optimal separation matrix.

1. Define the initial population Generate the population Xi randomly, determine the crossover probability Pc and the mutation probability Pm and the individual string length L.

2. Select the objective function. The individual is evaluated by the fitness

value. . To select the maximum of Fitness as the evaluation

of the optimal value, then record the optimal value and the corresponding individual W.

3.Genetic manipulation. According to the initialization fitness, to process the selection, crossover, mutation and evolve individuals.

4. Search and update. The fitness value of the objective function is calculated again after genetic operation, and the optimal value is updated. The search strategy used in this paper is the optimal preservation strategy.

5. Repeat step 3, step 4 until the termination condition is reached.

6. Find the optimal separation matrix W and extract the output signal by Y=X*W [7-10].

7. Do the spectral analysis with this model used in the paper, and analysis whether the result is consistent with the theoretical value.

8. Add the measured signal and extract the seismic precursor information.

Analyze the Experimental Results

0 1000 2000 3000 4000 5000 6000

-500 0 500

(a)sig₁(t)

AM

0 1000 2000 3000 4000 5000 6000

-500 0 500

(b)sig₂(t)

AM

0 1000 2000 3000 4000 5000 6000

-500 0 500

(c)sig₃(t)

AM

0 1000 2000 3000 4000 5000 6000

-2 0 2x 10

4

(d)sig₄(t)

AM

Figure 3. Input signal. 

0 1000 2000 3000 4000 5000 6000

-5 0 5

(a)O₁(t)

AM

0 1000 2000 3000 4000 5000 6000

-5 0 5

(b)O₂(t)

AM

0 1000 2000 3000 4000 5000 6000

-5 0 5

(c)O₃(t)

AM

0 1000 2000 3000 4000 5000 6000

-5 0 5

(d)O₄(t)

AM

Figure 4. Extracted signal.

and the geographical coordinates of sig3, sig2 are P2(102.74694°S,32°N), P3(102.74694°S,40°N). The acquisition of the three channels gravity earth tide signal is calculated by the closed formula, based on this, this paper introduces the fourth signal sig4 which is the actual detected data from the Black Dragon Pool seismic station in Kunming and has the same geographical coordinate with P1(102.74694°S,25.1483°N). The input signal is shown in Figure 3, the various components extracted by the ICA are shown in Figure 4.

In order to test the validity of this method, we need to do some spectral analysis to the extracted signal O(t). We can get Fig5 by doing FFT to the components of O(t) and also get the main frequency components in the frequency spectrogram.

2.15 2.2 2.25 2.3 2.35 2.4

x 10-5 0

1000 2000 3000

(a)The FFt of O₁(t)

AM

0 0.5 1 1.5 2 2.5 3 3.5 4

x 10-6 0

1000 2000 3000

(b)The FFTof O₂(t)

AM

2 4 6 8 10 12

x 10-6 0

200 400 600

(c)The FFT of O₃(t)

AM

1 1.05 1.1 1.15 1.2 1.25

x 10-5 0

1000 2000 3000

(d)The FFT of O₄(t) f/Hz

AM A B C D E A B C A B C D

Figure 5. The FFT of output.

0 1000 2000 3000 4000 5000 6000

-5 0 5

(a)O1(t)

AM

2880 2900 2920 2940 2960 2980 3000 3020 3040 0.5

1 1.5

(b)O2(t)

AM

0 1000 2000 3000 4000 5000 6000

-5 0 5

(c)O3(t)

AM

0 1000 2000 3000 4000 5000 6000

-5 0 5

(d)O4(t)

AM

A

The main frequency components of O1(t) are as follow: fA=21.93Hz, fB=22.35Hz, fC=22.8Hz, fD=23.15Hz; O2(t): fA=0.0693Hz, fB=0.4158Hz, fC=0.8316Hz, O4(t): fA=10.33Hz, fB=10.78

Hz, fC=11.19Hz, fD=11.54Hz, fD=11.61Hz, fE=11.54Hz. The harmonic frequency of the components above are corresponding with the theory value launched by DuSen in the range of allowable error. so it is feasible and effective to extract the gravity earth tide using the three-dimensional orthogonal decomposition model and ICA algorithm based on GA used.

There are four channels output as shown in Figure 4; namely, daily wave system harmonic component O4(t) and long period wave system harmonic component O2(t) and semidiurnal wave system harmonic component O1(t). The analysis shows that the long period wave system harmonic components O2(t) mainly exists in the FR that parallels to the earth’s rotation axis, daily wave system harmonic component O4(t) and semidiurnal wave system harmonic component O1(t) mainly existed in the FE that parallels to the equatorial plane. This result has confirmed the above assumption.

The noise interference is inevitable in the measurement process. As is shown in Figure 5, there are too many harmonic frequency of O3(t), which is tagraggery and can’t correspond to the theory value calculated by DuSen, so the O3(t) is noise. Therefore, we only analyze the other 3 channels signal except the noise O3(t). Analysis found there is a singularity in the long period wave O2(t) at a moment before the earthquake, as shown in Figure 6.

According to the data measured by Black dragon Pool seismic station in the Kunming, there was one earthquakes in 1999, which were detected in Chengjiang in November 25, 1999. If we converted a year into an horizontal coordinate with the unit of hour, then the earthquake occurred in about 4993 of the coordinates. As the A point shown in the Figure 6, singular value appeared in about 2953th, which is 2040 points(about 85 days ) before the earthquake. In order to verify whether the event is an happenchance, we analyzed several groups of data from the seismic stations, found that there will be one even more singular values in the long period waves before every earthquake point.

According to the data measured by the Black dragon pool Seismic Station (102.74694°S,25.1483°N) at Kunming, sampled 7 groups of data to analyze, the comparison of earthquakes points and singular value points are shown in the following table (precision is 1 hour):

Table 1. The comparison of earthquakes points and singular value points. earthquakes time Earthquake

location coordinate

earthquakes point [hour]

Singular point [hour]

How long before the earthquake

2000-04-03-23h-38m-37.0s 25.55°,101.07° 2257 1440 _{817h about 34 days} 2000-08-21-21h-25m-39.0s 25.82°,102.22° 5614 5113 _{501h about 21 days} 2001-07-15-02h-36m-05.0s 24.33°,102.63° 13468 12410 _{1058h about 44 days} 2001-10-27-13h-35m-40.0s 26.23°,100.57° 15975 14620 _{1325h about 55 days} 2002-05-13-09h-52m-06.2s 25.17°,103.05° 20723 18950 _{1773h about 74 days} 2003-07-21-23h-16m-30.0s 25.95°,101.23° 31152 29190 _{1962h about 82 days} 2003-10-16-20h-28m-03.0s 25.92°,101.30° 33237 32140 _{1097habout 46 days}

The data are taken from the same data package, and the starting point is the January 1, 2000, the precision is 1 hour

Summary 

tide signal into three components-the long period waves, daily waves and semidiurnal waves corresponds based on the three orthogonal components model, and validated the above hypothesis.

Further study on the harmonic component found that there are several singular values in the long period wave before the earthquake points, which makes us think that it may be associated with the earthquake. Studies have shown that daily wave and semidiurnal wave have some triggered influence to the earthquake in some regions [11]. Earthquake, however, is a long-term energy accumulation process, when the energy accumulation reached a state that is far away from the equilibrium state, the crustal plates also reached the highly unstable state, any tiny fluctuations may be amplified and cause an enormous energy gap, thus induce an earthquake.

The long period accumulates energy for a long time, however, all the experimental data shows that there isn’t a singular value at the earthquake point did in the long period wave. so we can infer that the long period wave participated the previous work of the earthquake, showing the process of the earthquake energy accumulation, and not triggered the earthquake directly.

The singularity in the long period wave is the energy accumulation reached a certain height and brought some unstable phenomenon, which provides some forecast for the earthquake. It just say the earthquake may come. But a large number of experiments show that each earthquake is not the same about how long before the earthquake the abnormal waveform will appear. that is, there is too much uncertainty about how long the earthquake will occur after the Singularity. And the connection between the singular value and the location and magnitude of the earthquake is still unknown, so this method can’t be used as a method of earthquake prediction recently.

Acknowledgement

This work is supported by National Natural Science Foundation of China (No. 41364002), State Science Foundation of Yunnan (No. 2009ZC048M) and Science Grant of Kunming University of Science and Technology (No. KKZ3201103022). The authors are graceful for the support of the grants.

References

[1] Zhao X.Y., Chen C.X. Gravity observation technique [M]. Beijing: Seismological Press, 1997: 20-26.

[2] Li Q.Y., Quan H.Y., Analysis on the signal of the Gravity Earth Tide based on ICA and extract the information of tidal harmonics [J]. Journal of Yunnan University(Natural Sciences Edition), 2015 (6) 845-850.

[3] Shun S.Y., Blind Signal Processing Foundation and It’s Applications [M]. Beijing: National Defend Industry Press, 2010.

[4] Yu X.C., Hu D., Blind Source Separation Theory and Application [M]. Beijing: Science Press, 2011.

[5] Shi X.Z., Blind Signal Processing Theory and Practice [M]. Shanghai: Profile of Shanghai Jiao Tong University Press, 2008.

[6] Jiang D., Information Theory and Coding (Second Edition) [M]. Hefei: Press of University of Science and Technology of China, 2004.

[7] Wang X.P., Cao L.M., Genetic Algorithm Theory, Application and Software Implementation [M]. Xi’an: Xi’an JiaoTong University Press, 1998:1-14.

[9] Shi F., Wang H., 30 Case Analysis of MATLAB Intelligent Algorithm [M]. Beijing: Beihang University Press, 2011:19-26.

[10] Peng S.F., The Research on Speech De-noising Based on ICA in High Noise Environment [D]. HuBei: Hubei University Of Technology, 2013.