ann methodology for 3d seismic parameters attenuation analysis

J. Wang et al. (Eds.): ISNN 2006, LNCS 3973, pp. 1223 – 1230, 2006. © Springer-Verlag Berlin Heidelberg 2006

Artificial Neural Network Methodology for Three-Dimensional Seismic Parameters

Attenuation Analysis

Ben-yu Liu1, Liao-yuan Ye1, Mei-ling Xiao1, Sheng Miao1, and Jing-yu Su2

1 Institute of Public Safety and Disaster Prevention, Yunnan University, Kunming 650091, China

{liubenyu, lyye, mlxiao, msheng}@ynu.edu.cn http://www.srees.ynu.edu.cn/structure/index.html

2 Civil Engineering Department, Beijing University of Technology, Beijing 100022, China [email protected]

Abstract. With the accumulating of the strong earthquakes records, it becomes practicable to achieve the more accurate attenuation relationships. Based on the seismic records of West American, the Radial Basis Function (RBF) and Back Propagation (BP) artificial neural networks model are respectively constructed for three-dimensional seismic parameters attenuation relationship. The RBF model is nice fitting for the training data, although it has great errors on other tested points. While the BP model is not good than the RBF model for the train-ing data, it possesses a better consecutive property in the whole area. It is a proper neural network model for the problem. After training with the selected records, the Neural Networks (NN) shows a good fitting with the training re-cords. And it is easy to construct three-dimensional model to predict the at-tenuation relationship. In order to demonstrate the efficiency of the presented methodology, the contrast is discussed for the results of the BP model and three typical traditional attenuation formulae.

1 Introduction

Taking from the seismic ground motion attenuation relationships, the movement can easily be predicted if certain earthquake occurred. Traditionally, there are two ways to get this special relationship. One is make a theoretical attenuation model and analyze its influence coefficients and parameters; the other is statistical way from the stations seismic records. Since the complicated nature of the problem, the predicted results of most relationships can not accord with the stations records nice.

As we know, Artificial Neural Networks (ANN) are highly parametric functions of the input variables through processing units, whose high connectivity makes them suitable for describing complex input-output mappings without resorting to a physical description of the phenomenon. Some studies in this problem have been reported. Zheng Guanfen discussed the earthquake intensity attenuation using Back Propaga-tion Neural Networks (BPNN) [1]. Wang Hushuang constructed a NN model to simu-late the peak seismic parameters attenuation relation and a NN to relate the intensity

1224 B.-y. Liu et al.

with peak seismic parameters [2]. By using the peak horizontal acceleration records acquired in Lancang-Gengma Earthquake in 1988, Cui Jianwen constructed a NN model to predict the peak ground acceleration attention relationship in Yunnan region [3].

This paper using the records collected in West America where is abundant in seis-mic records to study the three-dimensional (3D) attenuation relation of the ground seismic parameters. Up to now, it is very difficult to describe the 3D relationships in geophysics. The ANN model just presented a solution to this question. This paper only studied the three dimensions Peak Ground Acceleration (PGA), the peak ground velocity and peak ground displacement can be studied in the similar way. The 3D in the earthquake records are two horizontal directions and one vertical direction. In the paper, the horizontal directions are named as direction 1 and 2, the vertical direction as direction 3.

2 Experimental Statistical Model

The experimental models were simply regressed from the strong earthquakes records. As for the records in West America, the following models were famous.

Joyner-Boore [4]（West America, bedrock and hard soil, 1981）

2222 3.70025.0)3.7lg(249.002.1lg +−+−+−= DDMPGA (1)

This model did not include the magnitude saturation which is proved in many strong earthquakes. Huo Junrong [5] revised this model in order to consider the mag-nitude saturation, as following,

( ) 33268.0lg904.1046.0241.1935.0lg 6135.02 −+−−+−= MeDMMPGA (2)

In these two relations, the attenuation ratio is same when the magnitude is differ-ent. It means that the same magnitude space in the equations has the same variety even in different distance, which is different with the theoretical results and strong earthquakes observations. The fact is famous as magnitude saturation phenomenon. It says even with middle magnitude earthquake (such as M=5), the PGA in the near field may reach a high value; while with the more strong earthquakes, the PGA can’t ex-ceed an upper limit. The far field amplitude of the ground motion may attenuate with different ratio with respect to different magnitude [6]. Thus, Wang Guoxing presented the following equation,

3)84.8lg()251.0797.2(053.4lg −+−−= RMPGA (3)

Where PGA is peak ground acceleration, R is the distance from the observation site to the focal, D is the direct distance from the observation site to the striking fault and M is the Richter Magnitude of the earthquake.

The relations presented by Boore D. M. [6, 7] also included the fault types, the shear wave velocity of the soil where is 30 meters below the observation station. And he made the solution more complicated.

ANN Methodology for Three-Dimensional Seismic Parameters Attenuation Analysis 1225

3 ANN Analysis for the 3D Attenuation Relation

From the attenuation models presented above, we learned that the different statistical model implied different assumption of the relation that is why the given models dem-onstrated great discrepancy with the earthquake recordings. On the other side, the theoretical models are deduced from the very simplified assumptions, which is differ-ent greatly with the real seismic process and geology situation. How to minimize the assumptions in the models and reach a rather feasible attenuation relation for the seis-mic parameters is a valuable problem.

Magnitude Distance Soil Condition

Normalization of the Input Vector

Normalization of the Output Vector

PGA1 PGA2 PGA3

Prediction Training PredictionTraining Training Prediction

Fig. 1. The PGA, PGV and PGD should be constructed in three ANN models. This figure only demonstrated the architecture of the PGA. The PGV and PGD model can just be replaced the PGA with themselves. The number of perceptrons in the hidden layer was determined by net-works itself according to the training effect.

Since ANN is self-studied, self-organized and self-adapted, it is interesting to use this methodology for seismic parameters analysis. The method can learn experiences from the real observation records, so the sufficient learning data is required. The ANN model needs no assumption which may suitable for this seismic problem.

When used for data fitting, the NN model such as BP and Radial Basis Function (RBF) are often employed. The RBF network is a linear basis function method, which can present 100 percent accuracy for the training data; while for the testing data may exhibit great discrepancy. The BP network is limited in the [-1, 1], so it can not behave in great difference. This paper takes the BP network as main model for the problem.

Figure 1 is the ANN model constructed in this paper for the seismic ground pa-rameter analysis. The training samples are the records acquired after the strong earth-quakes. The Magnitude, Distance and Soil Condition are selected as input part. The intensity of the observation station was excluded because it can not be used in the prediction procedure. The output parameters were the seismic parameters at the ob-


servation station, such as PGA, Peak Ground Velocity (PGV) and Peak Ground Dis-placement (PGD). Because the difference nature of the PGA, PGV and PGD, three ANN model were needed to be constructed for the problem.

Fig. 2. RBF fitting with contrast to equation (1)

4 Data Processing

The data in this paper was coming from reference [9], which includes 63 items strong earthquakes of the West America. In order to avoid the deflection of one earthquake attenuation relation to the whole region relations, the records were selected. All the records in the earthquakes which had small data were accepted, while just part of the records was selected for those earthquakes which had excessive records. 186 PGA data were picked from the dataset. The magnitude changed from 4.3 to 7.7, the epi-center distance changed from 1 km to 214 km and the acceleration changed from 0.0081 to 1.2219 (g).

The RBF network was used to demonstrate its efficiency in data fitting. The train-ing data was from 6.0 to 6.5 in magnitude. And the result of the equation (1) was drawn in figure 2. It can easily be pointed that the RBF network can fit the data with certain satisfaction. While in the place with insufficient data, it demonstrate sudden jump of the line, which means the unexpected results may occur.

Because of the situations demonstrated in figure 2. The BP network was chosen for the 3D seismic parameters prediction analysis. In order to present a strong impression this method, the results of equations (1) – (3) are listed in Figure 3 -5.

The data for the network training were also included in these figures. The magni-tude of attenuation relation changed from 5.5 to 7.7, the epicenter distance changed from 5 km to 150 km. One of the horizontal direction results was listed in order to balance with other results.


Fig. 3. The prediction results of equation (1)




Fig. 6. Prediction of artificial neural network

Fig. 7. The ANN prediction curves of the three dimensional attenuation of PGA when the magnitude equal to 6.6

Because most of the earthquake records are collected at middle distance with mid-dle magnitude, the relationships introduced above at this area demonstrated favorable fitting results. But for the high magnitude data fitting, the results may be greatly dif-ferent. The result of equation (3) is the maximum, the equation (1) in the middle, and equation (2) is the minimum. With the increasing of the magnitude, the acceleration is increased which failed the magnitude saturation fact. The ANN model demonstrates the acceleration decrease at the high magnitude, which may represent the magnitude saturation phenomenon. Of course, the insufficiency of the records may be one reason for the acceleration decrease. For the detail situation of the attenuation relation, the three former equations are changed steady while the ANN model is different.


Furthermore, the ANN method can easily get the 3D seismic parameter attenuation relationships. The target of PGV and PGD can be attained just change the training target from PGA to PGV or PGD, and no more assumptions were need for this meth-odology.

In order to demonstrate the advantage of ANN method, the earthquakes data which magnitude is 6.6 is selected. There are 55 records for the hard soil site in the dataset. The ANN data fitting and the original data were pointed in figure 7.

In figure 7, the fitting curves of the direction 1 and direction 2 are relative close. This is because they represent the two horizontal directions. In the near field, they are a little different, and while in the far field they are similar. The direction 3 is the verti-cal direction, which has smaller value than the horizontal direction and has the similar attenuation relationship with the horizontal directions.

5 Conclusions and Suggestions

From the contrast with the traditional seismic parameter attenuation relationships, this paper presented an ANN model to simulate this special relation. After training with the data acquired in West America, the model demonstrated favorable results. Unlike the traditional method, this model involve the magnitude saturation and length influence of the focal just by training the model with the proper data, and the three dimensional vectors and three parameters such as PGA, PGV and PGD can easily be acquired.

From the ANN analysis of this paper, it can easily be found out that the attenuation curves of the horizontal and vertical are different. The results of this paper can provide three dimensional attenuation relationships for engineering usage.

By employed the RBF and BP networks to the training data, this paper demon-strated that the BP network is more suitable for this problem. The architecture of the BP network was constructed in this paper. By contrast with the traditional models, it demonstrated that the ANN model is more suitable for the problem. With the suffi-cient training data, the model may present a reasonable relationship for the seismic parameters attenuation with displacement.

Acknowledgements

This research is financial supported by the National Science Foundation of China under the grant number 40564002, the National Science Foundation of Yunnan Prov-ince under the grant number 2004E007R and the Science and Engineering Foundation of Yunnan University under the grant number 2004Z005B.

References

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2. Wang, H.S..: Intelligent Prediction of the Peak Seismic Parameters Based On ANN. Journal of Seismology 15(2) (1993) 208–216


3. Cui, J.W., Fan, Y.X., Wen, R.Z.: Establishment of Attenuation Law of Acceleration Peak Value by Using Neural Network. Earthquake Research 20(3) (1997) 296–306

4. Joyner, W.B., Boore, D.M.: Peak Attenuation and Velocity from Strong-Motion Records Including Records from 1979 Imperial Valley, California, Earthquake. Bulletin of Seismol-ogy Society of America 71(6) (1981) 2011–2038

5. Huo, J.R.: Near Field Ground Motion Attenuation Research. Ph. D. Thesis of the Institute Of Engineering Mechanics, China Earthquake Administration (1989)

6. Wang, G.X., Tao, X.X.: A New Two-Steps Method for Fitting Ground Motion Attenuation Relationship. Earthquake Engineering and Engineering Vibration 20(1) (2000)25–28

7. Boore, D.M., Joyner, W.B., Fumal, T.E.: Estimation of Response Spectra and Peak Accelera-tions from North America Earthquakes: an Interim Report. U. S. Geol. Surv. Open File Re-port (1993) 93–509

8. Boore, D.M., Joyner, W.B., Fumal, T.E.: Estimation of Response Spectra and Peak Accelera-tions from North America Earthquakes: Part 2, Interim Report. U. S. Geol. Surv. Open File Report (1994) 94–127

9. Hu, Y.X., Zhang, Y.M., Shi, Z.L.: Training Material for the Code of Evaluation of Seismic Safety for Engineering Sites. Engineering Earthquake Research Center (1994)

ann methodology for 3d seismic parameters attenuation analysis

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