A Neural Network Scheme For Earthquake. City University, Centre for Information Engineering(1), Department of Computer Science(2),

Transcription

1 A Neural Network Scheme For Earthquake Prediction Based On The Seismic Electric Signals Spiros Lakkos 1, Andreas Hadjiprocopis 2, Richard Comley 1, Peter Smith 2 City University, Centre for Information Engineering(1), Department of Computer Science(2), Northampton Square, London, EC1V 0HB, UK Introduction It has been reported that transient variations of the electrotelluric eld - called Seismic Electric Signals (SES) - are observed before an earthquake. The study of the physical properties of these signals is used for the determination of the parameters (epicentre and magnitude) of an impending event[1]. The occurrence of these precursors varies from a few hours to a few days before the earthquake and have a duration of one minute to a few hours. These signals appear as a transient change of the potential dierence measured between two electrodes (up to a few tenths of V/m) (Figure 1) depending on the earthquake magnitude, Ms, the epicentre, local geophysical inhomogeneities, source characteristics and travel path. The components of the electric eld are measured in two perpendicular directions (East-West and North-South) using dipoles with lengths varying from a few tenths of meters to a couple of kilometers. Very often, noise obstructs the clarity of SES. It can be classied into three categories depending on the nature of the cause: electrochemical, magnetotelluric and cultural. By using various techniques[9], [10] to eliminate the noise from the electrotelluric eld measurements and by applying 1

2 certain, well dened, criteria[2], the detection of SES is achieved. The study of the physical properties of SES and their correlation to the impending seismic activity leads to the construction of an empirical selectivity map for a monitoring station. Selectivity is dened as the sensitivity of a station to signals from a restricted number of seismic areas while remaining insensitive to SES from other areas[3]. In this paper a dierent approach is suggested for the construction of the selectivity maps based on the use of Articial Neural Networks. Articial Neural Networks The most basic function of Articial Neural Networks (ANN) is the mapping of an N-Dimensional space to M Dimensions. By adjusting the weights of the internal connections of the network, through training, a transformation function is approximated. The accuracy of the resultant mapping depends on the amount of the output error at the end of the training process, as well as, whether the training set is a representative sample of the domain of the application. The problem was to nd a suitable transformation which would map the two dimensional input data (the relative SES components [mv/m] in the directions East-West and North- South) collected by the monitoring station, into a three dimensional representation (the geographical location - longitude and lattitude - and the magnitude of the impending event), (Figure 2). The XERION software package[16] was used to simulate a feed-forward Network. Several combinations of network architectures and training algorithms were tested. The conguration that gave satisfactory results comprised of: Two input nodes corresponding to the two components of the SES, Fourty ve hidden layer nodes, Three output nodes corresponding to longitude, lattitude and magnitude information. 2

3 The Delta-Bar-Delta[16] training algorithm was employed. The training data was collected by a monitoring station based at Ioannina (western Greece) and presented in [1 to 8]. Due to its small size, expansion of the original set was necessary by addition of a small amount of Gaussian noise to each of the training vectors. The size of the data set has been increased by a factor of ve, (Figure 3). The mapping produced with the expanded data set works better since the network now has a better idea of what the input surface looks like and any misinterpretations due to restricted input data are avoided. Although the overall output error in this case increases, a continuous and smooth output is obtained, moreover, meaningless output values are avoided. After convergence, the network can be used to predict impending earthquakes and construct the selectivity map for a monitoring station. Interpretation of the Results The network has been tested using a small subset of the available data which has not been presented to the network during the training process. The majority of the training vectors was associated with earthquakes from the geographical area 20:0 o E? 21:5 o E; 37:5 o N? 40:0 o N. As a result the network prediction accuracy was higher in that area. The epicentre location can be predicted with an error of less than 0:3 o, and the magnitude with an error of less than 0.5 Ms. The most successful of the methods used so far for the same purpose, based on traditional statistical linear models have approximately twice as much error. Furthermore, by feeding the network with a data set occupying the whole input space, a surface related directly to the sensitivity properties of the station is obtained, thus, approximating its selectivity map, (Figure 4). A possible way of investigating the travel paths of the SES and certain geophysical characteristics of the monitoring area is to present the network with a set of data as above and plot only the epicentre information, discarding the magnitude. The obtained curves or family of curves indicate paths where SES 3

4 sensitive to that station possibly propagate, (Figure 5). Similarly, by discarding the epicentre information and plotting only the earthquake magnitude versus one component of the input vectors, while the other is kept constant, the relationship between the magnitude of the earthquake and the SES could be obtained, (Figure 6). Comments and Conclusions The method presented here is superior to the classical statistical method for the prediction of earthquakes based on the SES. The construction of the selectivity map has become a relatively easy and accurate task. Once the network is trained with a large data set, the results can be considered suciently accurate for practical purposes. Furthermore the trained network can be used as a model for geophysical research. More work can be done to further investigate the behaviour of the Neural Net under unconventional conditions. Other network topologies, such as Self Organised Maps, could be employed. It is also worth considering the idea of a network with inputs from more than one monitoring stations. Despite the fact that so far a single network was employed assuming a strong correlation between the magnitude and epicentre of the earthquake, it could be possible to use two separate networks. We would like to acknowlegde the help and advice of Mr. J.Makris, University of Athens. 4

5 Figure 1: Typical forms of Seismic Electric Signals. Earthquake Prediction [Ms] Eq. Mag. [o] Longitude [o] Latitude Artificial Neural Network E NS Seismic Electric Signals EEW Figure 2: Input to Output Space transformation by means of ANN. 5

6 noisy.examples basic.examples Ens [mv/m] Eew [mv/m] Figure 3: The input training vectors. Sensitivity_Area High_Sensitivity_Area Longitude E[o] Latitude N[o] Figure 4: Sensitivity map of a monitoring station. 6

7 IOA Station Coord. vs Ens Experimental_Data IOA_Station x Latitude N[o] Ens = 0 mv/m - Ens=+0.018mV/m 38 Ens=-0.026mV/m Longitude E[o] Figure 5: Epicentral location as a function of E N S constant. E EW with 7 Ms Ex.Data Eq. Magnitude [Ms] Ens [mv/m] Figure 6: Earthquake magnitude as a function of E N S with E EW constant. 7

8 References [1] Varotsos P. and Alexopoulos K.: Physical Properties of the Variation of the Electric Field of the Earth Preceding Earthquakes I and II, Techtonophysics, vol 110, (1984). [2] Varotsos P. and Lazaridou M.: Latest Aspects of Earthquake Prediction in Greece based on Seismic Electric Signals, Techtonophysics, vol.188 (1991). [3] Varotsos P., Alexopoulos K. and Lazaridou M.: Latest Aspects of Earthquake Prediction in Greece based on Seismic Electric Signals II, Techtonophysics (1993). [4] Varotsos P., Alexopoulos K., Lazaridou M., Nagao T.: Earthquake predictions issued in Greece by seismic electric signals since February 6, 1990, Techtonophysics (1993). [5] Varotsos P., Alexopoulos K., Lazaridou M.: Recent earthquake predictions issued by the VAN-network in Greece. Period: Feb. 6, May 31, 1991, submitted in Techtonophysics. [6] Shnirman M., Schreider S., Dmitrieva O.: Statistical evaluation of the VAN predictions issued during the period , Techtonophysics (1993). [7] Dologlou E.: A three year continuous sample of ocially documented predictions issued in Greece using the VAN method: Techtonophysics (1993). [8] Eftaxias K., Hadjicontis: Information material on earthquake prediction in Greece by means of seismic electric signals, Int. Conf. Measurement and Theoretical Models of the earth's electric eld variations related to earthquakes, Feb. 6-8 Athens). [9] Chouliaras G. and Rasmussen T.M.: The Application of the Magnetotelluric Impedance Tensors to Earthquake Prediction Research in Greece, Techtonophysics, vol. 152 (1988). 8

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