POPOVA_correctedOK:Layout 6 ANNALS OF GEOPHYSICS, 56, 3, 2013, R0328; doi:10.4401/ag-6224 R0328 Neural network approach to the prediction of seismic events based on low-frequency signal monitoring of the Kuril-Kamchatka and Japanese regions Irina Popova1,*, Alexander Rozhnoi1, Maria Solovieva1, Boris Levin2, Masashi Hayakawa3, Yasuhide Hobara3, Pier Francesco Biagi4, Konrad Schwingenschuh5 1 Institute of Physics of the Earth, RAS, Moscow, Russia 2 Institute of Marine Geology and Geophysics, RAS, Yuzhno-Sakhalinsk, Russia 3 University of Electro-Communications, Chofu, Tokyo, Japan 4 University of Bari, Department of Physics, Bari, Italy 5 Space Research Institute, Austrian Academy of Sciences, Graz, Austria ABSTRACT Very-low-frequency/ low-frequency (VLF/LF) sub-ionospheric radiowave monitoring has been widely used in recent years to analyze earthquake preparatory processes. The connection between earthquakes with M ≥5.5 and nighttime disturbances of signal amplitude and phase has been es- tablished. Thus, it is possible to use nighttime anomalies of VLF/LF sig- nals as earthquake precursors. Here, we propose a method for estimation of the VLF/LF signal sensitivity to seismic processes using a neural net- work approach. We apply the error back-propagation technique based on a three-level perceptron to predict a seismic event. The back-propagation technique involves two main stages to solve the problem; namely, network training, and recognition (the prediction itself ). To train a neural net- work, we first create a so-called ‘training set’. The ‘teacher’ specifies the correspondence between the chosen input and the output data. In the pres- ent case, a representative database includes both the LF data received over three years of monitoring at the station in Petropavlovsk-Kamchatsky (2005-2007), and the seismicity parameters of the Kuril-Kamchatka and Japanese regions. At the first stage, the neural network established the re- lationship between the characteristic features of the LF signal (the mean and dispersion of a phase and an amplitude at nighttime for a few days before a seismic event) and the corresponding level of correlation with a seismic event, or the absence of a seismic event. For the second stage, the trained neural network was applied to predict seismic events from the LF data using twelve time intervals in 2004, 2005, 2006 and 2007. The results of the prediction are discussed. 1. Introduction Low-frequency (LF) signals (range, 10-50 kHz) propagate between the Earth and the ionosphere as in a spherical waveguide. The bottom boundary of the waveguide is the Earth, and the top boundary is the lowest part of the ionosphere. The propagation of low-frequency signals is determined on the one hand by the electrical conductivity of the Earth surface, and on the other hand by the conductivity of the lower ionosphere and upper atmosphere. The analysis of the behavior of the amplitude and phase signals from very- low-frequency (VLF)/LF transmitters have shown the possibility for their use as precursors of earthquakes. A night disturbance of the signal amplitude and phase for the long paths has been observed before several strong earthquakes, as described by Gokhberg et al. [1987, 1989] and Gufeld et al. [1992] over two decades ago. More recently, the changes in the position in minima of the phase and amplitude daily variations during sunset and sunrise for a few days before strong earthquakes in Japan were describe [Hayakawa et al. 1996, Molchanov and Hayakawa 1998]. The usefulness of the sub-ionospheric VLF/LF signal propagation method for the detection of seismo- ionospheric perturbations from observations of ground stations has been demonstrated recently in Japan [Maekawa et al. 2006, Muto et al. 2009, Hayakawa et al. 2010], Italy [Biagi et al. 2007, 2008] and Russia [Rozhnoi et al. 2006, 2007a, 2009]. This method was used for the analysis of both ground-based transmitter signals detected onboard the DEMETER satellite above seismic regions, and ground observations [Muto et al. 2008, Rozhnoi et Article history Received October 9, 2012; accepted April 23, 2013. Subject classification: Wave propagation, Seismic risk. al. 2007b, Solovieva et al. 2009, Rozhnoi et al. 2012]. A statistical analysis was realized by Rozhnoi et al. [2004] for the purpose of determining the sensitivity threshold of LF signals to the magnitude of an earth- quake, and unearthing probable periods of observation of anomalies caused by seismic activity. They showed that the sensitivity of the LF signal to seismic processes becomes apparent for M ≥5.5. The signal anomalies for earthquakes with such magnitudes were observed in 20% to 25% of cases. In this study, we propose a method for the estima- tion of the LF signal sensitivity to seismic processes using a neural network approach. The trained neural network is applied in forecast mode for the automatic detection of abnormal changes in the signal, relating to seismic activity above a certain threshold. 2. Methods Historically, the first successful applications of the neural network method were implemented for a pat- tern-recognition problem; namely, the problems of recognition of printed text, image compression, and image recognition in the field of computer vision. Even- tually, the properties of neural networks proved to be useful to other areas of knowledge. The essential dif- ference between traditional computing and neurocom- puting is that neural networks can produce their own rules from incomplete and noisy data. When it is hard to find a traditional algorithm for the solution to a prob- lem, the ability of a neural network to extract the ‘rules of exit’, to effectively solve nonlinear tasks, and to per- form interpolation and extrapolation of an available database can be helpful for many tasks in geophysics. An excellent review of neural network paradigms and a detailed analysis of their application to various geo- physical problems was given by Poulton [2002]. Neural network methods have been used in geo- electrics for inversion of electromagnetic data in three- dimensional geoelectric structures [Spichak and Popova 2000]. Interpretation of multidimensional geophysical data generated during a geological exploration was car- ried out using the neural network method known as self-organizing mapping [Klose 2006]. A neural network application for seismic data processing was developed for first-break peaking and trace editing [McCormack et al. 1993]. Neural network technology has been used in various fields of geophysics for parameter estima- tion, filtering, classification and prediction. A back- propagated and associative neural network was applied to predict magnitudes of earthquakes from seismic net- work signals, electric preseismic signals, and average magnitudes of previous earthquakes [Dutta 2011]. The variation of the geomagnetic field declination, hori- zontal component, hourly relative humidity, ground temperature, rain rate per day, mean number of rainy hours per day, and ground temperature, were used to predict the magnitude of an earthquake two days be- fore its occurrence by means of a neural network [Suratgar et al. 2008]. We applied the back-propagation technique [Rumel- hart and McClelland 1986], based on the three-layer per- ceptron to estimate the sensitivity of the VLF/LF signal to seismic processes, as illustrated on Figure 1. This type of a neural network is known as ‘supervised’. This in- volves two main stages of solving a problem: the training of the network, and the recognition (the prediction it- self ). In the supervised scheme of teaching, the network is taught the relationship between the input and output pairs, which is called the training set. To train the neural network, we created a teach- ing database that included both the catalog of seismic events from 2005 to 2007 and the corresponding data (amplitude and phase of the LF signals), measured in the regime of monitoring at the receiving station in Petropavlovsk-Kamchatsky from the Japanese trans- mitter JJY (see Figure 2). The seismic events were ex- cluded from the database for the days when the index of the magnetic field activity, Dst, and the flux of rela- tivistic electrons exceeded the given thresholds. The op- timal properties for the formation of the teaching database were derived after many experiments on teaching and testing of the neural networks. As a re- sult, the training samples included the features calcu- lated from the amplitudes and phases of the signals, POPOVA ET AL. 2 Figure 1. Three layer perceptron of back-propagation neural net- work applied to prediction of seismic events. The input signal rep- resents the mean and dispersion values of the phases (MPh,t-n and DPh,t-n, respectively) and amplitudes (MA,t-n and DA,t-n, respectively) in the nighttime for five days before the seismic event (n varies from 1 to 5). The corresponding level of correlation with the seismic event Ct is used as the output data. 3 which were measured for five days before 40 seismic events of M ≥5.5 that occurred at a depth (H) of less than 150 km. The ratio of the radius (R) of the zone of precursors displayed to the distance (D) of the epicen- ter from the axis of the propagation path between the transmitter and receiver (R/D) was selected as >0.7, be- cause the preparation zone intersected the sensitivity zone in this case. Thus, the preparation activity can in- fluence the LF signal propagation. The radius of the zone of the precursor display was calculated using the relationship R = 100.43M, where M is the magnitude of an earthquake [Dobrovolsky et al. 1979]. The teaching database also included 40 examples of a lack of seismic events, because the neural network had to learn to distinguish between the seismic events of M ≥5.5 and their absence. Thus, the total teaching database contained 80 examples. Each example con- tained the input and output data for the teaching of the neural network. Below, we refer to the seismic events of M ≥5.5 as the ‘seismic event’, and to the rest as a ‘lack of the seismic event’. The mean and dispersion values of the phases and amplitudes in the nighttime for five days before the seis- mic event (or the lack of it) were used as the input data. Thus, the number of the input neurons in the three- layer perceptron was 20. The mean and dispersion val- ues of the amplitude are marked in Figure 1 as MA,k and DA,k, and those of the phase, as MPh,k and DPh,k, re- spectively. The index k refers to the number of days be- fore the seismic event (or lack of it) and this varies from t-1 to t-5, where t is the number of the day of a seismic event (or lack of it). The input signal X consisted of these values. The corresponding correlation level with the seismic event (where the correlation value was 1) or with a lack of the seismic event (where the correla- tion value was 0) were used as output data U. Thus, the value of the output neurons in the three-layer percep- tron was equal to unity. The level of correlation is marked as Ct on Figure 1. After the preparation of the input-output pair, the neural network was trained using 80 examples of the teaching database. The input signal X that is represented by the means and dispersions of the phases and amplitudes in the nighttime for five days, propagated forward from one layer to the next layer. Thereby, each neuron i of a next layer received the total signal from all of the neurons j of a previous layer: (1) where ui l is the output signal of neuron i of layer l, G is the neuron response function (e.g., hyperbolic tangent), Wi j l are the weight connections between the neurons of layers l - 1 and l, and xj is the value of the neuron j of the layer l -1. At the training state, we must obtain the output signal ui on the third layer that minimizes the total stan- dard error: (2) The summation was carried out for each training example p over all of the neurons i of the output layer. The ‘target’ value ui t represented the sample value of the correlation coefficient for the corresponding train- ing example. The real value ui represented the value of the output neuron formed as a result of signal propa- gation (Equation 1). Weight connections W1 and W2 between the lay- ers of the neural network were the parameters that de- fined the value of an error (Equation 2). Therefore, the essence of the teaching process was the search for the weight connections Wij for the error minimization. The weights were assigned random values within a certain range at the beginning of the teaching procedure. The teaching procedure was based on the gradient descent technique of the error minimization (Equation 2) be- tween the target values of the outputs specified by the ‘teacher’ and those produced by the neural network: (3) where DWij (n) is the increment of the weight connection at step n, DWij (n −1) is its increment at the previous step, and a and b are internal parameters of the neural net- work. This procedure was fulfilled for all of the teach- ing examples, and finished when it reached the NEURAL NETWORK PREDICTION OF EARTHQUAKES Figure 2. Map showing the position of the receiver Petropavlovsk- Kamchatsky (PTK) and transmitter JJY (40 kHz). Solid circles, posi- tions of the earthquake epicenters with M ≥5.5, D ≤150 km and R/D ≥0.7 for the period 2004-2007 (from USGS/NEIC http://neic. usgs.gov/neis/epic/epic_global.html); ellipse, projection of the fifth Fresnel sensitivity zone on the Earth surface. ,W W Er W( ) ( 1)ij n ij ij n 2 2 a bD D=- + - .Er u ui i t ip 2= -^ h// ,u G W xi l ij l j j = ` j/ accuracy threshold, eps, such that Er 0.5 for several days in a row before the earthquake. For six of the 12 time intervals (see Table 1 for the seismic events numbered from 1 to 6), the neural network detected changes in the LF signal for several days in a row (2-3 days) before an earthquake of M ≥5.5 and on the day itself. These examples are shown in Figure 3. For the next three time intervals (see Table 1 for POPOVA ET AL. 4 N Year Month Day Time Latitude (°) Longitude (°) Depth (km) M D (km) R/D 1 2006 9 28 1:36 46.5 153.3 11 5.9 154.7 2.22 2 2004 9 13 3:0 44 151.4 8 6.1 223.7 1.87 3 2004 7 21 0:11 40.9 143.1 30 5.5 127.9 1.81 4 2007 1 11 20:34 43.5 147.1 10 5.5 45.7 5.07 5 2005 3 11 18:47 43.1 144.7 54 5.5 187.7 1.23 6 2005 3 16 13:23 43.5 146.9 39 5.6 59.4 4.3 7 2004 5 29 3:47 37.7 141.9 29 5.8 51.9 5.9 8 2005 8 1 4:40 46.9 153.9 16 5.7 156.8 1.8 9 2004 11 2 13:4 38.8 142.8 23 5.6 26.1 9.8 10 2004 11 26 22:42 42.4 142.9 58 5.7 257.8 1.1 11 2004 5 6 13:43 42.5 145.0 28 5.6 116.8 2.2 12 2004 7 8 10:30 47.2 151.3 128 6.4 49.4 11.4 Table 1. The 12 seismic events of M ≥5.5 for considered twelve time intervals in 2004, 2005, 2006 and 2007. 5 the seismic events numbered from 7 to 9), the neural network detected changes in a signal that indicated an earthquake on the second or third day before the earth- quake, excluding the day itself. These results can also be considered as positive. For the remaining three time intervals (see Table 1 for the seismic events from 10 to 12), there were no correlations between the seismic events of M ≥5.5 and changes in the signal. We discuss the results of the prediction on the ex- ample presented in Figure 3a. The magnitudes of the earthquakes that occurred during the period of analy- sis are shown in the upper section of Figure 3a. If a magnitude is ≥5.5, the following parameters are given for the corresponding column: magnitude M, depth H, distance D from the epicenter of the earthquake to the axis of the transmitter–receiver line, and the ratio R/D. The dashed line represents the threshold at which M ≥5.5. The results of the prediction from January 6-11, 2007, are shown on the bottom section of Figure 3a. These results are formed as the output (single neuron) of the previously trained neural network. This output represents the correlation coefficient. In this way, we find the degree of the correlation with a seismic event of M ≥5.5. A procedure for recognition (prediction) is performed step by step with a shift in one day, up to the day of the seismic event of M ≥5.5. The dashed line in Figure 3a represents the threshold value of the correla- tion coefficient of 0.5. One can see from the bottom section of Figure 3a that the correlation coefficients are more than 0.5 for two days in a row before the earthquake and on the day of seismic event itself. Such behavior of the correlation coefficient indicates an earthquake of M ≥5.5. 4. Discussion and conclusions For nine of the twelve time intervals, the neural network successfully recognized changes in the LF sig- nal that indicated an earthquake of M ≥5.5 a few days before the earthquake. These results confirm that short- term prediction of seismic events based on changes in the LF signal is possible. A mean value and dispersion calculated from the amplitudes and phases of signals for the night period can be considered as indicators of seismic events. The LF signal sensitivity to seismic processes is seen for seismic events of M ≥5.5 that occur at a depth of <150 km. In addition, the ratio R/D should be >0.7. As an outlook, we suggest the use of several wave paths as input data of a neural network, as well as the additional output parameters, such as a magnitude value and a forecast probability. Acknowledgements. The study was supported by the Russ- ian Foundation for Basic Research, under grant No. 11-05-00155-a. Data and sharing resources – The earthquake catalog used in this study can be found at: http://earthquake.usgs.gov/earthquakes/eqarchives/ epic/ – Dst data were taken from the site: http://wdc.kugi.kyoto-u.ac.jp/dstdir/index.html The electron fluxes are on the site: http://www.swpc.noaa.gov/ftpmenu/lists/particle.html NEURAL NETWORK PREDICTION OF EARTHQUAKES Figure 3. The neural network prediction. (a) Result of prediction for January 6-11, 2007. (b) Result of prediction for July 16-23, 2004. (c) Result of prediction for September 8-14, 2004. Each column on the upper section represents the magnitude of the earthquakes that oc- curred on certain days of the time period considered. If M ≥5.5, the corresponding column is marked with the following parameters: magnitude M, depth H, distance D from the epicenter of the earth- quake to the axis of the ‘transmitter–receiver’ line, and the ratio R/D. Dashed line, threshold at which M ≥5.5. The corresponding values of the correlation coefficients are presented in the bottom section: dashed line, threshold of the correlation coefficient of 0.5. References Biagi, P.F., L. Castellana, T. Maggipinto, G. Maggipin- to, A. Minafra, A. Ermini, V. Capozzi, G. Perna, M. Solovieva, A. Rozhnoi, O.A. Molchanov and M. Hayakawa (2007). 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Fourth International Conference, 2008, 2, 448-452. *Corresponding author: Irina Popova, IInstitute of Physics of the Earth, RAS, Moscow, Russia; email: ipopova@trtk.ru. © 2013 by the Istituto Nazionale di Geofisica e Vulcanologia. All rights reserved. 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