A chilean seismic regionalization through a Kohonen neural network

arXiv:0812.1198v1 [physics.geo-ph] 5 Dec 2008 physics/08MMNNN A chilean seismic regionalization through a Kohonen neural network Jorge Reyes1∗and V´ıctor H. C´ardenas2† 1TGT, San Renato 217, Los Andes, Chile and 2Departamento de F´ısica y Astronom´ıa, Universidad de Valpara´ıso, Valpara´ıso, Chile A study of seismic regionalization for central Chile based on a neural network is presented. A scenario with six seismic regions is obtained, independently of the size of the neighborhood or the reach of the correlation between the cells of the grid. The high correlation between the spatial distribution of the seismic zones and geographical data confirm our election of the training vectors of the neural network. PACS numbers: 91.30.Px I. INTRODUCTION The idea of seismic regionalization can be traced back to 1941 when Gorshkov [1] published one of the first studies on seismic regionalization for the URSS. Based on these earlier studies, Richter [2], in a paper entitled “Seismic regionalization”, founded the basis of a method- ology that allows to have information dealing with pre- venting the potential damage that an earthquake may cause through the definition of hazard zones. In a seismic country like Chile, and based on the ur- gent goals established by Richter, a proper regionaliza- tion map is desirable. Attempts to fill the gap in these matters have been done from time to time. In [3] is found probably the first regionalization study for Chile where the authors Gajardo and Lomnitz used the same methods of seismic correlation Tsuboi used in the case of Japan. Later works on the subject were mainly focused on en- gineering aspects as Walkner [4], Labbe [5] and Barri- entos [6], discussing on seismic risk. Essentially, these studies used the technique proposed by Cornell [7] and Algermissen and Perkings [8]. A more recent study was made by Martin [9]. Here the author used a longitudi- nal division criteria for the country using the line that separates the deep and superficial earthquakes, which leads to a high degree of coupling between the Nazca and Southamerican plate. This criterium enable him to identify two macro-zones in the continental zone: In the coast, with hypocenters with depths lesser than 40km, and the mountain macro-zone. As a criteria for latitu- dinal division, Martin computed the b parameter of the Gutenberg-Richter law for an initial surface, and then he varied the surface iteratively. If b changes dramatically, it means that a seismic zone has been crossed. These are the nine regions Martin found: in the coast; three zones. In the deep mountain zone, he distinguished four zones. In the surface mountain zone, he distinguished a single zone. Finally, the method determined the aseismic zone of Magallanes. In this work we implement a Kohonen neural network ∗Electronic address: daneel@geofisica.cl †Electronic address: victor@dfa.uv.cl (from here on NN) to determine the seismic zones. In general, a neural network [12] can be defined as a com- puting system made up of a number of simple, highly interconnected processing elements, which processes in- formation by their dynamic state response to external inputs. NNs are typically organized in layers. Layers are made up of a number of interconnected ‘nodes’ which contain an ‘activation function’. Patterns are presented to the network via the ‘input layer’, which communicates one or more ‘hidden layers’ where the actual processing is done through a system of weighted ‘connections’. The hidden layers then link to an ‘output layer’ where the answer is output. Most NNs contain certain types of ‘learning rule’ which modify the weights of the connec- tions according to the input patterns which are exposed to. In this work we use a special NN appropriated to dis- criminate spatial distribution. A Kohonen NN [18](or as it is usually called a self organising map) is an arti- ficial neural network that is trained using unsupervised learning to produce a low-dimensional (typically two di- mensional), discretized representation of the input space of the training samples, called a map. The network must be fed a large number of example vectors that represent, as close as possible, the kinds of vectors expected dur- ing mapping. The examples are usually provided several times. In this way, the NN finds by itself the best distri- bution of zones, based on the training vectors, without any other specification than geographical characteristics. In the context of seismic hazard or seismic risk, there have been many attempts to use this technique. For ex- ample, in [15] the authors used artificial NN to discrim- inate between earthquakes and underground nuclear ex- plosions. Also for seismic detection [16], in which the NN is trained to recognize signal patterns, and also for earth- quake prediction [17]. This work is organized as follows. The next section discusses the election of the training vec- tors or training set, from which the NN starts its learn- ing process. Then, in sect

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