پیش بینی زلزله با استفاده از شبکه های عصبی: نتایج و کار آینده Earthquake Forecasting Using Neural Networks: Results and Future Work

1. Introduction When looking for analytical tools designed to forecast time series, one finds that the practical domain in which they are most commonly used is financial forecasting – especially for the prediction of trends in the stocks, bonds, commodities and currencies markets [1] – where technical analysts name these tools “financial oscillators”. Time-series of earthquake parameters are also of a chaotic nature [2], with comparable scaling laws [3, 4], and testing those financial oscillators on seismicity was a natural step. The transposition of scenery appears to be fairly straightforward. Instead of analysing a series of quotes in order to predict the next quote, one has to analyse a series of seismic parameters, namely those related to time, energy and epicentral locations, in order to predict the next time, effect and local. A natural doubt can arise: if a predictive model must be related to the process it tries to predict, and there is no relationship between the fluctuation mechanisms of markets and seismic mechanisms, why and how should this approach work? Indeed, there is an important relationship because both are deterministic non-periodic processes – chaotic processes. But there is still a more important reason for using these “financial” tools: they reduce the degree of chaos in the analysed sequence, making it more predictable. This happens because the fractal dimension of a system is a measure of its degree of chaoticity. The movement of a particle in the real plane can take dimensions between 1 (completely deterministic) and 2, in the case of Brownian movement (completely random). We expect that a sequence of, say, earthquake magnitudes, will have a fractal dimension between 1 and 2. If we calculate that dimension and then the dimension of the sequence of moving averages (the simplest oscillator, on which most others are based) we find such a reduction of fractal dimension – a reduction of chaos [5].