| Chaotic Properties and Fractal Analysis of The Marmara Earthquakes
The objects, which are self-similar and scale invariant are called as fractals. If a system does not have a characteristic length or scale, it is a good approximation to try to understand its behaviour using fractal analysis. Many phonemena in geophysics such as the spatial and temporal distribution of earthquakes show chaotic behaviour and can be analysed using fractal statistics. Fractal analysis requires that, the number of objects larger than a specified size, has a power-law dependence on the size. The power of the mentioned relation is called as fractal dimension, and is used to define the system.
Using power-law relations in the statistical seismicity studies is not a new subject in geophysics. The b-value of Gutenberg and Richter, which is a good example, defines a power-law relation between the cumulative number of earthquakes larger than a specified magnitude and the earthquake magnitude, and has been widely used in the seismicity studies. The p-value of Omori is also a power-law relation and defines the decay rate of earthquakes by the time.
In the present study, the fractal analysis is performed using the earthquakes in the area between 38.4º-41.6ºN latitudes and 25.2º-32.1ºE longitudes, in order to contribute to better understanding of occurrence systems of earthquakes. As the result of temporal and spatial analysis, it is proposed that the regional seismicity follows a fractal pattern and has experienced three behavioural phases. Moreover, the study intends to prove that the system is constantly on the critical stress level and background seismicity defines the general properties of regional seismicity. Finally, the relation between stress transfer, fractal dimension and background seismicity is shown, implementing a probabilistic fractal model approach.
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