Fractal Concepts and their Application to Earthquakes in Austria
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Fractal concepts have been applied widely in different scientific disciplines since their introduction. This paper discusses practical aspects of determining fractal dimensions, and their interpretation in terms of seismology. Firstly, several evaluation algorithms are investigated. Austria’s borderline is then used as an example for demonstrating the effect scale length can have on perimeter estimates. Derived fractal dimensions D concentrate at 1.18, but can vary by more than one decimal of a unit, depending on the algorithm employed. Comparing fractal dimensions across the literature and their interpretation in terms of underlying mechanisms is therefore extremely difficult.
Applying the fractal concept to earthquake statistics reveals that several factors need to be considered, thus leaving room for a variety of interpretations. The common approach estimates D of earthquakes from the b-value - the ratio of the number of small to large earthquakes. The relation between D and the b-value is not necessarily straightforward, but may deviate due to variations in stress drops of earthquakes, stress environments, the geometrical nature of rupture planes and the fault interactions. Therefore, further interpretations concentrated rather on the b-value than on the fractal dimension D.
Most regions in Austria exhibit b-values near unity, which implies normal stress drops and three-dimensional deformation processes. It is shown, that areas of low b-values do not necessarily call for alternative deformation processes, but rather for lower horizontal stresses or higher stress drops.
KeywordsFractal Dimension Stress Drop Focal Depth Rupture Plane Fractal Concept
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