Fractal Dimension
Fractal Dimension : A statistical quantity in fractal geometry that indicates of how completely a fractal appears to fill space, as one zoomes down to smaller and smaller scales. Although there exist many specific definitions the fractal dimension may be estimated from the exponent of a power law distribution such as the GutenbergRichter relation. Its b-value is about half of the fractal dimension of the considered complete random ensemble of earthquakes of different magnitude. Values of b = 1.5, 1 or 0.5, respectively, would indicate that the governing earthquake rupture process would be 3D, 2D or 1D (linear). b-values may vary with time and tend to be larger for aftershocks and swarm earthquakes than for main shocks of larger magnitudes. Values 0.7 < b < 1.4 have been reported by Neunh?fer and G?th (1989) within a major earthquake swarm
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