Fractal Density and Singularity Analysis of Extreme Geo-Processes
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Density is a fundamental physical parameter involved in most geodynamics models used for prediction in the earth sciences. A new concept of fractal density was proposed to characterize the extreme physical properties of complex geo-processes. As a generalization of the ordinary density concept, the fractal density has a unit of ratio of mass or energy over a fractal set (e.g., g/cm α and J/m α , where the singularity α can be a non-integer number). From a fractal density point of view the ordinary density becomes scale dependent with singularity which should be substituted by fractal density in dynamic models. We demonstrate that several extreme geo-processes occurred in the Earth’s crust originated from cascade earth dynamics (e.g., mantle convection) and self-organized criticality (e.g., slab breakoffs and faults as avalanches) can cause fractal density of mass accumulation or energy release. Examples shown in the paper include energy release of earthquakes and floods.
KeywordsPower-law Fractal and multifractals Extreme geo-events Mass density and energy density
This research has been supported by an NSERC Discovery Research “Research and development of multifractal methods and GIS technology for mineral exploration and environmental assessments” (ERC-OGP0183993).
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