SPATIAL AND DEPTH DISTRIBUTION CHARACTERISTICS OF GEOLOGICAL FAULTS
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This study investigates the spatial and depth distribution characteristics of geological faults using fractal and statistical analysis methods. A random point distribution model and the Lévy flight fractal model were employed to simulate the spatial arrangement of fault systems. Based on the Lévy flight model, the probability density and distribution functions of inter-fault distances were determined, and the fractal dimension parameter was calculated. The results confirmed that the spatial distribution of geological faults and earthquake epicenters represents a complex structural-geodynamic system exhibiting self-similar fractal properties. A strong relationship was identified between the degree of fault clustering, spatial density, depth distribution, tectonic stress fields, and seismic activity. The influence of systematic factors, including coordinate errors, boundary effects, statistical sample size, and spatial projection, was analyzed during the estimation of the correlation dimension. It was demonstrated that reduced coordinate accuracy at small scales may lead to inaccurate estimation of fractal parameters. The application of statistical filtering and scale-parameter optimization methods improved the accuracy of distribution pattern assessment. The obtained results are of significant scientific and practical importance for identifying seismic hazard zones and evaluating the geodynamic state of regions.
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