Fractal Dimension Study of Southern California Temporospatial Seismicity Patterns from 1982 to 2020

Abstract

Power-law scaling relationships concerning the earthquake frequency-magnitude distribution and the fractal geometry of spatial seismicity patterns may provide applications to earthquake forecasting and earthquake hazard studies. Past studies on the fractal characteristics of seismic phenomena have observed spatial and temporal differences in earthquake clustering and b value in relation to fractal dimension value. In this thesis, an investigation of the spatiotemporal seismicity patterns in southern California for the years 1982 to 2020 was conducted. The range and temporospatial distribution of b and D2 values for earthquake hypocenters contained in the Southern California Earthquake Data Center catalogue were calculated and shown in time series and spatial distribution maps. b values were calculated using both the Least SquaresMethod and the Maximum Likelihood Method while D2 values were calculated for length scales between 1 km to 10 km. A set of b and D2 values were calculated after declustering for foreshocks and aftershocks using Gardner and Knopoff’s declustering algorithm. b values decreased while D2 values increased on the dates of M > 6.0 earthquakes, whereas b values increased and D2 values decreased on the dates after M > 6.0 earthquakes. Declustering results suggest an influence of earthquake aftershocks to increase D2 values while decreasing b values. The role for b values and D2 values to delineate both the temporal and spatial extent of aftershock sequences for large earthquakes may prove to have an application in earthquake hazard studies.