Fractal geometry in the San Andreas Fault System

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Abstract
It has been noted that the spatial distribution of earthquakes and the mode of strain release in the San Andreas fault system is related to the complexity of fault geometry. Because of their rough appearance over many length scales, faults can be regarded as fractal surfaces. Direct estimates of fractal dimension D of portions of the San Andreas fault system between the northern Gabilan Range and the Salton Sea, including the postulated extent of the great 1857 Fort Tejon earthquake, are obtained from measured fault lengths, analogous to the lengths of coastlines as discussed by Mandelbrot. Regions characterized by complicated fault geometry are associated with larger values of D. Based on fault traces mapped at a scale of 1:750,000, D is 1.3 for this reach of the fault defined as a 30‐km‐wide band about a main fault trace. For that part near Parkfield which could be associated with the nucleation of the 1857 earthquake, D is 1.1; at this same scale, D is 1.4 for the San Andreas and related faults near San Bernardino where the 1857 rupture stopped, compared to 1.2 for the San Andreas‐San Juan fault segments near the point of arrest of the 1966 Parkfield earthquake. At finer map scales (1:24,000 and 1:62,500) critical lengths of ∼ 500 m and 1 km are identified which might relate to the extent of off‐San Andreas fault offsets. The critical lengths also suggest that fault geometry is not self‐similar. If this fractal geometry persists through the seismic cycle, it may be possible to use a quantitative measure of complexity to explain the occurrence of great and characteristic earthquakes along a given reach of fault.