Fractal analysis applied to characteristic segments of the San Andreas Fault

Abstract

Fractal theory is applied in a quantitative analysis of the San Andreas fault (SAF) geometry. The method, which directly measures the increase in total fault length with a decrease in ruler size, gives the fractal dimension D and scaling properties for the chosen length band 0.5–1000 km. A physical interpretation of D is that it measures the irregularity of the fault trace in the selected band. The fault is subdivided into six segments of distinctive seismic behavior. A “main” fault trace which shows either maximum coseismic slip or creeping was selected for analysis, with three alternative branches examined for the SAF system south of San Bernardino. Branches of the fault trace are not considered in this work. Fractal dimensions calculated for the different segments range from 1.0008 to 1.0191, and are different from 1.0 to the 95% confidence interval. These small changes reflect the overall smoothness of the main fault trace. Significant variations in D among segments indicate heterogeneities in the fault smoothness along strike. D also changes significantly from the short‐length band to the long‐length band where the demarcation point ranges from 1 to 2 km. The short‐length band has larger D values. A slight correlation is obtained between the fractal dimension of the main trace and the extent of subparallel faulting. This indicates some correspondence between the main fault trace irregularity and the complexity of subsidiary fault traces in plan view.