Earthquakes at seismogenic plate boundaries are a response to the differential motions of tectonic blocks embedded within a geometrically complex network of branching and coalescing faults. Elastic strain is accumulated at a slow strain rate of the order of $10^{-15}$ s$^{-1}$, and released intermittently at intervals $>100$ years, in the form of rapid (seconds to minutes) coseismic ruptures. The development of macroscopic models of quasi-static planar tectonic dynamics at these plate boundaries has remained challenging due to uncertainty with regard to the spatial and kinematic complexity of fault system behaviors. In particular, the characteristic length scale of kinematically distinct tectonic structures is poorly constrained. Here we analyze fluctuations in GPS recordings of interseismic velocities from the southern California plate boundary, identifying heavy-tailed scaling behavior. This suggests that the plate boundary can be understood as a densely packed granular medium near the jamming transition, with a characteristic length scale of $91 pm 20$ km. In this picture fault and block systems may rapidly rearrange the distribution of forces within them, driving a mixture of transient and intermittent fault slip behaviors over tectonic time scales.
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