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## A forest fire model of earthquake faulting

Cameron Saylor, & John B. Rundle

Published August 14, 2020, SCEC Contribution #10591, 2020 SCEC Annual Meeting Poster #165

Much is still unclear about the complex nature of earthquake faulting, such as rupture propagation across a fault from its original failure point which can give rise to nonuniform slip distributions. To gain insight into this problem, we introduce a model that utilizes the principles of both forest fire models and percolation theory. The rectangular fault plane is split into a lattice, with each site connected to its neighbors by a bond. The bond can be in either an unbreakable state, or in a breakable state with an associated bond strength. At each time step, an unbreakable bond can be converted to a breakable bond. It is also possible--with very low probability--that at any time step a single site is chosen to test its bonds for failure. The strength of each breakable bond is compared to a randomly generated number--if the strength is greater, the bond remains intact; otherwise, the bond is broken. If a bond is broken, the bonds of the previously connected site are tested for failure, while preventing any closed loops from forming. This process is repeated until no more bonds break or the edge of the fault is reached. Once the cluster has stopped growing, each site in the cluster is assigned a seismic moment, with the total moment release being the sum of each sites' moment. The amount of slip assigned to each site grows as the square root of the size of the cluster and the slip is used to compute surface deformation and the corresponding stress drops. As an example, Rundle et al. (2020) find that as the bond percolation probability approaches the critical value p = 0.5 in d = 2, the Gutenberg-Richter b-value approaches 1 from above. Moreover, the clusters become increasingly ramified as the critical point is approached. Our model therefore predicts that observed seismicity has a fractal dimension D^F = 1.89 < 2, in agreement with the observed value of D^F = 1.89. This model therefore predicts that earthquake seismicity is non-compact as is observed.

Key Words
earthquakes, faulting

Citation
Saylor, C., & Rundle, J. B. (2020, 08). A forest fire model of earthquake faulting. Poster Presentation at 2020 SCEC Annual Meeting.

Related Projects & Working Groups
Fault and Rupture Mechanics (FARM)