11:30 AM - 11:45 AM
[SSS06-10] Modeling dynamic rupture and statistical properties of earthquakes with cellular automaton models.
Keywords:Cellular automaton model, Gutenberg-Grichter law, nonequilibrium statistics, Dynamic rupture, Omega squared model
How to understand seismic activity from deterministic rupture mechanics is an important issue in seismology. In recent years, the development of rupture mechanics-based cycle simulations has been remarkable, and we are now at the stage where we need to figure out how to simulate more complex fault structures. However, due to issues such as understanding friction at high speeds and computational costs, rupture mechanics-based earthquake cycle simulations that fully incorporate realistic heterogeneous structures have not yet been realized. In this study, we tackle this issue by considering complex heterogeneous structures as a multibody problem, and using a statistical physics approach that understand the multibody system in a simplified way through good coarse-graining. The goal of this study is to develop a cellular automaton model that reproduces both the fracture and the statistical properties, and to improve our understanding of the coarse-graining that is useful for understanding complex seismic activity. Such an attempt can serve as a useful relay point for understanding seismic activity on a fracture mechanics basis.
Conventional studies of cellular automata models have focused on statistical properties and have not touched on dynamic behavior [Carlson and Langer,1989:Olami et al.] In addition, it has been pointed out that the BK model with a simple friction law has a pulsed rupture behavior with constant slip and does not show the characteristics of a regular earthquake as a rupture behavior [Ide and Yabe, 2019]. Therefore, the OFC model, which is said to reproduce the GR, was extended to include a finite time constant of the rupture chain to create a cellular automaton model that can handle rupture behavior (Dynamic OFC model). The rupture behavior of the Dynamic OFC model shows a behavior similar to that of the tremor, which is one of the slow earthquakes, rather than a regular earthquake.
The Dynamic OFC model that we have been using so far incorporates the assumption that the rupture threshold (corresponding to the strength) does not change even at the end of one rupture step.
This assumption implies that the strength recovery is very fast in relation to the rupture chain (i.e., the rupture chain is slow). In this study, the model was further extended to include a new parameter, the ratio of the time constant of loading and strength recovery to the time constant of the fracture chain. This model is capable of discussing slow phenomena (slow rupture propagation) and fast phenomena (fast rupture propagation) in a unified manner, using the competition between the two time constants of (1) fracture and stress accumulation, and (2) fracture and strength recovery as parameters.
We introduce that this model reproduces both the crack-like rupture behavior, where the moment rate spectrum is proportional to the square of the frequency, and the Gutenberg-Grichter law, where the size frequency distribution is the power law distribution. We will also discuss how such a cellular automaton model can provide a perspective on the coarse-graining of fracture phenomena. The results of the parameter range of the slow phenomenon (slow fracture propagation) will be introduced in the poster presentation in the S-CG39 session.
Conventional studies of cellular automata models have focused on statistical properties and have not touched on dynamic behavior [Carlson and Langer,1989:Olami et al.] In addition, it has been pointed out that the BK model with a simple friction law has a pulsed rupture behavior with constant slip and does not show the characteristics of a regular earthquake as a rupture behavior [Ide and Yabe, 2019]. Therefore, the OFC model, which is said to reproduce the GR, was extended to include a finite time constant of the rupture chain to create a cellular automaton model that can handle rupture behavior (Dynamic OFC model). The rupture behavior of the Dynamic OFC model shows a behavior similar to that of the tremor, which is one of the slow earthquakes, rather than a regular earthquake.
The Dynamic OFC model that we have been using so far incorporates the assumption that the rupture threshold (corresponding to the strength) does not change even at the end of one rupture step.
This assumption implies that the strength recovery is very fast in relation to the rupture chain (i.e., the rupture chain is slow). In this study, the model was further extended to include a new parameter, the ratio of the time constant of loading and strength recovery to the time constant of the fracture chain. This model is capable of discussing slow phenomena (slow rupture propagation) and fast phenomena (fast rupture propagation) in a unified manner, using the competition between the two time constants of (1) fracture and stress accumulation, and (2) fracture and strength recovery as parameters.
We introduce that this model reproduces both the crack-like rupture behavior, where the moment rate spectrum is proportional to the square of the frequency, and the Gutenberg-Grichter law, where the size frequency distribution is the power law distribution. We will also discuss how such a cellular automaton model can provide a perspective on the coarse-graining of fracture phenomena. The results of the parameter range of the slow phenomenon (slow fracture propagation) will be introduced in the poster presentation in the S-CG39 session.