1:45 PM - 3:15 PM
[SSS06-P13] Preliminary results of dynamic earthquake cycle simulations with the Nagata law for a fault under rate- and state-dependent friction law
Keywords:Dynamic earthquake cycle simulation, Rate- and state-dependent friction law, Nagata law
The slip behavior of a fault that repeatedly hosts earthquakes can be investigated by performing earthquake cycle simulation (ECS). Rice & Ben-Zion (1996) considered a planer fault embedded in a linear elastic medium as the boundary and proposed a simulation framework (spectral boundary integral equation method, SBIEM) for fully dynamic ECS, which simultaneously solves the fault constitutive law and the elastodynamics treated in the wavenumber domain. This method was improved in terms of computational cost by Lapusta et al. (2000), and further extended to simulations without the periodic boundary condition (Noda, 2020) and for non-elastic media (e.g., Miyake & Noda, 2019).
In many dynamic ECS using SBIEM, the rate- and state-dependent friction (RSF) law has been used as the fault constitutive law. The RSF law was proposed by Dieterich (1979) and Ruina (1983) to explain mechanical data obtained from laboratory rock experiments. Under the RSF law, the frictional force on a fault surface depends on slip the velocity and the state of the surface. In addition to two conventional state-evolution laws, i.e., the aging and the slip laws, previous studies have proposed many different evolution laws. In particular, Nagata et al. (2012) quantified the state directly, by assuming that the transmissivity of the P-wave during experiments is related to the state (real area of contact) of the fault surface. They introduced the stress-weakening term to the state-evolution equation, which was not considered in the previous evolution laws, to explain both the mechanical data and the transmissivity during friction experiments.
The choice of the evolution law significantly affects the modeling results of quasi-static nucleation (e.g., Ampuero & Rubin, 2008) and dynamic ECS (e.g., Rice & Ben-Zion, 1996). Kame et al. (2015) performed numerical calculations of quasi-static nucleation employing the Nagata law and compared the modeling results with those using the aging and slip laws. They reported that the nucleation of the Nagata law has characteristics similar to those of pulse-like rupture (the slip law) rather than crack-like rupture (the aging law), but the spatial size of the slip pulse is larger than that of the slip law. On simulation of earthquake cycle with the Nagata law, Kame et al. (2013) performed simulations of a one-dimensional spring-slider model without mass, whereas the dynamic ECS with the Nagata law has not been reported. Based on the results of those previous studies, the dynamic ECS with the Nagata law may yield solutions between those obtained using the aging and slip laws, while such an expectation may not be the case when the solution is sufficiently far from the steady state and nonlinearity dominates the behavior of the solution.
The goal of the present study is to investigate differences in the earthquake cycles of a fault governed by the Nagata law from those by the aging and slip laws. For this purpose, we implemented the Nagata law into the dynamic ECS using SBIEM, based on the code developed by Noda (2022). It should be noted that the frictional parameters of the original Nagata law in the form reported by Nagata et al. (2012) have a different mathematical meaning from those of the previous evolution laws. We reformulated the Nagata law in a form similar to the previous evolution laws by further modifying the reformulations made by Noda & Chang (submitted), in such a way that the stress-weakening term does not appear explicitly. In this formulation, the dependencies of the variables are exactly the same as the conventional friction laws, and thus the implementation to the dynamic ECS is straightforward. In this presentation, we present the methodology for implementing the Nagata law in a dynamic ECS and the preliminary results obtained.
In many dynamic ECS using SBIEM, the rate- and state-dependent friction (RSF) law has been used as the fault constitutive law. The RSF law was proposed by Dieterich (1979) and Ruina (1983) to explain mechanical data obtained from laboratory rock experiments. Under the RSF law, the frictional force on a fault surface depends on slip the velocity and the state of the surface. In addition to two conventional state-evolution laws, i.e., the aging and the slip laws, previous studies have proposed many different evolution laws. In particular, Nagata et al. (2012) quantified the state directly, by assuming that the transmissivity of the P-wave during experiments is related to the state (real area of contact) of the fault surface. They introduced the stress-weakening term to the state-evolution equation, which was not considered in the previous evolution laws, to explain both the mechanical data and the transmissivity during friction experiments.
The choice of the evolution law significantly affects the modeling results of quasi-static nucleation (e.g., Ampuero & Rubin, 2008) and dynamic ECS (e.g., Rice & Ben-Zion, 1996). Kame et al. (2015) performed numerical calculations of quasi-static nucleation employing the Nagata law and compared the modeling results with those using the aging and slip laws. They reported that the nucleation of the Nagata law has characteristics similar to those of pulse-like rupture (the slip law) rather than crack-like rupture (the aging law), but the spatial size of the slip pulse is larger than that of the slip law. On simulation of earthquake cycle with the Nagata law, Kame et al. (2013) performed simulations of a one-dimensional spring-slider model without mass, whereas the dynamic ECS with the Nagata law has not been reported. Based on the results of those previous studies, the dynamic ECS with the Nagata law may yield solutions between those obtained using the aging and slip laws, while such an expectation may not be the case when the solution is sufficiently far from the steady state and nonlinearity dominates the behavior of the solution.
The goal of the present study is to investigate differences in the earthquake cycles of a fault governed by the Nagata law from those by the aging and slip laws. For this purpose, we implemented the Nagata law into the dynamic ECS using SBIEM, based on the code developed by Noda (2022). It should be noted that the frictional parameters of the original Nagata law in the form reported by Nagata et al. (2012) have a different mathematical meaning from those of the previous evolution laws. We reformulated the Nagata law in a form similar to the previous evolution laws by further modifying the reformulations made by Noda & Chang (submitted), in such a way that the stress-weakening term does not appear explicitly. In this formulation, the dependencies of the variables are exactly the same as the conventional friction laws, and thus the implementation to the dynamic ECS is straightforward. In this presentation, we present the methodology for implementing the Nagata law in a dynamic ECS and the preliminary results obtained.