11:30 AM - 11:45 AM
[SSS10-08] Quantitative evaluation of discrete sizes to substitute for realistic heterogeneity using discrete cellular automata models
Keywords:GR law, Scaling law, Cellular automata model
Theoretical studies to elucidate the formation mechanism of the GR law can be categorized into two approaches: one based on continuum theory and the other on discrete models based on statistical physics. The former is based on geological features obtained by observation and friction laws obtained in the laboratory, and numerical calculations based on continuum mechanics. In this continuum theory-based approach, there is the problem of computational cost for calculations over many orders of magnitude of spatio-temporal scales, as well as the issue of how to formulate realistic spatial heterogeneity structures. On the other hand, the latter statistical physics approach, discrete model studies, takes the position that discreteness substitutes for realistic heterogeneous structures, including geological heterogeneity (Ben-Zion and Rice, 1993:1995), thereby avoiding the problems mentioned above and making it relatively easy to reproduce the GR law ( Carlson and Langer,1989:Ben-Zion and Rice, 1993:1995:Olami et al. 1992). However, the problem exists that there is no deductive explanation in terms of continuum theory as a basis for assuming that realistic heterogeneous structures can be substituted by discreteness. Conventional discrete model studies have not been able to provide even a quantitative argument for the essential discrete size that is assumed.
Therefore, this study attempts to tackle this problem by creating a new discrete model that reproduces the source features in addition to the GR law. By creating a new model that reproduces source features, which have not been dealt with well in conventional discrete models, it is possible to discuss the correspondence with observational studies more abundantly than in conventional discrete model studies.
The Olami-Feder-Christensen model (OFC model), a simple cellular automaton model that reproduces the GR law, is extended to include finite fracture propagation velocity. This allows us to create a discrete model describing the source process (Fukuda et al., 2022). Furthermore, by extending this model to describe the finite strength recovery effect, a discrete model can be created that reproduces both the GR law and a self-similar crack fracture image (hereafter referred to as the Dynamic OFC model). In this study, we quantitatively clarified the parameter conditions that reproduce both the GR law and the self-similar crack fracture image on the Dynamic OFC model. From these conditions, the range of discrete sizes required to reproduce the GR law and the crack fracture image was quantitatively obtained.
This discrete model does not reproduce the observed distribution of event waiting times or aftershocks (Omori-Utsu law). Therefore, the estimated discrete size range still contains uncertainties. However, if we can create a discrete model in the future that realizes these observational reproductions as well, it may be possible to make more quantitatively accurate estimates regarding discrete sizes that can substitute for realistic heterogeneous structures. This realization could provide an important benchmark for bridging the logical gap between the discreteness that forms the GR law and continuum theory.
Therefore, this study attempts to tackle this problem by creating a new discrete model that reproduces the source features in addition to the GR law. By creating a new model that reproduces source features, which have not been dealt with well in conventional discrete models, it is possible to discuss the correspondence with observational studies more abundantly than in conventional discrete model studies.
The Olami-Feder-Christensen model (OFC model), a simple cellular automaton model that reproduces the GR law, is extended to include finite fracture propagation velocity. This allows us to create a discrete model describing the source process (Fukuda et al., 2022). Furthermore, by extending this model to describe the finite strength recovery effect, a discrete model can be created that reproduces both the GR law and a self-similar crack fracture image (hereafter referred to as the Dynamic OFC model). In this study, we quantitatively clarified the parameter conditions that reproduce both the GR law and the self-similar crack fracture image on the Dynamic OFC model. From these conditions, the range of discrete sizes required to reproduce the GR law and the crack fracture image was quantitatively obtained.
This discrete model does not reproduce the observed distribution of event waiting times or aftershocks (Omori-Utsu law). Therefore, the estimated discrete size range still contains uncertainties. However, if we can create a discrete model in the future that realizes these observational reproductions as well, it may be possible to make more quantitatively accurate estimates regarding discrete sizes that can substitute for realistic heterogeneous structures. This realization could provide an important benchmark for bridging the logical gap between the discreteness that forms the GR law and continuum theory.