講演情報
[SCG56-53]Multi-scale rate-and-state friction and coarse-graining of hierarchical fault heterogeneity
*乘杉 玲壽1、野田 博之2 (1.京都大学、2.京都大学 防災研究所)
キーワード：
速度・状態依存摩擦構成則、階層的不均質の粗視化、動的地震サイクル計算、震源パラメータのスケーリング
When constructing a fault constitutive law to model fault slip, an essential step is the coarse-graining (CG) of underlying microscopic processes. In the conventional rate- and state-dependent friction (RSF) law, widely used to simulate earthquake sequences, the shear strength is interpreted as a function of the “averaged” contact lifetime at a specific spatial scale. However, whether such a CG process is appropriate is unclear. Given that we use limited computational resources to simulate earthquake sequences, without a plausible CG process or upscaling method, it is not straightforward to apply the same constitutive laws across scales, from rock-friction experiments to megathrust earthquakes. In this study, we summarize the previously proposed micromechanical derivation of the RSF law with an explicit CG process at the microscale and investigate its validity through dynamic earthquake sequence simulations based on different CG scales, evolution laws, and constitutive parameters.
To investigate the coarse-grainability of heterogeneity by the RSF framework, we first simulate dynamic earthquake sequences with the hierarchical distribution of seismic patches. The patch size and number of patches obey the power laws, and large/small patches have large/small fracture energy (or weakening distance). We change the brittleness of seismic patches, i.e., the ratio of patch size to nucleation size, and find the variety of complex seismic activities. These models exhibit reasonable scaling of macroscopic source parameters, including fracture energy scaling, a narrowly distributed stress drop and radiation efficiency, and self-similar potency-duration scaling. Secondly, we conduct numerical experiments to coarse-grain hierarchical heterogeneity using a multi-scale rate-and-state friction law, which accounts for small-scale heterogeneity below the CG scale by introducing new state variables that depend on the scale of seismic patches. The present process offers the CG without additional parameter tuning for a given heterogeneity and CG scale. Depending on the CG scale, the spatial distribution of parameters is simplified like a pixelization, and the effect of small-scale distribution is included in the constitutive law. We find that the CG of hierarchical fault heterogeneity does not change the scalings of macroscopic source parameters much, whereas it drastically changes the characteristics of earthquake sequences. In addition, the CG of small-scale heterogeneity reduces the high-frequency component of seismic radiation, thereby simplifying the rupture process. Both aging law and slip law exhibits the same tendency. We are now attempting to quantify the similarity and difference between earthquake sequences with different CG scales to evaluate the applicability of coarse-grained models. It should be emphasized that all numerical models for fault behavior based on continuum mechanics are coarse-grained models to some extent. Our results indicate that coarse-graining heterogeneity and upscaling the lab-scale constitutive law to large scales are not straightforward, while most models implicitly assume their validity. Further study may be required to appropriately incorporate the small-scale spatio-temporal heterogeneity into the constitutive law to mitigate the effect (artifact) of CG, which is crucial to understand and reproduce the complex dynamics of earthquake sequences.
To investigate the coarse-grainability of heterogeneity by the RSF framework, we first simulate dynamic earthquake sequences with the hierarchical distribution of seismic patches. The patch size and number of patches obey the power laws, and large/small patches have large/small fracture energy (or weakening distance). We change the brittleness of seismic patches, i.e., the ratio of patch size to nucleation size, and find the variety of complex seismic activities. These models exhibit reasonable scaling of macroscopic source parameters, including fracture energy scaling, a narrowly distributed stress drop and radiation efficiency, and self-similar potency-duration scaling. Secondly, we conduct numerical experiments to coarse-grain hierarchical heterogeneity using a multi-scale rate-and-state friction law, which accounts for small-scale heterogeneity below the CG scale by introducing new state variables that depend on the scale of seismic patches. The present process offers the CG without additional parameter tuning for a given heterogeneity and CG scale. Depending on the CG scale, the spatial distribution of parameters is simplified like a pixelization, and the effect of small-scale distribution is included in the constitutive law. We find that the CG of hierarchical fault heterogeneity does not change the scalings of macroscopic source parameters much, whereas it drastically changes the characteristics of earthquake sequences. In addition, the CG of small-scale heterogeneity reduces the high-frequency component of seismic radiation, thereby simplifying the rupture process. Both aging law and slip law exhibits the same tendency. We are now attempting to quantify the similarity and difference between earthquake sequences with different CG scales to evaluate the applicability of coarse-grained models. It should be emphasized that all numerical models for fault behavior based on continuum mechanics are coarse-grained models to some extent. Our results indicate that coarse-graining heterogeneity and upscaling the lab-scale constitutive law to large scales are not straightforward, while most models implicitly assume their validity. Further study may be required to appropriately incorporate the small-scale spatio-temporal heterogeneity into the constitutive law to mitigate the effect (artifact) of CG, which is crucial to understand and reproduce the complex dynamics of earthquake sequences.