講演情報
[P08-22]Multi-scale rate-and-state friction law and coarse graining of hierarchical fault heterogeneity preserving source parameter scaling
*乘杉 玲壽1、野田 博之2 (1. 京都大学 理学研究科、2. 京都大学 防災研究所)
Earthquakes are macroscopically characterized by several source parameters, and it is well known that they exhibit scaling relationship or scale-invariance. For example, fracture energy scales with coseismic slip in a power-law manner; stress drop and radiation efficiency is approximately constant for a wide range of moment magnitudes; and seismic moment follows a power-law scaling with event duration. Although there exists many physical mechanisms that realize at least some of these properties, we investigated the hierarchical fault heterogeneity. It is assumed that the fracture energy (or length-scale which determines the fracture energy) is distributed in a fractal manner on the fault, so that a large earthquake spans a wide area with large fracture energy while other source characteristic parameters are preserved. However, this model was constructed using simulations of single dynamic rupture with artificial initial conditions and stress distribution, and it is not verified that the source parameter characteristics are realized as designed in sequences of earthquakes and interseismic processes. Besides, this model is computationally very intense because of requirement of high resolution for regions with small fracture energy. Therefore, we investigated coarse graining of dynamic earthquake sequence simulation for a hierarchical heterogeneous fault. Firstly, we performed the dynamic earthquake sequence simulation, using a rate-and-state friction law with a single state variable and the hierarchical distribution of characteristic weakening distances, finding that the designed source parameter scalings were realized. And then, we constructed coarse-grained models based on spatial average of friction law with various length scales of spatial window and increasing the number of state variables, investigating how the earthquake sequence and the scaling relationships change or remain by the coarse graining.
The coarse graining is motivated by the slip- and time-dependent fault constitutive law which includes the effect of multi-scale fault roughness into the constitutive law. If a spatial window hosts regions of different state-evolution distances Ln, then the corresponding point in the coarse-grained model has multiple state variables (θn where n is the state mode), corresponding area-averaged frictional parameters bn and characteristic weakening distances Ln. Depending on the length scale of coarse graining, 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 coarse graining of the hierarchical fault heterogeneity does not change the scaling or scale-invariance of macroscopic source parameters much, while the characteristics of earthquakes drastically change. In addition, the coarse graining of the small-scale heterogeneity results in the reduction of high frequency component in seismic radiation, making the rupture process simpler. We are now attempting to quantify the similarity and difference between earthquake sequences with different length scale of coarse graining 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. Further study may be required to appropriately incorporate the small scale spatio-temporal heterogeneity into the constitutive law to mitigate the effect (artifact) of coarse graining, which is crucial to understand the complex dynamics of earthquake sequences.
The coarse graining is motivated by the slip- and time-dependent fault constitutive law which includes the effect of multi-scale fault roughness into the constitutive law. If a spatial window hosts regions of different state-evolution distances Ln, then the corresponding point in the coarse-grained model has multiple state variables (θn where n is the state mode), corresponding area-averaged frictional parameters bn and characteristic weakening distances Ln. Depending on the length scale of coarse graining, 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 coarse graining of the hierarchical fault heterogeneity does not change the scaling or scale-invariance of macroscopic source parameters much, while the characteristics of earthquakes drastically change. In addition, the coarse graining of the small-scale heterogeneity results in the reduction of high frequency component in seismic radiation, making the rupture process simpler. We are now attempting to quantify the similarity and difference between earthquake sequences with different length scale of coarse graining 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. Further study may be required to appropriately incorporate the small scale spatio-temporal heterogeneity into the constitutive law to mitigate the effect (artifact) of coarse graining, which is crucial to understand the complex dynamics of earthquake sequences.