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The lack of clarity regarding slip distribution within heterogeneous rupture areas has a significant impact on characterizing the seismic source and the role of heterogeneities in determining ground motion. One approach to understand the rupture process is through dynamic simulations, which require substantial computational resources, thereby limiting our comprehension of seismic rupture processes. Consequently, there is a need for methods that efficiently describe the spatial complexities of seismic rupture in a realistic manner. To address this, the statistics of real self-arrested ruptures that conform to the asperity criterion are investigated. This research demonstrates that power law distributions can describe the final slip statistics. Regarding the computational efficiency, a simple heterogeneous energy-based (HE-B) method is proposed. The HE-B method is characterized by the spatial correlation between the rupture parameters, such as the final slip or the rupture velocity, and the distribution of residual energy which determines the zones where the rupture could occur. In addition, the HE-B method defines the rupture area in those zones of the fault where the coupling function exceeds the energy required for rupture initiation. Therefore, the size of the earthquake is directly influenced by the distribution of coupling within faults. This method also leads to the successful reproduction of the statistical characteristics of final slip and generates slip rates that match the kinematic behavior of seismic sources. Notably, this kinematic rupture simulation produces seismic moment rates characterized byf−1{f}^{-1}andf−2{f}^{-2}spectra with a double corner frequency. Finally, it is observed that the maximum fracture energy value within the ruptured area is strongly correlated with both the magnitude and peak seismic moment rate. Thus, by employing this method, realistic rupture scenarios can be generated efficiently, enabling the study of spatial correlations among rupture parameters, ground motion simulations, and quantification of seismic hazard.

Geological earthquake simulations generated by kinematic heterogeneous energy-based method: Self-arrested ruptures and asperity criterion