Large nucleation before large earthquakes is sometimes skipped due to cascade-up-Implications from a rate and state simulation of faults with hierarchical asperities

Does a large earthquake have a large quasi-static preparation? A hierarchical asperity model in which a large tough patch (Patch L) contains smaller fragile patches (Patch S) enables a large earthquake to start with only small preparation because of cascade-up rupture growth. We realized such a model in a rate-and-state framework by heterogeneous distributions of the state evolution distance, and its consequences are investigated by earthquake sequence simulations. Focus is put on elementary processes, the interaction between two scales: one Patch L containing one Patch S is simulated, with their size ratio as a parameter. If Patch S is larger than the nucleation size of Patch L, the system falls into a limit cycle consisting of only one earthquake that starts with Patch S nucleation and grows dynamically to rupture entire Patch L. If Patch S is considerably smaller than the nucleation size of Patch L, small earthquakes never dynamically cascade-up, and the large earthquakes are initiated by large quasi-static nucleation. In between, large earthquakes start in various ways: by large nucleation, dynamic cascade-up, or delayed cascade-up. In the final stage of quasi-static nucleation, the preseismic moment release rate increases roughly inversely proportional to the time-to-failure t(f) with its amplitude depending on the nucleation size. For a Patch S rupture to cascade up, strength in the adjacent region must have been reduced, manifested by a higher creep velocity before the Patch S nucleation starts following 1/t(f) acceleration. Large nucleation sometimes has a precursory small earthquake characterized by larger afterslip than nonprecursory ones.