Seismic Cycles 3 - Adding more physics into the friction law, what are the implications about the seismic cycle?
Implementation of quasistatic viscoelasticity and poroelasticity using memory variables into dynamic earthquake sequence simulation with SBIEM
In a dynamic earthquake sequence simulation with SBIEM, storage of Fourier-transformed slip rate history and computation of dynamic stress transfer are limiting factors, which determine the maximum affordable problem size for restricted numerical resources. Calculation of static traction change on the fault does not cost significantly for an elastic medium because it depends only on the current slip distribution and thus temporal convolution is not needed. In inelastic medium, however, the static stress depends not only on the current slip distribution, but also on its history. Calculation of static stress by conducting temporal convolution would require additional storage of slip rate history, and thus affect the ability of numerical resolution for a given numerical resources. In this talk, a way of going around the temporal convolution is introduced by raising a couple of examples, Maxwell viscoelasticity (Miyake and Noda, 2019) and poroelasticity (revision submitted). Key tricks are definition of auxiliary memory variables and reformulation of the integral expressions of Fourier-transformed traction change to ODEs of the memory variables. In the present method, we have only to integrate the ODEs each timestep, similarly to integration of state variables in a rate- and state-dependent friction law.
Fault-size dependent fracture energy, seismogenesis, and cascading rupture on multi-scale fault networks
Fracture energy fundamentally affects all aspects of earthquake rupture, including fault seismogenesis. Seismological inferences of fracture energy [1-3] are seen to increase with both slip and the size of fault source. To explain these observations, refs [3-5] invoke co-seismic shear heating as the mechanism leading to continuing fault co-seismic weakening with slip on all scales. In this case, the observed correlation of fracture energy G with source/fault size R can be simply a consequence of larger faults been capable of hosting larger slip, and can otherwise be independent of individual fault properties (such as the thickness of the fault’s principal slip zone known to depend on fault maturity, total accrued fault slip, and fault size). While theoretically feasible at larger slip permissible on larger faults, such proposed fault-invariance of the fracture energy is questionable at smaller slip and/or smaller faults and fractures. It is the latter, i.e. the fracture energy at smaller values of slip, that governs dynamic rupture nucleation and is relevant to understanding seismogenesis.
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|When:||Friday 20 May, 2022, 9:00 am - 10:00 am PDT|