Topological properties of aftershock clusters in a viscoelastic model of quasi-brittle failure

Material failure at different scales and processes can be modeled as an emergent feature in terms of avalanche dynamics in micromechanical systems. 
Event-event triggering -or aftershocks- is common in seismological catalogs and acoustic emission experiments ^[1] among other phenomena.
Stochastic branching and linear Hawkes processes are used to model the statistical properties of catalogs.  In the micromechanical approach, viscoelastic stress transfer and after-slip are among the proposed mechanism of aftershocks. Here we ask this simple question: 'Do aftershock sequences in micromechanical models agree with such epidemic branching paradigm?'

We introduce two fibrous models as prototypes of viscoelastic fracture ^[2] which (i) provides an analytical explanation to the acceleration of activity in absence of critical failure observed in acoustic emission experiments ^[3]; (ii) reproduce the typical spatio-temporal properties of triggering found in field catalogs, acoustic emission experiments; but (iii) display discrepancies with the branching topological properties predicted by stochastic models ^[4], probably due to physical constrains.

[1] J. Baró et al., Phys. Rev. Lett. 110 (8), 088702 (2013).
[2] J. Baró, J. Davidsen, Phys. Rev. E  97 (3), 033002 (2018).
[3] J. Baró, et al., Phys. Rev. Lett. 120 (24), 245501 (2018).
[4] S. Saichev, et al., Pure and App. Geoph. 162 (6), 1113-1134 (2005).