A multiscale cellular automaton

Different cells at different level represent the state of fracturing at different scales. The dynamical system consists of a permanent interplay between the local strain rate and the state of fracturing at different scales.

A finite number of states

Different states represent fault segments with different faulting mechanisms or stable zones. A temporal iteration is associated with any transition of a microscopic element from one state to another. Then the time step is not constant.

A continuous time

At each iteration, the time step is calculated from the local strain rates and the number of active cells according to a set of constitutive rules. For example, the failure rate increases with respect to the strain rates (i.e. weakening) and the healing rate is constant (i.e. strengthening).

The fault

Each new active fault segment may interact with neighboring active fault segments to form a fault (i.e. short range interaction).

Fault interactions

The new fault interacts or not with neighboring faults according to its location within the fault population (interaction over a wide range of spatial scale).

The redistribution mechanism

In the neighborhood of a new fault, within a zone proportional to the length of the fault, the local strain rates are perturbed according to the magnitude of the fault interaction and the magnitude of the tectonic loading (long range interaction).