Despite considerable improvements of
the knowledge of the earthquake machine in various scientific
disciplines (tectonics, seismology, rock physics, etc..), a
complete understanding of seismic sequences and their prediction are
still out of reach.

In the upper seismogenic
crust, self-similar faulting and seismic patterns are observed worldwide
across many different types of geological environments.
Classical examples of power-law relationships include fracture-length
distributions, aftershock decay rates and the well-known
Gutenberg-Richter law between the magnitude of an earthquake and its
characteristic recurrence time.
Historically, self-organized criticality states
observed in sand-pile and slider block models have been used as a paradigm for
the earthquake-size distribution. These models
serve as an analogy for coseismic rupture propagation by illustrating
how short-range interactions and a random element can result in an
instability that can spread across the entire system.
These precursory works have also demonstrate that a cellular automaton
approach can be a useful complementary tool for the modelling of
earthquake dynamics.

In our work, we analyse the feedback mechanisms, positive or negative,
that can be involved in the brittle deformation processes of the
brittle upper crust (earthquake triggering, fault interactions,
fluid-rock interactions, aseismic transients). We develop discrete
numerical codes for the modelling of earthquake and faulting patterns.
This new generation of models combine long-range interactions that
mimics the continuum elastic solutions while retaining the inherently
discrete approach of statistical physics. In addition, we analyse the
earthquake phenomenology with a special interest on aftershock
sequences.

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