The model is a simplification of the
Burridge-Knopoff model, where the blocks move instantly to their balanced positions when submitted to a force greater than their friction. Let
S be a
square lattice with
L × L sites and let
Kmn ≥ 0 be the tension at site (m,n). The sites with tension greater than 1 are called critical and go through a relaxation step where their tension spreads to their neighbours. Through analogy with the Burridge-Knopoff model, what is being simulated is a
fault, where one of the lattice's dimensions is the flaw depth and the other one follows the flaw.
Model rules If there are no critical sites, then the system suffers a continuous drive, until a site becomes critical: : K_\max = \underset{(i,j)\in S}{\max} K_{ij} \, : K_{ij} \leftarrow K_{ij} + (1-K_\max) \, else if the sites
C1,
C2, ...,
Cm are critical the relaxation rule is applied in parallel: : K_{C_i} \leftarrow 0 ,\quad i=1,\ldots,m \, : K_j \leftarrow K_j + \alpha K'_{C_i}\, \forall\, j\in \Gamma_{C_i} ,\quad i=1,\ldots, m where K'
C is the tension prior to the relaxation and ΓC is the set of neighbours of site
C.
α is called the conservative parameter and can range from 0 to 0.25 in a square lattice. This can create a chain reaction which is interpreted as an earthquake. These rules allow us to define a time variable that is update during the driving step : t \leftarrow t + (1 - K_\max) \, this is equivalent to define a constant drive : \frac{dK_i}{dt} = 1 \,\forall\, i \in S and assume the relaxation step is instantaneous, which is a good approximation for an earthquake model. == Behaviour and criticality ==