THE TRANSIENT REGIME PATTERNS IN THE DISSIPATIVE CELL MODEL OF EARTHQUAKES

Abstract

The purpose of this work was to analyze the mechanisms of the growth of drop clusters,
leading on a finite-size lattice to a state close to a critical one with a power-law size distribution of
clusters similar to that observed in a seismic process. At the same time, the question of applicability
of this model to the description of processes in a real geophysical medium remains. Analysis of
the elements coupling in the one-dimensional OFC model with open boundary conditions allowsan estimation of the variability of the incoming energy to the lattice elements located at different
distances from the boundaries. The constructed computational model makes it possible to
estimate the size of the boundary areas of high average incoming energy variability at different
values of the coupling parameter α. It is shown that, as α grows, the boundary region of inhomogeneity
expands. It is shown that there are two different modes of synchronous drop fo rmation,
simulating an earthquake. Both mechanisms are determined by the capture of a neighboring
element and the subsequent synchronization of the drops. This process forms a stable
drop of a larger size. The presence of boundary regions with a high gradient of the input energy
rate is the main mechanism for the formation of clusters of lattice elements, demonstrating the
simultaneous drop of the accumulated energy. Such a synchronization is achieved due to the
high mutual variability of energy at each iteration step. The second important mechanism of
cluster growth is typical for the formed clusters that exceed the size of the near-boundary region
of high inhomogeneity of the energy inflow. As the cluster size grows, the capture area of
neighboring elements that are not included in the cluster expands. Accordingly, the probabi lity
that the energy of the neighboring element is in the capture area increases. The calculations
show that the mean time of reaching the given size of the cluster on the lattice at different sp atial
dimensions d and at different coupling parameters confirms the presence of two time intervals
with a different mechanism of cluster formation. In this case, the growth of large clusters has
a power-law character, with an exponent determined by the dimension d.