## 4 Discussion  
Most of the models used to describe post-seismic relaxation are based on the assumption of a single relaxation time estimated for each relaxation mechanism proposed [4; 11; 14; 60; 61]. A co-seismic deformation leaves the system in a metastable state taking place in the broad earthquake zone. In the present work, the post-seismic relaxation is viewed as a superposition of several different relaxation times, each one activated in different mesoscopic domains of the macroscopic relaxed seismic volume. The macroscopic relaxation observed is a result of the superposition of different relaxation times on the microscopic-mesoscopic  
Figure 6: The experimentally estimated \(\Omega(t)\) function for the first 400 days of the post-seismic relaxation after the Lefkas main event, along with the calculated one using Equation (16) for \(\tau_{min}\approx 3.5\) days and \(\tau_{max}\approx 350\) days, respectively. Figure 7: A comparison of the experimentally estimated \(\Omega(t)\) function with the calculated values \(R(t)/\mathrm{Ro}\) for the post-seismic relaxation period after the Lefkas main event for \(\tau_{min}\approx 3.5\) days and \(\tau_{max}\approx 350\) days, respectively (see text). scale. This slow thermodynamic recovery could be explained by a physical model based on the Arrhenius Equation [62]. The lithosphere as a dynamical system under a post-seismic relaxation is a complex systems with strong interactions between its mesoscopic \"subvolumes\" [63] and, thus, could be viewed as a macroscopic system driven by hierarchically constrained dynamics [28] involved in the macroscopically observed relaxation process as a sequential series of correlated mesoscopic processes. The view of hierarchical constrained dynamics could be a physical pathway to describe many of the complex systems that present logarithmic relaxation [64; 65; 66]. In the case of post-seismic phase, the applied tectonic load drives the system to fracture, and its relaxation creates a reorganization of the stress field in some selected mesoscopic regions of the system. The deformed subvolumes nearest to the fractured region are rearranged and the system reorganized. These new stress changes will affect the deformed subvolumes outside the area nearest to the fracture, permitting their relaxation, and so on. The above picture suggests that the relaxation in the fractured fault system is slow because it consists of a large number of correlated and strongly interacting reorganization steps with an increasing relaxation time. It seems to be appropriate to describe macroscopical post-seismic relaxation in terms of a lithosphere that presents a hierarchical pattern, with the faster relaxation to be associated with the subvolume close to earthquake focus regions and, due to strong correlations and long-range interactions, the slower relaxation time to be related with the \"outer\" deformed, but in the broad vicinity of epicenter, regions. The latter is in agreement with that proposed for complex relaxed systems with cluster interactions, where the relaxation time \(\tau\) scales with the relaxation volume as \(\tau\)-\(\mathrm{V}^{\alpha}\), where \(\alpha\) is an exponent related macroscopically with the fractal geometry of the subvolume distribution and the dynamical nature of relaxation [67; 68; 69]. This type of hierarchically constrained dynamics is able to derive the logarithmic relaxation frequently observed and associate it with thermally activated processes. We note that this behavior can result either from the parallel relaxation of subvolumes or by a sequential relaxation series of strongly correlated complex events [28]. Our results are in agreement with that presented in [70], where a Burridge-Knopoff (BK) model is used to describe the time dependence of the mean stress, assuming that a uniform statistical distribution of stress values is acting on each block (i.e., deformation in subvolumes) in the relaxing lithospheric system.