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Seismic process is usually considered as an example of occurrence of the regime of self-organizing criticality (SOC). A model of seismic regime as an assemblage of randomly developing episodes of avalanche-like relaxation, occurring at a set of metastable subsystems, can be the alternative of such consideration. The model is defined by two parameters characterizing the scaling hierarchical structure of the geophysical medium and the degree of metastability of subsystems of this medium. In the assemblage, these two parameters define a model

Seismic process is usually considered as an example of realization of the self-organized criticality—the SOC-model [

For quantitative statistic modeling of seismicity regime, the Generalized Omori law and the Epidemic-Type Aftershock-Sequence (ETAS) model are used at the present time [

The fundamental properties determining the process of seismicity are the scaling hierarchical properties of the structure of the Earth’s crust and the irreversibility of the processes ongoing in the Earth’s interior. A natural model for understanding of the process of seismicity would be a statistical model treating seismicity in terms of these fundamental characteristics. The model of seismic process as an assemblage of avalanche-like episodes of relaxation, occurring occasionally at a set of uniform metastable subsystems [

We will model seismic regime as an assemblage of episodes of avalanche-like relaxation, occurring occasionally at a set of statistically identical metastable subsystems. Let us describe this statistical earthquake model (SEM) in terms of recurrent scheme (or equivalently in terms of multiplicative process) as it was presented in [

Let us imagine that an ongoing stochastic process (here earthquake), that had released energy

For simplicity of the mathematical manipulations presented below, we will suggest that the constant

The scheme thus described treats a development of an earthquake as a process of sequential transition to higher hierarchical levels. At constant parameter

Thus, in terms of the SEM model, the

It is not difficult to pick up the values of

As an example, we take a case with weak (with amplitude 0.2) and periodic (

An example of realization of the SEM model of a seismic regime; (a) maximal magnitude values

It is easy to see that even such a very simple model is not trivial. It produces the well-known “prognostic” feature—the decrease in

Model relationship between the

An appearance of model correlation given in Figure

Thus the increase of the values of parameters

The SEM model is used below for examination of the seismic regime of the south of Sakhalin Island. However, before discussing the results of such examination, we should briefly characterize the seismicity of the Sakhalin Island and the used database.

Sakhalin Island (Russia) is located in the Pacific-Eurasia transition zone. In the island, on average 1 earthquake with magnitude

The seismicity of Sakhalin can be divided into shallow (

Within Sakhalin Island and the adjacent shelf, four major deep fault systems were identified that generate almost all crustal earthquakes with

Active faults of the Sakhalin region. Insert—regional scheme of plate boundaries in the model NUVEL-1A and its modifications [

The most complete data about the Sakhalin Island earthquakes during the historical and instrumental periods of observations are collected in the regional catalogue [

Map of crustal

Let us consider the main features of the spatial distribution of epicenters with

It can be noticed that localization of the strong earthquakes appears to agree with a suggested location of the boundary of Okhotsk Sea plate in this region. It is suggested [

Sources of large earthquakes at the western coast of Sakhalin Island (grey ovals) and the approximate location of the seismic gap (hatched rectangle).

More detailed information about the seismicity of the South Sakhalin area is available since 2003 because of the installation of the seismic networks “Datamark” and “DAT.” The catalog obtained from these networks is presented in unified

Gutenberg-Richter relations for both catalogs 1(a) and 2 (b); points—earthquakes of magnitude

We have used the catalogue 1 [

Having in mind the change in representativeness of the catalog 1 through time the different variants of time interval and magnitude limitation were used for

Scheme of changes of the values

For earthquake prediction, however, the time changes of probability

The estimation of time changeability of parameter of metastability

In Figure

Temporary component of the SEM model—sequence of values of parameter of metastability

Location of earthquakes with typical (

The groups of the epicenters with

The higher level of parameter of metastability revealed in the area of the Poyasok Isthmus can be connected probably with the Southern Sakhalin fault [

After the Nevelsk earthquake of August 2, 2007, the earthquakes with higher parameter

According to the catalog 1 [

Cumulative graphs of a number of the events (a) and of released seismic energy (b) inside the area 48°-49°N and 141.5°–143°E. Vertical lines and figures show the moments of the Nevelsk (1), Gornozavodsk (2) earthquakes, and the strongest earthquake of February 24, 2007,

In Figure

A nonlinear growth of a number of earthquakes takes place in the Poyasok Isthmus area also since 2010. Besides, the nonlinear growth of released seismic energy takes place here since the middle of 2010 (Figure

It should be noted also that the intervals of time of nonlinear growth of a number of events and of released seismic energy (occurring in 2007-2008 and since the middle of 2010) correspond to the intervals of time of occurrence of events with higher (>0.55) values of parameter of metastability

Seismic regime is usually considered in terms of the SOC-model. This model suggests the spontaneous evolution of dynamic system to a critical state. However, the physical mechanism of such evolution in the case of seismicity has not been suggested. It is also not clear how to explain the difference of seismically active and aseismic areas in terms of the SOC-model. The analogy between seismic regime and the second-order phase transitions also seems disputable. The principal feature of the second-order phase transitions is that the transformation goes without absorption (emission) of energy. In contrast to it, a huge explosion-like release of energy takes place during strong earthquakes.

The alternative model of the seismic regime as a set of episodes of avalanche-like relaxation of metastable sub-systems (SEM model) is suggested. In the case of seismicity the origin of metastable sub-systems is connected with storage of elastic energy. The discharge of accumulated elastic energy can be initiated by the excess of stress level [

In the simple variant of the SEM model (without memory of the medium), the geophysical medium is described by two parameters [

The presence of two latent parameters specifying one empirically determining characteristic

As a result of the estimate of the parameter of metastability

The results of parameterization of the seismic regime in the framework of the SEM model complement the results received previously from the examination of the seismic gaps. According to these results, the gap along the western coast of the South Sakhalin was only partly (in its southern part up to the latitude 47°N) closed as a result of the Nevelsk earthquake (Figure

Note that the revealed features in the behavior of parameters of the SEM model could be explained in terms of change of

Seismic regime is usually considered as an example of the regime of self-organizing criticality (SOC-conception). The alternative SEM model treats the seismic regime as an assemblage of random episodes of avalanche-like relaxation, taking place at a set of uniform metastable sub-systems. The SEM model in its simple form without memory of the system is defined by two parameters, characterizing scaling in spatial structure of the Earth’s crust and the degree of metastability of the geophysical medium. This model is used for the description of seismic regime of the south of Sakhalin Island. The models of spatial changeability of the scaling parameter and temporal changeability of the parameter of metastability are constructed. The anomalous growth of the parameter of metastability preceded the occurrence of the Gornozavodsk and Nevelsk earthquakes. At the present time, the anomalously high (and growing over time) values of this parameter are observed in the area of the Poyasok Isthmus (in the vicinity of latitude 48°N). Clear nonlinear growth of the flow of a number of seismic events and of seismic energy is noticeable in this area before the Gornozavodsk and Nevelsk earthquakes and after 2009.

This paper was supported by the Russian Foundation for Basic Research, Grant no. 11-05-00663, and the European Grant FP7 no. 262005 SEMEP.