**1. Introduction**

The study of the processes that determine the evolution of open physical systems has led scientists to understand the fact that their development is due to unstable dissipative nonlinear systems [1]. Moreover, the instability of open systems is

understood as such that, at characteristic observation times, as a result of the influence of minor external perturbations, it comes to a deviation in its state by an amount comparable to the characteristic values of the quantities that determine this state. In turn, an open nonequilibrium system that is in a stationary state far from thermodynamic equilibrium, which is provided by a balance between energy dissipation within the system itself and the influx of energy coming from outside, is called a dissipative system or a dissipative structure [1]. In addition, in an open system, due to the coordinated interaction of many of its elements through intensive (flow) exchange of matter and energy with the environment in nonequilibrium conditions, an ordering process (spatial, temporal, or spatio-temporal), called self-organization, can occur. In other words, in such systems, the coordinated behavior of subsystems is observed, as a result of which the degree of its ordering increases, i.e. entropy decreases. The conducted research in the field of "dissipative structures" led to the conclusion that the process of "self-organization" occurs much faster in the presence of external and internal disturbances (noise) in the system. Thus, noise phenomena lead to an acceleration of the self-organization process.

It is clear that any real open physical system is continuously under the action of small external and internal perturbations. Based on the most general considerations, it can be assumed that an earthquake is the result of a manifestation of a certain set of processes in the lithosphere, which is a nonlinear unstable system and which is under the action of the background field of external disturbances. A regular process, determined by compression or extension of the lithospheric plate, or other physical and chemical phenomena in a seismically active region on a global scale, is affected by a certain set of external disturbances in a consistent system of geospheres, determined by the system of solar-terrestrial relations. These perturbations excite the development of various instabilities, ultimately leading to local (in the volume of the focus) destruction of the structure, which is in a special limiting (critical) state. This state is characterized by a certain but rather complex balance between fluctuations in the system and its average characteristics, which determine the macroscopic state.

Thus, from the most general considerations, we can consider the preparatory stage of an earthquake as the development of instability that forms in local areas of the lithosphere against the background of external disturbances that arise in the chain "Sun—heliosphere—magnetosphere—ionosphere—neutral atmosphere—lithosphere."

The proposed work uses the catalog of earthquakes recorded by the Kamchatka regional network of seismic stations of the Kamchatka branch of the Geophysical Service of the Russian Academy of Sciences (KB GS RAS). This catalog can be divided into two parts [2]. The first part includes events from 1962 to 2009. By 2010, the approaches and methods for calculating the main parameters have changed, and the conditions for the formation of the catalog in close to real time have developed. This second part of the catalog contains data on earthquakes from 2010 to the present and is formed with a delay of 1–7 days. The Kronotskoe earthquake (1997-12-05) falls into the first part.

It should be noted that the greatest difficulties in processing the parameters of the catalog arise when determining the depth of an event. Each real value of the depth *hreal* is within the corresponding error interval Δ*hmist* relative to the depth *hmet* calculated by a certain method. Strictly speaking, the relation *hreal* ∈ *hmet* Δ*hmist* holds. That is, the real depth *hreal* can take any value from the set of values covered by the interval *hmet* Δ*hmist*. Therefore, in this fuzzy situation, we will be interested not in some undefined value of the depth *hreal*, which falls somewhere in the corresponding error interval, but in the depth value *hmet* itself, calculated according to *Investigation of the Dynamics of the Seismic Regime in the Kamchatka… DOI: http://dx.doi.org/10.5772/intechopen.109069*

a certain method, for which the error interval Δ*hmist* is calculated. In this case, the depth value *hmet* is a fixed value and will depend only on the method of its calculation. For a homogeneous catalog, this technique is the same for all calculated depths. In the analysis carried out in this chapter, we will follow the dynamics of the trend, which would indicate a tendency in the distribution of the depths of various "background" earthquakes that form on large spatial scales, to group at the depth of the source of the impending major event. In other words, we will be interested in the question: at what depths *hmet* do "background" events fall on the eve of a strong earthquake. At the same time, we believe that the trend *hmet* reflects the general tendency of the real depth *hreal* of "background" earthquakes to cluster at the source depth of a major event. We will study this trend by probabilistic methods using wavelet decomposition methods [3, 4].

If the error is taken into account and some of its numerical values Δ*hmist* are specified, then in this case, events for which this error is greater than the specified one will be filtered out of all earthquakes in the catalog for the period under consideration. Naturally, in this case, the statistics will be reduced. Moreover, the smaller the given error, the closer the value of the real depth *hreal* to the value *hmet*, the smaller the statistics. In what follows, unless otherwise specified, the event depth will be understood as *hmet.*
