arXiv subjects

O. D. Zotov

Publications and source records attributed to O. D. Zotov.

17 recordsLinked to original sources

arXiv2026

On four representations of the law of aftershock evolution

The relaxation of the earthquake source following the main shock has been investigated both theoretically and experimentally, based on data regarding the evolution of aftershocks. It is shown that Omori picture of aftershock evolution is not holistic, whereas the Hirano-Utsu representation contradicts observations. Linear and discrete representations are proposed. They are based on original concepts regarding deactivation and the proper time of the source. The difference between the linear and discrete representations lies in the procedure for processing experimental data on aftershocks. In the linear representation, proper time is calculated based on the frequency of aftershocks. In a discrete representation, the source's proper time is measured by an imaginary underground clock, the rate of which differs radically from that of universal time. In the linear representation, the frequency of aftershocks is described by the simplest nonlinear differential equation. In the discrete representation, the aftershock frequency is described by a first-order linear differential equation. It has been found that aftershock activity decays exponentially with the source's proper time. Keywords: earthquake source, foreshocks, mainshock, aftershock theory, Omori law, Utsu's law, proper time, underground clock, deactivation coefficient, source relaxation.

physics.geo-ph↗

arXiv2026

On the classification of triggers of dynamic processes in geophysics

In geophysics, the problem of classifying triggers of dynamic processes in the lithosphere, hydrosphere, atmosphere, ionosphere and magnetosphere has arisen and needs to be solved. Triggers that induce catastrophic events, such as destructive earthquakes, require special attention. Classification is necessary in order to express the diversity of triggers in a limited number of ordered and well-identifiable species. This paper proposes a project for collective work on the systematization of triggers, i.e., the formation of a unified classification and nomenclature. A simplified (basic) and extended classification table are proposed. The basic matrix uses the principle of binary opposition. The matrix contains three categories of descending rank: type (natural, artificial), class (endogenous, exogenous) and specie (periodic, aperiodic). Three additional categories have been added to the expanded classification table. This results in 128 trigger varieties. The heuristic significance of the classification of triggers is emphasized. New phenomena discovered during the classification process are indicated: excitation of a strong aftershock by a round-the-world seismic echo, modulation of global seismicity by spheroidal oscillations of the Earth, the weekend effect in earthquake activity. In the magnetosphere, a cause-and-effect chain of triggers has been identified, called a trigger cascade. The existence of so-called antitriggers is indicated, which do not excite, as usually happens, but interrupt the ongoing dynamic process. Key words: systematics, nomenclature, dynamic system, disturbance, lithosphere, hydrosphere, atmosphere, ionosphere, magnetosphere, earthquake, magnetic storm, trigger cascade, antitrigger.

physics.geo-ph↗

arXiv2025

Relativity of Time in Earthquake Physics

In this paper we develop an understanding of the proper time of the Tohoku earthquake source. The paper is dedicated to the 120th anniversary of Einstein's theory of relativity, but the dedication is symbolic, since we are investigating a purely non-relativistic geophysical object. We still found it possible to borrow the terms time relativity and proper time from the theory of relativity. The concept of the proper time of the source is developed by us within the framework of the phenomenological theory of earthquakes. The paper describes a procedure for measuring proper time using observation data of foreshocks and aftershocks. We synchronized the imaginary underground clock that counted the proper time and the clock that showed world time. The idea of a hypothetical underground clock turned out to be effective. We have shown that the proper time of the source flows unevenly relative to the flow of world time. Two phases of the evolution of the source before the main shock of the earthquake were discovered. This complements the picture of three-phase relaxation of the source after the main shock, which we established earlier. The uneven flow of proper time relative to world time indicates the non-stationarity of the source parameters. The overall conclusion is that the concept of the proper time of the source has enriched the possibilities of experimental study of earthquakes.

physics.geo-ph↗

arXiv2025

Evolution of the Tohoku earthquake aftershocks in the framework of the phenomenological theory of aftershocks

The aftershocks of the Tohoku earthquake are analyzed in light of the phenomenological theory of aftershocks. The theory is based on the concept of an earthquake source as a dynamic system, the state of which is described by a deactivation coefficient. The concept of the proper time of the source is used, which in general differs from world time. The "underground clock" and the clock showing world time have been synchronized. For an observer using the underground impacts as time markers, the flow of world time will be uneven. The admissibility and effectiveness of the idea of this specific relativity of time is shown. Three phases of relaxation of the source after the main shock were discovered. In the initial phase, the deactivation coefficient is zero. In the main phase, the deactivation coefficient has a finite value and does not change over time. In the recovery phase, the deactivation coefficient changes randomly over time. The sharp transitions between phases resemble the phenomenon of bifurcation.

physics.geo-ph↗

arXiv2025

On the three laws of earthquake physics

The paper provides a synoptic overview of a series of works carried out by a group of researchers at the Institute of Physics of the Earth RAS with the aim of finding new approaches to the problems of earthquake physics. The fundamental laws of Omori, Gutenberg-Richter and Bath have served as a constant support and reference point in the course of many years of research. The concept of the tectonic earthquake triad as a natural trinity of foreshocks, main shocks and aftershocks is used in the article to organise the thematic material. A classification of main shocks into six types of triads found in experience is given. The parameters appearing in the three laws for different types of triads are given. The axiomatic theory of the evolution of aftershocks is outlined. The concepts of source deactivation, Omori epoch and source bifurcation are introduced, and the notion of the proper time of unsteady lithospheric processes is introduced. Convergence of foreshocks and divergence of aftershocks are mentioned. The general conclusion is that the Omori, Gutenberg-Richter and Bath laws are reliable tools in the experimental and theoretical study of earthquakes. The laws have a depth of content that has been demonstrated by the ability to enrich the original formulations of the discoverers with interesting and important additional statements.

physics.geo-ph↗

arXiv2025

On the elementary theory of earthquake aftershocks

The elementary theory of aftershocks, being relatively simple mathematically, belongs to the basics of earthquake physics. The paper briefly outlines the concepts and ideas of the theory, provides equations for the relaxation of the source after the main shock, and emphasizes the effectiveness of the theory in the search for new approaches to the processing and analysis of aftershock observation data. The main attention is paid to the discussion of two new results obtained on the basis of elementary theory. Firstly, a two-stage relaxation mode of the earthquake source was discovered. In the first stage, called the Omori epoch, the Omori law is strictly observed. The first stage ends with a bifurcation of the source, and the second stage of relaxation begins, during which the evolution of aftershocks proceeds chaotically. Secondly, within the framework of the elementary theory of aftershocks, a fundamentally new concept of the proper time of the source was introduced. Keywords: earthquake source, deactivation coefficient, Omori law, dynamic system, inverse problem, relaxation, proper time. The source proper time has proven useful in experimental studies of seismic activity.

physics.geo-ph↗

arXiv2024

Classification of earthquakes main shocks

The concept of a triad of tectonic earthquakes as a natural trinity of foreshocks, main shock and aftershocks is introduced. The basis for classifying the main shocks is the belonging of the main shock to one or another category of triads. The basis for classifying triads is the ratio between the number of foreshocks and the number of aftershocks that occurred during equal periods of time before and after the main shock. The existence of three classes of triads has been discovered, called classical, mirror and symmetrical triads. Each class is divided into two species, called the full and shortened triad. Thus, the existence of three classes and six species of main shocks is established. The classification is natural, is made on one basis and is proportionate, i.e. the sum of classes and the sum of species are equal to the volume of the generic concept of the triad. The discovery of a small but obviously non-empty set of mirror triads is an interesting and important concrete result of classification. Confidence is expressed that the classification of main shocks opens up new perspectives for earthquake research. Key words: foreshocks, aftershocks, triad of earthquakes, taxonomy of triads, mirror triad.

physics.geo-ph↗

arXiv2024

Around-the-world seismic echo as a trigger for aftershocks and the main shock of an earthquake

The essence of the cumulative effect of a round-the-world seismic echo is that the echo can serve as a trigger for a second tremors in the epicentral zone of the earthquake that gave rise to the echo. According to the classification of triggers, the round-the-world echo is an endogenous force mechanical additive trigger. The round-the-world echo excited by the main shock as a trigger for aftershocks has been studied in detail previously. In this work, the question of whether a foreshock can excite a round-the-world echo, which will turn out to be a trigger for the main shock, is posed and experimentally studied. In the course of the study, the classification of the so-called triads of earthquakes was considered. When studying one of the six types of triads, indirect signs were found that the answer to the question posed may be positive Key words: earthquake source, main rupture, foreshock, triad of earthquakes, cumulative effect, free vibrations of the Earth.

physics.geo-ph↗

arXiv2024

Energy flows in the earthquake source before and after the main shock

We proceeded from general physical concepts based, on the one hand, on the Umoff-Poynting theorem, and on the other, on the phenomenological theory of earthquakes, and formulated the following question: What are the directions of energy flows in the earthquake source before and after the formation of a main rupture in it? A non-standard technique for experimental research of this issue has been developed. The epicentral zone of the main shock is considered as a kind of track detector, and foreshocks and aftershocks are considered as marks (tracers) marking the propagation in the source of some factor that has energy and stimulates the excitation of foreshocks and aftershocks in a stressed-strained rock mass. By processing and analyzing a large volume of observation data, it was found that over time, foreshocks, on average, approach the epicenter of the main shock, while aftershocks, on the contrary, move away from the epicenter. A method is indicated for verifying the result by studying the magnitude dependence of foreshock convergence and aftershock divergence. Keywords: foreshock, aftershock, main rupture, evolution equation, nonlinear diffusion waves, fault length.

physics.geo-ph↗

arXiv2022

About the waiting time for a strong earthquake

As an object of study, we chose the global activity of strong earthquakes (M > 7). The subject of the study is the waiting time for the next strong earthquake. The purpose of the study is to compare two distributions of waiting time, one of which is calculated when ordering events according to world time, and the second when ordering according to proper time. We have come up with unique underground clock to counting proper time. The average waiting time is 25 days in world time, and 10 ticks in proper time. We assert with a high degree of confidence that both distributions obey an exponential law. The coefficients of determination are 0.94 in the first case, and 0.98 in the second case. This is all the more surprising since our underground clock is a rather crude measuring instrument. We also consider general issues related to the chronologization of earthquakes. Keywords: proper time, deactivation factor, main shock, foreshocks and aftershocks, exponential and power distributions.

physics.geo-ph↗

arXiv2022

On the proper time of the earthquake source

The concept of proper time, which is different from universal time, has been introduced into the physics of earthquakes. The global activity of strong earthquakes was chosen as the object of study. We consider the sequence of earthquakes as a random process of the Poisson type. Comparatively weak earthquakes are used as the underground clock, the ticking of which marks the course of proper time. The Poisson distribution is compared with the distributions for two sequences of strong earthquakes. One of the sequences is ordered by calendar time, and the second by proper time. The result of the test showed that the distribution of events ordered by proper time is closer to the Poisson distribution than the distribution of events ordered by calendar time. We explain this by non-stationarity, which is an immanent property of the Earth's lithosphere.

physics.geo-ph↗

arXiv2022

On generalized models of earthquake evolution by the example of classical and mirror triads

The analysis of the classical and mirror triads of the sequence of earthquakes has been carried out in order to find the equations of evolution of foreshocks and aftershocks. The differential equation with cubic (quadratic) nonlinearity has been proposed to describe the activity of foreshocks (aftershocks). The solution of the governing equation for foreshocks indicates the explosive instability of rocks, leading to the main rupture and the main shock of the earthquake. It is suggested that explosive instability leads to a first-order phase transition, in which the main parameters of the earthquake source as a thermodynamic system change abruptly. A direction for further research has been outlined. Keywords: Omori law, evolution equation, earthquake triads, foreshocks, main shock, aftershocks , rise and fall in seismic activity.

physics.geo-ph↗

arXiv2022

Phenomenology of aftershocks: Once more on the Omori Law

Omori Law describes the evolution of the aftershocks of a strong earthquake. Established at the end of the century before last, it is characterized by the beauty of its form, quite definite clarity, as a result of which it still attracts considerable attention of the geophysical community. In recent years, we have accumulated considerable experience in studying the Omori law by theoretical and experimental methods. This paper summarizes the results of our study briefly. The main attention is focused on the phenomenological theory of aftershocks, the foundations of which were laid by Fusakichi Omori. Keywords: earthquake, source deactivation, logistic equation, nonlinear diffusion equation, Omori epoch, round-the-world echo, mirror triad.

physics.geo-ph↗

arXiv2021

Mirror triad of tectonic earthquakes

It is natural to call the trinity of foreshocks, main shock and aftershocks a classical triad. The magnitude of the main shock is always greater than the maximum magnitudes of foreshocks and aftershocks. In the classical triad, the number of foreshocks is less than the number of aftershocks. In many cases, foreshocks are completely absent even before very strong earthquakes. In this work, we found a rare but extremely interesting species of triad (we called it the mirror triad), in which the number of foreshocks is greater than the number of aftershocks at the interval of 24 h before and 24 h after the main shock. Quite often, aftershocks are absent in mirror triads at all. In this paper, we described the properties of mirror triads and made an attempt to understand their origin. A schematic classification of tectonic triads is proposed. Keywords: foreshock, main shock, aftershock, Gutenberg-Richter law, Bath law, Omori law, solitary earthquake.

physics.geo-ph↗

arXiv2021

Dependence of the source deactivation factor on the earthquake magnitude

Three fundamental laws of the physics of earthquakes, bearing the names of their discoverers Omori, Gutenberg, Richter and Bath, are widely used in original, review, monographic, and encyclopedic literature. In this paper, we have tried to look at laws from an unusual point of view. The idea behind our approach is as follows. Each of the three laws was established in the course of work on solving a specific research problem, and the result was expressed in a specific mathematical form. We asked ourselves whether it is possible to modify the statement of the problem, and/or modify the form of expression of the law in order to see new facets of a well-known scientific statement? The result was successful in relation to Omori's law, according to which the frequency of aftershocks hyperbolically decreases over time. The modified formulation of the problem was to find a differential equation describing the time evolution of aftershocks. We found a simple differential model, within the framework of which the concept of deactivation of the earthquake source is introduced. The question of dependence of the deactivation factor on the magnitude of main shock is analyzed theoretically and experimentally. A monotonic decrease in the deactivation factor with an increase in the magnitude of the main shock has been reliably established. Other possible applications of the proposed methodological technique are considered. In particular, it is indicated how to overcome the contradiction between the Omori law and the law of energy conservation. Keywords: Omori law, Gutenberg-Richter law, Bath law, main shock, aftershock, deactivation factor, Omori epoch, differential equation of evolution.

physics.geo-ph↗

arXiv2013

On the aftershocks of the Great Sumatra-Andaman earthquake

Analysis of the Sumatra-Andaman earthquake on 26.12.2004 (M = 9) has allowed us to identify two non- trivial properties of the dynamics of aftershocks. First, the strongest aftershock (M = 7.2) was likely triggered by the round-the-world seismic echo of the main shock. The idea is that the surface waves propagating outwards from the main shock return back to the vicinity of the epicenter after having made a complete revolution around the Earth and induce there the aftershock. The second property is the modulation of the aftershock sequence by the fundamental oscillation of the Earth 0S2 excited by the main shock. Both results are supported by analysis of the Tohoku earthquake (11.03.2011, M = 9), as well as by the statistical analysis of the USGS earthquake catalog.

physics.geo-ph↗

arXiv2006

On-off Intermittence as a Possible Mechanism of Geomagnetic Impulse Generation

Using the many-year observations at several high-latitude observatories in the Northern and Southern Hemispheres, the regularities in distribution of magnetic impulse events (MIEs) amplitudes are studied. It is shown that the tails of the functions of statistical distributions of impulse amplitudes are approximated by a power function of the form f (A) = A**(-b), where A is the impulse amplitude, and b is the power index laying in the range from 1 to 5. Experimental confirmation is obtained to the hypothesis suggested earlier that the impulse generation regime qualitatively corresponds to the model of on-off intermittency. It is assumed that the model of the on-off intermittency may be considered as one of the possible mechanisms of MIEs generation. It is found that the majority of the analyzed statistical distributions of MIEs amplitudes have the index b exceeding 2, the fact being typical for chaotic regimes called the strong turbulence. In some cases the index b is close to the unity, this fact being typical for the regimes generated in weakly turbulized medium. The results obtained make it possible to assume that: a) at higher magnetospheric latitudes, the plasma turbulence degree is higher that at lower latitudes, b) in the afternoon sector of the magnetosphere, the plasma is stronger turbulized than in the prenoon sector; c) in the Northern and Southern Hemispheres the magnetospheric plasma is stronger turbulized in summer and winter, respectively; d) at the growth phase of solar activity the magnetospheric plasma is stronger turbulized than at the declining phase. The dependence of the power index b on the solar wind parameters and IMF demonstrates the influence of interplanetary conditions on the high-latitude magnetosphere plasma where MIEs are formed.

physics.space-ph↗