arXiv subjects

A. V. Guglielmi

Publications and source records attributed to A. V. Guglielmi.

At least 19 recordsLinked to original sources

arXiv2026

Holistic law of aftershocks

The paper is devoted to the phenomenological theory of aftershocks occurring in the source of a tectonic earthquake following the main shock. The theory was developed by the author jointly with A.D. Zavyalov and O.D. Zotov during the course of a long-term study of aftershocks. The theory is based on the concepts of source deactivation and the source's proper time. The holistic law governing the decay of aftershock activity over proper time follows from the theory. The damping decrement is equal to the source deactivation coefficient. The main focus of this paper is the analysis of the logical structure of the theory. The paper also contains a brief description of the experimental results obtained using the theory. Keywords: earthquake source, aftershocks, Omori's law, Utsu's law, deactivation coefficient, proper time, underground clock, foreshock convergence, aftershock divergence.

physics.geo-ph↗

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↗

arXiv2026

The Pc1 geomagnetic pulsations in light of the Cepheid theory

It has been 90 years since the discovery of geomagnetic pulsations in the Pc1 range (0.2-5 Hz), widely known as pearls. In the second half of the last century, the concept of pearls as multiple echoes of a wave packet that propagates along the lines of the geomagnetic field, periodically reflecting off the ionosphere at magnetically conjugate points emerged. This paper proposes an alternative interpretation of the pearls. It is assumed that high above the Earth in the narrow equatorial zone of the outer radiation belt there is a pulsed generator of ion-cyclotron waves. The generator excites a discrete sequence of wave packets, which are recorded in the magnetosphere and on the Earth's surface as a series of pearls. The generator is a Q-modulated ion cyclotron resonator with active filling. The presence of opacity domains adjacent to the resonator's end faces is reminiscent of the opacity layer in the atmosphere of a Cepheid. This association was strengthened by the fact that in both cases the formation of opaque layers is associated with the presence in the medium of ions with different charge-to-mass ratios. Based on this association, the idea of a ponderomotive valve arose, periodically changing the width of the opacity domains, thereby forming a periodic sequence of pearls. The ponderomotive valve in pearl theory is analogous to the Eddington valve in Cepheid theory.

physics.geo-ph↗

arXiv2026

Trigger excitation of "pearls" in the Earth's magnetosphere: On the 90th anniversary of the discovery of Pc1 waves

Ultra-low-frequency electromagnetic waves Pc1 (0.2-5 Hz), widely known in the literature as pearls, are excited in the outer radiation belt and propagate to the Earth along the geomagnetic field lines in the form of Alfven waves. The study of pearls is of considerable interest for magnetospheric physics. Both spontaneous and stimulated pearl excitation are observed. The paper examines stimulated (trigger) excitation of pearls. A classification of triggers acting on dynamic systems of the magnetosphere is presented. 2 types, 4 classes and 8 species of triggers have been introduced. Examples of triggers of natural and artificial origin are given. The concept of a trigger cascade is introduced. Particular attention is paid to the anthropogenic periodic trigger of pearls. It manifests itself in the form of the so-called Big Ben effect. The essence of the effect is that a series of pearls is often excited immediately following the hour marker according to world time. It is claimed that the connection between the excitation of pearls and hour markers is not accidental, but represents a rather mysterious geophysical phenomenon. It is assumed that the Big Ben effect occurs as a result of the impact on the radiation belt of an unknown type of endogenous periodic artificial trigger. Key words: oscillations and waves, Alfven waves, ion-cyclotron resonator, radiation belt, instability, classification, natural and artificial, technosphere, Big Ben effect.

physics.geo-ph↗

arXiv2025

Toward a Phenomenological Theory of Earthquakes

An attempt to construct a phenomenological theory of earthquakes is being undertaken by a small research team, which includes the author. We have only taken the first steps towards goal, but the results already obtained convincingly demonstrate the feasibility of the project. This paper is a kind of commentary on the path taken. The paper explains the essence and character of phenomenological theory. It also contains critical comments on alternative approaches to describing earthquakes. The theory is based on the concept of an earthquake source as a dynamic system, the state of which is described by a small number of phenomenological parameters. Within the framework of elementary theory, the source is described by one parameter, called the deactivation coefficient. The most important concept of the proper time of the source has been introduced, the course of which, generally speaking, differs from the course of world time. Dynamic equations describing the evolution of the source are given. The inverse problem of the source is posed, the essence of which is to calculate the phenomenological parameters based on earthquake observation data. Elementary phenomenological theory has already become a practical tool for the experimenter studying specific earthquake time series. The Appendix provides a list of previously unknown properties and patterns of earthquakes that we discovered within the framework of elementary theory. At the same time, it is noted that phenomenology itself does not lead us to a deep understanding of the essence of earthquakes. Sooner or later, the results of a complex of geophysical and physical-mathematical disciplines will lead to such an understanding. We place particular hopes on the theory of phase transitions and the mathematical theory of catastrophes.

physics.geo-ph↗

arXiv2025

On the inverse problem of the earthquake source and the three-phase relaxation mode of the source after the formation of a main rupture in it

The fundamentals of the phenomenological theory of aftershocks are presented. The theory contains an original concept of the proper time of the earthquake source, the course of which, generally speaking, differs from the course of world time. Within the framework of the theory, a new method for processing and analyzing earthquakes has been developed. Analysis of the Tohoku earthquake demonstrated the effectiveness of the method. Three phases of relaxation of the source were discovered. In the initial phase, the deactivation coefficient, which characterizes the source as a dynamic system, is equal to zero. At the end of the initial phase, the deactivation coefficient suddenly acquires a positive value, which remains unchanged throughout the main relaxation phase. The transition from the main phase to the recovery phase is accompanied by a jump in the time derivative of the deactivation coefficient. The recovery phase differs from the initial and main phases by chaotic variations in the deactivation coefficient. Keywords: dynamic system, deactivation coefficient, proper time. synchronization, foreshocks, mainshock, aftershocks.

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

Elementary theory of earthquake source relaxation

The elementary theory of relaxation of the source cooling down after the main shock of an earthquake is presented axiomatically. The names of the objects under study are given and the relationships between them are determined. A new basic concept of earthquake source deactivation is introduced and a procedure for calculating the deactivation coefficient from aftershock frequency measurement data is indicated. An important property of the system is that the axioms do not contain statements regarding the actual process of source relaxation. From two simple axioms a number of meaningful statements (theorems) logically follow. A two-stage mode of source relaxation was discovered. The sharp transition between stages has the character of a bifurcation. It is shown that the classical Omori law has limited applicability. It describes the evolution of aftershocks only at the first stage of relaxation. The well-known Hirano-Utsu law is not applicable to describe aftershocks either at the first or second stages of relaxation. The conclusions of the elementary theory allow for interesting generalizations that expand the possibilities of experimental and theoretical study of the source. Keywords: earthquake source, foreshocks, main shock, aftershocks, source state, deactivation coefficient, bifurcation, Omori's law, Hirano-Utsu's law.

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

An axiomatic method for studying the truth or falsity of the Hirano-Utsu law describing aftershocks

The power law of aftershock evolution was proposed by Hirano in 1924 and introduced by Utsu into seismology in the second half of the last century. The Hirano-Utsu law is widely used in studying the relaxation of earthquake source after the main shock of an earthquake. The prevailing view in the literature is that the Hirano-Utsu law is an improved version of Omori's hyperbolic law, formulated in 1894. The author disagrees with this notion. The paper proposes an axiomatic approach to the study of aftershocks. A phenomenological parameter of the source, called the deactivation coefficient, was introduced. The theory is based on axioms that do not contain any a priori statements regarding the form of the law of aftershock evolution. Formulas for the deactivation coefficient are derived from the axioms, allowing one to experimentally establish the truth or falsity of the Hirano-Utsu and Omori laws. A two-stage mode of source relaxation was discovered. In the first stage, called the Omori epoch, the Omori law is strictly followed. The Omori epoch ends with a bifurcation, after which aftershock activity becomes unpredictable. Omori's law is not fulfilled at the second stage of evolution. The Hirano-Utsu law is not fulfilled either at the first or second stage. Keywords: earthquake source, main shock, relaxation, deactivation coefficient, evolution equation, inverse problem, Omori epoch, bifurcation, two-stage relaxation mode.

physics.geo-ph↗

arXiv2024

Method for processing and analyzing tectonic earthquake aftershocks: A new look at old problem

The deactivation coefficient has been introduced for the source that cools down after the mainshock of the earthquake. The deactivation coefficient satisfies two conditions. First, it can be computed from observed aftershock frequency data (axiom of computability). Second, the deactivation factor is independent of time if and only if Omori law is strictly satisfied (hyperbolicity axiom). From the two axioms follows an explicit expression for calculating the source deactivation factor from observed aftershock data. A simple and efficient method for processing and analyzing aftershocks using the deactivation factor has been developed. A two-stage mode of the source relaxation to a new equilibrium state after the formation of the main rupture of rock continuity in it was discovered. In the first stage, called the Omori epoch, the Omori law is strictly followed. The duration of the first stage is tentatively 10 to 100 days. In the Omori epoch, the average frequency of aftershocks is predictable with high accuracy. At the end of the Omori epoch, a bifurcation occurs. In the second stage, the deactivation factor changes with time in an unpredictable way. The phase portrait of the source allows us to visualize the complex dynamics of seismic activity in the second stage of the source relaxation. The experiment shows that the Hirano-Utsu law is inapplicable for describing the evolution of aftershocks neither at the first nor at the second stage of the source relaxation. Keywords: deactivation factor, evolution equation, phase portrait, Omori law, Hirano-Utsu law.

physics.geo-ph↗

arXiv2024

On the theory of earthquakes: Paradoxical contradiction of Omori's law to the law of energy conservation

After the main shock of an earthquake the aftershocks are observed. According to Omori's law, the frequency of aftershocks decreases hyperbolically over time. We noticed that, strictly speaking, Omori's law paradoxically contradicts the law of energy conservation. The contradiction is that the excitation of each aftershock consumes a finite portion of the source's energy, so that the total energy released by the source tends to infinity over time. The paradox is formally theoretical, but its analysis has proved useful. Eliminating the contradiction between Omori's law and the fundamental law of conservation of energy allowed us to further understand the nature of the phenomenological theory of aftershocks. We used the concept of deactivation of a source after the formation of a main rupture in it. We have based the theory on the original aftershock evolution equation, which has the form of a first-order linear differential equation. Two ways to eliminate the paradoxical situation are indicated. Key words: earthquake source, aftershock, evolution equation, deactivation coefficient, inverse problem, Omori epoch, source bifurcation, logistic equation, Hirano-Utsu formula.

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

On ponderomotive metallization of magnetospheric plasma

The problem of ponderomotive separation of ions with different charge-to-mass ratios under the influence of Alfven waves, which permanently exist in the magnetosphere in the form of geomagnetic pulsations, is posed. Formulas are derived for partial ponderomotive forces acting on light and heavy (metal) ions. In the quasi-hydrodynamic approximation, it was found that the Clarke number, which characterizes the metallicity of the plasma, is maximum at the minimum of the magnetic field on the field line along which the Alfvén wave propagates. Key words: ponderomotive forces, Alfvén waves, heavy ions, Clarke number.

physics.plasm-ph↗