arXiv subjects

B. I. Klain

Publications and source records attributed to B. I. Klain.

15 recordsLinked to original sources

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↗

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↗

arXiv2022

Alfvén waves: To the 80th anniversary of discovery

The paper is dedicated to the anniversary of the discovery of Alfvén waves. The concept of Alfvén waves has played an outstanding role in the formation and development of cosmical electrodynamics. A distinctive feature of Alfvén waves is that at each point in space the group velocity vector and the external magnetic field vector are collinear to each other. As a result, Alfvén waves can carry momentum, energy, and information over long distances. We briefly describe two Alfvén resonators, one of which is formed in the ionosphere, and the second presumably exists in the Earth's radiation belt. The existence of an ionospheric resonator is justified theoretically and confirmed by numerous observations. The second resonator is located between reflection points located high above the Earth symmetrically with respect to the plane of the geomagnetic equator. Keywords: Alfvén velocity, dispersion law, group velocity, geometric optics, heavy ions.

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

Cycles of paleomagnetic activity in the phanerozoic

Quasi-periodic changes of the paleointensity and geomagnetic polarity in the intervals of 170 Ma to the present time and of 550 Ma to the present time were studied, respectively. It is revealed that the spectrum of the basic variations in the paleointensity and of the duration of the polar intervals is discrete and includes quasi-periodic oscillations with characteristic times of 15 Ma, 8 Ma, 5 Ma, and 3 Ma. The characteristic time of these quasi-periodic changes of the geomagnetic field at the beginning and at the end of the Phanerozoic differed by no more than 10%. The spectral density of quasi-periodic variations of the geomagnetic field changed cyclically over geological time. The relation between the behaviors of the amplitude of paleointensity variations, the duration of the polar intervals, and their spectral density was shown. Quasi-periodic variations of the paleointensity (geomagnetic activity) had a relatively high spectral density in the interval of (150 - 40) Ma (in the Cretaceous - Early Paleogene). In this interval, both the amplitude of paleointensity variations and the duration of polar intervals increased. In the intervals of (170 - 150) Ma and of 30 Ma to the present, a quasi-periodic variation in the paleointensity practically did not detect against the background of its noise variations. At the same time, the amplitude of the paleointensity variations and duration of polar intervals decreased. An alternation of time intervals in which the paleointensity variations acquired either a quasi-periodic or noise character took place during the geomagnetic history.

physics.geo-ph↗

arXiv2021

Discrete Spectrum of ULF Oscillations of the Ionosphere

This work relates to the field of ultra-low-frequency (ULF) spectroscopy of near-Earth plasma. Our attention is focused on the Alfvén ionospheric resonator (IAR), the spectrum of which is a series of discrete lines. The aim of the study is to experimentally verify a well-defined theoretical prediction. Within the framework of an idealized resonator model, a hypothesis about the relationship between the frequencies of spectral lines has been formulated. To test the hypothesis, observations of ULF oscillations at the mid-latitude Mondy observatory were used. The result of the analysis confirmed the hypothesis that odd harmonics of the IAR discrete spectrum are observed on the Earth's surface. Key words: electromagnetic oscillations, Alfvén waves, ionospheric Alfvén resonator, ultra-low-frequency spectroscopy.

physics.geo-ph↗

arXiv2021

A Paradox of Whistling Atmospherics

Analyzing paradoxes is interesting and instructive. Sometimes the analysis leads to non-trivial results. This methodological note sets out a paradox arising in the theory of propagation of electromagnetic waves in moving plasmas. The paradox is interesting in itself, and, generally speaking, it should be taken into account when analyzing geoelectromagnetic waves. The paradox is as follows: contrary to expectations, the group velocity of the waves is the same in the comoving and laboratory frames of reference. The condition for the appearance of the paradox is the quadratic dependence of the frequency on the wave number. A paradoxical property manifests itself in the theory of the propagation of radio waves (in particular, whistling atmospherics), Langmuir waves and Alfvén waves. From a cognitive point of view, it is interesting that the paradox can be traced in relation to de Broglie waves. An explanation of the paradox is proposed. Keywords: group velocity, moving plasma, Doppler Effect, dispersion, longitudinal waves, transverse waves.

physics.geo-ph↗

arXiv2020

The Phenomenology of Aftershocks

The presented paper is devoted to the search for mathematical basis for describing the aftershock evolution of strong earthquakes. We consider the experimental facts and heuristic arguments that allow to make a choice and to focus on the nonlinear diffusion equation as the master equation. Analysis of the master equation indicates that, apparently, the selected mathematical basis makes it possible to simulate two important properties of the aftershock evolution known from the experiment. We are talking about the Omori law and the slow propagation of aftershocks from the epicenter of the main shock. Keywords: earthquakes, propagation of aftershocks, Omori law, deactivation coefficient, nonlinear diffusion, master equation, inverse problem

physics.geo-ph↗

arXiv2019

Global Magnitude of the Earthquakes

The idea of the global daily magnitude (GDM, unit designation is Mg) of earthquakes is introduced. The formula is given for calculating Mg from earthquake strength data, characterized by the classic magnitude M on the Richter scale. An example of the calculation of Mg is given. It is noted that the Mg index may be useful in studying a number of seismological problems.

physics.geo-ph↗

arXiv2017

Peculiarities of geomagnetic field behavior near boundary of the mesozoic - cenozoic

The results of paleointensity determinations of the geomagnetic field, which are obtained by sedimentary rocks in the Middle Jurassic - Neogene (167-12) Ma, are summarized. It was found that in the interval (167-67) Ma (Middle Jurassic - Cretaceous) mean values and amplitudes of paleointensity variations increased. Mean values of paleointensity reached a maximum in front of the Cretaceous-Paleogene boundary. During the Paleogene the mean values and amplitudes of paleointensity variations decreased. In the Cretaceous - the beginning of the Paleogene cyclic changes in the amplitudes of paleointensity variations with characteristic times of several million years have been observed. It is shown that the duration of cycles of the paleointensity changes coincided with transgressive-regressive cycles (T-R cycles). This can be considered as a confirmation of the hypothesis on a relation between processes in the Earth's core and tectonic processes.

physics.geo-ph↗

arXiv2014

Geomagnetic field intensity in the middle jurassic - oligocene

The present paper summarizes results of the studies on the intensity of geomagnetic field in the (167 - 23) Ma interval by sedimentary rocks of the Russian Plate and adjacent territories. The joint analysis of the data paleointensity obtained by sedimentary and thermomagnetized (from PINT12) rocks within this temporal interval is conducted. It is shown that the changes of the paleointensity were occurred chaotically. Alternating bursts and periods of quiet regime of the geomagnetic field are typical for intermittent processes and is a characteristic of the geological interval Jurassic-beginning of Paleogene. The distributions of the paleointensity corresponding to different intervals of geologic time were investigated. It is revealed that the cumulative distribution function (CDF) of the paleointensity values is best approximated by a power function. The indices of the power functions varied depending on geologic time intervals.The analysis of the paleomagnetic data suggests that the medium in which the geomagnetic field is generated is turbulent. Turbulence in the Earth's liquid core is enhanced in the Cretaceous compared with Jurassic and Paleogene.

physics.geo-ph↗

arXiv2013

Variations of paleointensity in the Paleogene

Behavior of the geomagnetic field intensity in the Paleogene from sedimentary rocks of the Russian Plate was investigated. It is revealed that in the beginning of the Paleogene alternating of paleointensity variations of little amplitude (about 0.5 Ho, where Ho is the value of modern geomagnetic field taken as 40 mkT) and bursts of large amplitude (up to 5 Ho) took place. At the end of the Paleogene paleointensity variations occur only with a little amplitude.

physics.geo-ph↗

arXiv2008

Factors Influencing the Earth's Magnetic Field Evolution

The relationship between the behavior of an ancient geomagnetic field characteristics (paleointensity and frequency of inversions) and cyclic recurrence of endogenic and cosmogeneous processes which are conceivably connected with radial mantle heat transmission and the Earth rotation speed has been studied. It is shown that endogenic processes affect the behavior of the paleointensity and frequency of inversions. Large basalt effusions identified with plumes are accompanied by the changes in paleointensity (by 30-40)% and the frequency of inversions. Characteristic time intervals of paleointensity variations caused by the formation of plumes makes up 10-20 Ma. The paleointensity varies (by 15-30)% according to phases of the riftogenesis activization and tension - compression cycles. The dependence of geomagnetic field behavior on changes of the Earth rotation speed which occurred as a result of the Earth - Moon - Sun system evolution has been analyzed. Thus, in accordance with phases of the Earth - Moon distance changes (periodicity about 200 Ma) average values of the paleointensity varied by a factor of two. Besides, the frequency of inversions, asymmetry of polarity and features of paleointensity variations changed too.

physics.geo-ph↗

arXiv2007

On Interdependence of the Paleomagnetic Field Characteristics

The behaviour of the geomagnetic field characteristics (mean values of the paleointensity, amplitude of its variations and reversal frequency) during the last 170 million years was analyzed. It was found that the mean values of the paleointensity were in direct relation to amplitude of its variations and in reverse relation to reversal frequency. The most considerable changes of the Earth magnetic field characteristics occurred in Early Cretaceous, Middle Paleogene and Neogene. The analysis of conformity of the reconstructed characteristics behaviour of a geomagnetic field to an alfa-omega- dynamo model was made.

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↗