Inertial effects in the Earth’s crust and magnetosphere

A review of studies devoted to the problem of exciting magnetic signals in the crust associated with the formation of the major rupture in an earthquake source and with the propagation of seismic waves was given in [Sgrigna et al., 2004]. However, this review contains incorrect citations from original papers and several erroneous statements concerning inertial and inductive mechanisms of conversion of the energy of rock motion into magnetic field energy. These mistakes are analyzed in the present paper. The formal and physical similarity between seismomagnetic waves in the crust and Alfvén waves in the magnetosphere is used in the analysis. A comparative analysis of the inertial and inductive mechanisms of seismomagnetic field generation is performed. The Cherenkov criterion of Alfvén wave generation due to the ionospheric effect of acoustic waves from earthquakes and explosions is derived. Attention is also given to nonlinear phenomena (nonlinearity of a mechanomagnetic conversion in the crust and anharmonicity and self-focusing of Alfvén waves in the magnetosphere).     

Character of turbulence in the boundary regions of the Earth’s magnetosphere

The statistical features of the magnetic field and ion flux fluctuations in the boundary regions of the Earth’s magnetosphere have been studied on different timescales based on the Interball satellite measurements. Changes in the form and parameters of the probability density function have been studied for the periods when the satellite was in the solar wind plasma, different magnetosheath regions, and the turbulent boundary layer (TBL) at the polar cusp outer boundary. Variations in the probability density function maximum (P ₀) and the kurtosis value as characteristics of the turbulence property evolution on different timescales have been studied. Two asymptotic regimes of P ₀, which are characterized by different power laws, have been found. The structural functions of different orders and the types of diffusion processes in different regions, depending on time variations in the generalized diffusion coefficient, have been studied in order to analyze the character of diffusion processes. For the magnetosheath regions, TBL, and polar cusp, it has been found that the diffusion coefficient increases in the course of time (i.e., the regime of superdiffusion has been obtained). In the foreshock region before the main shock, turbulent processes are described by the Kolmogorov model of classical diffusion.     

Determining the thickness of the low-latitude boundary layer in the Earth’s magnetosphere

We describe a method for determining the thickness of the low-latitude boundary layer (LLBL) of the Earth’s magnetosphere at the dayside near the equatorial plane based on the data gathered by a single satellite that traverses the layer and measures the plasma velocity. The method may be applied when the position of the magnetopause and the magnetosheath parameters fluctuate. The necessity of taking the presence of outer and inner LLBL regions into account is analyzed. The developed method is tested using the analysis results of two almost simultaneous close traverses of the magnetopause completed by the THEMIS mission satellites that provided relatively precise data on the LLBL thickness. It is shown that the developed method makes it possible to determine the LLBL thickness with an accuracy of ～10%.     

Hydrogen and helium isotope inner radiation belts in the Earth’s magnetosphere

Radial transport theory for inner radiation zone MeV ions has been extended by combining radial diffusive transport and losses due to Coulomb friction with local generation of D, T and ³He ions from nuclear reactions taking place on the inner edge of the inner radiation zone. Based on interactions between high energy trapped protons and upper atmospheric constituents we have included a nuclear reaction yield D, T and ³He flux source that was numerically derived from a nuclear reaction model code originally developed at the Institute of Nuclear Researches in Moscow, Russia. Magnetospheric transport computations have been made covering the L-shell range L=1.0–1.6. The resulting MeV energy D, T and ³He ion flux distributions show a strong influence of the local nuclear source mechanism on the inner zone energetic D, T and ³He ion content.     

Convection in anelastic models of the Earth’s liquid core

The effects of adiabatic cooling on the convection in the anelastic model of the liquid core of the Earth are considered. It is shown that even minor adiabatic cooling causes significant changes in the pattern of the convection, shifting the peak in the convection intensity to the inner part of the core. Just as in the Boussinesq model, both direct and inverse kinetic energy cascades are simultaneously present, and the direct cascade of entropy is observed.     

Some sources of plasma inhomogeneities in the solar wind in front of the Earth’s magnetosphere

The origination of various plasma inhomogeneities in the magnetosheath in front of the Earth’s magnetosphere is analyzed within classical magnetohydrodynamics. The effect of directional discontinuities or tangential and rotational discontinuities of the solar wind on plasma is studied. The origination of inhomogeneities of the type of secondary MHD waves in the magnetosheath is shown; the former equalize plasma parameters when restoring the stationary state. The effect of a rotational discontinuity on the bow shock–Earth’s magnetosphere system is of special interest, with distinguishing of plasma inhomogeneities of the plateau type observed in the near-Earth space.     

A contribution to the theory of the equatorial noise generation in the Earth’s magnetosphere

This work is devoted to the study of the generation of the equatorial noise—electromagnetic emission below the LHR frequency observed near the equatorial plane of the magnetosphere at distances of ~4R_E. According to accepted views, the generation of the equatorial noise is related to the instability of ring current protons. In this work, a logarithmic distribution of energetic protons over the magnetic moment with an empty loss cone is proposed, and arguments for the formation of such a distribution are presented. The main result of the work is the calculation and analysis of the instability growth rate of waves forming the equatorial noise. The growth rate obtained in this work significantly differs from that encountered in the literature.     

Efficiency of electron acceleration in the Earth’s magnetosphere by whistler mode waves

The efficiency of energetic electron cyclotron acceleration in the Earth’s magnetosphere in different regimes of electron resonant interaction with parallel propagating whistler mode waves of variable frequency, specifically, with chorus ELF-VLF emissions, is considered. The regime of stochastic acceleration, typical of the interaction between particles and noise-like emissions, and particle acceleration in the regime of nonlinear trapping by a quasimonochromatic wave field are discussed. The specific feature of the latter regime consists in its non-diffuse character, i.e., the definite sign of the energy variation depending on the frequency variation in the wave packet. The trapped electron energy becomes higher if frequency increases within an element, which is typical of chorus emissions. For the parameters typical of chorus emissions (the amplitude of a wave magnetic field B _～ = 10² nT, the initial frequency ω ～ 0.3ω _H , and the frequency variation &;Dω ～ 0.15ω _H , where ω _H is the electron gyrofrequency), the energy increase during one act of such an interaction at L = 4?5 exceeds the rms variation in the energy of untrapped electron (during stochastic acceleration) by one-two orders of magnitude. The estimates indicate that a considerable fraction (several tens of percent) of the chorus element energy can be absorbed by electrons accelerated in the trapping regime during a single hop.     

Recent advances in radiation belt dynamics and wave-particle interactions in the Earth’s inner magnetosphere

<正>Radiation belt dynamics and the related wave-particle interactions in the Earth’s inner magnetosphere are a very important research field in space physics.Since the launch of Van Allen Probes on August 30,2012,many substantial advances have been achieved,and some of them are briefly reviewed in this paper.Using Van Allen Probes data soon after its launch,Baker et al.(2013)discovered a relativistic electron storage ring that was embedded in Earth’s outer Van Allen belt.The     

Impact of solar wind tangential discontinuities on the Earth’s magnetosphere

The collision of a solar wind tangential discontinuity with the bow shock and magnetopause is considered in the scope of an MHD approximation. Using MHD methods of trial calculations and generalized shock polars, it has been indicated that a fast shock refracted into the magnetosheath originates when density increases across a tangential discontinuity and a fast rarefaction wave is generated when density decreases at this discontinuity. It has been indicated that a shock front shift under the action of collisions with a tangential discontinuity is experimentally observed and a fast bow shock can be transformed into a slow shock. Using a specific event as an example, it has been demonstrated that solar wind tangential discontinuity affects the geomagnetic field behavior.     

Nonlinear phenomena related to the solar shock motion in the Earth’s magnetosphere

The motion of the MHD nonlinear shock in the Earth’s magnetosphere is considered in the scope of magnetic hydrodynamics. This wave comes from the solar wind and is refracted into the magnetosphere, generating a fast return rarefaction wave. It has been indicated that a wave refracted into the magnetosphere is a weak fast dissipative shock, propagating in magnetospheric plasma at a velocity higher than its propagation velocity in a solar wind stream. The wave motion near the Earth-Sun line with regard to the effect of the geomagnetic field transverse component is described. In this case, shock damping follows the generalized Crussard-Landau law and a wave retains its shock character up to the plasmapause, interacting with this region when an arbitrary MHD discontinuity is disintegrated. It is stated that an MHD shock loses its shock character when moving in a strongly inhomogeneous plasma within the plasmasphere and a weak shock reflected from the plasmapause can combine with a return secondary shock in the magnetosheath, promoting the experimentally observed backward motion of the bow shock front.     

Perturbation of the magnetic field in the Earth’s magnetosphere due to plateau creation in the radial distribution of plasma pressure

The nonlinear perturbation of a dipole field by a system of transverse currents, which arises due to the radial pressure distribution when the pressure is almost independent of the radial distance, is analyzed. This distribution of pressure was observed in the experiment. The radial dependences of the magnetic field depression, transverse current density, and volumes of magnetic flux tubes have been obtained at different values of the plasma parameter via nonlinear simulation. It is shown that a dependence of the volume of magnetic flux tube on the radial distance can change and a region of the negative gradient of volume can appear at some plasma-parameter values.     

Comparison of Earth’s magnetospheric magnetic field models in the context of cosmic ray physics

Over the last two decades, models of the Earth’s magnetospheric magnetic field have been continuously improved to describe more precisely the different magnetospheric current systems (magnetopause current, symmetric and partial ring currents, tail currents and field aligned currents). In this paper we compare the different Tsyganenko models and the Alexeev and Feldstein model in the context of cosmic ray physics. We compare the vertical cutoff rigidity and asymptotic direction of vertical incidence obtained with these models for the January 20, 2005, ground level enhancement and for the big magnetic storm of April 6, 2000. For the event of January 20, 2005, we study the impact of the differences in asymptotic direction obtained with the models on the radiation dose computation at aircraft altitude. For the magnetic storm of April 6, 2000, we discuss the importance of the different magnetospheric current systems in causing cutoff rigidity variations. Finally we summarise the advantages and drawbacks of the different models in the context of space weather.     

Constraining the focal mechanism of the Lushan earthquake with observations of the Earth’s free oscillations

The amplitudes of the Earth's free oscillations have a close relationship to earthquake focal mechanisms. Focal mechanisms of large earthquakes can be well analyzed and constrained with observations of long period free oscillations. Although the 2013 Lushan earthquake was only moderately sized, observable spherical normal modes were excited and clearly observed by a superconductive gravimeter and a broadband seismometer. We compare observed free oscillations with synthetic normal modes corresponding to four different focal mechanisms for the Lushan earthquake. The results show that source parameters can be analyzed and constrained by spherical normal modes in a 2.3–5 mHz frequency band. The scalar seismic moment M0 has a major influence on the amplitudes of free oscillations; additionally, the strike, dip, rake and depth of the hypocenter have minor influences. We found that the synthetic modes corresponding to the focal mechanism determined by the Global Centroid Moment Tensor show agreement to the observed modes, suggesting that earthquake magnitudes predicted in this way can readily reflect the total energy released by the earthquake. The scalar seismic moment obtained by far-field body wave inversion is significantly underestimated. Focal mechanism solutions can be improved by joint inversion of far- and near-field data.     

Cyclic variations in the Earth’s flattening and questions of seismotectonics

For more than a decade, the global network of GPS stations whose measurements are part of the International GPS Service (IGS) have been recording cyclic variations in the radius vector of the geodetic ellipsoid with a period of one year and amplitude of ~10 mm. The analysis of the figure of the Earth carried out by us shows that the observed variations in the vertical component of the Earth’s surface displacements can induce small changes in the flattening of the Earth’s figure which are, in turn, caused by the instability of the Earth’s rotation. The variations in the angular velocity and flattening of the Earth change the kinetic energy of the Earth’s rotation. The additional energy is ~10²¹ J. The emerging variations in the flattening of the Earth’s ellipsoid lead to changes in the surface area of the Earth’s figure, cause the development of deformations in rocks, accumulation of damage, activation of seismotectonic processes, and preparation of earthquakes. It is shown that earthquakes can be caused by the instability of the Earth’s rotation which induces pulsations in the shape of the Earth and leads to the development of alternating-sign deformations in the Earth’s solid shell.     

Dynamics of solar protons in the Earth’s magnetosphere during magnetic storms in November 2004–January 2005

The processes of penetration, trapping, and acceleration of solar protons in the Earth’s magneto-sphere during magnetic storms in November 2004 and January 2005 are studied based on the energetic particle measurements on the CORONAS-F and SERVIS-1 satellites. Acceleration of protons by 1–2 orders of magnitude was observed after trapping of solar protons with an energy of 1–15 MeV during the recovery phase of the magnetic storm of November 7–8, 2004. This acceleration was accompanied by an earthward shift of the particle flux maximum for several days, during which the series of magnetic storms continued. The process of relativistic electron acceleration proceeded simultaneously and according to a similar scenario including acceleration of protons. At the end of this period, the intensification was terminated by the process of precipitation, and a new proton belt split with the formation of two maximums at L ～ 2 and 3. In the January 2005 series of moderate storms, solar protons were trapped at L = 3.7 during the storm of January 17–18. However, during the magnetic storm of January 21, these particles fell in the zone of quasi-trapping, or precipitated into the atmosphere, or died in the magnetosheath. At the same time, the belts that were formed in November at L ～ 2 and 3 remained unchanged. Transformations of the proton (and electron) belts during strong magnetic storms change the intensity and structure of belts for a long time. Thus, the consequences of changes during the July 2004 storm did not disappear until November disturbances.     

Penetration of the Earth’s free oscillations at 54 minute period into the atmosphere

It is known that the fundamental spheroidal mode ₀S₂ of the Earth free oscillation with a period of about 54 min forces atmospheric oscillations. We present a certain phase relationship for components of the ₀S₂ multiplet, which is based on synchronous collocated microbarograph and seismograph observations. This relationship is both the first observational manifestation of the Pekeris mode of global atmospheric oscillations with the 54 min period and a further proof of the Earths ₀S₂ mode penetrating into the atmosphere. We show that the linear non-dissipative model of steady forced oscillations in isothermal atmosphere at rest does not describe the penetration of the ₀S₂ mode into the atmosphere adequately.     

Manifestation of solar and geodynamic activity in the dynamics of the Earth’s rotation

The relationships between different manifestations of solar and geomagnetic activity and the structural peculiarities of the dynamics of the pole wobble and irregularities in the Earth??s rotation are studied using singular spectrum analysis. There are two close major peaks and several lower ones in the same frequency range (1.1?C1.3 years) in the Chandler wobble (CW) spectrum. Components in the geomagnetic activity were distinguished in the same frequency band (by the Dst and Ap indices). Six- to seven-year oscillations in the Earth??s rotation rate with a complex dynamics of amplitude variations are shown in variations in geomagnetic activity. It is revealed that secular (decade) variations in the Earth??s rotation rate on average repeat global variations in the secular trend of the Earth??s geomagnetic field with a delay of eight years during the whole observation period.     

Ranges of AGW propagation in the Earth’s atmosphere

The propagation of atmospheric gravity waves (AGWs) is studied in the context of geometrical optics in the nonisothermal, viscous, and thermal-conductive atmosphere of Earth in the presence of wind shifts. Parametric diagrams are plotted, determining the regions of allowed frequencies and horizontal phase velocities of AGWs depending on the altitude. It is shown that a part of the spectrum of AGWs propagates in stationary air in an altitude range from the Earth’s surface through the ionospheric F1 layer. AGW from nearearth sources attenuate below 250 km, while waves generated at altitudes of about 300 km and higher do not reach the Earth’s surface because of the inner reflection from the thermosphere base. The pattern changes under strong thermospheric winds. AGW dissipation decreases with an adverse wind shift and, hence, a part of the wave spectrum penetrated from the lower atmosphere to the altitudes of F2 layer.     

Model of muon generation in the Earth’s atmosphere

The muon fluxes on the Earth’s surface and at depths of 7, 20, and 40 m of water equivalent are calculated based on a simple model of pion generation by primary particles with different energies. This generation model is based on the known concepts of multiple pion production. The model parameters are compared with the data obtained using accelerating machines.