Verification of magnetic field models based on measurements of solar cosmic ray protons in the magnetosphere

Measurements of solar cosmic ray (SCR) protons in the magnetosphere can be used to verify models of the Earth’s magnetic field. The latitudinal profiles of precipitating SCRs with energies of 1–90 MeV were measured on the CORONAS-F low-orbiting satellite during a strong magnetic storm on October 29–30, 2003. A flux of precipitating protons can remain equal to the interplanetary flux only due to a strong pitch angle diffusion that originates when the radius of the field line curvature is close to that of the particle rotation Larmor radius. The observed boundaries of the strong diffusion region can be compared with the boundaries anticipated according to the models of the magnetic field of the Earth’s magnetosphere. The adiabaticity parameter values, calculated for several instants of the CORONAS-F satellite pass based on the TS05 and parabolic models, do not always correspond to measurements. How possible changes in the model configurations of the magnetic field can allow us to eliminate discrepancies with the experiment and to explain why solar protons with energies of several megaelectronvolts penetrate deep in the Earth’s inner magnetosphere is considered here.     

Formation of strong stationary vortex turbulence in the terrestrial magnetosheath

The microscopic consequences of the presence of nonlinear vortex structures in the near-Earth plasma dispersive medium are studied in this work. In dispersive media, strongly localized vortex structures contain trapped particles, cause pronounced density fluctuations, and intensify transfer processes, mixing in a medium; i.e., they can form strong vortex turbulence. Turbulence is represented as a gas in the ensemble of strongly localized (therefore, weakly interacting) identical vortices composing the ground state. Vortices with different amplitudes are randomly located in space (since they interact with one another) and are described statistically. It is assumed that the steady turbulent state is formed through a balance of mutually competing effects: spontaneous generation of vortices due to nonlinear steepening of the disturbance front, ^noise transfer to small scales, and collisional or collisionless damping of disturbances in the HF region. Noise scaling in the inertial interval takes place since structures merge during their collision. A magnetized plasma medium in the magnetosheath is considered. A new type of turbulent fluctuation spectra with respect to wavenumbers k ^−8/3, which is in satisfactory agreement with satellite observations in space plasma, has been determined. The medium particle diffusion on an ensemble of vortices has also been studied. It has been established that the interaction between structures themselves and between structures and medium particles causes anomalous diffusion in the medium. The effective diffusion coefficient square roothly depends on the noise stationary level.     

Investigation of the broadband ELF turbulence by observations of the FAST satellite

Scaling properties of variable electric fields in the topside ionosphere have been investigated on scales s from ∼30 m to 2 km by FAST electric field observations with sample rate of 512 s⁻¹, in sixteen events of the broadband ELF turbulence. It is shown that down to scales of a few hundred meters, the power of turbulent electric fluctuations is a power law, ∼s ^α. Scaling index α derived from the slope of logarithmic diagrams (LD) constructed by the discrete wavelet transform of data can be estimated as α = 2.2 ± 0.3, which is close to α estimate earlier reported for scales 1–30 km by electric field observations of the Dynamics Explorer 2 satellite. The behavior of α index is analyzed near the scale of the order of electron inertial length λ_e = c/ω₀ (ω₀ being the electron plasma frequency). At altitudes considered (700–2500 km), λ_e makes 100–900 m. We demonstrate that at scales ≤λ_e, a decrease of LD slope and deviation from the power law are typically observed. As pointed out in the discussion, this feature cannot be identified as a transition to the diffusion range, where dissipation of the turbulence occurs.     

Induced polarization: Simulation and inversion of nonlinear mineral electrodics

Graph-theoretic representations are used to model nonlinear electrodics, while forward and inverse simulations are based on reaction rate theory. The electrodic responses are presented as distorted elliptical Lissajous shapes obtained from dynamic impedance over a full cycle. Simulations show that asymmetry in reaction energy barrier causes slight asymmetry in the shape of the response ellipse and hardly affects the phase angle of the complex electrode impedance. The charge transfer resistance and the diffusion constraints tend to have opposite effects. The former causes reduction in the phase angle, tending to make the impedance purely resistive. Both of these mechanisms show saturation effects. Charge transfer resistance at its limit forces a thin S-type symmetry on the Lissajous patterns, while with diffusion control the size of the Lissajous patterns begins to reduce after saturation. The fixed layer causes substantial increase in the phase angle and tends to “enlarge” the Lissajous patterns. It is responsible for the hysteresis-like shapes of the Lissajous patterns when superimposed on strong charge transfer resistance. This study shows that it is quite possible to deduce the mechanisms that control the electrodic processes by inverting electrodic parameters from “observed” distorted, nonelliptical Lissajous patterns characteristic of nonlinear electrodics. The results and qualities of the inversion technique are discussed.     

Investigation of the amplitude features of high-latitude magnetic impulse events

The features of the amplitude distributions of magnetic impulse events have been investigated using the observations from a number of high-latitude observatories in the Northern and Southern hemispheres. It has been shown that the tails of the statistical distribution functions of the impulse amplitudes are approximated by a power law of the form f(A) = A ^−α, where A is the impulse amplitude and α is the exponent. Therefore, the magnetic-impulse generation regime corresponds to the features of the on-off intermittency model. The distribution of the magnetic impulse amplitudes has been analyzed for various geomagnetic latitudes, local times, seasons, solar activity cycle phases, and interplanetary conditions. It has been found that most statistical distributions of magnetic impulse amplitudes have the exponent α larger than 2, which is typical of the chaotic regimes called “strong turbulence.” In some cases, the exponent α is close to 1, which is typical of the regimes generated in a weakly turbulent medium. Qualitative estimates of the plasma wave turbulence level in the high-latitude magnetosphere have been obtained.     

Rhyolite magma degassing: an experimental study of melt vesiculation

 The vesiculation of a peralkaline rhyolite melt (initially containing ∼0.14 wt.% H₂O) has been investigated at temperatures above the rheological glass transition (T _g≈530  °C) by (a) in situ optical observation of individual bubble growth or dissolution and (b) dilatometric measurements of the volume expansion due to vesiculation. The activation energy of the timescale for bubble growth equals the activation energy of viscous flow at relatively low temperatures (650–790  °C), but decreases and tends towards the value for water diffusion at high temperatures (790–925  °C). The time dependence of volume expansion follows the Avrami equation ΔV (t)∼{1–exp [–(t/τ_av) ⁿ ]} with the exponent n=2–2.5. The induction time of nucleation and the characteristic timescale (τ_av) in the Avrami equation have the same activation energy, again equal to the activation energy of viscous flow, which means that in viscous melts (Peclet number <1) the vesiculation (volume expansion), the bubble growth process, and, possibly, the nucleation of vesicles, are controlled by the relaxation of viscous stresses. One of the potential volcanological consequences of such behavior is the existence of a significant time lag between the attainment of a super-saturated state in volatile-bearing rhyolitic magmas and the onset of their expansion. Received: March 20, 1995 / Accepted: October 24, 1995     

A universal field equation for dispersive processes in heterogeneous media

When formulated properly, most geophysical transport-type process involving passive scalars or motile particles may be described by the same space–time nonlocal field equation which consists of a classical mass balance coupled with a space–time nonlocal convective/dispersive flux. Specific examples employed here include stretched and compressed Brownian motion, diffusion in slit-nanopores, subdiffusive continuous-time random walks (CTRW), super diffusion in the turbulent atmosphere and dispersion of motile and passive particles in fractal porous media. Stretched and compressed Brownian motion, which may be thought of as Brownian motions run with nonlinear clocks, are defined as the limit processes of a special class of random walks possessing nonstationary increments. The limit process has a mean square displacement that increases as t^α+1 where α > −1 is a constant. If α = 0 the process is classical Brownian, if α < 0 we say the process is compressed Brownian while if α > 0 it is stretched. The Fokker–Planck equations for these processes are classical ade’s with dispersion coefficient proportional to t^α. The Brownian-type walks have fixed time step, but nonstationary spatial increments that are Gaussian with power law variance. With the CTRW, both the time increment and the spatial increment are random. The subdiffusive Fokker–Planck equation is fractional in time for the CTRW’s considered in this article. The second moments for a Levy spatial trajectory are infinite while the Fokker–Planck equation is an advective–dispersive equation, ade, with constant diffusion coefficient and fractional spatial derivatives. If the Lagrangian velocity is assumed Levy rather than the position, then a similar Fokker–Planck equation is obtained, but the diffusion coefficient is a power law in time. All these Fokker–Planck equations are special cases of the general non-local balance law.     

Modification by lateral mixing of the Warm Deep Water entering the Weddell Sea in the Maud Rise region

Deep water originating in the North Atlantic is transported across the Antarctic Circumpolar Current by eddies and, after circumnavigating of the Antarctic, enters the Weddell Gyre south of Africa. As it does so, it rises up from mid-depth towards the surface. The separate temperature and salinity maxima, the Upper and Lower Circumpolar Deep Waters, converge to form the Warm Deep Water. Cores of this water mass on the southern flank of the eastern Weddell Gyre show a change in characteristic as they flow westward in the Lazarev Sea. Observations have been made along four meridional sections at 3° E, 0°, 3° W and 6° W between 60 and 70° S during the Polarstern Cruise ANTXXIII/2 in 2005/2006. These show that a heterogeneous series of warm and salty cores entering the region from the east both north and south of Maud Rise (65° S, 3° W) gradually merge and become more homogeneous towards the west. The gradual reduction in the variance of potential temperature on isopycnals is indicative of isopycnic mixing processes. A multiple regression technique allows diagnosis of the eddy diffusivities and, thus, the relative importance of isopycnic and diapycnic mixing. The method shows that the isopycnic diffusivity lies in the range 70–140 m² s⁻¹ and the diapycnic diffusivity reaches about 3 × 10⁻⁶ m² s⁻¹. Scale analysis suggests that isopycnic diffusion dominates over diapycnic diffusion in the erosion of the Warm Deep Water cores.     

Stress Changes due to Recent Seismic Events in the Central Apennines (Italy)

The Central Apennines, Italy, are characterized by moderate seismic activity on normal faults, oriented in directions parallel to the Apenninic chain. The subject of this study is the Umbria-Marche Apennines, a segment approximately 200-km long, where three main seismic events occurred in the last three decades. The 1979 Norcia earthquake was a M_w = 5.8 event, taking place at the south end of the considered segment. The 1984 Gubbio earthquake was a M_w = 5.6 event which took place at the north end. The 1997-1998 Colfiorito sequence constituted 8 main shocks with magnitudes M_w between 5 and 6 and epicenters located between the Gubbio and the Norcia earthquake areas. A model made of an elastic half-space is considered, in which the seismic sources are represented by rectangular dislocations which have the appropriate values of source parameters, and in which the static stress field produced by each event is calculated. The analysis of the Coulomb stress change (ΔC) as a function of time shows that the coseismic stress transfer and fault interaction played an important role in the region during the past three decades: 7 earthquakes of the 9 considered took place where ΔC>0. Such an interaction has been confirmed by the analysis of the aftershocks in the Colfiorito zone post September 26, 1997: about the 61% of the aftershocks considered took place where ΔC>0. The comparison between the ΔC^s due to the coseismic stress transfer and the rate ΔĊ^t due to the tectonic stress allows us to quantify the time advance of the earthquakes. The ΔC^s pattern shows positive values in two areas that can be regarded as historical seismic gaps.     

Probabilistic assessment of earthquake recurrence in the January 26, 2001 earthquake region of Gujrat, India

Kutch region of Gujrat is one of the most seismic prone regions of India. Recently, it has been rocked by a large earthquake (M _w = 7.7) on January 26, 2001. The probabilities of occurrence of large earthquake (M≥6.0 and M≥5.0) in a specified interval of time for different elapsed times have been estimated on the basis of observed time-intervals between the large earthquakes (M≥6.0 and M≥5.0) using three probabilistic models, namely, Weibull, Gamma and Lognormal. The earthquakes of magnitude ≥5.0 covering about 180 years have been used for this analysis. However, the method of maximum likelihood estimation (MLE) has been applied for computation of earthquake hazard parameters. The mean interval of occurrence of earthquakes and standard deviation are estimated as 20.18 and 8.40 years for M≥5.0 and 36.32 and 12.49 years, for M≥6.0, respectively, for this region. For the earthquakes M≥5.0, the estimated cumulative probability reaches 0.8 after about 27 years for Lognormal and Gamma models and about 28 years for Weibull model while it reaches 0.9 after about 32 years for all the models. However, for the earthquakes M≥6.0, the estimated cumulative probability reaches 0.8 after about 47 years for all the models while it reaches 0.9 after about 53, 54 and 55 years for Weibull, Gamma and Lognormal model, respectively. The conditional probability also reaches about 0.8 to 0.9 for the time period of 28 to 40 years and 50 to 60 years for M≥5.0 and M≥6.0, respectively, for all the models. The probability of occurrence of an earthquake is very high between 28 to 42 years for the magnitudes ≥5.0 and between 47 to 55 years for the magnitudes ≥6.0, respectively, past from the last earthquake (2001).     

Simulating the transfer and fate of hexachlorocyclohexane in recent 50 years in Beijing,China

Huge amounts of organic chlorine pesticides (OCPs) had been applied to agricultural area in China during 1950s―1980s, and resulted in serious environmental pollution because of their tendency to accumulate in organisms and persistence in the environment, which caused highly risk potential to the ecosystem and long-term residue in the polluted area. There are still higher HCHs residues in the environment even 20 years after the prohibition of HCHs from 1984[1,2]. It is necessary to investi…     

Temporal migration of earthquakes in Koyna–Warna (India) region by pore-fluid diffusion

Continuous occurrences of several thousands of earthquakes in Koyna–Warna region since the initial impoundment (1962) of the Koyna reservoir has attracted the attention of seismologists all over the world to know the exact earthquake physical processes involved. The area has been a site for reservoir-triggered earthquakes for the last four and half decades. Major bursts of seismic activity occurred during 1967, 1973, 1980, 1993, and 2000 and recently in 2005 with magnitudes exceeding 5.0 in the region. A notable southward migration of seismicity has been observed following the impoundment of another reservoir, the nearby Warna reservoir. All the mainshocks suggest that the significant southward migration might be due to pore-pressure diffusion. We have divided the entire period from 1967 to 2007 in several sequences starting by a mainshock of M >5. Each sequence is critically analyzed in terms of triggering by the diffusion process through the fractured medium. The pore-fluid diffusion tensor D for each sequence is estimated based on Darcy’s law. The direction of temporal migration of seismicity of each sequence except 1980 is correlated well with the eigenvectors of diffusion. The fluid flow eigenvectors are constrained with one of the strike directions of the focal mechanisms. The frequency magnitude distribution shows the b value to vary from 0.5 to 1.2. Spatial distribution of the b value further indicates that the area along the major faults is more prone to future earthquake.     

Model calculations of the total electron content for the system of GPS satellites

The numerical global self-consistent model of the Earth’s thermosphere, ionosphere and protonosphere (GSM TIP), which makes it possible to calculate all the main parameters of the near-Earth plasma, is used to calculate the total electron content (TEC). Calculations have been performed along the radiosignal propagation trajectory between a surface receiving point and a GPS satellite. The TEC value calculated from the satellite data have been compared with such a “true model” TEC value for magnetically quiet conditions of the spring equinox and moderate solar activity. The relative errors in determining the satellite data-based TEC for two European (Troms have been calculated. It has been indicated that an increase in the number of satellites not always results in an increase in accuracy of the TEC value measured on satellites.     

Chemical and geochemical studies of Lake Biel

The mixing and transport processes in Lake Biel have been studied using the heat and excess Rn-222 as natural tracers. The mixing parameters were established in terms of coefficients of eddy diffusion in a two-dimensional box model. To account for observed transient Rn-222 distribution, transport by advection had to be included in the model calculations. Part I: Peter W. Santschi and Paul W. Schindler: A mass balance for Lake Biel and its implications for the rates of erosion of the drainage area. Schweiz. Z. Hydrol.39, 182–200 (1977).     

Properties of electric turbulence in the polar cap ionosphere

Small-scale (scales of ∼0.5–256 km) electric fields in the polar cap ionosphere are studied on the basis of measurements of the Dynamics Explorer 2 (DE-2) low-altitude satellite with a polar orbit. Nineteen DE-2 passes through the high-latitude ionosphere from the morning side to the evening side are considered when the IMF z component was southward. A rather extensive polar cap, which could be identified using the ɛ-t spectrograms of precipitating particles with auroral energies, was formed during the analyzed events. It is shown that the logarithmic diagrams (LDs), constructed using the discrete wavelet transform of electric fields in the polar cap, are power law (μ ∼ s ^α). Here, μ is the variance of the detail coefficients of the signal discrete wavelet transform, s is the wavelet scale, and index α characterizes the LD slope. The probability density functions P(δE, s) of the electric field fluctuations δE observed on different scales s are non-Gaussian and have intensified wings. When the probability density functions are renormalized, that is constructed of δE/s ^γ, where γ is the scaling exponent, they lie near a single curve, which indicates that the studied fields are statistically self-similar. In spite of the fact that the amplitude of electric fluctuations in the polar cap is much smaller than in the auroral zone, the quantitative characteristics of field scaling in the two regions are similar. Two possible causes of the observed turbulent structure of the electric field in the polar cap are considered: (1) the structure is transferred from the solar wind, which is known to have turbulent properties, and (2) the structure is generated by convection velocity shears in the region of open magnetic field lines. The detected dependence of the characteristic distribution of turbulent electric fields over the polar cap region on IMF B _y and the correlation of the rms amplitudes of δE fluctuations with IMF B _z and the solar wind transfer function (B _y ² + B _z ²)^1/2sin(θ/2), where θ is the angle between the geomagnetic field and IMF reconnecting on the dayside magnetopause when IMF B _z < 0, together with the absence of dependence on the IMF variability are arguments for the second mechanism.     

Numerical studies of dispersion due to tidal flow through Moskstraumen, northern Norway

The effect of horizontal grid resolution on the horizontal relative dispersion of particle pairs has been investigated on a short time scale, i.e. one tidal M ₂ cycle. Of particular interest is the tidal effect on dispersion and transports in coastal waters where small-scale flow features are important. A three-dimensional ocean model has been applied to simulate the tidal flow through the Moskstraumen Maelstrom outside Lofoten in northern Norway, well known for its strong current and whirlpools (Gjevik et al., Nature 388(6645):837–838, 1997; Moe et al., Cont Shelf Res 22(3):485–504, 2002). Simulations with spatial resolution down to 50 m have been carried out. Lagrangian tracers were passively advected with the flow, and Lyapunov exponents and power law exponents have been calculated to analyse the separation statistics. It is found that the relative dispersion of particles on a short time scale (12–24 h) is very sensitive to the grid size and that the spatial variability is also very large, ranging from 0 to 100 km² over a distance of 100 m. This means that models for prediction of transport and dispersion of oil spills, fish eggs, sea lice etc. using a single diffusion coefficient will be of limited value, unless the models actually resolves the small-scale eddies of the tidal current.     

Active phase of a substorm as a chain of two types of reconnection: In the closed plasma sheet and in the open tail lobes

The maps of the field-aligned current (FAC) density distribution in the ionosphere obtained by the TIM-2 magnetogram inversion technique are used to investigate the August 27, 2001 substorm. The open magnetic flux Ψ and intensity J of the substorm current wedge (SCW) have been determined with a step of 1–5 min. The substorm onsets are divided into two types, PSR (plasma sheet reconnection) and TLR (tail lobe reconnection). The fast expansion tailward of the PSR region is described as the transition from PSR to PSR+TLR. Assuming that the SCW FACs flow down into the ionosphere from the edges of the disruption region of the cross-tail dawn-dusk current, several parameters of the disruption region have been estimated. The disrupted magnetic field has been found to be ∼5% of the undisrupted one for PSR and ∼95% for PSR+TLR. The disturbance power Q for PSR is an order of magnitude lower than that for PSR+TLR. The abrupt growth of Q during the transition from PSR to PSR+TLR is observed over the entire SCW area from its near-Earth part to the midtail and distant tail.     

Morphology and causes of the Weddell Sea anomaly

The zone of anomalous diurnal variations in foF2, which is characterized by an excess of nighttime foF2 values over daytime ones, has been distinguished in the Southern Hemisphere based on the Intercosmos-19 satellite data. In English literature, this zone is usually defined as the Weddell Sea anomaly (WSA). The anomaly occupies the longitudes of 180°–360° E in the Western Hemisphere and the latitudes of 40°–80° S, and the effect is maximal (up to ∼5 MHz) at longitudes of 255°–315° E and latitudes of 60°–70° S (50°–55° ILAT). The anomaly is observed at all levels of solar activity. The anomaly formation causes have been considered based on calculations and qualitative analysis. For this purpose, the longitudinal variations in the ionospheric and thermospheric parameters in the Southern Hemisphere have been analyzed in detail for near-noon and near-midnight conditions. The analysis shows that the daytime foF2 values are much smaller in the Western Hemisphere than in the Eastern one, and, on the contrary, the nighttime values are much larger, as a result of which the foF2 diurnal variations are anomalous. Such a character of the longitudinal effect mainly depends on the vertical plasma drift under the action of the neutral wind and ionization by solar radiation. Other causes have also been considered: the composition and temperature of the atmosphere, plasma flows from the plasmasphere, electric fields, particle precipitation, and the relationship to the equatorial anomaly and the main ionospheric trough.     

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.