Numerical simulation of the <Emphasis Type="Italic">F</Emphasis>2-layer stratification and appearance of the <Emphasis Type="Italic">F</Emphasis>3 and <Emphasis Type="Italic">G</Emphasis> layers in the equatorial ionosphere: The morphology of the phenomena

This work is devoted to a numerical simulation of the equatorial ionosphere, performed using the GSM TIP model completed with a new block for calculating the electric field. It has been indicated that the usage of the wind system calculated according to the MSIS-90 model makes it possible to reproduce the electromagnetic drift velocities at the equator, the effect of the F2-layer stratification, and the appearance of the F3 layer in the equatorial ionosphere. The calculations performed using the modified GSM TIP model made it possible to detect a maximum in the electron density vertical profile at an altitude of ∼1000 km, formed by H⁺ ions, which we called the G layer. If this layer actually exists, it can be observed during sounding the low-latitude ionosphere from satellites during dark time of day.     

Mechanism of formation of <Emphasis Type="Italic">Q</Emphasis>-disturbances in the <Emphasis Type="Italic">F</Emphasis><Subscript>2</Subscript> region of the equatorial ionosphere

Using model simulations, the morphological picture (revealed earlier) of the disturbances in the F ₂ region of the equatorial ionosphere under quiet geomagnetic conditions (Q-disturbances) is interpreted. It is shown that the observed variations in the velocity of the vertical E × B plasma drift, related to the zonal E _y component of the electric field, are responsible for the formation of Q-disturbances. The plasma recombination at altitudes of the lower part of the F ₂ region and the dependence of the rate of this process on heliogeophysical conditions compose the mechanism of Q-disturbance formation at night. The daytime positive Q-disturbances are caused exclusively by a decrease in the upward E × B drift, and this type of disturbances could be related to the known phenomenon of counter electrojet. Possible causes of formation of the daytime negative Q-disturbances are discussed.     

Origination of <Emphasis Type="Italic">G</Emphasis> conditions in the ionospheric <Emphasis Type="Italic">F</Emphasis> region depending on solar and geomagnetic activity

The dependence of the origination of G conditions in the ionospheric F region on solar and geomagnetic activity has been determined based on numerical simulation of the ionosphere over points 50° N, 105° E and 70° N, 105° E for summer conditions at noon. It has been found that the threshold value of the Kp geomagnetic activity index (Kp _S ), beginning from which a G condition can originate, is minimal for a low solar activity level at relatively high latitudes during the recovery phase of a geomagnetic storm. On average, Kp _S increases with increasing solar activity, but G conditions can originate at high solar activity levels and be absent at moderate ones for certain Kp values, which was apparently predicted for the first time. These properties of the origination of G conditions do not contradict the known results of a G-condition statistical analysis performed based on the data from the global network of ionospheric stations.     

Vertical structure of the midlatitude winter <Emphasis Type="Italic">F</Emphasis> region of the ionosphere during postmidnight enhancements in <Emphasis Type="Italic">NmF</Emphasis>2

The behavior of the vertical structure of the ionospheric F2 layer, including the variations in the heights of the maximum and bottom of the layer, its half-thickness, and electron content at some fixed heights during postmidnight enhancements in the electron density at the F2 layer maximum (NmF2), has been studied based on the data of the ionospheric vertical sounding, conducted in Alma-Ata (76°55′ E, 43°15′ N) in 2005–2006. The analysis of the amplitude and phase relationships between the measured parameters of the layer made it possible to qualitatively complete the existing concepts of the mechanisms by which the discussed effect is maintained. It is shown that the accelerated decrease in the electron density of the layer within a short time interval preceding the beginning of the postmidnight increase in NmF2 is governed not only by recombination processes but also by the plasma redistribution over the increasing thickness of the layer. The regularly observed effect of the delay in the moment of reversal in the motion direction of the layer bottom relative to the corresponding moment for the layer maximum made it possible to conclude that the meridional wind asynchronously reverses its direction from the poleward daytime to the equatorward nighttime in the entire layer: the direction changes later with decreasing height.     

Regular changes in the critical frequency of the <Emphasis Type="Italic">F</Emphasis>2 layer of the quiet midlatitude ionosphere

A method for constructing the empirical model of the F2 layer critical frequency (foF2) under magnetically quiet conditions, aimed at analyzing disturbances of any nature, is proposed. This method has been analyzed, and typical features of regular changes in foF2 of the quiet ionosphere and day-to-day foF2 variability are analyzed using the data from Irkutsk and Slough stations as an example. In particular, it has been obtained that this model differs from the international IRI model, and this difference is mainly caused by the fact that the foF2 values in the IRI model do not correspond to quiet conditions. Therefore, this model gives a larger amplitude of the annual and semiannual variations in foF2 than the IRI model. In addition, this model more accurately reproduces the rate of foF2 annual variations at a fixed local time, especially in equinoxes, when foF2 variations can exceed 1 MHz within one month.     

Combined Method of <Emphasis Type="Italic">F</Emphasis>-, <Emphasis Type="Italic">S</Emphasis>-, and <Emphasis Type="Italic">R</Emphasis>-Approximations of Increased Dimensionality in Solving the Problems of Geophysics and Geomorphology

The interrelation between different variants of the method of linear integral representations in the spaces of an arbitrary dimension is considered. The combined approximations of the topography and geopotential fields allows the selection of the optimal parameters of the method in solving a wide range of inverse problems in geophysics and geomorphology, as well as a most thorough use of the a priori information about the elevations and elements of anomalous fields. A method for numerically solving an inverse problem on finding the equivalent, in terms of the external field, mass distributions in the ordinary three-dimensional (3D) space and in the four-dimensional (4D) space is described.     

Unstable plasma irregular structures in the topside ionosphere and spread-<Emphasis Type="Italic">F</Emphasis>

The results of the Cosmos-900 satellite observ ations of plasma density inhomogeneities in the geomagnetic equator region and the longitudinal distributions of the equatorial spread-F, according to the Intercosmos-19 satellite data are presented. It is show n that the dependence of radiosignal propagation in the ionosphere on geophysical parameters is related to development of the electrostatic instability of the inhomo-geneous ionospheric plasma. The longitudinal dependence of the spread-F, can reflect the influence of the energetic sources, located outside the ionospheric layer that scatters a radio pulse, on the ionosphere. The manifestation of the longitudinal effect in the equatorial spread-F, in the Atlantic region can be explained by the influence of the cone instability on the plasma electrodynamics in the South Atlantic geomagnetic anomaly.     

Combined method of <Emphasis Type="Italic">F</Emphasis>-, <Emphasis Type="Italic">S</Emphasis>-, and <Emphasis Type="Italic">R</Emphasis>-approximations in solving the problems of geophysics and geomorphology

The interrelation between different modifications of the method of linear integral representation is studied. Combined approximations of the topography and geopotential fields enable more refined tuning of the method in solving inverse problems of geophysics and geomorphology and provide a more complete allowance for the a priori information about the surface elevation data and elements of anomalous fields. A technique for finding the numerical solution for the inverse problem for determining the mass distributions equivalent in terms of the external field is presented. The results of the mathematical experiment are discussed.     

Behavior of <Emphasis Type="Italic">foF</Emphasis>2 and <Emphasis Type="Italic">hmF</Emphasis>2 after sunset

The time behavior of the foF2 and hmF2 values at the time moment T(ss + 2 h) 2 h after sunset is considered. It is assumed that at this moment, the horizontal winds in the thermosphere in the strongest way influence hmF2 and, therefore, foF2. It is found that a fairly well pronounced and statistically significant change (trend) is observed for the foF2(ss + 2)/foF2(14) ratio, the sign of the change being different for different stations and even different seasons at the same station. A similar picture is obtained for the value of hmF2(ss + 2). It is shown that a positive correlation between the trends of these two values is observed. This confirms the initial concept of the paper that the foF2 and hmF2 trends are caused by long-term trends in the thermospheric dynamics.     

Numerical modeling of the behavior of super-small-scale irregularities in the ionospheric <Emphasis Type="Italic">F</Emphasis>2 layer

Using a mathematical modeling method, evolutions of super-small-scale irregularities of electron concentration stretched along the geomagnetic field which could be formed in the magnetized ionospheric plasma of the F2 layer both in a natural way and at an artificial impact on it, in particular, during heating experiments, are studied. Evolution in time of the initially formed irregularities of two types having different shape of the cross sections lateral to the magnetic field (types of direct narrow long band and with a circular cross section) is calculated. It is found that such irregularities during times tens of times shorter than the time of the electron free path time spread out and disappear, accomplishing thereby periodic attenuating oscillations. The period of these oscillations can be equal to both the period of Langmuir oscillations of electrons and the period of cyclotron oscillations of electrons depending on the irregularity type and its initial parameters.     

Studying the spread <Emphasis Type="Italic">F</Emphasis> effect before earthquakes

The observations of spread F during the nighttime hours (0000–0500 LT) have been statistically analyzed based on data of Tokyo, Akita, Wakkanai, and Yamagawa Japan vertical ionospheric sounding stations for the time intervals a month before and a month after an earthquake. The disturbances in the probability of spread F appearance before an earthquake are revealed against a background of the variations depending on season, solar activity cycle, geomagnetic and solar disturbances. The days with increased solar (Wolf number W > 100) and geomagnetic (ΣK > 30) activity are excluded from the analysis. The spread F effects are considered for more than a hundred earthquakes with magnitude M > 5 and epicenter depth h < 80 km at distances of R < 1000 km from epicenters to the vertical sounding station. An average decrease in the spread F occurrence probability one-two weeks before an earthquake has been revealed using the superposed epoch method (the probability was minimal approximately ten days before the event and then increased until the earthquake onset). Similar results are obtained for all four stations. The reliability of the effect has been estimated. The dependence of the detected effect on the magnitude and distance has been studied.     

Long-term changes in the relation between <Emphasis Type="Italic">foF</Emphasis>2 and <Emphasis Type="Italic">hmF</Emphasis>2

The change in the dependence of the F2-layer critical frequency on its height hmF2 is considered based on two sources of initial data used earlier by the authors. It is found that the slope k of the foF2 dependence on hmF2 systematically decreases from the earlier (“etalon”) period, 1958–1980, to the later periods of 1988–2010, 1998–2010, and 1998–2014. Since the foF2 value depends on the atomic oxygen concentration in the F region much more strongly than hmF2, the found decrease in k confirms the concept of a decrease in the atomic oxygen concentration in the thermosphere with time previously formulated by the authors.     

Variations in the fractal dimension of fluctuations of the ionospheric <Emphasis Type="Italic">F</Emphasis>2 layer critical frequency

The 40-year period of observations of short-term variations (with characteristic times of up to 1–2 days) in the critical frequency of the ionospheric F2 layer (foF2) is analyzed. The continuous (with a step of 1 h) series of fluctuations (F) of the foF2 critical frequency (with eliminated daily variations) has been calculated using the hourly variations in foF2 at Moscow stations. The fractal dimension (FRH) of the fluctuations, characterizing short-term variations in foF2, has been determined and analyzed on a 30-day interval, using the Higuchi method. It has been established that FRH estimates substantially change in time. The 11-year cycle, which is in antiphase with the solar cycle, and the total annual and semiannual variations, similar to the variations observed in the normalized critical frequency of the E region and in the electron density of the D region, are clearly defined in these changes. Thus, the parameters of fast variations in the ionospheric F2 layer are affected by the phase of the 11-year solar cycle and by the position of the Earth in the orbit or seasonal variations in the atmosphere.     

Dynamics of the midlatitude ionospheric <Emphasis Type="Italic">F</Emphasis> region at sunrise

The behavior of the F2 layer at sunrise has been studied based on vertical-incidence ionospheric sounding data in Almaty (76°55′E, 43°15′N). Records with small amplitudes of electron density background fluctuations were selected in order to exactly estimate the onsets of a pronounced increase in the electron density at different altitudes. It has been indicated that the electron density growth rate is a function of altitude; in this case, the growth rate at the F2 layer maximum is much lower than such values at fixed altitudes of ～30–55 km below the layer maximum. The solar zenith angle (χ) and the blanketing layer thickness (h ₀) at the beginning of a pronounced increase in the electron density at altitude h are linearly related to the h value, and these quantities vary within ～90° < χ < 100° and 180 km < h ₀ < 260 km, respectively.     

<Emphasis Type="Italic">R/S</Emphasis> analysis of the <Emphasis Type="Italic">Dst</Emphasis> index

The paper addresses estimation of the Hurst exponent for time series of the hourly values of the Dst index for the period from 1957 to 2011. It is found that the Hurst exponent is 0.79–0.94 for yearly intervals and 0.8–1.0 for monthly intervals. Based on R/S graphs, the Dst cycles are identified; they range from 3–4 months to 2.2 years and from 8.5 to 22 years in length. It is shown that a Dst time series can be quite satisfactorily described by an α-stable Levy process.     

Relationship between the daytime critical frequencies of the <Emphasis Type="Italic">F</Emphasis><Subscript>2</Subscript> layer and thermospheric characteristics

The relationship between the critical frequency of the F ₂ layer and the atmospheric characteristics has been obtained in a general form. It has been shown that this relation makes it possible to sufficiently accurately describe the daytime values of foF2 while comparing them with the observed monthly median values. Such comparisons were performed, first, for the data of measurements in Irkutsk using the DPS-4 digital ionosonde in 2003–2006 and, second, based on the annual variations in the noon foF2 values at 24 stations of the Northern Hemisphere in 1984. The calculations were performed using the MSIS-86 thermospheric model [Hedin, 1987].     

Dispersion Measurements of <Emphasis Type="Italic">P</Emphasis> Waves and their Implications for Mantle <Emphasis Type="Italic">Q</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>

We analyze the anelasticity of the earth using group delays of P-body waves of deep (>200 km) events in the period range 4–32 s for epicentral distances of 5–85 degrees. We show that Time Frequency Analysis (TFA), which is usually applied to very dispersive surface waves, can be applied to the much less dispersive P-body waves to measure frequency-dependent group delays with respect to arrival times predicted from the CMT centroid location and PREM reference model. We find that the measured dispersion is due to: (1) anelasticity (described by the P-wave quality factor Q _p ), (2) ambient noise, which results in randomly distributed noise in the dispersion measurements, (3) interference with other phases (triplications, crustal reverberations, conversions at deep mantle boundaries), for which the total dispersion depends on the amplitude and time separation between the different phases, and (4) the source time function, which is dispersive when the wavelet is asymmetrical or contains subevents. These mechanisms yield dispersion ranging in the order of one to 10 seconds with anelasticity responsible for the more modest dispersion. We select 150 seismograms which all have small coda amplitudes extending to ten percent of the main arrival, minimizing the effect of interference. The main P waves have short durations, minimizing effects of the source. We construct a two-layer model of Q _p with an interface at 660 km depth and take Q _p constant with period. Our data set is too small to solve for a possible frequency dependence of Q _p . The upper mantle Q ₁ is 476 [299–1176] and the lower mantle Q ₂ is 794 [633–1064] (the bracketed numbers indicate the 68 percent confidence range of Q _p ^–1). These values are in-between the AK135 model (Kennett et al., 1995) and the PREM model (Dziewonski and Anderson, 1981) for the lower mantle and confirm results of Warren and Shearer (2000) that the upper mantle is less attenuating than PREM and AK135.     

Reaction of the critical frequency of the <Emphasis Type="Italic">F</Emphasis>2 layer to a sharp depletion in atmospheric pressure

Changes in the critical frequencies of the F2 layer at several midlatitude stations of ionospheric vertical sounding during a sharp depletion in atmospheric pressure under quiet solar and geomagnetic conditions are analyzed. It is shown that in such periods, the observed foF2 values differ from the mean values by approximately 10–15% and the deviations from the mean could be both negative (in the daytime hours) and positive (at night). Such variations in foF2 could be referred to the known class of ionospheric disturbances observed under a quiet geomagnetic situation, that is, to the so-called “Q-disturbances.” Analysis of wavelet spectra of foF2 variations shows the presence in the F region of oscillations of various periods (from 0.5 to 10 days). The decrease in the amplitude of daily variations during pressure depletion is found. Presumably, the observed effect is caused by the dynamic impact of waves formed in the lower atmosphere on the ionospheric F2 layer.     

Relation of long-period variations in the critical frequencies of the <Emphasis Type="Italic">F</Emphasis><Subscript>2</Subscript> layer to geomagnetic activity

The relation of the long-period variations in the midnight and noon values of the critical frequency of the ionospheric F ₂ layer at three midlatitude stations (Irkutsk, Moscow, and Boulder) to the daily mean index of geomagnetic activity in years of different solar activity has been studied. It has been found that the correlation coefficients between the above parameters depend on time of day, season, and solar activity level. The correlation coefficients are higher at night than in the daytime, especially at low solar activity. The highest absolute values of the correlation coefficient most often appear during equinoxes: April–May and September–October. It has been shown that the variability of the critical frequencies of the midlatitude ionospheric F ₂ layer depends not only on geomagnetic activity but also (to a considerable degree) on the effect of the lower atmosphere.