Midlatitude <Emphasis Type="Italic">Pc</Emphasis>1 Geomagnetic Pulsations: Results of Observations and Statistical Estimates

An algorithm is developed for automated detection of the short-period Pc1 geomagnetic pulsations (frequency band f = 0.2–3 Hz) from the continuous time series of digital recording during 1998–2014 at the midlatitude Borok station. A digital catalog with the indication of time intervals of the presence and main morphological characteristics of Pc1 pulsations is created. Based on this catalog, the annual, seasonal, and diurnal dynamics of the midlatitude Pc1 pulsation activity is studied for 1998–2014. It is shown that the annual variation of the Pc1 occurrence has a maximum in 2005, i.e., at the end of the solar cycle decay phase, just as in the previous cycles. It is found that the minimum of the cases of Pc1 occurrence is observed in 2009, i.e., not at the maximum, just was the case in the previous cycles, but during the deep minimum of solar activity, which testifies to the untypical conditions in the magnetosphere during the unusually long minimum of the 23rd cycle. The seasonal variation of the Pc1 occurrence has a summer minimum when the series of Pc1 pulsations occur almost thrice as rarely as in winter. Besides, there are relatively small maxima at equinox. The diurnal behavior of Pc1 pulsations has the maxima in the morning and midnight sectors of the magnetosphere. By the superposed epoch analysis technique it is established that the maximal number of the cases of occurrence of Pc1 pulsations at the Borok observatory is observed on the fourth day after the global geomagnetic disturbances. The statistical distributions of pulsations amplitude and duration are obtained.     

<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.     

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.     

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.     

Mechanisms of stratification of the <Emphasis Type="Italic">F</Emphasis>2 layer and formation of the <Emphasis Type="Italic">F</Emphasis>3 and <Emphasis Type="Italic">G</Emphasis> layers in the equatorial ionosphere

The paper is dedicated to the studies of formation mechanisms of additional layers in the equatorial ionosphere carried out using numerical simulations with use of the Global Self-Consistent Model of the Thermosphere, Ionosphere, and Protonosphere (GSM TIP) modified in the part of the solution of the electric field equation in the Earth’s ionosphere. Calculations were preformed for quiet geomagnetic conditions using the MSIS-90 model for the calculation of thermospheric parameters. The obtained spatio-temporal pattern of thermospheric circulation and the variations in the dynamo electric field obtained on its basis make it possible to reproduce the stratification effect of the F2 layer and the appearance of the F3 layer in the equatorial ionosphere due to the action of the nonuniform in height zonal electric field at the geomagnetic equator. On the basis of the earlier presented results of calculations using the modified GSM TIP model, the appearance of a maximum in the vertical profile of the electron density at a height of ∼1000 km formed by H+ ions, which we called the G layer, has been predicted. Numerical simulations showed that this layer is formed by the meridional component of the thermospheric wind and is related to the formation of the nighttime midlatitude maximum at heights of the ionospheric F region.     

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.     

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.     

Linear transformations of anomalous potential fields using <Emphasis Type="Italic">S</Emphasis> and <Emphasis Type="Italic">R</Emphasis> approximations

Methods for linear transformations of anomalous physical fields based on R and S approximations of the elements of the initial field are described. The results of the numerical experiment and analytical extension of the gravity field measured in a detailed gravity survey in two regions of Russia are presented.     

Ponderomotive Force of Ion Cyclotron Waves in the <Emphasis Type="Italic">Pc</Emphasis>1 Frequency Range with Magnetosonic Dispersion

Nonlinear properties of the Pc1 geomagnetic pulsations with anomalous (magnetosonic) dynamic spectrum are studied. The nonlinear properties of the waves are reflected in the emergence of ponderomotive force proportional to the squared amplitude of the waves. Just as in the case of the Alfven waves, at small values of parameter ν₀ = ω/ω_ci0 < 0.4 (ratio of the carrier frequency to proton gyrofrequency in the equatorial plane), the ponderomotive force leads to the modification of the background plasma through increasing its density towards the equator. At ν₀ > 0.4, plasma is expelled from the equator towards the higher latitudes. The dependence of the nonlinear modification of background plasma for the different parameters of the magnetosphere is studied.     

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.     

Attenuative Dispersion of <Emphasis Type="Italic">P</Emphasis> Waves and Crustal <Emphasis Type="Italic">Q</Emphasis> in Turkey and Germany

We have measured group delays of the spectral components of high-frequency P-waves along two portions of the North Anatolian Fault Zone (NAFZ) in Turkey and in a region of southern Germany. Assuming that the observed dispersion is associated with attenuation in the crust and that it can be described by a continuous relaxation model, we obtained Q and the high-frequency relaxation times for those waves for each of the three regions. Individual P-wave Q values exhibit large scatter, but mean values in the NAFZ increase from about 25 to 60 over the distance range 5–90 km. Mean Q values are somewhat higher in the eastern portion of the NAFZ than in the western portion for measurements made at distances between 10 and 30 km. P-wave Q values in Germany range between about 50 and 300 over the hypocentral distance range 20–130 km. In that region we separated the effects of Q for basement rock (2–10 km depth) from that of the overlying sediment (0–2 km depth) using a least-squares method. Q varies between 100 and 500 in the upper 8–10 km of basement, with mean values for most of the distance range being about 250. Q in the overlying sediments ranges between 6 and 10. Because of large scatter in the Q determinations we investigated possible effects that variations of the source-time function of the earthquakes and truncation of the waveform may have on Q determinations. All of our studies indicate that measurement errors are relatively large and suggest that useful application of the method requires many observations, and that the method will be most useful in regions where the number of oscillations following the initial P pulse is minimized. Even though there is large scatter in our Q determinations, the mean values that we obtained in Turkey are consistent with those found in earlier studies. Our conclusions that Q is significantly higher in the basement rock of Germany than in the basement rock of Turkey and that Q is lower in western Turkey than in eastern Turkey are also consistent with results of Q studies using Lg coda.     

Multi-scale Tomography for Crustal <Emphasis Type="Italic">P</Emphasis> and <Emphasis Type="Italic">S</Emphasis> Velocities in Southern California

Seismic tomography is a viable tool in building depth-velocity models in the presence of strong lateral velocity variations. In this study 3-D P- and S-velocity models for the crust of southern California are constrained using more than 1,000,000 P-wave first arrivals and 130,000 S-wave arrivals from local earthquakes. To cope with the uneven distribution of raypaths, a multi-scale tomography is applied with overlapping model cells of different sizes. Within the 300 × 480 × 39 km³ model volume, the smallest cell size is 10 × 10 × 3 km³. During the iterations of velocity updating, earthquake hypocenters are determined using both P and S arrivals, and full 3-D ray tracing is implemented. Except near the edges and in the lower crust, the resultant models are robust according to various tests on the effects of reference models, resolution and signal-to-noise ratio. The tomographic velocities at shallow depths correlate very well with the regional geology of southern California. In the upper crust the P-wave and S-wave models exhibit slow velocities in major sedimentary basins and fast velocities in areas of crystalline rocks. Mid-crustal low velocity zones are present under the Coso Range, San Gabriel Mountains, and a large portion of the Mojave Desert. P- and S-velocity patterns maintain their similarity in the lower crust though the models are less reliable there.     

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.     

Dayside auroras during unusually large positive values of the IMF <Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">z</Emphasis></Subscript> component

The characteristics of dayside auroras during the large (16–24 nT) positive values of the IMF B _z component, observed on January 14, 1988, during the interaction between the Earth’s magnetosphere and the body of the interplanetary magnetic cloud, have been studied based on the optical observations on Heiss Island. A wide band of diffuse red luminosity with an intensity of 1–2 kilorayleigh (kR) was observed during 6 h in the interval 1030–1630 MLT at latitudes higher than 75° CGL. Rayed auroral arcs, the brightness of which in the 557.7 nm emission sharply increased to 3–7 kR in the postnoon sector immediately after the polarity reversal of the IMF B _y component from positive to negative, were continuously registered within the band. Bright auroral arcs were observed at the equatorward edge of red luminosity. It has been found out that the red auroral intensity increases and the band equatorward boundary shifts to lower latitudes with increasing solar wind dynamic pressure. However, a direct proportional dependence of the variations in the auroral features on the dynamic pressure variations has not been found. It has been concluded that the source of bright discrete auroras is located in the region of the low-latitude boundary layer (LLBL) on closed geomagnetic field lines. The estimated LLBL thickness is ∼3 R _e . It has been concluded that the intensity of the dayside red band depends on the solar wind plasma density, whereas the position of the position equatorward boundary depends on the dynamic pressure value and its variations.     

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.     

Sampling uncertainties and source <Emphasis Type="Italic">b</Emphasis> likelihood for the Gutenberg-Richter <Emphasis Type="Italic">b</Emphasis> value from the Aki-Utsu method

The Aki-Utsu method of Gutenberg-Richter (G-R) b value estimation is often misapplied so that estimations not using the G-R histogram are often meaningless because they are not based on adequate samples. We propose a method to estimate the likelihood Pr(b?b _m , N, M ₁, M ₂) that an observed b _m estimate, based on a sample of N magnitudes within an [M ₁????≤?ΔM/2,?M ₂?+?ΔM/2) range, where ΔM?=?0.1 is the usual rounding applied to magnitudes, is due to a “true” source b value, b, and use these likelihoods to estimate source b ranges corresponding to various confidence levels. As an example of application of the method, we estimate the b values before and after the occurrence of a 7.4-magnitude earthquake in the Mexican subduction zone, and find a difference of 0.82 between them with 100% confidence that the b values are different.     

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.     

Features of <Emphasis Type="Italic">Pc</Emphasis>5 pulsations in the geomagnetic field,auroral luminosity,and Riometer absorption

Simultaneous morning Pc5 pulsations (f ~ 3–5 mHz) in the geomagnetic field, aurora intensities (in the 557.7 and 630.0 nm oxygen emissions and the 471.0 nm nitrogen emission), and riometer absorption, were studied based on the CARISMA, CANMOS, and NORSTAR network data for the event of January 1, 2000. According to the GOES-8 satellite observations, these Pc5 geomagnetic pulsations are observed as incompressible Alfvén waves with toroidal polarization in the magnetosphere. Although the Pc5 pulsation frequencies in auroras, the geomagnetic field, and riometer absorption are close to one another, stable phase relationships are not observed between them. Far from all trains of geomagnetic Pc5 pulsations are accompanied by corresponding auroral pulsations; consequently, geomagnetic pulsations are primary with respect to auroral pulsations. Both geomagnetic and auroral pulsations propagate poleward, and the frequency decreases with increasing geomagnetic latitude. When auroral Pc5 pulsations appear, the ratio of the 557.7/630.0 nm emission intensity sharply increases, which indicates that auroral pulsations result from not simply modulated particle precipitation but also an additional periodic acceleration of auroral electrons by the wave field. A high correlation is not observed between Pc5 pulsations in auroras and the riometer absorption, which indicates that these pulsations have a common source but different generation mechanisms. Auroral luminosity modulation is supposedly related to the interaction between Alfvén waves and the region with the field-aligned potential drop above the auroral ionosphere, and riometer absorption modulation is caused by the scattering of energetic electrons by VLF noise pulsations.     

Dependence of geomagnetic disturbances on extreme values of the solar wind <Emphasis Type="Italic">E</Emphasis><Subscript><Emphasis Type="Italic">y</Emphasis></Subscript> component

The dependence of the zonal geomagnetic indices (AE, Ap, Kp, Kn, and Dst) on the solar wind parameters (the electric field E _y component, dynamic pressure P _d and IMF irregularity σB) has been studied for two types of events: magnetic clouds and high-speed streams. Based on the empirical relationships, it has been established that the AE, Ap, Kp, and Kn indices are directly proportional to the E _y value at E _y < 12 mV m^?1 and are inversely proportional to this value at E _y > 12 mV m^?1 for the first-type events. On the contrary, the dependence of Dst on E _y is monotonous nonlinear. A linear dependence of all geomagnetic indices on E _y is typical of the second-type events. It has been indicated that the specific features of geoeffectiveness of magnetic clouds and high-speed solar wind streams are caused by the dependence of the electric field potential across the polar cap on the electric field, solar wind dynamic pressure, and IMF fluctuations.     

On the <Emphasis Type="Italic">P</Emphasis> and <Emphasis Type="Italic">S</Emphasis> Receiver Functions Used for Inverting the One-Dimensional Upper Mantle Shear-Wave Velocities

The teleseismic P receiver functions are customarily inverted to attain the seismic velocities beneath a seismic station. Surface wave dispersion data are often added to reduce the effect of the non-uniqueness. The combination of P receiver function and surface wave works well in resolving the structures in the crust and uppermost mantle, but is less effective in characterizing greater (lithosphere and asthenosphere) depths due to the interference from crustal multiples. A solution to this problem is jointly to model teleseismic S receiver functions with surface wave and P receiver functions. This study adopts a fast, one-dimensional (1-D) inversion scheme. To avoid the effect of multidimensional structures away from the seismic station, we eliminate multiples that reverberate between the surface and interfaces below a restriction depth (RD), as well as S-to-P conversions below an inversion depth (ID). P-to-S conversions off the interfaces above the half-space and S-to-P conversions above the ID and multiples above the RD are properly modelled. This approach favours ray paths travelling close to stations and is, therefore, more suitable for 1-D inversions. We perform numerical experiments with and without noise and highlight the advantages of a joint receiver function and surface wave analysis.