Models of density and mechanical <Emphasis Type="Italic">Q</Emphasis>-factor distributions according to new data on the nutations and free oscillations of the Earth: 2. Comparison with astrometric data

In the first part of the paper [Molodenskii, 2011], we considered the problem of ambiguity in the solution of the inverse problem of retrieval of density distribution in the Earth’s core and mantle and determination of the Q factors in the mantle from the entire set of modern data on seismic velocities (V _p and V _S ), the frequencies f _i and quality factors Q _i of free oscillations of the Earth, and the amplitudes and phases of its forced nutations. We have constructed the model distributions of these parameters, in which the root-meansquared (rms) deviations of all observed values from the predicted ones are much smaller than in the PREM model. Below, we compare the observed amplitudes of the forced nutation with the values predicted by our model. In order to understand how rigid are the constraints imposed by the amplitudes of forced nutation, we not only calculate the deviations of the observed amplitudes of nutation from the predictions by our model but also estimate the changes in these deviations caused by small variations in several parameters of the model. To the parameters to be varied we refer those which have no or barely any effect on the periods and damping constants of free oscillations but have a pronounced effect on the amplitudes of forced nutation. These parameters include (1) the rheological properties of the mantle in the interval of periods from an hour to a day; (2) the dynamical flattening of the liquid core; (3) the dynamic flattening of the solid inner core; (4) the viscosity of the liquid core; and (5) the moment of inertia of the solid inner core. In addition, we estimate the effects of variations in the moment of inertia of the liquid core to be small (±0.2%) and not to affect, within the observation error, the periods of free oscillations. We show that the uncertainty in the model depth distributions of density considerably decreases when the new data on the amplitudes and phases of the forced nutation of the Earth are taken into account. With these data, it is possible to estimate the creep function for the lower mantle in a wide range of periods from a second to a day.     

The density and Q-factor models based on the new data on the nutations and overtones of the free oscillations of the earth: 2. The results of the numerical modeling of the solution of the inverse problem

In the first part of the paper, we obtained the refined estimates for the periods and Q-factors of the fundamental modes and overtones of spherical and toroidal oscillations with periods longer than 3 min from the data on the free oscillations of the Earth, which were excited by the earthquakes with magnitude 9 that occurred in Sumatra, Japan, and the Sea of Okhotsk. In (Molodenskii et al., 2013), we analyzed the limits of the admissible density distributions in the mantle and liquid core of the Earth, using the data on the amplitudes and phases of the forced nutations, as well as the periods and attenuation factors of the fundamental modes of the free spheroidal and toroidal oscillations of the Earth. These studies were conducted with the fixed values of the total mass and total moment of inertia of the Earth and the fixed distributions of the body seismic waves in the mantle and in the core. The solution was obtained by orthogonalizing the kernels of the integral equations that link the residuals of the observed frequencies and attenuation factors of the free oscillations, as well as the amplitudes and phases of the forced nutations, with the sought densities and Q-factors of the mantle and liquid core. Below, we present the solution of the same problem with allowance for the results obtained in the first part of this paper, namely, the new data on the periods and attenuation factors of the fundamental modes of free oscillations of the Earth and on the periods of the first four overtones of the free spheroidal and toroidal oscillations. Despite the involvement of the new data on the overtones, which have not been considered in our calculations, the weighted root mean square deviations of the theoretical predictions from the observed periods and attenuation factors of the free oscillations, as well as the amplitudes and phases of the forced nutations, have significantly decreased. This is due to (1) the noticeable reduction of the real errors in estimating the parameters of the free oscillations described in the first part of the paper and (2) the inclusion of the quantities determining the depth- and frequency dependences of the Q-factor in the mantle in the set of the independently varied parameters.     

The density and Q-factor models based on the new data on the nutations and overtones of the free oscillations of the earth: 1. The analysis of the new GSN data for the Sumatra,Tohoku, and Okhotsk earthquakes

We discuss the problem of the ambiguity of gravity inversion, i.e., finding the depth distribution of density and the depth and frequency dependences of the Q-factor from the entire set of the present-day seismic and astrometric data on the travel times of seismic waves, the periods and attenuation factors of the free oscillations of the Earth, as well as the amplitudes and phases of the forced nutations. In the first part of the paper, we present the new and more accurate determinations of the periods and Q-factors for the fundamental tones and overtones of the spheroidal and toroidal oscillations of the Earth, which have periods longer than 3 min. These determinations are based on analyzing the signals from the Sumatra, Tohoku, and Okhotsk earthquakes of magnitude 9, which were recorded by the stations of the Global Seismographic Network (GSN) in Obninsk and Kazakhstan. It is shown that, although the Okhotsk earthquake had a lower magnitude than the other quakes analyzed (since its seismic source was extremely deep (about 600 km)), the amplitudes of the overtones excited by this event are significantly higher than the amplitudes of the overtones caused by the Sumatra and Tohoku events of magnitude 9. Moreover, the amplitudes of the overtones from the Okhotsk earthquake exceed the amplitudes of the overtones of the free oscillations caused by the other seismic events of magnitude 9 that occurred in the second half of the 20th century. Due to this, the data on the Okhotsk Sea earthquake are of utmost importance for the solution of the inverse problems of reconstructing the vertical profiles of Q-factor in the ultra-low frequency (ULF) range and for reconstructing the vertical distribution of density. Based on the new empirical data, we obtained new and more accurate estimates for the periods and attenuation factors of the free oscillations of the Earth.     

On the admissible range for the mass and inertia moments of the liquid core: I. Solving the inverse problem of nutations and free oscillations of the Earth by decomposition of mechanical parameters in an orthogonalized basis

The results of solving the inverse problem of forced nutations and free oscillations of the Earth by decomposing the Q-factor and small depth variations in density in a system of orthogonal functions are considered. These functions are determined by orthogonalization of the functional derivatives of the observed parameters with respect to the depth distributions of the sought parameters (assuming there are no distributions of the velocities of body seismic waves V _p and V _S with depth and unchanged total mass M and inertia moments I of the Earth). The examples are presented to illustrate the numerical solution of the inverse problem on finding the density distributions in the mantle and core of the Earth using orthogonalization of the integral constraints for the probable depth distributions of density describing the conditions of unchanged M and I, as well as the constraints posed by the data on the periods of the free low-order oscillations of the Earth.     

Magnetic field variations and spatial configurations of long-period sunspot oscillations according to the SOHO data

The phenomenon of long-period sunspot oscillations with periods from several tens to a thousand minutes is studied using data on the magnetic field strength and sunspot coordinates obtained based on the SOHO MDI data. It has been indicated that oscillations of the sunspot magnetic field strength are related to relative and absolute horizontal oscillation modes, as a result of which certain limitations are imposed on the interpretation of the phenomenon.     

Specific features of long-period oscillations of sunspots and photosphere according to the MDI (SOHO) data

Long-period oscillations of the magnetic field and the line-of-sight velocity have been detected in sunspots based on the synchronous 90-h time series of magnetograms and dopplergrams obtained with the MDI(SOHO) device. The sunspot eigenmode (12–30 h), the periods of which nonlinearly depend on the magnetic field strength, predominates in the magnetic field oscillation spectrum. The mode, which is probably induced by motions of supergranulation cells (33 h), predominates in the sunspot line-of-sight velocity oscillation spectrum. A strong mode (33 h), which indicates that long-period quasi-oscillations of supergranulation exist, was also detected in the velocity power spectrum for a quiet photosphere, together with the known 5-min mode.     

The admissible interval for the Q factor in the solid inner core: Constraints from new data on the nutation and free oscillations of the earth

The models of the mechanical Q factor of the inner solid core of the Earth are reconstructed from the amplitudes and phases of forced nutation and the periods and damping constants of the high-order overtones of free radial modes. The admissible range of the Q-factor in the solid core is estimated and the stability of the obtained distributions is analyzed. The real accuracy of the obtained model distributions is estimated on the basis of the previous conclusions concerning the uncertainty in the solution of the inverse problem of reconstructing the internal structure of the Earth in the low-frequency range.     

Field-aligned currents of zones 1 and 2 in the magnetosphere according to the experimental data

The discrepancy between the model and measured magnetic fields, which can be described by the contribution of field-aligned currents, has been determined. The division of the initial data array into the individual data sets with different IMF values makes it possible to estimate the dependence of field-aligned currents on IMF.     

Check of Earth’s free oscillations excited by Sumatra-Andaman Large Earthquake and discussions on the anisotropy of inner core

Sumatra-Andaman Large Earthquake on Dec. 26, 2004 generated not only the Indian Ocean Tsunami but also the Earth’s free oscillations (EFO). The signals of Earth’s free oscillations were perfectly recorded by the superconducting gravimeter C0-32 at Wuhan station in China. After the pre-treatment and spectral analysis on the observational data from Wuhan station, we obtained more than ninety EFO modes including 42 fundamental modes, 2 radial modes and 49 harmonic modes. On the basis of the discussions on some observed harmonic modes and abnormal splitting phenomena, we considered that the real rigidity might be lower than the theoretical prediction of PREM model in the inner core and however the anisotropy of compressive wave was brightly higher than the present estimations in the inner core. This suggested that the anisotropy of the inner core could be much more complicated than our present understanding, and there might be some new geophysical phenomena in the formation process of the inner core. Supported jointly by the National Natural Science Foundation of China (Grant Nos. 40404005 and 40374029) and the Excellent Prize of President Scholarship and Hundred Talents Program of the Chinese Academy of Sciences     

Wave emission during a plasma density jump in the auroral zone of the topside ionosphere according to the APEX satellite data

The intensity of the wave emission in the 0.1–10 MHz band measured in the ionosphere (the APEX satellite experiment) has been presented. A jump of the plasma density and an increase in the emission intensity at a plasma frequency have been registered at altitudes of ～1300 km in the topside auroral ionosphere. The emission intensity in the whistler-mode band nonmonotonically increased along the satellite trajectory near the plasma jump wall. It has been indicated that waveguides could be formed near the wall during damping of electrostatic oscillations generated by precipitating electron fluxes. A spatially nonmonotonous separation of waveguides from the plasma inhomogeneity stretched along geomagnetic field lines is possible in this case.     

Long-term solar cycles according to data on the cosmogenic beryllium concentration in ice of central Greenland

Data on the concentrations of the cosmogenic ¹⁰Be isotope and Na⁺ and Ca²⁺ ions, as well as on ice accumulation rates in central Greenland, obtained by the GISP2 collaboration were studied in a time interval spanning about 40 000 recent years. Joint analysis of the indicated glacial and chemical paleoseries demonstrated that in a period from 12 008 to 24 008 years ago, the ¹⁰Be flux variations were most free of influence of climate and changes in the geomagnetic dipole moment. As a consequence, this time interval is most suitable for studying periodicities of purely solar nature. Statistical analysis of the ¹⁰Be flux data has revealed significant variations with periods of 500–800 years and 1300–1600 years in the time interval from 12 008 to 17 008 years ago. This evidence favors the existence of the appropriate cycles of solar activity in the mentioned epoch. Similar periodicities are also revealed in the time interval from 3288 to 8008 years ago.     

Geochemical constraints on the model of the composition and thermal conditions of the Moon according to seismic data

A new method of reconstruction of the temperature profile in the lunar mantle from the velocities of seismic P- and S-waves for different models of chemical composition is developed. The procedure of the solution of an inverse problem is realized with the help of the minimization of the Gibbs free energy and the equations of state of a mantle substance, taking into account phase transformations, anharmonicity, and the effects of inelasticity. The geophysical and geochemical constraints on composition and temperature distribution in Moon’s mantle are established. The upper mantle can be composed of olivine pyroxenite, depleted by low-volatile oxides (∼2 wt % of CaO and Al₂O₃). On the contrary, the lower mantle must be enriched by low-volatile oxides (∼4–6 wt % of CaO and Al₂O₃). Its composition can be represented by a mineral association of the olivine + clinopyroxene + garnet or olivine + orthopyroxene + clinopyroxene + garnet type, which is close in composition to pyrolite. The temperature distribution at depths 50–1000 km are approximated by the equation: T(°C) = 351 + 1718[1–exp (−0.00082H)]. The constraints inferred make it possible to conclude that the published values of the velocities of P- and S-waves for the lunar mantle, obtained by processing the data of seismic experiments of the Apollo lunar mission are inconsistent with each other at depths below 300 km. Otherwise, the variations in the velocities of P- and S-waves disturb the symmetry between the petrological model (composition), the temperature profile, and the seismic profile.     

Analysis of Turkish precipitation data: homogeneity and the Southern Oscillation forcings on frequency distributions

The homogeneity of newly compiled 212 precipitation records in Turkey for the period 1973‐2002 was checked by the Standard Normal Homogeneity Test (SNHT) and Pettitt Test. Stations were considered inhomogeneous if at least one of the tests rejects the homogeneity. As a result, 43 out of 212 stations were found to be inhomogeneous. In addition, the previously detected Southern Oscillation (SO)‐related precipitation anomalies by the authors were quantified at each station using the gamma distribution. The observed SO‐related shifts in the median precipitation amounts expressed as gamma percentiles may be considered as a typical SO response of that station. The results of this study confirm the wet responses of Turkish precipitations to El Nino events, whereas those for La Nina events seem to be masked by sampling variations within the study period. Copyright © 2007 John Wiley & Sons, Ltd.     

Estimation of the deep density distribution in the lithosphere of central and Southern Asia using data about free mantle surface depth

The results of the selection of a model of the deep density distribution in the lithosphere of Central and Southern Asia, which explains the previously revealed dependence of the free mantle surface depth on the thickness of the crust [Artemjev, 1975], are described. It is shown that this dependence can be caused by variations in the mantle’s density with depth. Models of the continental and oceanic mantles with an increase in the linear density over depth are selected for the region of Asia. The level of the free surface depth in the oceanic mantle is higher than in the continental mantle. The observed dependence on the crustal thickness can also be used for determining nonlinear density variations with depth under the assumption that lateral density variations in this dependence are of a random character.     

On the dynamics and structure of Earth’s oscillations in December 2004 from seismic gravimeter observations in St. Petersburg

The paper describes phenomena of large-scale deformations, in particular, long-term deformation, observed on the planet during December 1–12, 2004, before a cycle of enhanced seismic activity. The spectrum of seismic vibrations with periods of 1 to 9 hr is calculated. A high correlation is established between the frequency distribution of significant vibrations recognizable in this spectrum and vibrations that should be excited most frequently in accordance with the statistical spectrum of the seismogravitational oscillations of the Earth.     

Relationship between the aerosol concentration in the stratosphere and ionization according to the data on conductivity and nitrate content of Greenland ice

This paper studies the data on the conductivity and concentration of nitrates (ions) in an ice core from central Greenland obtained with high time resolution. The performed analysis indicates that the abrupt increase in the concentration of sulfate aerosols in the stratosphere due to additional ionization resulted from precipitation of solar cosmic ray energetic particles is one of the main factors that cause simultaneous origination of powerful peaks in the nitrate conductivity and concentration. Thus, coincidences of peaks in both studied paleoseries are manifestations of the effect that has been experimentally registered with lidar and satellite equipment for the last 25 years. This demonstrates that the relationship between the aerosol concentration and the ionization rate in the stratosphere is real and makes it possible to expand the interval where this relationship exists to more than 200 years. The possible physical mechanisms of the observed phenomenon are discussed.     

Irregularities in unstable plasma of the upper atmosphere according to the data of sounding on board the Intercosmos-19 satellite

The profiles of the plasma density in the topside ionosphere, according to the data of sounding on board the Intercosmos-19 satellite, are presented. It is shown that the large-scale fluctuations of the plasma density can be related to the propagation and attenuation of the atmospheric waves (e.g., acoustic gravity waves) in the dynamo region of the ionosphere. In the topside ionosphere, suprathermal particle fluxes can be formed and the plasma density can be modulated at an attenuation of small-scale electrostatic fluctuations of the plasma electron component in plasma pits. Plasma vortices can be formed when polarization fluxes of charged particles escape from regions of heating. The vortex field imparts stability to the inhomogeneous plasma structure, necessary for experimental detection of this structure.