Home – Home – Jornals – Russian Geology and Geophysics 2018 number 8

Geological, geochemical, and isotope (Sr, Nd, and O) parameters of Early Devonian (405 Ma) volcanics of southeastern Gorny Altai (Aksai and Kalguty volcanotectonic structures) are discussed. The studied igneous rock association comprises magnesian andesitoids, Nb-enriched basaltic andesites, and A-type peraluminous silicic rocks (dacites, rhyolites, granites, and leucogranites). Magnesian andesitoids (mg# > 50) are characterized by a predominance of Na among alkalies (K2O/Na2O ≈ 0.1-0.7), medium contents of TiO2 (~0.8-1.3 wt.%) and Al2O3 (~12-15 wt.%), enrichment in Cr (up to 216 ppm), and low Sr/Y ratios (4-15). The Nb-enriched (Nb = 10-17 ppm) basaltic andesites have high contents of TiO2 (1.7-2.7 wt.%) and P2O5 (0.4-1.4 wt.). The A-type granitoids are characterized by high contents of K (K2O/Na2O ≤ 60) and alumina (ASI ≤ 2.9) and depletion in Ba, Sr, P, and Ti. The magnesian andesitoids and Nb-enriched basaltic andesites are products of melts generated in the metasomatized lithospheric mantle; silicic magmas formed through the melting of Cambrian-Ordovician metaturbidites of the Gorny Altai Group and, partly, Early-Middle Cambrian island-arc metabasites. The above rock association might have resulted from a plume impact on the lithospheric substrates of the continental paleo-margin during the evolution of the Altai-Sayan rift system.

Precisional analyses of the abundances of La, Ce, and major elements in thermal waters and rocks of the Uzon-Geyzernaya volcanotectonic depression, supplemented by published data on a number of modern high-temperature hydrothermal systems of Kamchatka and two other areas of the world, allowed defining genetically important patterns of rare-earth elements (REE) distribution. The La and Ce abundances positively correlate with silica contents both in fresh igneous rocks of the study areas and in the products formed by hydrothermal processes. All studied hydrothermal clays are enriched in La and Ce. The general enrichment trend is similar to the pattern of positive correlation between the La and Ce abundances. Geothermal waters display a strong relationship between REE enrichment and pH. Enhanced REE enrichment trend is observed in thermal waters with abundant SO₄^2- and K. The REE versus Cl and B diagrams show two individual fields reflecting the level of acidity-alkalinity of thermal waters. These data demonstrate that La and Ce concentrations in the products of modern hydrothermal systems (in fluids and secondary mineral phases) are governed by wallrock composition, anionic water composition, and pH/Eh-dependent adsorption processes.

In the alluvial deposits of the Prizhlimny Creek (southern part of the Koryak Highland), grains of platinum-group minerals are found along with gold. We have established that the grains are native platinum (Pt, Fe) containing Cu (up to 5 wt.%), Os (up to 8 wt.%), and Rh (up to 2 wt.%). Inclusions in the platinum are native osmium (the content of Ir impurity reaches 12 wt.%, the average content being 0.2-4 wt.%), an unnamed intermetallic compound of composition PtRh, sulfides and arsenides of PGE (cooperite, laurite, malanite, cuproiridsite, cuprorhodsite, sperrylite, hollingworthite, unnamed compounds PdS, (Ir,Ru)S2, (Ir,Pt)S2), Cu, and Fe (bornite, chalcopyrite), chromite, and Cr-magnetite. Replacement of native-osmium crystals by compound IrO2 is described. It has been established that this compound formed during oxidation accompanied by the replacement of isoferroplatinum by native platinum. The data obtained agree with the results of study of platinum-group mineral assemblages from placers localized in weakly eroded Ural-Alaskan-type massifs whose apical parts formed under high oxygen activity conditions. Clinopyroxenites of the Prizhimny massif are considered to be the potential source of PGE.

The source of sulfur in giant Norilsk-type sulfide deposits is discussed. A review of the state of the problem and a critical analysis of existing hypotheses are made. The distribution of δ³⁴S in sulfides of ore occurrences and small and large deposits and in normal sedimentary, metamorphogenic, and hypogene sulfates is considered. A large number of new δ³⁴S data for sulfides and sulfates in various deposits, volcanic and terrigenous rocks, coals, graphites, and metasomatites are presented. The main attention is focused on the objects of the Norilsk and Kureika ore districts. The δ³⁴S value varies from -14 to +22.5‰ in sulfides of rocks and ores and from 15.3 to 33‰ in anhydrites. In sulfide-sulfate intergrowths and assemblages, δ³⁴S is within 4.2-14.6‰ in sulfides and within 15.3-21.3‰ in anhydrites. The most isotopically heavy sulfur was found in pyrrhotite veins in basalts (δ³⁴S = 21.6‰), in sulfate veins cutting dolomites (δ³⁴S = 33‰), and in subsidence caldera sulfates in basalts (δ³⁴S = 23.2-25.2‰). Sulfide ores of the Tsentral’naya Shilki intrusion have a heavy sulfur isotope composition (δ³⁴S = 17.7‰ ( n = 15)). Thermobarogeochemical studies of anhydrites have revealed inclusions of different types with homogenization temperatures ranging from 685ºC to 80ºC. Metamorphogenic and hypogene anhydrites are associated with a carbonaceous substance, and hypogene anhydrites have inclusions of chloride-containing salt melts. We assume that sulfur in the trap sulfide deposits was introduced with sulfates of sedimentary rocks (δ³⁴S = 22-24‰). No assimilation of sulfates by basaltic melt took place. The sedimentary anhydrites were “steamed” by hydrocarbons, which led to sulfate reduction and δ³⁴S fractionation. As a result, isotopically light sulfur accumulated in sulfides and hydrogen sulfide, isotopically heavy sulfur was removed by aqueous calcium sulfate solution, and “residual” metamorphogenic anhydrite acquired a lighter sulfur isotope composition as compared with the sedimentary one. The wide variations in δ³⁴S in sulfides and sulfates are due to changes in the physicochemical parameters of the ore-forming system (first of all, temperature and P _CH4) during the sulfate reduction. The regional hydrocarbon resources were sufficient for large-scale ore formation.

Results of this study of titanite samples collected from silicate rocks and apatite-nepheline-(sphene) ores from Paleozoic polyphase alkaline nepheline syenite complexes of the Khibiny and Lovozero massifs revealed the possibility of their in-situ U-Pb dating using sensitive high-resolution ion microprobe SHRIMP-II with an accuracy of 1.0-1.5%, which is comparable with that of U-Pb zircon analysis. Employing different approaches to age determination of the formation of the U-Pb system of titanites, the combined isochrons and mixing lines were plotted from the data obtained from the differentiated complex samples (121 analyses of five Khibiny samples and 52 analyses of one Lovozero sample) and apatite-nepheline ores (120 analyses of five Khibiny samples and 88 analyses of three Lovozero samples). They indicate synchronous crystallization of titanite in silicate rocks throughout the complexes: 374.1 ± 3.7 Ma for the Khibiny massif and 380.9 ± 4.5 Ma for the Lovozero massif, and attest to the later formation of phosphate-rare-metal ores: 371.0 ± 4.2 and 361.4 ± 3.2 Ma, respectively. The relatively delayed ore mineralization specific to the Lovozero massif can be accounted for the significantly lower volumes of magmatic melt and ore fluid involved, different thermal conditions, and the pattern of the investigated mineralization. As such, the obtained U-Pb data from titanite make it possible to limit significantly the time interval (most likely, not exceeding 15-20 Ma) comprising the evolution and activity of the ore-magmatic system of major agpaitic complexes, which is probably associated with plume magmatism.

Homologous series of alkenes and dimethylalkanes mostly with the odd or even number of carbon atoms in the molecule have been identified in chloroform extracts from the organic matter of the Upper Paleozoic deposits of the Vilyui syneclise, penetrated by the superdeep well SV-27 at depths below 5 km. It is assumed that these unusual hydrocarbons resulted from the destruction of asphaltene occlusions under severe P-T conditions at great depths and that the hydrocarbon generation began in the zone of postdiagenetic transformations of sediments. This hypothesis was tested in the sections of deposits whose organic matter underwent catagenesis of different grades. On the basis of these results, zones of emergence, transition, and destruction of occlusions have been recognized.

The Eldorado low-sulfide gold-quartz deposit, with gold reserves of more than 60 tons, is located in the damage zone of the Ishimba Fault in the Yenisei Ridge and is hosted by Riphean epidote-amphibolite metamorphic rocks (Sukhoi Pit Group). Orebodies occur in four roughly parallel heavily fractured zones where rocks were subject to metamorphism under stress and heat impacts. They consist of sulfide-bearing schists with veins of gray or milky-white quartz varieties. Gray quartz predominating in gold-bearing orebodies contains graphite and amorphous carbon identified by Raman spectroscopy; the contents of gold and amorphous carbon are in positive correlation. As inferred from thermobarometry, gas chromatography, gas chromatography-mass spectrometry, and Raman spectroscopy of fluid inclusions in sulfides, carbonates, and gray and white quartz, gold mineralization formed under the effect of reduced H2O-CO2-HC fluids with temperatures of 180 to 490 °C, salinity of 9 to 22 wt.% NaCl eq, and pressures of 0.1 to 2.3 kbar. Judging by the presence of 11% mantle helium (3He) in fluid inclusions from quartz and the sulfur isotope composition (7.1-17.4 ‰ δ34S) of sulfides, ore-bearing fluids ascended from a mantle source along shear zones, where they «boiled». While the fluids were ascending, the metalliferous S- and N-bearing hydrocarbon (HC) compounds they carried broke down to produce crystalline sulfides, gold, and disseminated graphite and amorphous carbon (the latter imparts the gray color to quartz). Barren veins of milky-white quartz formed from oxidized mainly aqueous fluids with a salinity of <15 wt.% NaCl eq at 150-350 ºC. Chloride brines (>30 wt.% NaCl eq) at 150-260 ºC impregnated the gold-bearing quartz veins and produced the lower strata of the hydrothermal-granitoid section. The gold mineralization (795-710 Ma) was roughly coeval to local high-temperature stress metamorphism (836-745 Ma) and intrusion of the Kalama multiphase complex (880-752 Ma).

Scintillation arc atomic-emission spectrometry (SAES) is used to study noble metals (NM), including Au, Ag, Pt, Pd, Ir, Os, Rh, and Ru, in black shales of the Sukhoi Log gold deposit (Irkutsk Region, Russia), with a focus on total NM contents in samples and on the compositions and sizes of NM-bearing particles. The estimated sizes of gold particles and their distribution are confirmed by results of scanning electron microscopy combined with energy dispersive X -ray microanalysis (SEM-EDX). The SAES results are in satisfactory agreement with earlier SEM-EDX data on NM species but reveal a much greater number and diversity of element associations.

The Rudny Altai and Gorny Altai regions had different geologic histories and differ in metallogenic patterns. The Vendian-Early Cambrian to Permian-Triassic multistage evolution of Gorny Altai included subduction, accretion-collision, and rifting events accompanied by magmatism and related mineralization. Metallogeny evolved in discrete pulses, with especially abundant Late Paleozoic-earliest Mesozoic mineralization. The Devonian-Carboniferous pulse produced diverse mineral deposits (iron, mercury, gold, silver, molybdenum, tungsten, cobalt, complex ores, and rare earths), some of considerable economic value. The territory of Gorny Altai includes several large ore districts that belong to different zones. They are the Beloretsk-Kholzun iron district in the west, the Kayancha-Sinyukha fluorine-gold district in the northeast, the Kurai gold-mercury and Yustyd rare-metal-silver districts in the southeast, and the Kalguty rare-metal-tungsten and Ulandryk U-REE-Cu districts in the south. The largest mineral deposits are Kholzun (Fe, P2O5), Karakul (Co, Bi), Sinyukha (Au), Aktash and Chagan-Uzun (Hg), Ozernoe and Pogranichnoe (Ag), Kalguty (Mo, W), Alakha (Li, Ta), Rudnyi Log (Y,Fe-specularite), and Urzarsai (W-scheelite). Mineralization in Rudny Altai is mainly pyritic: copper-pyrite, pyrite-complex ore, and barite-complex ore. It resides in suprasubduction basalts and rhyolites and in Emsian to Frasnian island-arc volcanics at different stratigraphic levels of Devonian volcanosedimentary sequences in six ore districts. The Kurchum high-grade metamorphic block hosts copper-pyrite and gold-quartz mineralization related to Late Paleozoic-Early Mesozoic volcanism.

An algorithm for estimating the node coordinates of deformed lattices of quasiperiodic textures with subpixel accuracy is proposed. The algorithm consists of two steps. In the first step, the vectors of the frequencies and initial phases of a polyharmonic brightness function model are calculated from the characteristics of spectral outliers of image fragments. The obtained estimates are used to determine the coordinates of the nodes of local lattices. In the second stage, the local lattices are combined into a global lattice for the entire image of the quasi-periodic texture. Using high-accuracy estimates of model parameters from small image fragments ensures stable operation of the algorithm for significant deformations of the lattice and sub-pixel accuracy in estimating the coordinates of its nodes. Results of computer simulation and processing of real halftone images of quasiperiodic textures are given demonstrating the effectiveness of the proposed algorithm.

The errors of estimates of the size, depth, and magnetization of a local source of a simply shaped magnetic anomaly are studied by means of a comprehensive analysis of the magnetic survey performed at different altitudes. Numerical simulations show that the values of magnetic induction induced by the presence of a magnetic source measured at different altitudes provide a more accurate estimate of some parameters of this source than the measurements performed at one altitude.

This paper touches upon the problem of a compact polygonal description of objects. A method of lossless compression of geometric data based on perturbation functions is proposed. Advantages of this approach over the known algorithms of transformation of three-dimensional models for fast transmission of information and its compact storage are demonstrated.

A selective segmentation method is developed that correctly recovers the boundaries of an object in the plan and estimates the depth range of its location. This method assumes the processing of electrical profiling data: shallow electrical profiling and vector patterns of dominant directions of changes in the medium resistance. The boundary of the object is estimated on the basis of using a fuzzy c-means clustering algorithm, adapted to analyze the multidimensional electrical profiling data. The depth range of the object location in the soil is estimated on the basis of using the scalar product function with respect to the vector patterns of dominant directions, adjacent in depth. The effectiveness of the method is confirmed by the computer simulation results and the example of processing of the full-scale experiment on an archaeological site, which is a medieval fortified settlement.

This paper describes the concept and methods of space-time processing of radio images of small objects in a multi-position system of radiometers, which make it possible to increase the performance of this system. The spatial processing is carried out in each overlook cycle of scanning radiometers in order to determine the spatial coordinates of objects and mutual orientation of coordinate systems. The time processing is carried out in a sequence of overlook cycles of radiometers for determining the trajectory parameters of the objects that change mutual positions.

When it comes to a two-position system detecting the amplitude and difference of instances at which a wave arrives at receiving positions, there is a new method for determining the range and location of radiation sources. This paper presents equations that make it possible to study the procedural error and accuracy characteristics of the method for various observation conditions and the results of a computational experiment. Recommendations on the application of the method are given.

A model of simultaneous tonal masking that isolates speech signal components perceived by a human's auditory system is under study. An algorithm of simultaneous masking on the basis of this model. It is shown that, after simultaneous masking, a signal is represented by a binary structure reflecting the harmonic structure of a vocalized sequence. It is experimentally proved that this structure can be used to isolate key (in terms of perception of the auditory system) speech sections. This structure serves as a basis for the algorithm of high-quality speech signal division into vocalized and unvocalized sections, which does not require training before use. According to the results of testing of the joint use of algorithms for simultaneous masking and division of speech signals, the quality of their performance is obtained.

This paper proposes and theoretically justifies a method for noncontact operational measurement of specific electric conductivity and dielectric and magnetic permeabilities of materials via pulse sensing of the controlled surface. An electromagnetic pulse reflected from a controlled object carries information in its spectral composition about measured parameters that can be calculated by the proposed technique.

A tunable (in terms of the angle of convergence of intersecting light beams) two-beam interferometer with fixed mirrors and a fixed photosensitive element is considered. The photosensitive element is based on a symmetric beam-splitter block where tuning of the interference pattern period is ensured by only one type of motion: interferometer rotation with respect to the motionless source of the collimating light beam. It is demonstrated that the period can be controlled in this way for convergence angles from 30 to 180º; the beam diameter should be at least 10 % of the beam-splitter block length. In this region, the greatest width of the range of convergence angle tuning can exceed 40º, and the admissible beam diameter approaches 40 % of the beam-splitter block length. Comparisons with a similar interferometer based on a beam-splitter cube are performed, and possible areas of application of the considered interferometer are determined.

This paper presents the results of development and investigation of compact waveguide electro-optical modulators using original synthesized chromophore-containing polyimides with covalently attached commercial DR-13 dye. Fully polymer electro-optical planar structures with phase-polarization and amplitude modulators in the form of a Mach - Zehnder interferometer were developed and implemented. The characteristics of the developed modulators at a wavelength of 1.3 μm were investigated, and a half-wave voltage of 24 B for the active part of the modulator 1.3 cm long was achieved.

A method used for calibration of scanning modules on the basis of galvanometric deflectors is considered. The method is based on an iterative two-step algorithm of processing of the profilometry map of the test recording of the calibrated module. It is demonstrated that high accuracy and robustness of determining the coordinates of the reference points of the test recording can be obtained by means of finding the approximate positions of such points and identifying the fragment in the vicinity of these points at the first step and searching for the exact values of the coordinates by the correlation method at the second step. The use of this method and a simple algorithm of piecewise-planar interpolation offers a possibility of laser beam positioning with a relative error of 10^-5 from the recording field.

An experimental structure of an optoelectronic system for contactless measurements of micro- and nanodisplacements of moving MEMS elements is considered.The system is based on a heterodyne interferometer with a frequency-stabilized He-Ne laser and an acousto-optical modulator of laser radiation. A resolution of less than 1 nm in terms of the moving element displacement is reached in experiments by applying voltage pulses with amplitudes up to 1 V on the MEMS structure; moreover, the displacement amplitude is found to be a linear function of the control voltage with sensitivity of 100-200 nm/V. No hysteresis is observed on the curve plotted in the coordinates of the element location and control voltage.

The photoextraction of rubidium atoms from the volume of a photonic crystal has been investigated. It has been found that in the case of crystal irradiation in the stop zone where the desorbing light does not penetrate deeply, the separation of atoms occurs practically from its surface, so that the density of desorbed atoms in the cell decreases only exponentially. In the case of irradiation of the crystal outside the stop zone, the volume of the crystal is irradiated almost completely. In this connection, the exponential decrease in the density of atoms in the cell is replaced by its relatively slow reduction of diffusion nature. The volume diffusion coefficient rubidium atoms in the photonic crystal was measured to be 2 x 10^-8 sm²/s.

Channels with and without memory in the simplest Gaussian noise distribution model are compared. It is shown that both channels have similar dependences of the capacity on the average signal power. At the same time, the optimal input alphabet for the channel with memory changes. The applicability of the model with nonlinear memory to the QPSK communication line with a periodic dispersion compensation is demonstrated numerically.

The formation and dynamics of excitations in an atomic or molecular nano chain of a helical shape is studied. The dipole-dipole interaction of the circular polarizations of optical transitions of neighboring molecules is taken into account. The derived Bloch equations are solved in a continuum approximation using the Frenet - Serret coordinate system. Solutions that describe the formation of stable localized structures, solitons, due to the curvature of the chain, which can have a critical influence on the luminescent properties of the chiral medium.

The results of the astroclimate characteristics measurements in the Special Astrophysical Observatory of RAS (SAO, North Caucasus) in 2012 and 2016 are presented. The experimental results are obtained from long-term observation series of the day and night astroclimate in SAO. The presence of non-Kolmogorov coherent turbulence was detected over SAO territory, in which the quality of telescope images improves. The influence of an underlying surface type and a wind speed direction on the formation mode of coherent turbulence is explained. It was found that the causes for coherent turbulence formation are the mountainous terrain and the uneven heating of underlying surface. The airflow velocity distribution inside the dome room of the Big Telescope Alt-azimuth (BTA) had been experimentally researched. Numerical simulation of the air mass motions inside the BTA dome room had been performed to analyze the influence of a temperature regime and a form of constructions. The solutions of the boundary value problem confirm the existence of the experimentally registered vortex structure with a vertical rotation axis. The causes for its formation are the temperature gradients of the dome surfaces.

A new complex for spectrometric measurements of atmospheric anthropogenic emissions is presented, which has been designed and is used for the study of optical characteristics of anthropogenic sols. The derived spectral dependences of effective absorption, scattering, radiation attenuation cross sections are used to retrieve the microstructure of anthropogenic sols and to detect the influence of the relative humidity of the radiation propagation medium on the optical characteristics of its dispersed phase. Atmospheric emissions of combustion products of wood, power enterprises, air carriers, and products of thermal decomposition of asbestos-cement plates during their calcination are analyzed.

The results of measurements of the light-scattering phase function in the tropical Atlantic are represented. The parameters of the scattering functions in water of the principal large-scale tropical currents are presented. The relations of the scattering function asymmetry coefficient with the total scattering coefficient and the total scattering coefficient with the beam attenuation coefficient are established.

We discuss the results of comparison of the average physical-chemical aerosol characteristics in the neighboring regions: in the Arctic settlement Barentsburg (Spitsbergen Archipelago) and over the Barents Sea. A small (less than 0.02) excess of the atmospheric aerosol optical depth in the island area over the maritime region is noted. The aerosol microphysical characteristics differ stronger in the near-ground layer: the black carbon concentrations are (a factor of 4) larger in Barentsburg, and particle concentrations are (a factor of 2.4) larger over sea. The absolute concentrations of ions in the atmosphere of Barentsburg are several-fold smaller than over sea. However, with respect to the relative content, Na⁺, Cl^- and NH₄⁺, SO₄^2- ions predominate in both regions, indicating equivalent contributions of continental and maritime sources.

The paper describes the creation and use of a geoinformation system (GIS) for long-term monitoring of agricultural development of a territory using the Lake Baikal basin as an example. The functional structure of GIS consists of measuring, information, technological, and analytical subsystems. The analysis results of retrospective maps as the main documents for the long-term metric assessment of the nature use dynamics are given. A technique for geometric correction of the retrospective maps on the modern topographic basis is described. A methodology for creating and using cartographic information resources for environmental monitoring is developed. A practical example of monitoring results in the form of a map of the arable land dynamics in the XX century is presented.

The investigation in spatiotemporal variability of ocean-atmosphere heat fluxes in the area of the Barents Sea was carried out over the period 1976-2014. Seasonal changes in the sea ice cover in the Arctic sector of Siberia was also derived. Sea ice area reduction during last decades in the Arctic basin corresponds to sea surface temperature increase, in contrast to which sensible and latent heat fluxes decrease, which was the most pronounced in January. The most intensive changes in ocean-atmosphere heat exchange in the sea under study were indicated during last several years. In the beginning of XXI century, in winter season, advection from the Barents Sea took place mainly through its east border, and advection to West Siberia, through its north border (1%). However, the contribution of advection to the air temperature and humidity in the region increased over last years. It is supposed, that, first of all, the weakening of heat and moisture advection to West Siberia from its south border played an important role in winter cooling here. The influence of the Barents Sea on heat fluxes changes was indirectly shown through large-scale circulation variability over the adjacent territories, as a consequence of intensified heat exchange due to the increase in the open sea area.

One of the strongest stratospheric ozone depletion events over the Antarctic was observed in October-November 2015. The increase in the ozone hole was associated with the eruption of Calbuco volcano (Chile) in April 2015 with a maximum plume altitude of  17 km. Based on the ERA-Interim reanalysis data and the NOAA HYSPLIT trajectory model, we estimated the possibility of penetration of volcanic aerosols inside the polar vortex. It was shown that volcanic aerosols could not contribute to the intensification of ozone depletion reactions, because it was outside the stable polar vortex.

The relationship between snow cover and surface ozone concentration is studied on the basis of measurements near Tomsk in 1990-2017. Four types of the seasonal ozone variations are revealed: (1) concentration growth which ends with a spring maximum (53.9% of cases); (2) slow growth and a surge in the concentration after the snow cover melting (19.2%); (3) neutral behavior during the snow cover period and a sharp surge in the concentration after the snow cover melting (15.4%); and (4) neutral behavior without spring maximum (11.5%). Thus, at the end of the snow cover period, the spring maximum of ozone concentration is observed in 88.5% of cases. Differences in the seasonal variations in different years are explained by the temperature dependence of photochemical ozone generation in the atmosphere.

The long-term variability of carbon dioxide concentration at different altitudes during the summer period is analyzed on the basis of data of aircraft sounding over Southwestern Siberia. The monitoring data show that summer values of carbon dioxide concentration at an altitude of 7.0 km grew with a rate of 1.90 ppm/year over the region under study. In the atmospheric boundary layer, the CO₂ concentration grew insignificantly during summer periods from 1997 to 2004 (0.32 ppm/year). Form 2005 to 2017 inclusive, the growth rate sharply increased and was 2.55 ppm/year. The analysis of possible causes of such long-term behavior has shown that it is not due to reduction of the area of forests, wildfires, or diseases of trees. It is also impossible to assert that the carbon dioxide sink was caused by the impact of climatic parameters on forest vegetation. It is probable that the amount of carbon dioxide accumulated in the atmosphere by 2004 makes impossible its further absorption by Siberian forests.

The problem of numerical differentiation of functions with large gradients in the boundary layer is investigated. The problem is that in the case of functions with large gradients and a uniform grid, the relative error of the classical difference formulas for derivatives can be significant. It is proposed to use the Shishkin mesh to obtain a relative error of the formulas independent of a small parameter. Error estimates that depend on the number of nodes of the difference formulas for a derivative of a given order are obtained. It is proved that the error estimate is uniform in terms of a small parameter. In the case of the uniform grid, the region of the boundary layer is allocated, outside of which the numerical differentiation formulas have an error that is uniform in terms of a small parameter. The results of the numerical experiments are presented.

The concept of a regularizing decomposition was introduced by R. Horn and V. Sergeichuk. This means the representation of a square matrix by a direct sum of the Jordan blocks with zero on the principal diagonal and a non-singular matrix. Such a representation is attained via congruent transformations and differs from the Jordan normal form. For the reasons explained in this paper, we prefer to speak about the SN-decomposition of a matrix (in other words, singular-non-singular decomposition) rather than the regularizing decomposition. Accordingly, the algorithms providing the former decomposition are called SN-algorithms. We propose a rational algorithm that considerably simplifies the SN-algorithms proposed by Horn and Sergeichuk.

The method to obtain solutions of the two-dimensional eikonal equation has been developed for the case when the velocity of wave propagation in a medium depends only on one spatial coordinate. We present several examples, where the initial problem is transformed to one or several ordinary differential equations using the substitution of the solution into a suitable general form. The dynamics of the wave propagation for each solution obtained is illustrated.

A survey of algorithms for approximation of multivariate functions with radial basis functions (RBF) splines is presented. Algorithms of interpolation, smoothing, selecting the smoothing parameter, and regression with splines are described in detail. These algorithms are based on the properties of conditional positive definiteness of the spline radial basis function. Several families of the radial basis functions generated by means of conditionally complete monotone functions are considered. Recommendations for the selection of the spline basis and on the preparation of the initial data for approximation with the help of the RBF spline are given.

An inverse boundary value problem for a nonlinear parabolic equation is considered. Two-way estimates for the norms of values of a nonlinear operator in terms of the norms of values of the corresponding linear operator are obtained. Consequent by the two-way estimates are established for the modulus of continuity of a nonlinear inverse problem in terms of the modulus of continuity of the corresponding linear problem. The auxiliary boundary conditions method to construct stable approximate solutions to the nonlinear inverse problem is used. An accurate in order error estimate for the auxiliary boundary conditions method on a uniform regularization class has been obtained.

The boundary conditions that are used for the numerical modeling of the tsunami generation and propagation have been studied. This study focuses on the generating boundary conditions which make it possible to simulate the tsunami wave with desired characteristics (amplitude, time period and, generally speaking, waveform). Taking into account the fact that the water flow velocity in the propagating tsunami wave is uniquely determined by its height and the ocean depth, it is possible to simulate the wave which propagates inward from the boundary into the area of simulation. This can be done by setting the wave height and the water flow velocity over the boundary. By such a way the numerical modeling of the tsunami propagation from a source up to the coast was implemented on a sequence of refining grids. In the conducted numerical experiment, the wave parameters are transmitted from a bigger area into a subarea via boundary conditions. In addition, such a method allows generating a wave that has certain characteristics on a specified line.

In this paper, we investigate a posteriori error estimates of a mixed finite element method for elliptic optimal control problems with an integral constraint. The gradient for our method belongs to the square integrable space instead of the classical H(div; Q) space. The state and co-state are approximated by the P²-P₁ (velocity-pressure) pair, and the control variable is approximated by piecewise constant functions. Using a duality argument method and an energy method, we derive residual a posteriori error estimates for all variables.