Том 53, № 2 (2017)

The question of ambiguity in the solution of the inverse problem for determining the Brünt-Väisäla frequency in the Earth’s mantle from the entire set of the up-to-date data on seismicity, free oscillations, and forced nutations of the Earth, as well as the data on the Earth’s total mass and total moment of inertia, is considered. Based on the results of a series of numerical experiments, the band of admissible distributions of the Brünt-Väisäla frequency and mantle density with depth is calculated. This estimate is used for investigating the convective and gravitational stability of the different regions of the mantle against relatively small adiabatic and nonadiabatic perturbations. The generalization of the known Rayleigh criterion of convective stability of homogeneous and a nonself-gravitating incompressible viscous fluid for the case of a compressible self-gravitating fluid is given. A system of the ordinary eight-order differential equations with complex coefficients and homogeneous boundary conditions, whose eigenvalues determine the transition from the stable state to instability, is obtained. Examples of the numerical determination of these eignevalues are presented. For interpreting the data about the band of the admissible distributions of the Brünt-Väisäla frequency with depth, the notion of the effective bulk modulus of the medium at different depths is introduced. This quantity governs the depth changes in temperature in a convecting mantle and allows us to make a conclusion about the role of heat conduction and the radial heterogeneity of the mantle composition without imposing any constraints on the convection mechanism. It is shown that within the present-day observation errors in the frequencies of the Earth’s free oscillations, the simplest reasonable model is that in which the ratio of the effective bulk modulus to its adiabatic value in the lower and middle mantle is 1.043 ± 0.05. The closeness of this value to unity indicates that convection in the lower and middle mantle is fairly close to adiabatic. At the same time, when the analysis only relies on seismic data and on the information about the periods of the free oscillations of the Earth, there is a significant uncertainty in the models of the effective bulk modulus distribution in the upper mantle and crust. This uncertainty precludes us from making purely empirically derived conclusions that reliably and unambiguously describe the role of the effects of heat conduction and radially heterogeneous material composition in the convection in the upper mantle.

For studying the structure of the lithosphere in southern Ukraine, wide-angle seismic studies that recorded the reflected and refracted waves were carried out under the DOBRE-4 project. The field works were conducted in October 2009. Thirteen chemical shot points spaced 35–50 km apart from each other were implemented with a charge weight varying from 600 to 1000 kg. Overall 230 recording stations with an interval of 2.5 km between them were used. The high quality of the obtained data allowed us to model the velocity section along the profile for P- and S-waves. Seismic modeling was carried out by two methods. Initially, trial-and-error ray tracing using the arrival times of the main reflected and refracted P- and S-phases was conducted. Next, the amplitudes of the recorded phases were analyzed by the finite-difference full waveform method. The resulting velocity model demonstrates a fairly homogeneous structure from the middle to lower crust both in the vertical and horizontal directions. A drastically different situation is observed in the upper crust, where the V_p velocities decrease upwards along the section from 6.35 km/s at a depth of 15–20 km to 5.9–5.8 km/s on the surface of the crystalline basement; in the Neoproterozoic and Paleozoic deposits, it diminishes from 5.15 to 3.80 km/s, and in the Mesozoic layers, it decreases from 2.70 to 2.30 km/s. The subcrustal V_p gradually increases downwards from 6.50 to 6.7–6.8 km/s at the crustal base, which complicates the problem of separating the middle and lower crust. The V_p velocities above 6.80 km/s have not been revealed even in the lowermost part of the crust, in contrast to the similar profiles in the East European Platform. The Moho is clearly delineated by the velocity contrast of 1.3–1.7 km/s. The alternating pattern of the changes in the Moho depths corresponding to Moho undulations with a wavelength of about 150 km and the amplitude reaching 8 to 17 km is a peculiarity of the velocity model.

A new class of algorithms for solving the inverse problems of gravity prospecting is considered. The best interpretation is selected from the set Q of the admissible versions by the optimality criteria that are borrowed from the solution-making theory and adapted for the geophysical problems. The concept of retrieving the information about the sources of gravity anomalies, which treats the result of the interpretation as a set of locally optimal solutions of the inverse problem but not as a single globally optimal solution is discussed. The locally optimal solutions of the inverse problem are sort of singularity points of set Q. They are preferable to the other admissible solutions by a certain criterion formulated in terms of the geologically important information about the anomalous bodies. The admissible versions of the interpretation of the gravimetry data that meet the criteria of the decision-making theory are the primary candidates for the singularity points. The results of the numerical calculations are presented. The set of the admissible solutions from which the locally optimal versions of interpretation are selected is formed by the modifications of the assembly method developed by V.N. Strakhov.

The possibility of identifying the fault plane in the case when the source of an earthquake is described in the second-moment-based approximation is analyzed. The commonly occurring type of the earthquake source whose major axis and rupture propagation are directed along the strike axis is analyzed in detail. The possibility of identifying the fault plane of this source depending on the focal mechanisms of the earthquake is explored. The inferred conclusions are verified by the results obtained for two strong earthquakes: the Chilean earthquake that occurred in Maule on February 27, 2010 and the Sumatra offshore earthquake of April 11, 2012.

Based on the data from the GPS receiving networks in Japan and America which have a high time resolution (2 min), two-dimensional (2D) distributions of the variations in the ionospheric total electron content (TEC) are constructed both close to and far from of the epicenter of the submarine earthquake of March 11, 2011 in Japan. Above the epicenter, a diverging multi-period disturbance appears after the main shock due to the acoustic gravity waves. Far from the epicenter, the wave trains associated with the tsunamigenic atmospheric internal gravity waves are revealed. These atmospheric waves significantly advance the arrival of the tsunami signal initially on the Hawaiian islands and then on the western coast of North America. The presence of the tsunami precursor in the form of atmospheric gravity waves is supported by the numerical calculations and by the analysis of the dispersion relation for the waves in the atmosphere. The detected ionospheric responses close and far from the epicenter can be used in the early tsunami warning systems.

The results of numerous rock magnetic and paleomagnetic studies of Pleistocene deposits in the Loess Plateau in China which were obtained over a period of a few decades are analyzed. It is shown that two important problems remain unsolved. These are (1) developing the particular mechanism of “magnetic enhancement” in the soils, probably with a more accurate assessment of the level of effect of various natural factors causing qualitative changes in the magnetic fraction of the soil. Here, both the chemical composition of the newly crystallized magnetic mineral causing this enhancement and the parameters of the corresponding secondary (chemical) magnetization process should be determined. (2) Fixing the exact climate-stratigraphic position of the main paleomagnetic benchmarks of the Pleistocene, primarily the Matuyama–Brunhes reversal. In contrast to many conclusions, it is inferred that the Pleistocene paleoclimatic loess-soil record in China generally disagrees with the oxygen isotope (OI) record in the deep-sea sediments. This inconsistency is particularly significant for the Matuyama chron deposits.