Vol 54, No 6 (2018)

This work criticizes the entrenched views according to which the orientation of the principal tectonic stress axes can be determined from local (in time and space) observations of the kinematic indicators which jointly allow estimating the strain rate of a crustal block under study. The criticized approach ignores or replaces by subjective assumptions the following factors: (1) The block’s interaction with a hosting medium expressed in terms of the equilibrium conditions of the block; (2) The stress rate which (in addition to stresses) can affect the strain rate; (3)The specific macroscopic mechanical properties of the block’s material under the unknown sought stresses, including the ratio of the stress relaxation time to the period of observations. This approach, which is developed in some Solid Earth sciences and mainly in tectonophysics, is referred to in our paper as the method of local kinematic reconstruction (MLKR) of stresses. After briefly surveying the concept of forces and stresses and discussing the importance of studying the tectonic stresses, this paper refutes the MLKR notions based on general arguments and by the example of certain thought experiments. It is shown that the use of the MLKR for the conditions of the Earth’s interior does not guarantee against obtaining the results that fundamentally and drastically differ from the true tectonic stresses. In the studied rock block, depending on the factors ignored in the MLKR, the principal axes of the strain rate tensor, on one hand, and the principal stress axes, on the other hand, can be oriented discordantly in any arbitrary given fashion. In particular, in the processes accompanied by the release of elastic energy, the maximal rate of elongation can be oriented along the axis of maximal compression, whereas the maximal rate of shortening can be aligned with the axis of the maximal tension. In this paper, the deformation processes that are most detrimental to the results of stress reconstruction by the MLKR are revealed. We introduce the notion of the inherited stress-state regime in which the orientation of the axes of principal stresses during the observation period does not depend on the deformation process and, hence, cannot be in principle determined by the MLKR. An attempt to directly locally recover the stress axes from the kinematic data is a false objective because neither the physical meaning of the stress tensor nor the way it is introduced has anything to do with strains. It is concluded that the MLKR is physically inadequate and that the tectonophysical concept of locality should be abandoned in favor of returning to the notions of classical physics, namely, to using the conservation laws. By the example of several guides on tectonophysics, this paper exposes typical errors in understanding the stress reconstruction problem.

The laboratory experiments with rock samples show that creep under small strains is transient and can be described by the linear hereditary rheological Andrade model. The flows that recover isostasy (including the postglacial rebound flows) cause the strains in the crust and mantle, which are as low as at most 10^–3 and, hence, demonstrate transient creep. The effective viscosity characterizing the transient creep is lower than that at the steady creep and depends on the characteristic time of the considered process. The characteristic time of restoration of isostatic equilibrium (isostatic rebound) after the initial perturbation of the Earth’s surface topography is at most 10 kyr and, therefore, the distribution of the rheological properties along the depth of the mantle and the crust differs from the distribution that corresponds to the slow geological processes. When considering the process of isostatic rebound, the upper crust can be modeled by a thin elastic plate, whereas the underlying crust and the mantle can be modeled by the halfspace with transient creep in which the rheological parameter is inhomogeneous with depth. For this system, the continuum mechanics equations are solved by means of the Fourier and Laplace transforms. The vertical displacements that violate the isostasy propagate from the area of the initial perturbation along the Earth’s surface and can be considered as the mechanism of the present-day vertical movements of the crust. Comparing the obtained results with the observation data allows estimating the Andrade parameter. The use of the Andrade rheological model makes it possible to quantify the relationship between the effective viscosity of the asthenosphere corresponding to the postglacial flows and the seismic Q-factor of this layer.

A new approach to identify the signals of the Earth’s main magnetic field (core field) based on the magnetic observatory data processing is suggested. The algorithms implemented in the approach are based on the Discrete mathematical analysis (DMA). The developed method is used to analyze the data from 49 midand low-latitude observatories of the INTERMAGNET network collected in 2011–2015. The results are compared with the classical method for determining the periods of low magnetic activity of external origin which is adopted by the International Association for Geomagnetism and Aeronomy (IAGA). The advantages of the suggested new approach are demonstrated. Based on the data records for the selected time intervals, the time series of the core field components and their secular variations are obtained for each observatory. These data are compared to the values predicted by the most accurate core field models: SIFM, CHAOS-6, and EMM-2015. The accuracy of the models is estimated using a set of statistical parameters: Pearson’s coefficient of linear correlation, Spearman’s and Kendall’s coefficients of rank correlation, the mean and median values over the data sets, and the mean difference between the data obtained by the suggested method from observatory measurements and the model predictions.

Spatial distribution of principal stresses in a layered elastic medium is considered in the paper. Transformations of the principal stresses across an interface between the layers are analyzed. A method for reconstructing the spatial stress distributions in layered medium from several spot measurements is proposed. The introduced approach is capable of obtaining the stable solution of the stress reconstruction problem with respect to the noise in input data. A typical layered medium is considered for which the stresses are reconstructed from few independent spot measurements of the stress state. The proposed approach may be used for solving an inverse problem of tectonic stresses reconstruction from the borehole logging data.

In seismology according to Båth’s well-known law, the magnitude of the strongest aftershock is on average by unity lower than the magnitude of the main shock. At the same time, most of the strongest aftershocks typically occur within a few hours after the main shock. From the practical standpoint, this activity is quite naturally perceived as a direct continuation of the main earthquake. The subsequent strong aftershocks occur against the rarer background shocks, are less expected, and therefore constitute a separate hazard. The average difference in magnitudes between the main shock and the strongest aftershock that occurs a certain time after the main shock gradually increases. In this work, we consider the problem of estimating the magnitudes of the strongest future aftershock at the successive instants of time after the main shock without taking into account the information about the aftershocks that have already occurred before a given time. For these estimates, we construct the theoretical distributions whose shape proves to be independent of time, whereas the time dependence of the shift in the magnitude proves to be known a priori. The predetermination of these dependences at the moment of the strong earthquake gives us grounds to characterize the constructed theoretical model as Båth’s dynamic law.

The results of studying the deep structure of the Earth’s crust and upper mantle in the central part of the Russian platform from receiver functions are presented. The records of teleseismic waves by the Monakovo small-aperture seismic array in the region of the northwestern slope of the Tokmovskii Arch of the Volga–Kama anteclise are used. The modification of the P-receiver function method (Vinnik, 1977) suggested in (Sanina et al., 2014) for analyzing the receiver functions in the regions with a complexly structured upper part of the section and the presence of a thick sedimentary cover is applied. The method is based on separating the high- and low-frequency components of the seismic record and successive reconstruction of the V-s velocity section in the upper part of the crust, which is performed first and, next, the entire deep section of the crust and the mantle down to a depth of ~300 km. The positions of the seismic conversion boundaries in the crust and upper mantle beneath the Monakovo array are determined. The upper mantle velocity section constructed based on the observations at the Mikhnevo array (Sanina et al., 2014) is compared with the world data on the ancient Precambrian platform.