Sh. A. Mukhamediev

Structure of the present-day velocity field of the crust in the area of the Central-Asian GPS network

The structure of the vector field of present-day horizontal velocities on the Earth’s surface is investigated with the use of the territory covered by the Central-Asian GPS network as an example. A method of identification of groups of GPS points (statistically rigid clusters), for which the rate of change in distances between them is virtually zero, is proposed and realized. Sites of the Earth’s surface (regions) containing such groups of GPS points, within the required measurement accuracy, move in the horizontal plane as two-dimensional rigid bodies. The clustering algorithm, which is based on the Student t statistics in determining the so-called statistical “sample cost,” is developed and carefully tested. The results of identification of regions take into account possible random errors in velocity measurements and do not depend on the chosen frame of reference. The method of identification of regions is sufficiently stable with respect to variations in the number of GPS sites used for clustering. Of all the sites of the Central-Asian GPS network, 323 points were selected for clustering. These sites were measured from 3 to 11 times over an 11-year interval of observations (1995–2005). The estimates of errors of velocity measurement for these sites must not exceed 1.0 mm/yr. As a result, 29 statistically rigid clusters, containing from 3 to 17 GPS sites, were identified, and the kinematic regimes of motion of regions corresponding to these clusters were determined with respect to the stable part of Eurasia. With the general direction of the translatory motion of regions toward the north, the majority of them rotate counterclockwise. Nearly one third of GPS sites do not participate in the formation of clusters; these points fall into the interregional space (IRS), which is characterized by increased strain rates. The IRS structure is partitioned into zones with four directions, of which two directions virtually coincide with directions of the principal axes of the regional strain rate tensor, and the two other directions are oriented diagonally to the principal axes. The axis of the maximum rate of the regional shortening has a north-northwestern orientation. It is in this direction (mainly along the IRS) that the crust’s contraction takes place. There is no spatial correlation between IRS zones and geological faults; however, their angular distributions and the directions of strike-slips on them are interrelated. The resulting patterns of regional motions and IRS deformations consistently reflect the dynamic action of the Indian plate on the territory under investigation.

Nonstationary dynamic control of seismic activity of platform regions by mid-ocean ridges

The plot of temporal variation in the seismic activity level in the central and eastern North American platform (NAP) is shown to be similar to that for the Mid-Atlantic Ridge (MAR). This fact was previously noted for Fennoscandia [Skordas et al., 1991]. The characteristic features of the MAR plot recur approximately every three years for Fennoscandia and every four to eight years for the NAP. These data indicate that the mid-ocean ridge largely controls the seismic activity of the adjacent platforms. The control is provided by the ridge push force. As a result of variations in this force due to the nonstationary process of dike intrusion in the axial zone of the ridge, disturbances of the stationary stress-strain state of the lithosphere migrate from the ridge. Using the Elsasser model, the observed time shift can be used for estimating the viscosity of the asthenosphere, amounting to 1017 Pa s with an accuracy of ±30% in the case considered. The disturbance amplitudes decaying away from the ridge are high enough to change the seismic activity of the adjacent platforms.

Prevention of strong earthquakes: Goal or utopia?

In the present paper, we consider ideas suggesting various kinds of industrial impact on the close-to-failure block of the Earth’s crust in order to break a pending strong earthquake (PSE) into a number of smaller quakes or aseismic slips. Among the published proposals on the prevention of a forthcoming strong earthquake, methods based on water injection and vibro influence merit greater attention as they are based on field observations and the results of laboratory tests. In spite of this, the cited proofs are, for various reasons, insufficient to acknowledge the proposed techniques as highly substantiated; in addition, the physical essence of these methods has still not been fully understood. First, the key concept of the methods, namely, the release of the accumulated stresses (or excessive elastic energy) in the source region of a forthcoming strong earthquake, is open to objection. If we treat an earthquake as a phenomenon of a loss in stability, then, the heterogeneities of the physicomechanical properties and stresses along the existing fault or its future trajectory, rather than the absolute values of stresses, play the most important role. In the present paper, this statement is illustrated by the classical examples of stable and unstable fractures and by the examples of the calculated stress fields, which were realized in the source regions of the tsunamigenic earthquakes of December 26, 2004 near the Sumatra Island and of September 29, 2009 near the Samoa Island. Here, just before the earthquakes, there were no excessive stresses in the source regions. Quite the opposite, the maximum shear stresses τmax were close to their minimum value, compared to τmax in the adjacent territory. In the present paper, we provide quantitative examples that falsify the theory of the prevention of PSE in its current form. It is shown that the measures for the prevention of PSE, even when successful for an already existing fault, can trigger or accelerate a catastrophic earthquake because of dynamic fault propagation in the intact region. Some additional aspects of prevention of PSE are discussed. We conclude that in the near future, it is too early to consider the problem of prevention of a forthcoming strong earthquake as a practical task; otherwise, the results can prove to be very different from the desired ones. Nevertheless, it makes sense to continue studying this problem. The theoretical research and experimental investigation of the structure and properties of the regions where the prevention of a forthcoming strong earthquake is planned in the future are of primary importance.

Tectonic and geomechanical control of dikes and sill-like bodies: Evidence from the northwestern part of the Kola Peninsula

A study of the meticulously documented Paleoproterozoic swarms of basic dikes and sill-like bodies, as well as granite veins crosscutting Archean granite-gneiss country rocks of the Central Kola Geoblock of the Fennoscandian Shield, elucidates the question of geomechanical control of the spatial location of syntectonic sheetlike magmatic bodies intruding into heterogeneous structured geomedium. Based on structural analysis and mapping results, the succession of emplacement of several dike generations has been reconstructed and linked to structural parageneses of the corresponding deformation stages. We evaluate the effect of geomechanical and tectonic factors as well as the structural elements of enclosing strata on the places of dike localization, the character of their spatial distribution, morphology of particular bodies, and patterns of swarm systems. Geomechanical problems on the intrusion of single bodies and their communities are solved taking into account their interaction and the heterogeneity of the medium. The conditions necessary for transition of nearly vertical dikes into sills are discussed.

The geometry of a dyke swarm as a result of dyke interaction with each other and with external stresses

In the framework of plane elastic problem we use a numerical approach to study the forms of opening and paths of growth of three parallel magma fractures as a model of dyke swarm formation and development. As expected, the internal dynamic mechanism of dyke interaction distorts their shapes in comparison with a single dyke shape, and curves their paths combining them into a divergent or a convergent system. The external dynamic mechanism of regional stress tends to align the growing dyke paths in parallel to the axis of the maximum compressive stress. The external and internal mechanisms compete with each other. The impact of the internal mechanism is stronger when the ratio of the distance between dykes to their length is less, the initial parallel dyke shift in relation to each other is larger, and the differential regional stress is less. Under the opposite conditions, the external mechanism prevails.

Conditions and mechanisms of origination of gravitational instability in layered bulk-elastic geomasses

Various geophysical processes which can lead to the origination of gravitational instability of the Rayleigh-Taylor type in layered bulk-elastic geomasses are analyzed. The analysis is based on obtained by the authors general results of theoretical study of two-layer systems of heavy bulk-elastic materials which are arbitrarily stratified over depth and occupy domains of arbitrary shape. Additionally some presented in a number of recent publications erroneous assertions related to considered issues of stability, are criticized.

What kind of information about stresses and rheology is supplied by fracture processes in the Earth’s crust?

Contrary to popular belief, fracture processes, when their spatial expression is sufficiently detailed, supply information not only about stresses, but also about the effective rheological properties of the rock mass. Based on the fracture pattern geometry, the trajectories of principal stresses are plotted, which in turn may allow rejecting definitely inappropriate classes of the effective rheological models. By studying kinematics of fracture processes (and, in general, by analysis of any type of kinematic data giving rise to determination of the inhomogeneous deformations), it is possible to identify specific constitutive relations within the rheological classes that are compatible with the observations and equilibrium conditions. The common practice of prescribing a priori rules of how the effective geophysical medium responds to the applied load should be replaced by the development of approaches to extracting these rules from observations.

Refraction of the principal stress trajectories and the stress jumps on faults and contact surfaces: Part 1. Non-constrained regular trajectories

Rock masses contain ubiquitous multiscale heterogeneities, which (or whose boundaries) serve as the surfaces of discontinuity for some characteristics of the stress state, e.g., for the orientation of principal stress axes. Revealing the regularities that control these discontinuities is a key to understanding the processes taking place at the boundaries of the heterogeneities and for designing the correct procedures for reconstructing and theoretical modeling of tectonic stresses. In the present study, the local laws describing the refraction of the axes of extreme principal stresses T1 (maximal tension in the deviatoric sense) and T3 (maximal compression) of the Cauchy stress tensor at the transition over the elementary area n of discontinuity whose orientation is specified by the unit normal n are derived. It is assumed that on the area n of discontinuity, frictional contact takes place. No hypotheses are made on the constitutive equations, and a priori constraints are not posed on the orientation on the stress axes. Two domains, which adjoin area n on the opposite sides and are conventionally marked + and −, are distinguished. In the case of the two-dimensional (2D) stress state, any principal stress axis on passing from domain − to domain + remains in the same quadrant of the plane as the continuation of this axis in domain +. The sign and size of the refraction angle depend on the sign and amplitude of the jump of the normal stress, which is tangential to the surface of discontinuity. In the three-dimensional (3D) case, the refraction of axes T1 and T3 should be analyzed simultaneously. For each side, + and −, the projections of the T1 and T3 axes on the generally oriented plane n form the shear sectors S+ and S−, which are determined unambiguously and to whose angular domains the possible directions p+ and p− of the shear stress vectors belong. In order for the extreme stress axes T1+,T3+ and T1−, T3− to be statically compatible on the generally oriented plane n, it is required that sectors S+ and S− had a nonempty intersection. The direction vectors p+ and p− are determined uniquely if, besides axes T1−, T3− and T1+, T3+, also the ratios of differential stresses R+ and R− (0 ≤ R± ≤ 1) are known. This is equivalent to specifying the reduced stress tensors TR+ and TR− The necessary condition for tensors TR+ and TR− being statically compatible on plane n is the equality p+ = p−. In this paper, simple methods are suggested for solving the inverse problem of constructing the set of the orientations of the extreme stress axes from the known direction p of the shear stress vector on plane n and from the data on the shear sector. Based on these methods and using the necessary conditions of local equilibrium on plane n formulated above, all the possible orientations of axes T1+, T3+ are determined if the projections of axes T1−, T3− axes on side — are given. The angle between the projections of axes T1+, T1− and/or T3+, T3− on the plane can attain 90°. Besides the general case, also the particular cases of the contact between the degenerate stress states and the special position of plane n relative to the principal stress axes are thoroughly examined. Generalization of the obtained results makes it possible to plot the local diagram of the orientations of axes T1+, T3+ for a given sector S−. This diagram is a so-called stress orientation sphere, which is subdivided into three pairs of areas (compression, tension, and compression-extension). The tension and compression zones cannot contain the poles of T3+ and T1+ axes, respectively. The compression-extension zones can contain the poles of either T1+ or T3+ axis but not both poles simultaneously. In the particular case when the shear stress vector has a unique direction p− on side −, the areas of compression-extension disappear and the diagram is reduced to a beach-ball plot, which visualizes the focal mechanism solution of an earthquake. If area n is a generally oriented plane and if the orientation of the pairs of the statically compatible axes T1−, T3− and T1+, T3+ is specified, then, the stress values on side + are uniquely determined from the known stress values on side −. From the value of differential stress ratio R−, one can calculate the value of R+, and using the values of the principal stresses on side −, determine the total stress tensor T+ on side +. The obtained results are supported by the laboratory experiments and drilling data. In particular, these results disclose the drawbacks of some established notions and methods in which the possible refraction of the stress axes is unreasonably ignored or taken into account improperly. For example, it is generally misleading to associate the slip on the preexisting fault with the orientation of any particular trihedron of the principal stress axes. The reconstruction should address the potentially statically compatible principal stress axes, which are differently oriented on opposite sides of the fault plane. The fact that, based on the orientation of the intraplate principal stresses at the base of the lithosphere, one cannot make a conclusion on the active or passive influence of the mantle flows on the lithospheric plate motion is another example. The present relationships linking the stress values on the opposite sides of the fault plane on which the orientations of the principal stress axes are known demonstrate the incorrectness of the existing methods, in which the reduced stress tensors within the material domains are reconstructed without allowance for the dynamic interaction of these domains with their neighbors. In addition, using the obtained results, one can generalize the notion of the zone of dynamical control of a fault onto the case of the existence of discontinuities in this region and analyze the stress transfer across the system of the faults.

Formation of systems of incompact bands parallel to the compression axis in the unconsolidated sedimentary rocks: A model

Uniaxial compression of poorly lithified rocks leads to the formation of thin incompact layers (or bands, in the two-dimensional case) parallel to the compression axis, which are characterized by increased porosity. The standard model of the formation of such bands, as well as deformation bands of other types, associates them with the narrow zones of localization of plastic deformations. In the case of decompaction, it is assumed that transverse tensile deformations are localized within the band, which cause the band to dilate. Here, the formation of a band of localized deformations is treated as a loss-of-stability phenomenon. Based on observations, we propose a fundamentally different model of incompact bands formation, according to which the microdefects in sediment packing (pores) rather than the deformations are localized in the narrow zones. The localization of pores, which are initially randomly distributed in the medium, occurs as a result of their migration through the geomaterial. The migration and subsequent localization of pores are driven by a common mechanism, namely, a trend of a system to lower its total energy (small variations in total energy are equal to the increment of free energy minus the work of external forces). Migration of a single pore in a granular sedimentary rock is caused by the force f driving the defect. This force was introduced by J. Eshelby (1951; 1970). An important feature of our model is that the formation of an incompact band here does not have a sense of a loss of stability. Quite the contrary, the formation of incompact bands is treated as a gradual process spread over time. In this context, the origination of incompact band systems directly follows from our model itself, without any a priori assumptions postulating the existence of such systems and without any special tuning of the model parameters. Moreover, based on the proposed model, we can predict the incompact bands to always occur in the form of systems rather than as individual structures. A single incompact band may only be formed when the force resisting the pore motion, fc, is absent.The calculations were conducted for the case of a plane strain in an infinite elastic medium loaded by uniaxial compressive stress, p. At the initial state, a random spatial distribution of N round pores having a diameter a was specified in some bounded domain Ω. At each iteration for each pore the driving force on a defect, f, was calculated, which is caused by the influence of all other pores. The position of the pore was varied along the direction of the acting force f if |f| > fc. The iterative process for the given initial conditions was terminated when the criterion |f| < fc had been met for all pores. Our calculations showed that the migration of pores results in the formation of a relatively regular structure composed of quasi-parallel linear elements extended along the axis of compression. We associate these formations with the systems of incompact bands. Several series of calculations were carried out. Each series was characterized by its own values of N, fc, and spatial average pore density, ρ. With fixed N, the pore density ρ was varied by changing the size of the initial domain ω within which the pores are distributed. Each series of calculations included 960 case computations of the formation of an incompact band. The cases within the series differ by the initial random distribution of pores. For each series, the frequency histograms were compiled for distances h between the incompact bands. Our results show that the initial pore density ρ (excluding its critically small values) does not have any effect on the shape of the histogram. In particular, this means that the typical distance hm between the incompact bands does not depend on ρ. Quite the opposite, variation in the resisting force, fc, with the other conditions being the same, drastically changes the frequency distribution of distances h. As fc decreases, hm increases; the his-tograms become more diffused, and their maxima become lower.

On the nature of the junction zone between the Vienna and Pannonian sedimentary basins

The results of long-term (2001–2009) measurements of fractures in sedimentary rocks of the Badenian and Pannonian age within the Rust-Fertorakos Highland and adjacent areas are presented and interpreted in terms of paleostresses in the study. The Rust-Fertorakos Highland has a nearly north-south trending strike and separates the Vienna and Pannonian Basins. It is expressed not only in the topography but also in the thickness of the sedimentary cover. Faults in the basement of the Rust-Fertorakos Highland have a nearly north-south strike diagonal to the general NE-SW strike of the faults of the basement of the Vienna Basin. The data of measurements of joints made in quarries and on road slopes that were subsequently computer processed using two independent techniques indicate that, along with joint systems, which are orthogonal to the rock bedding and are of a primary lithogenetic origin, joints joining to form systems obliquely oriented to the bedding are quite common in the region. These secondary joint systems have been formed at later stages of development of already lithified rocks under the influence of tectonic paleostresses. Interpreting pairs of secondary systems as conjugated shear joints, the authors have reconstructed the orientations of the axes of the relevant tectonic paleostresses. At some observation points, the identification of conjugated shear systems has been ambiguous. In these cases, two possible solutions for the paleostress axes have been drawn. Despite some ambiguities, all of the solutions obtained have a steady tendency in terms of the orientation of the minimum compression axis T3. This axis is subhorizontal and is oriented nearly east-west with some variation. The maximum compression axis T1 and the intermediate principal stress axis T2 are normally inclined to the horizontal, and the orientation of these axes depends on the observation point.The results obtained indicate that the Rust-Fertorakos Highland developed as a syndepositional anticlinal fold of the foundation in the zone of transition from the pull-apart Vienna Basin to the rift-type Pannonian Basin.