Vol 52, No 5 (2016)

Viscosity is a fundamental property of the mantle which determines the global geodynamical processes. According to the microscopic theory of defects and laboratory experiments, viscosity exponentially depends on temperature and pressure, with activation energy and activation volume being the parameters. The existing laboratory measurements are conducted with much higher strain rates than in the mantle and have significant uncertainty. The data on postglacial rebound only allow the depth distributions of viscosity to be reconstructed. Therefore, spatial distributions (along the depth and lateral) are as of now determined from the models of mantle convection which are calculated by the numerical solution of the convection equations, together with the viscosity dependences on pressure and temperature (PT-dependences). The PT-dependences of viscosity which are presently used in the numerical modeling of convection give a large scatter in the estimates for the lower mantle, which reaches several orders of magnitude. In this paper, it is shown that it is possible to achieve agreement between the calculated depth distributions of viscosity throughout the entire mantle and the postglacial rebound data. For this purpose, the values of the volume and energy of activation for the upper mantle can be taken from the laboratory experiments, and for the lower mantle, the activation volume should be reduced twice at the 660-km phase transition boundary. Next, the reduction in viscosity by an order of magnitude revealed at the depths below 2000 km by the postglacial rebound data can be accounted for by the presence of heavy hot material at the mantle bottom in the LLSVP zones. The models of viscosity spatial distribution throughout the entire mantle with the lithospheric plates are presented.

Constructing detailed models for postseismic and coseismic deformations of the Earth’s surface has become particularly important because of the recently established possibility to continuously monitor the tectonic stresses in the source zones based on the data on the time variations in the tidal tilt amplitudes. Below, a new method is suggested for solving the inverse problem about the coseismic and postseismic deformations in the real non-ideally elastic, radially and horizontally heterogeneous, self-gravitating Earth with a hydrostatic distribution of the initial stresses from the satellite data on the ground surface displacements. The solution of this problem is based on decomposing the parameters determining the geometry of the fault surface and the distribution of the dislocation vector on this surface and elastic modules in the source in the orthogonal bases. The suggested approach includes four steps: 1. Calculating (by the perturbation method) the variations in Green’s function for the radial and tangential ground surface displacements with small 3D variations in the mechanical parameters and geometry of the source area (i.e., calculating the functional derivatives of the three components of Green’s function on the surface from the distributions of the elastic moduli and creep function within the volume of the source area and Burgers’ vector on the surface of the dislocations); 2. Successive orthogonalization of the functional derivatives; 3. Passing from the decompositions of the residuals between the observed and modeled surface displacements in the system of nonorthogonalized functional derivatives to their decomposition in the system of orthogonalized derivatives; finding the corrections to the distributions of the sought parameters from the coefficients of their decompositions in the orthogonalized basis; and 4. Analyzing the ambiguity of the inverse problem solution by constructing the orthogonal complement to the obtained basis. The described approach has the following advantages over the method of steepest descent which was used in our previous works: 1. Application of the perturbation method significantly reduces the volume of the computations in the real problems of coseismic and postseismic deformations (by three to four orders of magnitude when the data from a few dozens of observation points are used); 2. In contrast to the method of steepest descent, the suggested method always provides stable results. This means that adding the new satellite data does not alter the previously calculated coefficients in the low-order harmonics of the distributions of the sought parameters in the orthogonalized basis; this only changes the coefficients of the increasingly higher harmonics which determine the smallscale details in the sought distributions. 3. In contrast to the method of steepest descent, the suggested method is not only capable of constructing stable partial solutions of the inverse problem but also estimating the ambiguity of these solutions. The ambiguity is represented in terms of the superposition of the known functions contained in the orthogonal complement and, hence, with the growth of the amount of the analyzed data it is determined by the linear combination of the increasingly higher harmonics. In the second part of the paper, we present the results of the model numerical computations of Green’s function for the elastic displacements of the ground surface, which correspond to the case of the arbitrary geometry of the dislocation surface and arbitrary orientation of the dislocation vector for the real model of the radially heterogeneous gravitating Earth with the hydrostatic distribution of the initial stresses. The numerical calculations of the creep function in the upper mantle for the coseismic deformations and the ambiguity of the models of postseismic deformations in the vicinity of the source of the Great Tohoku earthquake (Japan) of March 11, 2011 are illustrated by the examples.

A series of laboratory experiments have been carried out with a model of two granite blocks under biaxial compression loading. The experiments are mainly intended for assessing the possibilities of partially releasing the accumulated potential energy. The model was subjected to calibrated mechanical impacts (strokes) which induced elastic impulses. The mechanical stresses, strains, and acoustic emission were recorded. The strokes caused both large slips releasing the stresses down to their initial level and small slips which reduced the stresses by 5–8%. The small slips mostly occurred after the precursory emergence of the low frequency oscillations having low amplitudes. Before the large slips, the stages of speeding-up of the relative motion of the sides of the block contact was observed, similar to those emerging before the natural slips unrelated to the strokes. This feature was not universal: in some cases, the model recovered to the stationary state of the block contact without a large slip. All the slips occurred with a time delay after the stroke. The time delay was shorter when the energy of the blow was higher. With the shorter time delays, the small slip is more likely to occur. The energy of the impacts was by three orders of magnitude lower than the energy accumulated by the model, which points to the triggering mechanism of slip initiation. The series of strokes resulting in the small displacements partially reduced the accumulated energy and prevented the emergence of large motions such as the stick-slip events. If after a series of such blows a large sliding event still occurred, its energy was higher than in the slips unrelated to the impacts. The experiments revealed the difficulties in solving the problem of earthquake hazard reduction by elastic impacts.

New methods for solving the three-dimensional inverse gravity problem in the class of contact surfaces are described. Based on the approach previously suggested by the authors, new algorithms are developed. Application of these algorithms significantly reduces the number of the iterations and computing time compared to the previous ones. The algorithms have been numerically implemented on the multicore processor. The example of solving the structural inverse gravity problem for a model of four-layer medium (with the use of gravity field measurements) is constructed.

Peculiarities of the fluid regime in the source and in the area of preparation of an earthquake which accommodates the evolution of the precursors are considered. The qualitative characteristics and the conditions of migration of the fluids, as well as their influence on the disjunctive deformations of the crust are discussed. During the development of the earthquake source, the fluid regime in this area depends on the redistribution of the fluids and their inflow from the outside. The fluid inflow and the increase in the fluid pressure are mainly due to the filtering from the subvertical permeable faults and the metamorphic dehydration of the rocks in the walls of the main fault. The fluids may also be supplied to the source from the near-surface horizons, and most of the induced earthquakes are associated with this process. These earthquakes can be considered as large-scale natural experiments which can shed light on the contribution of fluids in this phenomenon. A particular role in the mechanism of natural seismicity is played by the inflow of high-pressure fluids through the faults from the deep zones of the section.

The mechanism and dynamics of the deformation and fracture of quartz, granite, and marble samples under the striker blow on their surface and electric discharge inside them are studied by the fractoluminescence (FL), electromagnetic (EME), and acoustic emission (AE) methods with 10-ns resolution. The impact excites a forced deformation wave with a velocity within 0.8 to 2 km/s depending on the mineral. The atomic bonds rupture and microcracks are formed at the nodes of the wave, which leads to the emergence of the FL flashes and disruption of the time dependences of EME. Based on the intensity of the flashes, the dimensions of microcracks are estimated to vary from 2 to 70 µm depending on the mineral. In turn, the emergence of microcracks initiates additional deformation waves.The discharge inside the studied samples excites a pressure shock wave which transforms into the tension wave after reflection from the surface. According to the analysis of FL spectra, this leads to the breakdown of the rocks into positively charged ions and electrons. The shock wave velocity in granites is measured at 4.8 km/s, which is close to the velocity of the longitudinal acoustic vibrations ~5 km/s. The microcracks in the rock have not enough time to form with this loading velocity. It is supposed that the shock wave stretches the deformed interatomic bonds at the dislocation nuclei in the crystal lattices of the minerals up to their breakdown into positively charged ions.

The well-known Omori law is represented in the form of the differential equation describing the evolution of the aftershock activity. The interpretation of the evolution equation is suggested. It is based on the idea of deactivation of the faults in the vicinity of the main shock of the earthquake. The generalization of the Omori law with the allowance for the nonstationarity of the medium in the source, which is cooling after the main shock, is presented.