Izvestiya, Physics of the Solid Earth最新文献

Abstract—Currently, bending deformations of lithospheric plates and bending vibrations of structures in earthquakes are studied based on the Kirchhoff–Love theory for thin plates with a thickness-to-length ratio h/L < 1/10 formulated by G. Kirchhoff in 1850. However, even for long oceanic plates, the effective h/L ratio is about 1/8. Therefore, the paper considers the possibility of using bending theories for thick plates. In engineering, for calculating bends of thick plates, along with numerical solutions of general elasticity equations, the Timoshenko’s (1922) and Reissner’s (1945) equations found by variational method have been used for the last 80 years. However, in papers, textbooks and reference books on the theory of elasticity, these equations are given with notes indicating their approximate nature and systematic error due to neglect of transverse deformation at bending. In this paper, we derive a system of two-dimensional (2D) second-approximation bending equations for thick plates by direct transformation of the initial general elasticity equations using a method of successive approximations. It is noteworthy that the obtained second-approximation equations refining the Timoshenko and Reissner equations do not become more complicated, since only the numerical coefficient in the differential equation for the plate deflection function changes and additive terms are introduced in the algebraic expressions for stresses and displacements. Significantly simplifying the solution compared to the general partial differential equations of elasticity, the derived ordinary differential bending equation neglects only small terms of higher than third order of smallness (h/L)³. The comparison of the solutions of the new equations with the test analytical solution of the exact general equations of elasticity has shown their complete coincidence to the fourth order of smallness. For thick plates at h/L = 1/3, compared to the exact solutions of the general elasticity equations, the solutions of the Kirchhoff equation give a systematic error for the deflection function up to 20%, the Timoshenko–Reissner’s equations up to 5%, while the new refined equations have an uncertainty of solutions below 1%. The paper presents the example of using the obtained equations for a refined calculation of the bending of oceanic plates, in which the solution is obtained in an analytical form.

Abstract—A two-dimensional thermoelasticity problem for a half-plane with a periodic relief is considered: on the relief line, the temperature changes with time according to a harmonic law with a period of 1 year. The results obtained by the authors earlier for the temperature field were used. A perturbation theory has been constructed that allows one to obtain almost exact values of stresses and deformations in a wide class of cases. Formulas for longitudinal deformation and tilt in first-order perturbation theory are written out. It is shown that they can be interpreted as asymptotics that are valid at a sufficiently large depth.

Abstract—The article considers the possibilities of using the telluric tensor in magnetotellurics, determined from the linear relationships of the electric field at the local and base points. Particular attention is paid to the local-regional decomposition of the telluric tensor, which allows separating the influence of near-surface inhomogeneities and the studied deep structures. We have adapted approaches widely used in analyzing the impedance tensor to analyzing the telluric tensor, tested on synthetic data calculated for a three-dimensional model with a deep conductive structure and a nonuniform near-surface layer. The phase tensor determined from the telluric tensor, free of surface effects, is considered. It is shown that maps of invariant parameters and polar diagrams make it possible to estimate the dimensionality of the medium, localize deep structures, and estimate their extent.

Abstract—Transient creep, which occurs during small deformations, leads to a small thickness of the upper elastic crust and low viscosity of the underlying layer. The solution to the problem of the distribution of strains and stresses in the upper layers of the Earth is obtained using a thin elastic plate as a model of the upper elastic crust and a viscous half-space as a model of the underlying layer. It is shown that stress waves attenuate very quickly and cannot propagate over long distances.

Abstract—A number of published papers have suggested that the influence of electromagnetic action on the seismic regime in natural conditions or on crack formation in laboratory experiments can be explained by the role of Joule heating when an electric current passes through fluid-saturated rocks. Heating of the fluid in the pore space can lead to an increase in fluid pressure in pores and cracks, which in turn can trigger additional cracking of the solid skeleton and decrease in rock strength. In this paper, the results of direct heating of artificial sandstone samples under uniaxial compression conditions are presented in order to identify the role of the thermal factor in rock fracture. The samples were taken from the same batch as previously studied in experiments on the effect of passing an electric current through a sample on the acoustic emission (AE) characteristics and on its failure process. In the presented experiments, the heat flow was supplied to the opposite side faces of the sample using Peltier elements, which are reverse thermoelectric converters. The heat flow density on the sample surface reached almost 10⁴ W/m²; the local temperature of the outer surface of the sample near the heating element increased during the heating process by 10–15°C depending on the duration of the switched-on current. Experiments have shown that even with such significant heat flows, the effect of heating is only evident for loads close to fracturing (Kp ≥ 0.95–0.97). The effect of heating was that the process of crack formation in the sample intensified and the sample itself gradually passed into a overcritical state, eventually failing. At lower loads, direct heating of the sample does not have a noticeable effect on the crack formation process.

Abstract—The review considers seismoelectromagnetic and seismoionospheric phenomena, the potential of which for earthquake forecasting and exploration geophysics was anticipated by the remarkable Russian geophysicist G.A. Sobolev. His works has focused geophysicists all over the world to the research in these fields, and by now they have developed rapidly. The directions of research, the origin of which modern geophysics owes much to G.A. Sobolev, include the study of the relationship between seismic and electromagnetic noise and vibrations, electromagnetic response of rock to loading, perturbations in the electrotelluric fields during the preparation of a seismic event, anomalies on radio paths and ionospheric disturbances before strong earthquakes, and trigger phenomena in geophysics. The development of the ideas in the later research proved the general value of the pioneering ideas of G.A. Sobolev. The current state of research in these fields and the problems faced by geophysicists are considered.

Abstract—A number of negative consequences are associated with a pore pressure drop in permeable fluid-saturated rocks: sudden coal outbursts, destruction of the borehole surrounding rock in oil producing wells, methane emissions as a result of permafrost degradation, etc. The article discusses results of a series of model laboratory experiments to study the destruction of a porous fluid-saturated material of low strength during rapid pressure release at its boundary. The rate of pressure release, the strength properties of the material, the presence of gas, and the position of the boundary between the gas and fluid were varied. The conditions for the formation of microcracks and permeability increase during repeated cycles of pressure growth-release were found. It has been established that with an increase in the rate of pressure release, the number of cracks formed, and the depth of destruction increases. Numerical modeling of the formation of macrocracks during pressure release in gas-filled samples was carried out.

Abstract—The heterogeneous structure of a future rupture surface plays an important role at all stages of the development of dynamic instability in the rock masses. The presence of inhomogeneities leads to the formation of stress concentration patches on large-scale irregularities (asperities) and relatively unloaded sections of the interface with radically different frictional properties. Interaction of such zones may produce a more complex effect than solely stress concentration. The published data of geodetic and seismological observations suggest that with certain structural configurations of the fault zone, various modes of fault movements may occur, from slow slip events to supershear rupture. The article presents the results of laboratory experiments on the displacement of meter-scale rock blocks whose contact interface contained zones of increased strength with velocity-weakening behavior. The laboratory results were compared with the effects observed in nature using a database containing rupture models for more than 150 earthquakes in different regions of the world was. A joint analysis of the results of laboratory experiments and seismological observations has shown that rupture develops by several scenarios determined by relative locations of asperity zones. Information about the locations of such zones required for numerical modeling of the deformation process in a specific crustal region can be derived from the results of satellite and seismological observations. In areas of preparation of relatively small earthquakes where geodetic observations are ineffective, the necessary information can be acquired from microseismicity observations.

Abstract—The essay prepared for the issue of the journal to honor the memory of G.A. Sobolev reflects the history of creation and describes the physical foundations of the method for detecting precursory RTL anomalies of seismicity proposed by G.A. Sobolev in 1995. The physical ideas precursory patterns in RTL parameter and Gutenberg–Richter b-value are discussed from the standpoint of the avalanche-unstable fracture formation (AUF) concept. The previous results on the comparison of the RTL and b-value anomalies revealed in a number of regions pertaining to different tectonic types (subduction zones, rift and shear zones) are summarized. Issues associated with RTL and b-value calculation methods are discussed. The manifestations of the anomalies in the regions pertaining to different tectonic types share common patterns and have regional differences. In the shear zones, the temporal sequence of the beginnings of seismic quiescence stages (RTL parameter) and changes in the energy “spectrum” of seismicity (b-value) proved to be inverse to the temporal sequence of stages observed in the subduction zones and in the rift zone. At the same time, in all regions, irrespective of their tectonic type, the temporal sequence of the stages of b-value anomaly formation and seismicity activation is identical: activation begins later than the b-value begins to decrease. This pattern corresponds to the scenario following from the AUF concept, thus confirming the validity of this concept in tectonically diverse regions.

Abstract—A computer method for systematic earthquake prediction is considered. The forecast is calculated regularly and for a constant time interval. The result is a map of the alarm zone in which the epicenters of the target earthquakes are expected. The forecast is considered successful if all epicenters of target earthquakes in a given interval fall within the alarm zone. The method of the minimum area of alarm is used to train the forecast. The method optimizes the probability of a successful forecast within a limited alarm zone, making it possible to estimate the probability of a successful decision at the next forecast interval and providing an explanation of the alarm zone using logical implication and a list of previous earthquakes with similar precursor values. An example of a systematic forecast of earthquakes in Kamchatka is considered.