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No 5 (2025)
Articles
Fuzzy Mathematics Methods for Comprehensive Analysis of Geophysical Data
Abstract
Discrete Mathematical Analysis (DMA) is a method of analyzing discrete data that actively uses fuzzy mathematics (FM) and fuzzy logic (FL), which allows it to take into account the opinion and experience of the researcher to a much greater extent than classical methods. The latest results of DMA in studying discrete functions using FL, clustering in complex multidimensional arrays, as well as a constructive description of the variety of solutions to systems of linear algebraic equations (SLAE) allowus to propose a new version of geophysical integration, in which FMandFL, and therefore the researcher, play a major role. The work is devoted to the presentation of the concept of geophysical integration. It is based on the theoretical apparatus of DMA, FMand FLand practical, geophysical results of using DMA as demonstrative examples.
Izvestiya, Physics of the Solid Earth. 2025;(5):3-26
3-26
Equations of Elastic 2D-Bending of Thick Plates
Abstract
At present, bending deformations of lithospheric plates and bending vibrations of structures during earthquakes are studied on the basis of the theory of bending of thin plates with a thickness-to-length ratio h/L <1/10 formulated by Kirchhoff in 1850. However, even for long oceanic plates, the effective ratioh/Lis about 1/8. Therefore, this paper considers the possibility of using theories of bending of thick plates. In technology, the equations of Timoshenko (1922) and Reissner (1945) found by the variational method have been used for calculating the bending of thick plates (along with numerical solutions of the general elasticity equations) over the past 80 years to the present day. However, in articles, textbooks and reference books on elasticity theory, these equations are given with indications of their inaccuracy and systematic error due to the neglect of transverse deformation during bending. In this paper, a system of equations for 2D bending of thick plates of the second approximation is derived by directly transforming the original general equations of elasticity using the method of successive approximations. It is noteworthy that, by refining the Timoshenko and Reissner equations, the obtained equations of the second approximationdo not become more complicated, since only the numerical coefficient in the differential equation for the bending function is changed and additive terms are added to the algebraic expressions for stresses and displacements. Significantly simplifying the solution compared to the general elasticity equations in partial derivatives, the obtained differential ordinary equation of bending neglects only small terms above the third order of smallness (h/L)3 . Comparison of the solutions of the obtained equations with the test analytical solution of the exact general elasticity equations showed their complete coincidence with an accuracy ofup to the fourth order of smallness. For thick plates at h/L=1/3, compared to exact solutions of general elasticity equations, the solutions of the Kirchhoff equation give a systematic error for the bending function ofup to 20%, the solutions of the Timoshenko–Reissner equation - upto 5%, and the obtained refined equations have an inaccuracy of solutions ofless than 1%. An example of using the obtained equations for a refined calculation of the bending of oceanic plates is given, in which the solution is obtained in analytical form.
Izvestiya, Physics of the Solid Earth. 2025;(5):27-46
27-46
Mechanism of Propagation of Deformations and Stresses in the Earth’s Crust
Abstract
Transient creep, which occurs at small deformations, leads to a small thickness of the upper elastic crust and low viscosity of the underlying layer. The solution to the propagation problem of deformations and stresses in the upper layers of the Earth is obtained by 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 decay very quickly and cannot propagate over large distances.
Izvestiya, Physics of the Solid Earth. 2025;(5):47-55
47-55
On the Influence of Relief on Thermoelastic Deformations and Slopes in the Upper Layer of the Earth’s Crust
Abstract
A two-dimensional thermoelasticity problem for a half-plane with a periodic relief is considered: on the relief line, the temperature changes in time according to the harmonic law with a period of 1 year. The results obtained earlier by the authors for the temperature field were used. A perturbation theory is constructed that allows obtaining practically exact values of stresses and deformations in a wide class of cases. Formulas for longitudinal deformation and slope in the first order of perturbation theory are written out. It is shown that they can be interpreted as asymptotics that are valid at a sufficiently large depth.
Izvestiya, Physics of the Solid Earth. 2025;(5):56-76
56-76
Influence of Inductive Masses of Conductive Objects Based on Numerical Three-Dimensional Modeling of Signals in the Method of Transient Processes
Abstract
The problem of modeling a non-stationary electric field in a spatially inhomogeneous medium with three closely located conductive ore objects is considered for an installation in which the generator loop covers the entire area with ore objects, and measurements are carried out inside it. Based on the numerical modeling data, their influence on the electromotive forces (emf) measured using the transient process method is studied. Analysis of the received signals showed that the significant influence of conductive objects is local in nature with time and manifests itself in the zone of projection of objects onto the daylight surface. The magnitude of the electromotive force (emf) anomaly and its duration in time correlate with the number of conductive objects.
Izvestiya, Physics of the Solid Earth. 2025;(5):77-92
77-92
Complex Analysis of Geophysical Data in Comparison with Seismic Activity in the Junction Zone of the Chui Basin and the Foothills of the Kyrgyz Ridge
Abstract
When studying the distribution of earthquake epicenters in the Northern Tien Shan region, a tendency for weak seismic events to cluster in relatively small areas was discovered. To understand the conditions of earthquake occurrence and their clustering, it is necessary to analyze various geophysical features in relation to seismic event data. Using the Kohonen neural network, which allows the multidimensional classification of data, clusters were identified according to various sets of geophysical environment characteristics directly in the space of geographic coordinates. A comparison of cluster maps obtained by one or several geophysical parameters simultaneously with data on seismic events in the region under study was carried out. Such an integrated analysis allowedus to discover that there is a spatial correlation between clusters formed by a set of such parameters as electrical resistivity, temperature, vertical gradient of the ratio of longitudinal and transverse velocities of seismic waves, and the distribution of seismic events in the area under study.
Izvestiya, Physics of the Solid Earth. 2025;(5):93-106
93-106
Seismotectonics and Seismicity in the Area of the Tsagan Earthquake (1862, M7.5, the Selenga Delta, Baikal)
Abstract
The paper analyzes the results of shallow geophysical studies and seismicity of the Selenga delta and adjacent areas of the South Baikal depression, where the catastrophic Tsagan earthquake of 1862 with M7.5 occurred. This study area is characterized by the formation of epicentral zones, substituting each other in an echelon manner, as well as seismic “silence” of the eastern segment of the Deltaic fault, to which the dislocations of the Tsagan earthquake are confined. The distribution of seismicity, as well as the similarity of coseismic effects during the Tsagan and Middle Baikal (1959, M6.8) earthquakes, allowus to assume that the shock of 1862 was caused by a fault slip within the water area, either along the flank Beregovoy fault or along the intra-depression Middle Baikal fault, which length allows an earthquake with M > 7 to occur. The activation of one of these faults in 1862 led to the subsidence of the northeastern block of the Delta trough with the opening of ruptures along its perimeter, including along the Delta fault. The consequence of the activation of the environment after strong events and the clustering of strong shocks in time is a large number of weak shocks, which is reflected in the increased value of the recurrence graph slope (γ = –0.54 ± 0.01). According to geophysical data, the range of vertical movements during the last cycle of seismotectonic activation reaches 35 m.
Izvestiya, Physics of the Solid Earth. 2025;(5):107-125
107-125
Impact of the Series of Kahramanmaras Catastrophic Earthquakes (February 6, 2023) on the Regime of Recent Movements of the Caucasus Earth’s Crust
Abstract
Coseismic displacements and deformations of the Earth’scrust from the world’sstrongest earthquakes spread to significant distances from their epicenters. Assessment of the impact of earthquakes on the characteristics of movements and deformations of the Earth’scrust in remote areas is of great scientific and practical interest. The article is devoted to the analysis of the impact of the Turkish Kahramanmaras earthquake (February 6, 2023) on the crustal movements and deformations of the Earth’scrust of the Caucasus region by analyzing the time series of continuous GNSS observations. The velocities of motions in the region, before and after the Kahramanmaras earthquakes were determined. The research results show a significant (and statistically significant) impact of earthquakes on horizontal and vertical crustal movements in remote areas. The following has been confidently recorded: a clockwise reversal of the horizontal movement velocity vectors, a decrease in horizontal velocities, and, predominantly, an increase in vertical movements. The general direction of horizontal movements of the Caucasus GNSS stations is consistent with the postseismic velocity vector of the ANTP station, the closest to the Kahramanmaras epicentral zone, in agreement with the tendency of the Arabian tectonic plate movement. General trends in the combination of pre- and post-seismic movements show the effect of counteraction of the Lesser Caucasus mountain structures to the northeastern pressure of the Arabian tectonic plate wedge. The obtained results provide important information for explaining the mechanisms of regional actuotectonics and the role of strong seismic events in the regime of modern movements of the earth’scrust in the Caucasus.
Izvestiya, Physics of the Solid Earth. 2025;(5):126-138
126-138
Determination of Paleointensity of Geomagnetic Field on the Red Sea Basalts by the Thellier-Coe Method when Heating in Argon and Air
Abstract
The paleointensity of geomagnetic field was determined by the natural residual magnetization of Holocene basalts from the Red Sea rift zone using the Thellier method in the Coe modification when heating in air and argon. It was shown that when basalts are heated in air, mineralogical changes occur in titanomagnetite, the carrier of residual magnetization, at temperatures that are 50–100°Clower than the maximum blocking temperature, which complicates the determination of paleointensity. It has been established that carrying out the ThellierCoe procedure in argon allows avoiding the oxidation of titanomagnetite and thus significantly improving the quality of paleointensity determination. When heating in air, only 50–60% of the natural residual magnetization can be used to calculate paleointensity, while when heating in an argon environment, upto 87% can be used, with the quality factor being 1.5–3 times higher. The calculated value of paleointensity determined by heating in argon is 10–20% lower than by heating in air. The paleointensity of 62±1 μTobtained for the Red Sea basalts turned out to be approximately 1.7 times higher than the modern field in this region according to the IGRF13 model. The high value of paleointensity allows usto attribute the formation period of the studied basalts to the time of the Levantine Iron Age Anomaly of 1.5–0.5 thousand years BC.
Izvestiya, Physics of the Solid Earth. 2025;(5):139-153
139-153
Properties of Orthogonal Diagrams and Arai-Nagata Diagrams on Titanium-Magnetite-Containing Basalts with Laboratory-Induced Mutually Perpendicular Thermoremanent and Chemical Remanent Magnetizations
Abstract
The role of secondary magnetization for determining the characteristic component and paleointensity in basaltic rocks in which the carrier of remanent magnetization is titanomagnetite of varying oxidation states is assessed. For this purpose, laboratory experiments were performed on basalt from the Reykjanes underwater ridge (North Atlantic) to create the “primary” total thermoremanent magnetization TRM (formed after holding the samples at 600°Cfor some time with subsequent cooling in a magnetic field of 50 μT) and the «secondary» chemical remanent magnetization CRM perpendicular to it (imposed during subsequent 200-hour exposure at 350°Cin the field of the same size). The time monitoring of changes in the TRM and CRM components was carried out directly at the temperature of 350°C. Thellier experiments were performed on samples with laboratorygenerated total remanent magnetizations, and the results were used to construct Arai–Nagata and Zijderveld diagrams. It was shown that CRM is formed on new ferrimagnetic phases resulting from the oxidation of the unstable titanomagnetite fraction, and its intensity critically depends on the oxidation state of the original material. In all the obtained diagrams, differently inclined linear segments are distinguished in the following intervals: low-temperature (LT) from 20–350°Cto 450°C, medium-temperature (MT) from 450–475°Cto 500–530°C, and high-temperature (HT) from 500–530°Cto 560–600°C. It is shown that the presence of a secondary component leads to errors in determining both paleodirection and paleointensity based on the primary component, and these errors are the greater, the larger the secondary CRM is in relation to the primary TRM. A new criterion for the reliability of paleomagnetic data is proposed, which applies to both paleointensity and paleodirections: the secondary component should be several times smaller in magnitude than the primary one.
Izvestiya, Physics of the Solid Earth. 2025;(5):154-169
154-169
Laboratory Modeling of Archaeomagnetic Recording in the Thellier-Coe Experiments
Abstract
The influence of the laboratory magnetic field magnitude in the Thellier-Coe method on the results of determining the “archeointensity” of the magnetic field was studied. The experiments were conducted on the same samples of artificial “Neolithic” ceramics and medieval bricks from Veliko-Tаrnovo town in laboratory magnetic fields of 20, 35, 50, 75 and 100 μT. The obtained results show that for the studied samples the magnitude of magnetic field induction determined in the Thellier-Coe experiments (“archeointensity”) depends on the magnitude of the laboratory magnetic field induction in the Thellier-Coe method (increases approximately according to a quasi-logarithmic law). It is assumed that the reason for the obtained dependence is the nonlinear dependence of thermoremanent magnetization on the magnetic field magnitude (in the range of 20-100 μT) in which it was created.
Izvestiya, Physics of the Solid Earth. 2025;(5):170-186
170-186
Detailed magnetostratigraphy of Ordovician sections in the Leningrad region: on the question of the fine structure presence in the Ordovician geomagnetic Moyero superchron
Abstract
By the mid-2000s, a large amount of magnetostratigraphic evidence had been accumulated, suggesting the existence of a geomagnetic superchron of reversed polarity in the Early to Middle Ordovician (the Moyero Reversed Polarity Superchron). The subsequent studies generally supported this hypothesis. However, there were also isolated reports that could either indicate the presence of a fine structure in the superchron, i.e., the existence of several short intervals of normal polarity within the superchron, or significantly limit its duration. Meanwhile, study of geomagnetic superchrons, further substantiation of the very existence of the Ordovician super-chron and establishing its time limits is crucial for the development of the physical theory of geomagnetism, geological correlation, etc. Therefore, any information related to this issue should be carefully considered and verified. This paper presents the results of the detailed magnetostratigraphic study of some intervals from several Ordovician Ladoga sections. These intervals are coeval to those from the Ordovician of the northwestern Russia, Baltic region, and Scandinavia whose age corresponds to the Moyero reversed polarity superchron but which were previously reported to contain separate levels of normal polarity. Combined with the recent data on the Mishina Gora section of the Pskov region, these results provide yet another significant argument supporting the existence of the Moyero Ordovician geomagnetic superchron and its lack of fine structure.
Izvestiya, Physics of the Solid Earth. 2025;(5):187-202
187-202
Construction of Temperature Model Along the Sub-Latitude Profile in the Chuiskaya Depression of the Northern Tien Shan Based on Seismotomography Data
Abstract
A new approach to constructing a two-dimensional model of the temperature of the earth’sinterior is proposed in the article, based on solving the heat conductivity equation in a stationary mode with variable coefficients. For this purpose, a lithotype model was constructed based on seismic wave velocities measured along the sub-latitudinal profile of the Northern Tien Shan, which was later used to estimate the two-dimensional distribution of thermal conductivity of rocks in the section, taking into account its dependence on the background temperature.
Izvestiya, Physics of the Solid Earth. 2025;(5):203-210
203-210