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0UDC 550.34.034
ANALYSIS OF THE PHYSICAL NATURE OF THEMODYNAMIC AND RHEOLOGICAL PARAMETERS IN EARTHQUAKE SPOTS AND THE UNIVERSALITY
OF THEIR CALCULATION METHODOLOGY
LYUTIKOVA VERONIKA SERGEEVNA Junior Research Fellow, Master of Engineering and Technology
LITOVCHENKO IRINA NIKOLAEVNA Leading Researcher
National Science Center seismological observations and research of the Ministry of Emergency Situations of the Republic of Kazakhstan, Almaty, Kazakhstan
Abstract: The paper presents an analysis of the physical nature of thermodynamic and rheological parameters in earthquake foci and the universality of the method for their calculation.
Key words: magnitude, earthquake source, rheological, thermodynamic parameters
The paper analyzes the physical nature of thermodynamic and rheological parameters in earthquake foci, and proves the universality of the calculation method. The numerical values of rheological and thermodynamic parameters in earthquake foci are studied. It should be noted that the papers [1, 2, 5, 10] previously considered the issue of rheological and thermodynamic conditions in earthquake foci. In the course of the conducted research, graphical dependencies of thermodynamic and rheological parameters on magnitude and temperature were constructed according to various sources [3, 7, 10] (see Fig. 2).
The initial data for the conducted research is the world catalog of earthquakes with M>2.5 for 1973-2024 [11], according to which some parameters in focal zones were calculated.
Relevance research justified activation seismicity For of the entire Earth as a whole over the past decades. In the course of the analysis of the physical essence of thermodynamic and rheological parameters, we note that: earthquakes are sources of information about the physical parameters of the earth's crust and its stratification , the initial data For definitions physical characteristics parameters are the magnitude and energy class of the earthquake. Physical parameters V focal zones strong earthquakes can be calculated using known and original equations [1,2, 3, 9, 10]. Accordingly, the equations should meet the specifics seismicity in any region of the Earth [1,2, 5, 9]. Rheological and thermodynamic parameters in earthquake foci are considered V next sequences: energy seismic waves; temperature of the environment of the source; temperature stresses, deformation of the volume and shape of the source; density of deformation energy; potential energy of deformation of the source; ultimate strength environment in the destruction volume; determination of the ratio of the magnitude of potential deformation energy, destruction energy, viscosity, etc.
According to the universal calculation method from [7, 9, 10], the values of thermodynamic and rheological parameters in the focal zones of earthquakes with a magnitude greater than 2.5 were obtained. Figure 1 shows the epicenters earthquakes with M>2.5 for 1973-2024 by depth and the viscosity parameter is presented in different colors (3-D representation of the viscosity logarithm parameter, see scale). The color indicates increased and decreased viscosity values for the Northern and Southern hemispheres of the Earth. Other rheological and thermodynamic parameters were also calculated parameters V focal zones earthquakes with different magnitudes (NEIC) [11].
Using the calculation method from [9,10], quantitative values of physical parameters in the focal zones of earthquakes with a magnitude greater than 2.5 were obtained. The diagrams of the relationships between physical parameters are shown in Figure 2. As can be seen, the dependencies between the parameters are observed for both strong and moderate and weak earthquakes: (1) -according to Tuliani L. (1999), (2) - according to Litovchenko I., Lyutikova V. (2024), (3) -according to Amirov N. (2022) [1, 3, 5-7, 9, 10]. Moreover, a change in magnitude by one unit is
equivalent to an increase (decrease) in the earthquake energy by 32 times. Magnitude M=8.0 corresponds to E=6.3*10 23 Erg.; M=7.0; E=2.0*10 22 Erg . etc. There are many equations for determining the relationship between earthquake energy or energy class and magnitude [10]. All of them are proposed for different seismogenic regions of the Earth [1-10]. The quantitative values of the parameters are considered and it turns out that the average energy value calculated using the equations of the method from [9, 10] covers the largest volume of the initial seismological material [1,2, 5, 10].
The theoretically possible maximum energy class is 27.49. The physical meaning of the calculated parameters follows from the differences: in the change in the critical value of the source volume V and the energy density per unit volume U. From the analysis of the parameter values, it is evident: the logarithm of the critical dimensions of the source volume ( lgV ) is in a quadratic dependence on the magnitude ( M ). In our case, in the magnitude range from 2.5<M<9.2, the calculated values of lgV change within 12.44<lgV<21.95. The presence of parameters E and V made it possible to calculate the density of potential energy of seismic waves per unit volume U (in erg/cm3 ) ( see Fig. 2 (1), (2), (3)) [1-11]. Moreover, lgU = lgE - lgV V range magnitude from 2.5<M<9.2 the values of lgU vary within the range from 2.947<lgU<3.609. Note that the logarithm of the specific (volume) energy density of seismic waves ( lgU ), unlike ( lgV ), is in a linear dependence on the magnitude (see Fig. 2). There are two types of specific energy hearth earthquakes, related With: 1) change volume, 2) change forms foci that differ by one order of magnitude for the same magnitude [1-10].
Северное
Figure 1 - 3- D projections of the hypocenters of the Earth's earthquake foci for the Northern and Southern Hemispheres, with the logarithm of viscosity parameter shown in different colors
In theory plan probability interrelations between energy And magnitude earthquakes with the thermodynamic parameters of the source can be assumed from the very nature of the accumulation of thermoelastic stresses in the upper layers of the Earth. Such accumulation is a consequence of uneven temperature distribution and differences in the physical properties of the geological environment [2]. An indicator of stress concentration at depth is their discharge in the form of an earthquake [1; 2; 4; 5, 10]. Graphs connections temperatures V hearth earthquakes ( see Fig . 2) V moment dropping additional elastic stresses with energy at the source: T(K)=196.8K( lgEmax - lgE ), where 196.8K is a constant that determines the number of degrees corresponding to a change in energy (Erg) by one order of magnitude; lgE - logarithm energy seismic waves, calculated according to the universal method [9]. lgE max - logarithm maximum meanings energy seismic waves are used And at viscosity calculation. As follows from Figure 2, some assumptions are necessary: 1) a conditional assumption outside the real existing range of magnitudes. It follows from the calculation that 1) the maximum energy value corresponds to a magnitude of 13.5 and the corresponding value
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of E max = 10 27 erg. 2) an analysis of the distribution of hypocenters of earthquakes with magnitudes M < 5.0 by depth shows their concentration in elongated quasi-vertical large and small volumes (see Fig. 1).
1000
3 t
Figure 2 - Addiction thermodynamic parameters from temperatures, magnitudes: (1) - according to Tuliani L. (1999), (2) - according to Litovchenko I., Lyutikova V. (2024), (3) - according to Amirov N. (2022): 1 — M, 2 — E (Erg), 3 — V(cm 3 ), 4 — U (Erg/ cm3 ), 5 — E k , 6 — G *10 11 (dyne/cm 2 ), 7 — a v 10 -5 K -1 , 8 — t Cr *10 8 (dyn/cm2 ) , 9 — e , 10 — a *10 9 (dyn/cm2 ) , 11 — n (P), 12 — N
3) The calculated values of temperatures (T) for earthquakes with magnitudes 5.0< M< 9.0 correspond to the crystallization temperatures of the constituent elements of the crust.
1
2
Based on the results of the analysis of the physical essence of thermodynamic and rheological parameters, it follows that:
- comparing the calculated quantitative values of the parameters s, o and G with temperature (T°(C)) it is found that the first two of them experience an increase as the temperature rises, while the third - the bulk modulus of elasticity G - on the contrary, decreases.
The dependences of the parameters o, a v on temperature (T) are shown by straight lines (Figure 2: 1, 2, 3). As follows from the presented relationship, the dependence G=f(T) is curvilinear, and s = f(T) is piecewise rectilinear (see Figure 2 (1), (2), (3)).
Like this in this way, theoretical calculations quantitative values thermodynamic and rheological parameters using a universal method, which determine emergence strong earthquakes in the earth's crust, and statistical processing of experimental data indicate: the existence of universal dependencies between physical conditions in earthquake focal zones. Similar relationships are fulfilled for relatively weak (5>M>2.5) earthquakes. Physical and numerical dependencies of thermodynamic and rheological parameters have been determined. According to these rheological and thermodynamic parameters, elastic, elastic-viscous layers of the earth's crust are distinguished.
The obtained results are necessary for practical purposes of identifying zones that are ready for the occurrence of strong earthquakes.
Application of results will help:
1) find out the functional dependencies physical parameters from the magnitude of the earthquake, temperature.
2) evaluate quantitative meanings rheological And thermodynamic parameters in the centers of ongoing earthquakes.
The work was carried out within the framework of fundamental research in the laboratory of physics of geodynamic and seismic processes of the National Scientific Center of Seismic Research of the Ministry of Emergency Situations of the Republic of Kazakhstan within the framework of the 2024-2026 PCF on the topic BR 24992763 "Assessment of the seismic hazard of the territories of regions and cities of Kazakhstan on a modern scientific and methodological basis."
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