Comparison of the earth’s crust geothermal field in Northern Tien Shan region with seismic characteristics

The deep crustal temperatures of the Northern Tien Shan region are being calculated on the basis of direct measurements of the heat flow and empirical relation of geothermal parameters and seismic velocities. For this purpose the applied method of numerical solution of conductive heat transfer equation takes into account additional sources of heat release due to radioactive decay. Thermoelastic deformations, reaching 20-40% of the total lithostatic pressure at depths of 35-60 km, are determined. The criteria controlling the distribution of hypocenters of earthquakes have been determined in accordance with the morphology of the regions of excess temperatures and thermal stresses.


Introduction
The temperature field largely determines the physical state of the Earth's lithosphere material. The study of the thermal state of the earth's interior is especially important for areas where intensive tectonic movements occur, accompanied by strong and catastrophic earthquakes. Northern Tien Shan is one of such areas. This is evidenced by the earthquakes occurred in the region: Vernenskoye (Ms = 7.1, 1887), Chilik (Ms = 8.1, 1889), Kemin (Ms = 8.0, 1911), Zhalanash (Ms = 6.8, 1978), Bisorun (Ms = 5.9, 1990), etc. The aim of this paper is to examine the distribution of the deep thermal field of the Earth's crust of Northern Tien Shan to assess the seismic activity of the region.

Methods and Materials
The method used for the research implied numerical modelling of the Earth's crust temperatures based on the results of heat transfer equations with the use of experimental thermophysical parameters -heat flow, thermal conductivity coefficient, radiogenic heat generation. A comparative analysis of the parameters of the calculated geothermal model with the distribution of earthquakes of the territory has been performed.
Mathematical model. The basic equation of stationary conductive heat transfer for longterm geological processes in a heterogeneous anisotropic elastic medium can be expressed as [1]: (1) where k is the thermal conductivity of the rocks at the point with coordinates (x,y,z), T is the temperature, and A (x,y,z) is the radioactive generation of heat in a unit volume. The symbol  denotes the differential Laplace operator in three-dimensional space (2) The coefficient of thermal conductivity at the point (x, y, z), taking into account the temperature dependence, was calculated for the Northern Tien Shan region as follows: where Vp -velocity of seismic waves (km/s), T -initial temperature in o K. Radiogenic heat release in the Earth's crust due to the decay of radioactive elements 40 K, 238 U and 232 Th was calculated from the empirical relationship between the heat generation A (μW/m 3 ) and the velocity Vp (km/s) for the earth crust of the Northern Tien Shan: Equation (1), with allowance for (3,4), is solved using the numerical method of finite differences on the grid 41x31x20 in the variable direction scheme [2]. The heat flow determined from well measurements was taken as a boundary condition for heat transfer on the surface; according to meteorological data, the average annual temperature of the earth's surface is 10 °C at a depth of 1 m. The initial temperature distribution corresponded to a linear geothermal gradient. The lateral boundary conditions the heat flow to zero through the vertical boundaries of the model. At the lower boundary of the modelling region, the mantle component of the heat flow was determined as the difference between the flow on the surface and the radiogenic component from the decay of the U, Th, K-containing rocks, as well as constant temperature, assuming the presence of the rock at the depth of 120 km with Solidus temperature (1370 °C).
To calculate the effective thermal stresses in the earth's crust, the working formula is applied [3] where -3β is the volume coefficient of thermal expansion of the rocks, K is the bulk modulus, ρ is the density, g is acceleration of gravity, and (T-T 0 ) is the temperature deviation from the initial linear distribution. The product 3βK (T-T 0 ) denotes thermal stresses caused by a combination of a nonlinear temperature change. The bulk modulus K is calculated from the ratio of the P-waves and S-waves velocities in the conditions of natural bedding of the rocks: where Vp/Vs = 2.04 stands for the rocks of the Northern Tien-Shan, Density of rocks is defined in each node of the grid model according to the law of linear approximation: Taking into account the sphericity of the surface and the considerable spatial dimensions of the model, equation (1) was solved in spherical coordinates relative to the center of the Earth:

Results and Discussion
Thermophysical model. Geologically, the region is a part of the Alpine neotectonic belt and includes the longitudinally extending mountain ranges Kungei and Zailiyskiy Ala-Tau separated by intermontane depressions [4]. From the east, the region is bordered by spurs of the Dzhungar Ala-Tau mountain ranges, and from the west by the eastern end of the Chu-Ili Mountains. In the earth's crust, according to geophysical data, sedimentary, granite (upper and lower), and basalt layers are distinguished. The thickness of the earth's crust varies from 42 km to 55-60 km, increasing southeastward towards the mountain structures of the Tien Shan and Dzungaria.
Structure of seismic velocities field. The initial experimental base of the deep structure of the earth's crust was P-waves velocities data to the depth of 100 km within the region with coordinates determined by the methods of the DSS, the DSS-MOVZ [4,5]. (Fig. 1).  Geothermal model. The distribution of heat flow, the coefficient of thermal conductivity of rocks and radiogenic heat generation were used to calculate the field of deep crustal temperatures of the Northern Tien Shan (Fig. 4). The structure of the thermal field was studied by dividing the calculated temperatures into a stationary (linear) and anomalous. The anomalous (excess) temperatures are determined by subtracting the stationary component corresponding to a linear geothermal gradient of 12 °C/km from the calculated field.
There is a linear decrease in temperatures from the south to the north from the mountain structures to the platform part of the area. The horizontal temperature gradients decrease from 1.5 °C/km for mountain ranges to 0.5 °C/km in this direction. The absolute temperature is 600-800 °C at the depth of 40 km, 850-1050 °C at the depth of 80 km and 1200 °C at the depth of 100 km. In the depth interval from 20 km to 45 km, a temperature anomaly with increased values of excess temperatures up to 250 °C relative to the linear distribution was determined. The anomaly of excess temperatures is elongated in the sub latitudinal direction just above the boundary of M. Thermoelastic stresses. The operating pressure is calculated as the sum of the lithostatic pressure resulting from the mass of overlying rocks and thermoelastic stresses due to uneven heating and inhomogeneity of physical-mechanical properties (equation 5).
At depths of 30÷50 km, the contribution of temperature stresses is 12%÷27% of the lithostatic pressure and reaches 0.45 GPa (Fig. 5). The ratio of the total pressure (with allowance for thermobaric) and lithostatic pressure in the region of anomalous temperatures is 1.3÷1.4. The calculations are in the range of the experimental data of mineral equilibrium, showing that the tectonic pressure can reach up to 100% of the lithostatic and the values of the first gigopascals [11].  A comparison of the heat flow distribution and earthquakes of the average energy class (9.0-10.5) distribution on the plan shows that the epicenters are concentrated mainly in the regions of low HF values (Fig. 7). The increased density of epicenters here can be explained by the lower viscosity properties of the earth's crust and increased fragility of the rocks. We can assume a fragile mechanism of the earthquakes formation by reducing the plasticity limit of the material of the crust. The question requires further study.

Conclusion
Geothermal modelling allows us to conclude that temperature regime has the prevailing influence on the development of the seismic processes in continental conditions. One of the crucial aspects is determining the high-temperature regions with excess temperatures of 100-250 °C above the solidus, which can lead to partial melting of rocks. The accumulation of thermoelastic stresses in the earth's crust can be considered as one of the criteria of seismic activity observed in the Northern Tien Shan region. The distribution of the average energy class earthquakes hypocenters is controlled by the region of excess temperatures up to 230 °C and the isobar of thermal stresses less than 0.35 GPa. The combination of numerical simulation of the earth's crust temperature regime in the Northern Tien Shan region and seismic data provides additional information for predictive results on the possible mechanisms and physical parameters of the seismoactive environment of the region.