Tectonic Earthquake Source Mechanism Model Based on Moment Theory
Authors: Atabekov I. U. 
Published: April 2024

During the construction of strategic facilities, micro zoning is required to determine the peak values of terrain acceleration due to possible earthquakes. The acceleration of the soil in this case strongly depends not only on the power of the earthquake, but also on the earthquake source mechanism and the geodynamic state of the terrain. The known dislocation models of a single dipole with a moment and a pair of dipoles without a moment of the earthquake source mechanism satisfactorily describe the observed effects of the quadrant stress distribution on the Earth’s surface during earthquakes. When carrying out calculations within the framework of the theory of elasticity, the actions of the dipoles are expressed through volumetric forces. There are two known models of replacing the moments with equivalent forces: one of them is based on the equilibrium equations for an infinitely elastic space (Landau and Lifshitz,1965; Maruyama,1963), and the other is based on the representation theorem for elastic bodies, by introducing a singular internal volume, at the boundary of which there are dislocations (Vvedenskaya, 1969; Aki and Richards, 1983). Although these models involve moment effects, they themselves are derived from the momentless theory of elasticity. In our work, we propose a double dipole effect without a moment based on the moment theory of elasticity. The proposed model of the earthquake source mechanism is applied to solve the problem of stress variations in the Earth’s crust in Central Asia using the example of a particular earthquake with a simplified orientation of the rupture plane. Stress variation is understood as the difference in stresses in problems with and without an earthquake mechanism. Static stresses are obtained by solving the inverse elasticity problem with partially unknown boundary conditions. The lithosphere is a prismatic body consisting of several homogeneous blocks, the upper surfaces of which correspond to the relief of Central Asia. Verification of the results of the numerical solution is carried out by comparing the obtained stresses with previously established empirical values. As a priori stresses for solving the inverse problem, we used the solution of the elastic plane problem, the boundary conditions in which correspond to the lateral compression of the lithosphere of the region of the Indian and Arabian plates on the one hand, and the Eurasian plate on the other hand. The obtained solutions of the problem were used to analyze the geodynamic state of Central Asia. Based on the results of laboratory experiments, the unambiguity of the conclusions about the geodynamic state of the Earth’s crust (compression, extension) according to the Lode-Nadai coefficient, which are currently used by many researchers, is questioned. It is shown, contrary to earlier statements, that the values μσ = +1 and μσ = –1 can correspond simultaneously to both tension and compression cases, depending on the spatial form (ellipsoid) of the stress state. Geodynamic analysis of the Earth’s crust is carried out according to the Anderson method.