## 2 Research Significance  
Investigation of pre-seismic anomalies in geophysical fields is of high practical significance for the development of the methods of early notification on seismic hazard. Geophysical field intensity variations in seismically active regions are known to be associated with stress-strain state near earthquake sources during their preparation. In this case, pre-seismic anomalies are often recorded at the distances of hundreds of kilometers from preparing earthquake epicenters. That corresponds to the cases of acoustic emission of rock anomalies recorded in kilohertz frequency range. However, signals at such frequencies cannot propagate from preparing earthquake epicenters due to strong attenuation. Thus, they occur as the result of medium response at the recording site on the change of its stress-strain state. It appears that the changes of stress-strain state near earthquake sources propagate at the distances up to hundreds of kilometers. Undoubtedly, that requires theoretical, model and experimental confirmation. Such investigations of the fields of the Earth's crust stress and deformation are topical in order to obtain new knowledge on the physical processes occurring during earthquake source preparation. The basic concepts of plate tectonics, theory of elasticity and rock plastic deformations were described by [PERSON] and [PERSON] [19]. [PERSON] [20] formulated the basic concepts of deformation and destruction of fractured rocks under static and dynamic load. [PERSON] [1] described in detail the modern understanding of earthquake mechanics. The theory of earthquake-induced seismic wave propagation and modern method of observation data interpretation and processing were considered in detail by [PERSON] and [PERSON] [21]. Analytical solutions of the mathematical model, describing the Earth's crust deformations in medium elastic approximation under earthquake source effect, were considered in detail by [PERSON] [22; 23]. [PERSON] [24] introduced the notion of precursor manifestation zone and showed that its size is determined by the energy of a preparing earthquake. [PERSON] [25] also suggested limiting the dimensionsof this zone by the boundaries, behind which anomalies in deformations do not exceed the deformation process background values of the order of \(10^{-8}\). [PERSON] and his co-authors [26] connected the geophysical field anomalies, occurring in seismically active regions, with the appearance of zones of geo-environment nonlinear loosening (dilatancy). Dilatancy zones, which are formed in the vicinity of earthquake sources during the stresses close to destructive values for rocks, were modeled in the approximation of elastic half-space [26]. Three-dimensional block visco-elastic model of the south-eastern Tibetan Plateau was constructed [27]. Earth's crust model taking into account friable-plastic transitions in the Earth's crust was constructed. This model is based on Maxwell and Kelvin-Voigt models [28]. Visco-elastic fault-based model of crustal deformation was proposed for the 2023 Update to the \"U.S. National Seismic Hazard Model\" [29]. Earth's crust deformations model under earthquake source impact in the form of a rectangular plane was developed. In this model the Earth is a homogeneous elastic sphere [30]. Some complication of this model was made. It was generalized to the case of a layered elastic sphere [31]. The pre-seismic deformations before the Japanese earthquake occurred on 11 March 2011 in the Tohoku region were estimated [32]. An analysis of seismic anomalies associated with Ludian earthquake on 3 August 2014 was made [33]. Post-seismic deformations after Kokoxili earthquake occured on 14 November 2001 in the Northern Tibetan Plateau were estimated using satellite data [34]. A wide review of articles on the estimates of the Earth's crust deformations based on satellite data was made in 2018 [35]. Simulation of stress fields formed around Kamchatka earthquake sources was carried out earlier.