Geoacoustic emission is the emission of elastic waves by rocks as a result of their dynamic restructuring. Geoacoustic emission zones are areas of the Earth’s crust surface with relative deformations from to . These strain values are higher than tidal ones, but below the threshold of rock strength. In this paper, we propose a model of the formation of these zones in an elastic approximation of a medium under the influence of a distributed stress source with a given distribution function. The source of the impending earthquake is considered as a source of stress. The source is described by a double couple force system distributed over a certain differentiable surface located inside an elastic homogeneous isotropic half-space. The stochastic component affects the shape of the force distribution surface. The model is based on the Navier form of the equilibrium equations. To solve the boundary value problem, we use the Green functions obtained by Mindlin and the Volterra theory of dislocations. The model takes into account the total elastic potential energy of the medium accumulated during earthquake preparation. Using the developed model, numerical modeling of geoacoustic emission zones for a number of Kamchatka earthquakes was carried out.
Gapeev, M.I., Solodchuk, A.A. Mathematical Model of the Formation of Geoacoustic Emission Zones in the Elastic Approximation of the Medium // In: Parovik, R., Zunnunov, R.T. (eds) Hereditary Models of Dynamic Processes in Geospheres. Mathematics of Planet Earth, vol 12. Springer, Cham, 2024. P. 109-120. DOI: 10.1007/978-3-031-70114-6_6
