Some aspects of the qualitative analysis of the high-frequency geoacoustic emission model

Geoacoustic emission is an indicator of the stress-strain state of the geosphere, so it plays an important role in the development of methods for predicting strong earthquakes in seismically active regions such as Kamchatka. The paper investigates some aspects of the qualitative analysis of the mathematical model of high-frequency geoacoustic emission. The mathematical model of high-frequency geoacoustic emission is a chain of two coupled oscillators, which is described by a system of two second-order linear ordinary differential equations with non-constant coefficients. Non-constant coefficients have the property of continuous damping at large times. Each differential equation describes a pulse of high-frequency geoacoustic emission with its own characteristics, and the interaction between pulses – energy exchange is carried out using a linear coupling coefficient. For a mathematical model, the existence and uniqueness of a solution were investigated, and the corresponding theorem was proved based on the contraction mapping principle from functional analysis. The stability of the zero solution of the mathematical model of geoacoustic emission was studied, the results were formulated in the form of a theorem, and the stability at large times was also studied using the Routh-Hurwitz criterion. A study of stiffness was carried out, it was shown which parameters in the model can affect the stiffness of the system of differential equations under study, and visualization of studies of the dependence of stiffness on time is given. Using the Rosenbrock numerical method implemented in the Maple computer mathematics environment, oscillograms and phase trajectories were constructed under various conditions: the presence of rigidity, instability, etc. The results of the study are interpreted and directions for further research of the mathematical model of high-frequency geoacoustic emission are given.