Geodesic
Some aspects of the qualitative analysis of the high-frequency geoacoustic emission model
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 42 (2023) no. 1, pp. 191-206 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: high-frequency geoacoustic emission, Berlage function, rigidity, existence and uniqueness, stability, Routh-Hurwitz criterion, mathematical model, oscillograms. 
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D. F. Mingazova; R. I. Parovik. Some aspects of the qualitative analysis of the high-frequency geoacoustic emission model. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 42 (2023) no. 1, pp. 191-206. http://geodesic.mathdoc.fr/item/VKAM_2023_42_1_a13/

[1] Marapulets Yu. V., Shevtsov B. M., Mezomasshtabnaya akusticheskaya emissiya, Dalnauka, Vladivostok, 126 pp.

[2] Marapulets Yu. V., Tristanov A. B., “Primenenie metoda razrezhennoi approksimatsii v zadachakh analiza signalov geoakusticheskoi emissii”, Tsifrovaya obrabotka signalov, 2011, no. 2, 13-17

[3] Marapulets Yu. V., Larionov I. A., Mischenko M. A., Scherbina A. O., Solodchuk A. A., Shevtsov B. M., “Otklik vysokochastotnoi geoakusticheskoi emissii na aktivizatsiyu plasticheskikh protsessov v seismoaktivnom regione”, Uchenye zapiski fizicheskogo fakulteta, 2014, no. 6, 146311

[4] Vodinchar G. M., Perezhogin A. S., Sagitova R. N., Shevtsov B. M., “Modelirovanie zon geoakusticheskoi emissii”, Matematicheskoe modelirovanie, 19,:11 (2007), 59-63

[5] Gapeev M. I., Solodchuk A. A., Parovik R. I., “Svyazannye ostsillyatory kak model vysokochastotnoi geoakusticheskoi emissii”, Vestnik KRAUNTs. Fiz.-mat. nauki, 40:3 (2022), 88-100 DOI: 10.26117/2079-6641-2022-40-3-88-100 | DOI

[6] Gapeev M. I., Parovik R. I., Solodchuk A. A., “Matematicheskaya model vysokochastotnoi geoakusticheskoi emissii na osnove svyazannykh ostsillyatorov”, Ufimskaya osennyaya matematicheskaya shkola - 2022, Materialy mezhdunarodnoi nauchnoi konferentsii, Ufa, 28 sentyabrya – 01 2022 goda, v. 2, RITs BashGU, Ufa, 2022, 322-324 DOI:10.33184/mnkuomsh2t-2022-09-28.120

[7] Tristanov A., Lukovenkova O., Marapulets Yu., Kim A., “Improvement of methods for sparse model identification of pulsed geophysical signals”, Conf. proc. of SPA-2019, IEEE, Poznan, 256–260 DOI:10.23919/SPA.2019.8936817

[8] Senkevich Yu. I., Lukovenkova O. O., Solodchuk A. A., “Metodika formirovaniya Reestra geofizicheskikh signalov na primere signalov geoakusticheskoi emissii”, Geosistemy perekhodnykh zon, 2:4 (2018), 409-418

[9] Krylov V. V., Landa P. S., Robsman V. A., “Model razvitiya akusticheskoi emissii kak khaotizatsiya perekhodnykh protsessov v svyazannykh nelineinykh ostsillyatorakh”, Akusticheskii zhurnal, 39:1 (1993), 108-122

[10] Parovik R. I., “Mathematical Models of Oscillators with Memory”, Oscillators — Recent Developments, InTech, London, 2019, 3-21 . DOI: 10.5772/intechopen.81858

[11] Parovik R. I., “Fractal parametric oscillator as a model of a nonlinear oscillation system in natural mediums”, International journal of communications, network and system sciences, 6:3 (2013), 134-138 . DOI:10.4236/ijcns.2013.63016 | DOI