Russian Journal of Earth Sciences Russian Journal of Earth Sciences Russian Journal of Earth Sciences 1681-1208 52549 10.2205/2023ES000845 ОРИГИНАЛЬНЫЕ СТАТЬИ ORIGINAL ARTICLES ОРИГИНАЛЬНЫЕ СТАТЬИ Analytical model of small fluctuations of compressible magma with Maxwell rheology in the feeding system of a volcano. Part 1. Density oscillation Аналитическая модель малых колебаний сжимаемой магмы с реологией Максвелла в питающей системе вулкана. Часть 1. Осцилляции плотности https://orcid.org/0000-0002-6934-6873 Радионов Анатолий Анатольевич Radionoff Anatoly Anatolievich aar200772@mail.ru

кандидат технических наук;

candidate of technical sciences;

 Южный математический институт – филиал Федерального государственного бюджетного учреждения науки Федерального научного центра «Владикавказский научный центр Российской академии наук» Владикавказ Россия Southern Mathematical Institute – the Affiliate of Vladikavkaz Scientific Center of Russian Academy of Sciences Vladikavkaz Russian Federation 29 06 2023 29 06 2023 23 2 1 14 17 10 2022 03 04 2023 https://ras.editorum.ru/en/nauka/article/52549/view

Представлена аналитическая математическая модель, описывающая один из возможных механизмов возникновения длиннопериодных сейсмических событий, часто регистрирующихся вблизи активных вулканических центров. Питающая система вулкана моделируется в простейшей форме канала цилиндрической формы, заполненного сжимаемым магматическим расплавом с реологией тела Максвелла. Показано, что такое магматическое тело может испытывать гармонические затухающие колебания, коэффициент затухания которых определяется временем релаксации магматического расплава. Эти колебания могут появляться как реакция на возмущение плотности, вызываемое поступлением более плотной магмы из глубинных слоев или изменением давления в питающей системе вулкана. Показана зависимость собственной частоты колебаний от физических характеристик магматического расплава и геометрических размеров питающего канала. При учете сжимаемости магматического расплава, возмущения плотности зависят от размера питающей системы и характеризуются периодическими осцилляциями, наиболее выраженными вблизи оси канала. Колебания также испытывает компонента скорости течения, направленная вдоль радиуса цилиндра. Обсуждается механизм источника длиннопериодных сейсмических событий. Модель применяется для описания длиннопериодных землетрясений вулкана Сантьягуито, Гватемала.

The analytical mathematical model is presented that describes one of the possible mechanisms for the occurrence of long-period seismic events that are often recorded near active volcanic centers. The feeding system of the volcano is modeled in the simplest form of a cylindrical channel filled with a compressible magmatic melt with the rheology of a Maxwell body. It is shown that such a magmatic body can experience harmonic damped oscillations, the damping coefficient of which is determined by the relaxation time of the magmatic melt. These fluctuations may appear as a response to a density perturbation caused by the influx of denser magma from deep layers or a change in pressure in the supply system of the volcano. The dependence of the natural oscillatory frequency on the physical characteristics of the magmatic melt and the geometric dimensions of the feed channel is shown. When the compressibility of the magmatic melt is taken into account, density perturbations depend on the size of the feeding system and are characterized by periodic oscillations, which are most pronounced near the channel axis. Oscillations are also experienced by the flow velocity component directed along the radius of the cylinder. The source mechanism of the long-period seismic events is discussed. The model is used to describe long-period oscillations recorded near Santiaguito (Guatemala).

 вулканические длиннопериодные землетрясения питающая система вулкана реоло- гия Максвелла сжимаемое магматическое тело аналитическая модель Volcanic low-frequency earthquakes volcano feeding system magmatic melt rheology compressible magmatic body analytical model нет no

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