Mathematical Model of the Stick-Slip Effect for Describing the "Drumbeat" Seismic Regime During the Eruption of the Kizimen Volcano in Kamchatka

TL;DR

This paper develops a mathematical model to explain the 'drumbeats' seismic pattern observed during the Kizimen volcano eruption, linking it to the stick-slip movement of lava flow front.

Contribution

It introduces a novel fractional nonlinear oscillator model to describe the self-oscillating stick-slip dynamics of volcanic lava flow.

Findings

The model explains the quasi-periodic seismic 'drumbeats' observed.

The movement of the lava flow front is linked to the stick-slip mechanism.

Qualitative agreement between the model and observed seismic patterns.

Abstract

During the eruption of the Kizimen volcano in 2010-2013. There was a uniform squeezing of the viscous lava flow. Simultaneously with its movement, earthquakes with an unusual quasi-periodicity were recorded, the "drumbeats" mode. In this work, we show that these earthquakes were generated by the movement of the flow front, which was observed for the first time in the practice of volcanological research. We represent the movement of the flow as an intermittent slip with the inclusion of the "stick-slip" mechanism with the initiation of a self-oscillating process. The plausibility of the phenomenological model at the qualitative level is confirmed by the mathematical model of a fractional nonlinear oscillator.