Modeling eruptions of Karymsky volcano

A model is proposed to explain temporal patterns of activity in a class of periodically exploding Strombolian-type volcanos. These patterns include major events (explosions) which follow each other every 10-30 minutes and subsequent tremor with a typical period of 1 second. This two-periodic activity is thought to be caused by two distinct mechanisms of accumulation of the elastic energy in the moving magma column: compressibility of the magma in the lower conduit and viscoelastic response of the almost solid magma plug on the top. A release of the elastic energy happens when a stick-slip dynamic phase transition in a boundary layer along the walls of the conduit occurs; this phase transition is driven by the shear stress accumulated in the boundary layer. The first-order character and intrinsic hysteresis of this phase transition explains the long periods of inactivity in the explosion cycle. Temporal characteristics of the model are found to be qualitatively similar to the acoustic and seismic signals recorded at Karymsky volcano in Kamchatka. A wide variety of types of volcanic activity exists: from devastating explosions separated by calm periods of many years or even centuries to a steady continuous outpouring of magma. In this paper we study mechanisms that give rise to a Strombolian-type volcanic activity, which is somewhere between these two extremes and characterized by regularly repeated explosions (10-400 per day) followed by relatively calm periods. Often in the course of a longer explosion, the gas and ash emission exhibits audible and visible modulations with a rather robust period of about 1 second. These modulations, often found on the seismograms of Strombolian-type eruptions, received a special name, "chugging" (Benoit and McNutt, 1997), because they resemble a periodic noise produced by a steam engine. An example of a volcano exhibiting such activity, we consider Karymsky volcano on Kamchatka peninsula in the Far East of Russia. We believe that these Strombolian-type eruption patterns are caused by peculiarities of the motion of the magma column, and propose a model that describes the magma motion in a volcanic conduit as a creep flow of viscoelastic compressible medium with shear-stress-dependent boundary conditions. We show that the dynamics of the model indeed exhibits 2 levels of quasiperiodic behavior and resembles the eruption patterns of the Strombolian-type volcanos both on long and short time scales. The physical transparency of the suggested model allows us to express the observed time scales using the material properties of the magma. Our paper is organized in the following way: first, we briefly describe geological aspects of the current eruption of Karymsky volcano. Then, after referring to the existing explanations of Strombolian-type activity, the model is formally introduced. We derive simple analytical expressions for a dormant time, a duration of explosion , and a typical period of tremor, and then present a numerical solution to a system of dynamical equations describing the motion of the magma column. The paper is concluded with a discussion of results and possible directions for further studies.