Volcanic two-phase flow instability: Pressure-drop oscillation model for tilt-steps at Miyakejima volcano

Periodic step-like tilt changes were observed at intervals of 12 to 60 hours during the caldera_fs formation stage preceding the 2000 Miyakejima volcano eruption. Our analysis suggests that these phenomena were caused by the cyclic expansion of a subsurface sill-like magma plumbing system. The sill reservoir is connected to the summit conduit with a gas-pocket at its upper part, having a cap at its top. As a source model of the tilt-steps, we propose a gas-liquid flow in this sill-conduit system. The instability of such a two-phase flow triggers a phenomenon called _gpressure-drop oscillation._h We define the gas pressure and the pressure at the exit of the sill as Pg and Pe, respectively and their difference as dP=Pg-Pe. The state of dP and the flux f in the sill experiences the periodical trace, 1: when f is small, the magma head gradually rises and dP increases, then, 2: when dP reaches a threshold, over which the system becomes unstable, the flux runs off toward an another stable state with a large flux, then, 3: the dP gradually decreases and the flux decreases and after that, 4 the system goes again back to the state 1. We believe that the observed tilt-steps correspond to the run-off from 2 to 3, causing a rapid increase of the flux with the opening of the sill. This phenomenon is fundamentally characterized by the Van del Pol_fs equation and its non-linear character governs the system response. The capacity of the gas-pocket mainly determines the period of the change of the flux and dP. The observed intervals of tilt-steps suggest the uplift and descent of magma head in the conduit.