Modeling the Failure of Magmatic Foams and Application to Infrasonic Signals at Stromboli Volcano, Italy

Abstract:

The failure of magmatic foams appears to be a fundamental eruption process at open-conduit, basaltic volcanoes. We applied the fiber bundle model using global load sharing to model the failure of magmatic foams. The fiber strengths in the model were taken from bubble wall widths measured in four computer-simulated foams and by X-ray tomographic microscopy in three foams produced in the laboratory by heating hydrated basaltic glasses at 1 atm. to 1200 °C. The strengths of the modeled foams were calibrated based upon the correlation of the strength of one foam with published experimental data. The fiber bundle model successfully reproduced measured tensile strengths of porous volcanic rocks studied by other researchers and confirms published findings of the primary importance of foam porosity, as well as the secondary importance of structural details that affect the number and size of bubble walls and permeability. The success of the fiber bundle model in reproducing foam strengths encouraged us to compare its predictions with infrasonic measurements associated with bubbles at Stromboli (Italy). We found that within uncertainty the power-law exponents of the infrasonic energies and of the fiber bundle model energies are in agreement. They both show a cross-over from an exponent of 5/2 associated with the bursting of small bubbles in the infrasonic measurements to an exponent of 3/2 for normal Strombolian eruptions associated with infrasonic signals from meter-scale bubbles. The infrasonic signals for major explosions and a paroxysmal eruption at Stromboli fall near the extrapolation of the power law defined by the low-amplitude, bubble bursting events. The measurement of small-amplitude infrasonic events at Stromboli thus appear useful in predicting the recurrence interval of paroxysmal eruptions at this volcano and may also provide a tool that uses common, small-amplitude infrasonic events to constrain the frequency of larger eruptions at other volcanoes.