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"abstract": "The 2004-5 eruption of Mount St. Helens exhibited \nsustained, near-equilibrium behavior characterized by nearly \nsteady extrusion of a solid dacite plug and nearly periodic \noccurrence of shallow earthquakes. Diverse data support the \nhypothesis that these earthquakes resulted from stick-slip \nmotion along the margins of the plug as it was forced incrementally upward by ascending, solidifying, gas-poor magma. \nI formalize this hypothesis with a mathematical model derived \nby assuming that magma enters the base of the eruption \nconduit at a steady rate, invoking conservation of mass and \nmomentum of the magma and plug, and postulating simple \nconstitutive equations that describe magma and conduit compressibilities and friction along the plug margins. Reduction \nof the model equations reveals a strong mathematical analogy \nbetween the dynamics of the magma-plug system and those of \na variably damped oscillator. Oscillations in extrusion velocity \nresult from the interaction of plug inertia, a variable upward \nforce due to magma pressure, and a downward force due to \nthe plug weight. Damping of oscillations depends mostly \non plug-boundary friction, and oscillations grow unstably if \nfriction exhibits rate weakening similar to that observed in \nexperiments. When growth of oscillations causes the extrusion \nrate to reach zero, however, gravity causes friction to reverse \ndirection, and this reversal instigates a transition from unstable \noscillations to self-regulating stick-slip cycles. The transition \noccurs irrespective of the details of rate-weakening behavior, \nand repetitive stick-slip cycles are, therefore, robust features of \nthe system\u2019s dynamics. The presence of a highly compressible \nelastic driving element (that is, magma containing bubbles) \nappears crucial for enabling seismogenic slip events to occur \nrepeatedly at the shallow earthquake focal depths (<1 km) \nobserved during the 2004-5 eruption. Computations show that fluctuations in magma pressure accompanying such slip events \nare <3 kPa, indicating that deviations from mechanical equilibrium are slight and that coseismic force drops are <108\n N. \nThese results imply that the system\u2019s self-regulating behavior \nis not susceptible to dramatic change--provided that the rate \nof magma ascent remains similar to the rate of magma accretion at the base of the plug, that plug surface erosion more or \nless compensates for mass gain due to basal accretion, and that \nmagma and rock properties do not change significantly. Even \nif disequilibrium initial conditions are imposed, the dynamics \nof the magma-plug system are strongly attracted to self-regulating stick-slip cycles, although this self-regulating behavior \ncan be bypassed on the way to runaway behavior if the initial \nstate is too far from equilibrium.",
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