Dynamics of seismogenic volcanic extrusion , Mount St . Helens , 2004 - 2005

behaviour characterized by nearly steady extrusion of a solid dacite plug and nearly periodic shallow earthquakes. Diverse data motivate the hypothesis that these earthquakes resulted from stick-slip motion along the margins of the plug as it was forced incrementally upward by ascending, solidifying, gas-poor magma. We formalize this hypothesis with a dynamical model that reveals a strong analogy between behaviour of the magma-plug system and that of a variably damped oscillator. Small oscillations in extrusion velocity grow unstably because plug friction exhibits rate weakening, but friction reverses direction when magma pressure relaxes sufficiently and the plug velocity declines to zero. This reversal transforms unstable oscillations into repetitive stick-slip cycles, irrespective of other frictional effects. Dynamical attraction to this self-regulating behaviour is strong, and inferred magnitudes of recurrent slip events help constrain the balance of forces governing the earthquakes and eruption. 2 Silicic volcanoes are famous for explosions and other disequilibrium behaviour, but the dome-building eruption of Mount St. Helens (MSH) that began in October 2004 and continues today has exhibited prolonged, near-equilibrium behaviour that affords unique opportunities for understanding volcano dynamics. A remarkable feature of the eruption has been persistence of nearly steady, solid-state extrusion (1-2 m 3 /s) accompanied by nearly periodic earthquakes with shallow (< 1 km) focal depths. The repetitive nature of these earthquakes implies the existence of a nondestructive seismic source, and it provides an exceptional opportunity to link seismicity and extrusion dynamics 1,2. Here, we summarize seismic, geodetic, photogrammetric, petrologic, geochemical, and thermal data collected during the 2004-2005 MSH eruption, and we hypothesize a mechanistic link between magma influx, nearly steady extrusion, and nearly periodic earthquakes. A new mathematical model formalizes our hypothesis and reveals a strong analogy between the behaviour of MSH and that of variably damped oscillators. We exploit this analogy to probe unobserved aspects of eruption dynamics. Eruptive behavior and seismicity Although MSH erupted explosively on 18 May1980, dome-building activity that began in 2004 is consistent with the volcano's recent geologic history 3. Over the past ~ 4000 years MSH has extruded rock at a mean rate ~ 0.2 m 3 /s while constructing a 26 km 3 edifice composed primarily of andesite and dacite lava flows and domes and their detritus (Supplementary Figure 1). From 1980-1986 a dacite dome grew episodically in the 1980 crater, and its volume ultimately reached 74×10 6 cubic metres 4. From 1987-2004 MSH 3 did not …