HR: 11:05h
AN: V52B-04    [Abstracts]
TI: A Dynamical Model of Seismogenic Dome Extrusion, Mount St. Helens, 2004-2005
AU: * Iverson, R M
EM: riverson@usgs.gov
AF: U.S. Geological Survey, 1300 SE Cardinal Ct. #100, Vancouver, WA 98683 United States
AB: A new mathematical model aims to explain the relationship between two key aspects of the 2004-2005 eruption of Mount St. Helens: (1) for many months the eruption was characterized by nearly constant rates of extrusion (~ 2 m³/s) of a solid dacite plug surfaced with striated fault gouge; and (2) this extrusion was accompanied by repetitive, small (M < 2), shallow (< 1 km) earthquakes that occurred at regular intervals (~ 100 s). The persistence of these nearly periodic earthquakes (dubbed "drumbeats") motivates the hypothesis that they resulted from discrete slip events (< 1 cm each) along the margins of the plug as it was forced incrementally upward by a nearly steady influx of ascending, solidifying magma. This hypothesis is formalized mathematically by considering conservation of mass and momentum of the solid plug and underlying magma, and by adopting simple constitutive relations for the compressibilities of the magma and conduit walls and for the frictional resistance F of the plug sliding against the conduit walls. The resulting model reduces to a nonlinear system of three ordinary differential equations describing simultaneous evolution of the upward plug velocity, u, basal magma pressure, p, and volume of the liquid-filled portion of the conduit, V. In general these equations must be solved numerically, but they also yield analytical results showing that u will persistently oscillate, provided that F does not increase as u increases. Predicted oscillation periods correspond well with the observed interval between drumbeat earthquakes. Moreover, if F decreases nonlinearly as u increases (representing a decay from static to rate-dependent dynamic friction), numerical solutions show that oscillations of u sharpen into discrete stick-slip cycles capable of producing earthquakes. The magma-plug system can be attracted to this type of near-equilibrium, oscillatory behavior even if it begins in a disequilibrium state, as is necessary to instigate a volcanic eruption. However, initial conditions far from equilibrium will cause ejection of the magma plug and a probable transition to explosive behavior.
DE: 4410 Bifurcations and attractors
DE: 4445 Nonlinear differential equations
DE: 8414 Eruption mechanisms and flow emplacement
DE: 8425 Effusive volcanism
SC: Volcanology, Geochemistry, Petrology [V]
MN: Fall Meeting 2005