1. Conduit length Conduit top Tilt: 17 µrad due to pressure 50 MPa 100 MPa P Tilt  Pressure Conduit length Conduit top τ Tilt  Traction  Strain rate  Magma velocity (Green et al., 2006) Continuity equation for compressible fluids : t    0    U  reference Dome collapse July 12, 2003 Photo: J. Neuberg Generation of interface waves: --30m-- const (ρ c =2680 kg m -3 χ c = 30 %) const (~1,5 10 -5 Pa s)  b  m  g  c   g  g  c  c Magma = Melt + Crystals + Gas ρg ηgρg ηg ρm ηmρm ηm f(Cm, P) (Hess & Dingwell,1996) const (~ 2300 kg m -3 ) b ηbb ηb ρ c χ c mP/RT ηbηb ηmηm Melt viscosity Magma viscosity (Collier & Neuberg, 2006) Reaction to volume change Reaction to shear stress = 0 with λ = K – 2/3 η b K: volume viscosity η b : magma shear (dynamic) viscosity Modelling: Compressible Navier Stokes equation melt gas crystals 30m conduit 50m 30m Observations & Model in summary: ττ Gas diffusion No seismicity Pressure increasing 1 2 Seismicity Pressure decreasing 4 ττ No seismicity Magma slowing Gas diffusion (Green et al., 2006) 3 ττ Diffusion lags behind Gas loss Each instrument is a filter Seismometer: differentiation bandpass limitation Lee’s Yard St George’s Hill Lee's Yard 0 24 6 Time (s) Normalised Amp. Data Analysis. From seismograms to magma: interpreting broadband seismic signals in terms of magmatic processes EGU, Vienna, April 2007. J. Neuberg 1, P. Smith 1, D. Green 1, M. Collombet 1, L. Collier 1, C. Hammer 2 & J. Key 1. 1. School of Earth and Environment, University of Leeds. UK. (J.Neuberg@see.leeds.ac.uk) 2. Institute of Geosciences, University of Potsdam, Germany. (Chammer@rz.uni-potsdam.de) Seismic wavefield modelling. Magma flow modelling. 50m conduit Ultra-long period signals. Trigger mechanism and seismic moment tensor analysis. Deformation. 90% CLVD Compensated linear vector dipole Ring dyke Near field terms & single forces → Source mechanism that is non- destructive, repeatable and with a stationary source location. Characteristics of low-frequency events Similar waveforms Repetitive Tight clusters of source locations Swarms precede dome collapse Family members: normalised & stacked Overlain, Normalized Traces Link seismicity rate with magma movement at depth. Pre- cursor to dome collapse Conduit filled with melt, gas & crystals Montserrat topography Onset contains information on trigger mechanism Conduit resonance Comparison of a 30m and 50m wide conduit: illustrating the change in frequency content with widening conduit 2-D Finite-Difference Model : Fluid-filled conduit (rather than crack) Physical properties are depth & time dependent Viscoelastic model includes effects of intrinsic attenuation and damping ● Seismicity correlates with tilt/deformation Sources are dependent on pressure Models for seismicity & tilt: Modelling parameters: conduit top & pressure 3-D detail - cut out to see tilt source (vertically exaggerated x 3) References and Acknowledgements. Collier, L. & Neuberg, J., 2006, Incorporating seismic observations into 2D conduit flow modelling. J. Volcanol. Geotherm., 152, pp331-346 Green, D., Neuberg, J., & Cayol, V., 2006, Shear stress along the conduit wall as plausible source of tilt at Soufrière Hills Volcano, Montserrat. GRL., 33, L10306. Jousset, P., Neuberg, J. & Jolly, A., 2004, Modelling low-frequency volcanic earthquakes in a viscoelastic medium with topography. J. Geophys. Int., 159, pp776-802. Neuberg, J., Tuffen, H., Collier, L., Green, D., Powell T. & Dingwell D., 2006, The trigger mechanism of low-frequency earthquakes on Montserrat. J. Volc. Geotherm., 153, pp37-50. (Jousset et al., 2004) (Neuberg et al, 2006) Determine: pressure, density, temperature, viscosity, gas volume %, magma velocity, velocity gradient (= strain rate) Employ: Navier Stokes equation for compressible flow, gas loss – permeability, temperature loss & friction, water solubility, viscosity Magma velocity profiles for 30m and 50m wide conduit Moment tensor inversion with corresponding radiation pattern Cylindrical shear fracturing at the edge of the conduit as triggering mechanism? The resulting particle motion pattern should be symmetrical, centred around the conduit location, with downward motions in the inner ring and upward motions in the outer ring Only upward particle motions Particle motions compatible with a " shallow " event Fit two stations: use ratio of displacement for ground deformation modelling Models of shear stress for conduits with depth dependent geometries – using a constant magma viscosity 2-D conduit model: narrowing from 60m to 30m 3-D conduit model: 30m wide pipes joined by 10m deep sill and : displacement components : wavenumber and : potentials of the P- and S-waves Trigger mechanism velocity profile Magma ruptures if   Pa 7 at constant depth Conduit resonance where viscosity is low Shear stress Tilt: 17 µrad due to traction 0.5 MPa 1 MPa