Conduit length

Con

du

it t

op

Tilt: 17 µraddue to pressure

50 MPa

100 MPa

P

Tilt Pressure

Conduit length

Con

du

it t

op

τ

Tilt Traction Strain rate Magma velocity

(Green et al., 2006)

gUUUPdt

dU T

b

Continuity equation for compressible fluids: t 0

U

reference

Dome collapseJuly 12, 2003Photo: J. Neuberg

Generation of interface waves:

--30m--

const(ρc=2680 kg

m-3

χc= 30 %)

const(~1,5 10-5 Pa s)

bmgcggcc

Magma = Melt + Crystals + Gas

ρg ηgρm ηm

f(Cm, P)(Hess &

Dingwell,1996)

const(~ 2300 kg m-3)

b ηb ρc χc

mP/RT

ηbηm

Melt viscosity Magma viscosity

(Collier & Neuberg, 2006)

Reaction to volume change

Reaction toshear stress

= 0

with λ = K – 2/3 ηb

K: volume viscosity ηb : magma shear (dynamic) viscosity

Modelling: Compressible Navier Stokes equation

• melt• gas• crystals

30m conduit

50m

30m

Observations & Modelin summary:

τ τ

Gas diffusion

No seismicity

Pressure increasing

1

2

Seismicity

Pressuredecreasing

4

τ τ

No seismicity

Magma slowing

Gas diffusion

(Green et al., 2006)

3

τ τ

Diffusion lagsbehind

Gas loss

Each instrument is a filter

Seismometer:• differentiation• bandpass limitation

Lee’s Yard

St George’s Hill

Lee's Yard

0 2 4 6Time (s)

Nor

mal

ised

Am

p.

Data Analysis.

From seismograms to magma: interpreting broadband

seismic signals in terms of magmatic processesEGU, Vienna, April 2007.

J. Neuberg1, P. Smith1, D. Green1, M. Collombet1, L. Collier1, C. Hammer2 & J. Key1.1. 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% CLVDCompensated 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 motionsOnly 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

xu

tizikxl

Sxl

zz

tizikxlz

xlcx

eeelekiu

eeeikelu

zSP

zSP

xu zuand : displacement components

: wavenumber

and : potentials of the P- and S-waves

zk pzP Vkfl ,,: SzS Vkfl ,,:

Trigger mechanism

velocityprofile

Magma ruptures if

Pa7

at constant depth

Conduit resonance whereviscosity is low

Shear stress

Tilt: 17 µraddue to traction

0.5 MPa

1 MPa