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IUGG 2007
An amplitude battle: attenuation in bubbly magma versus conduit
resonance
Patrick Smith and Jürgen Neuberg
School of Earth and Environment,
The University of Leeds.
IUGG 2007
Outline of Presentation
• Background: low-frequency seismicity, seismic attenuation in gas-charged magma
• Methodology: Viscoelastic finite-difference model & Coda Q analysis
• Results and Implications
Low frequency seismicity
High frequency onset
Coda:• harmonic, slowly decaying• low frequencies (1-5 Hz)
→ Are a result of interface waves originating at the boundary between solid
rock and fluid magma
What are low-frequency earthquakes?
Specific to volcanic environments
IUGG 2007
Why are low frequency earthquakes important?
• Have preceded most major eruptions in the past
• Correlated with the deformation and tilt - implies a close relationship with pressurisation processes (Green & Neuberg, 2006)
• Provide direct link between surface observations and internal magma processes
IUGG 2007
IUGG 2007
Conduit Properties
seismic signals(surface)
Magma properties(internal)
Seismic parameters
Signal characteristics
Incorporate flow model data into wavefield models
Combining magma flow modelling and seismicity
Conduit geometry
+Properties of the magma
Attenuation via Q
IUGG 2007
Seismic attenuation in magma
(i) Generation of low-frequency events: Can seismic energy travel through a highly viscous magma to produce resonance - or is it too highly attenuated?
(ii) Allows us to link signal characteristics, e.g. amplitude decay of the coda, to properties of the magma such as the viscosity.
Why is attenuation is important?
Definitions:
Apparent (coda) Intrinsic (anelastic) Radiative (parameter contrast,geometric spreading)
IUGG 2007
Amplitude decay of codaComparison of approaches:1. Kumagai & Chouet: used Sompi method to
calculate complex frequencies to derive apparent Q from signals → resonating crack finite-difference model using bubbly water mixture to reproduce signals. Only radiative Q – no account of intrinsic Q
2. Our approach – viscoelastic finite-difference model, with depth dependent parameters: includes both intrinsic attenuation of magma and radiative energy loss due to elastic parameter contrast.
Kumagai & Chouet (1999)
IUGG 2007
Intrinsic Q• Intrinsic Q is directly dependent on properties of the attenuating
material: but if these are unknown can be equivalently calculated from phase lag
between applied stress and resulting strain:
• Q is dependent on the properties of the magma:
• Viscosity• Gas content• Diffusivity
Am
plitude
Phase lag
Applied stressResultant strain
time
Collier et al. (2006)
IUGG 2007
Modelling Intrinsic Q• To include anelastic ‘intrinsic’ attenuation – the finite-difference code uses a viscoelastic medium: stress depends on both strain and strain rate.
• Parameterize material using Standard Linear Solid (SLS): viscoelastic rheological model
whose mechanical analogue is as shown:
• Use parallel array to model Q with frequency
IUGG 2007
Finite-Difference Method
Domain Boundary
Solid medium(elastic)
Fluid magma(viscoelastic
)Variable Q
Damped Zone
Free surface
Seismometers
Source Signal:
1Hz Küpper wavelet
(explosive source)
ρ = 2600 kgm-3
α = 3000 ms-1
β = 1725 ms-1
•2-D O(Δt2,Δx4) scheme based on Jousset, Neuberg & Jolly (2004)
• Volcanic conduit modelled as a viscoelastic fluid-filled body embedded in homogenous elastic medium
IUGG 2007
Determining apparent (coda) Q
Coda Q methodology:
• Decays by factor (1 Q) each cycle
Aki & Richards (2003)
Model produces harmonic, monochromatic synthetic signals
0 1 2 3 4
0
Time [number of cycles]A
mpl
itude-A0
A0
A1
A2
A3
Take ratio of successive peaks,
e.g.A1
A2
= Q
Q =A2
A1 – A2
IUGG 2007
Calculation of coda QCalculating Q using logarithms
Gradient of the line given by:
Unfiltered data
Hence Q is given by:
0 2 4 6 8 10 12-24
-23.8
-23.6
-23.4
-23.2
-23
-22.8
-22.6
Time [cycles]
log(
Am
plitu
de)
Q value based on envelope maxima
Gradient of line =-0.10496
Q value from gradient = 31.5287
Linear Fit
Data
IUGG 2007
Results
0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
90
100
Intrinsic Q
App
aren
t Q
Intrinsic Q vs Apparent (coda) Q
For a fixed parameter contrast
2 SLS in array
Apparent Q less than intrinsic Q:
Radiative energy loss dominates
Apparent Q greater than intrinsic Q:
Resonance dominates
IUGG 2007
Future Work and developments
• Compare attenuation of acoustic waves with interface waves, both intrinsic & radiative
• Use flow magma models to derive viscosities – examine impact on seismic amplitude decay
• Link observables, e.g. coda decay & frequency content to magma properties such as the viscosity, gas content & pressure → ‘magma flow meter’ idea