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BGA 2007
Different aspects of seismic amplitude decay in viscous magma
Patrick SmithSupervisor: Jürgen Neuberg
School of Earth and Environment,
The University of Leeds.Photo : R Herd, MVO
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BGA 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: plus some discussion of future work
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Low frequency seismicity
High frequency onset
Coda:• harmonic, slowly decaying• low frequencies (0-5 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
BGA 2007
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Source
Propagation of seismic energyConduit Resonance • Energy travels as interface waves along conduit walls at velocity controlled by magma properties
• Top and bottom of the conduit act as reflectors and secondary sources of seismic waves
• Fundamentally different process from harmonic standing waves in the conduit
Trigger Mechanism = Brittle Failure of MeltBGA 2007
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Propagation of seismic energy
BGA 2007
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P-wave
S-wave
Propagation of seismic energy
BGA 2007
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Interface waves
P-wave
S-wave
Propagation of seismic energy
BGA 2007
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Interface waves
Propagation of seismic energy
BGA 2007
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Interface waves
Propagation of seismic energy
BGA 2007
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Interface waves
Propagation of seismic energy
BGA 2007
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Interface waves
Propagation of seismic energy
BGA 2007
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Propagation of seismic energy
BGA 2007
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reflections
Propagation of seismic energy
BGA 2007
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reflections
Propagation of seismic energy
BGA 2007
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Propagation of seismic energy
BGA 2007
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Low frequencies
High frequencies
FAST MODE: I1NORMALDISPERSION
SLOW MODE: I2INVERSEDISPERSION
Low frequencies
High frequencies
Acoustic velocity of fluid
Propagation of seismic energy
BGA 2007
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I1
I2
Propagation of seismic energy
BGA 2007
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I1
I2
S
Propagation of seismic energy
BGA 2007
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S
I1
I2
Propagation of seismic energy
BGA 2007
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S
I1
I2
Propagation of seismic energy
BGA 2007
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‘Secondary source’
I2
Propagation of seismic energy
BGA 2007
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Surface-wave
‘Secondary source’
Propagation of seismic energy
BGA 2007
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Surface-wave
Propagation of seismic energy
BGA 2007
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I1R1
Propagation of seismic energy
BGA 2007
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I1R1
Propagation of seismic energy
BGA 2007
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I2
I1R1
Propagation of seismic energy
BGA 2007
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I2
‘Secondary source’
Propagation of seismic energy
BGA 2007
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‘Secondary source’
Propagation of seismic energy
BGA 2007
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Propagation of seismic energy
BGA 2007
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Propagation of seismic energy
BGA 2007
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Propagation of seismic energy
BGA 2007
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Most of energystayswithin the conduit
Propagation of seismic energy
BGA 2007
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Most of energystayswithin the conduit
Propagation of seismic energy
BGA 2007
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Most of energystayswithin the conduit
Propagation of seismic energy
BGA 2007
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Most of energystayswithin the conduit
Propagation of seismic energy
BGA 2007
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Propagation of seismic energy
BGA 2007
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R2
Propagation of seismic energy
BGA 2007
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R2
Events are recorded by
seismometers as surface
waves
Propagation of seismic energy
BGA 2007
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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
BGA 2007
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BGA 2007
Conduit Properties
seismic signals(surface)
Magma properties(internal)
Seismic parameters
Signal characteristics
Context: combining magma flow modelling & seismicity
Conduit geometry
+Properties of the magma
Attenuation via Q
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BGA 2007
Seismic attenuation in magma
Provides information about magma properties
Why is attenuation important?
Definitions:
Apparent (coda) Intrinsic (anelastic)
Radiative (parameter contrast,
geometric spreading)
true damping amplitude decay
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BGA 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:
Intrinsic Q is dependent on the properties of the magma:
Viscosity (of melt & magma)Gas content
Diffusivity
Use in finite-difference code to model frequency dependent Q
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BGA 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
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BGA 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
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BGA 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
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Results
BGA 2007
Apparent (coda) Intrinsic (anelastic)
An amplitude battle: competing effects
Radiative (parameter contrast,geometric spreading)
High intrinsic attenuation overcome by resonance effect – but need better understanding of how energy of interface waves is trapped
Determines behaviour at high intrinsic Q – shifts the curve vertically
0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
90
100
Intrinsic Q
Ap
pa
ren
t Q
Intrinsic Q vs. Apparent (coda) Q
2 SLS in array
0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
90
100
Intrinsic Q
Ap
pa
ren
t Q
Intrinsic Q vs. Apparent (coda) Q
2 SLS in arrayFor a fixed parameter contrast
Apparent Q greater than intrinsic Q:
Resonance dominates
Apparent Q less than intrinsic Q:Radiative energy loss dominates
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BGA 2007
Future Work and developments• Compare attenuation of acoustic waves with interface waves, both intrinsic & radiative – aim to understand the different components of amplitude loss.
• Relate amplitudes at surface to slip at source → ‘magma flow meter’ idea
• 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