low frequency coda decay: separating the different components of amplitude loss. patrick smith...
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Low frequency coda decay: separating the different
components of amplitude loss.
Patrick SmithSupervisor: Jürgen Neuberg
School of Earth and Environment,
The University of Leeds.
Outline of Presentation
• Background: low-frequency seismicity, project context, quantifying amplitude losses
• Methodology: Viscoelastic finite-difference model & Coda Q analysis
• Results and Implications: plus some discussion of future work
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
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 Melt
Low frequencies
High frequencies
FAST MODE: I1NORMALDISPERSION
SLOW MODE: I2INVERSEDISPERSION
Low frequencies
High frequencies
Acoustic velocity of fluid
Propagation of seismic energy
ESC 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)
• One of the few tools that provide direct link between surface observations and internal magma processes
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
depth of brittle failure
slip
slipplug flow gas loss
parabolic flow
Seismic trigger mechanism
Collier & Neuberg, 2006; Neuberg et al., 2006
Stress threshold:
Pa7
Swarm structure
Increased event rates
Linked to magma extrusion
Similar earthquake waveforms
Swarms preceding dome collapse
Seismic attenuation in magmaWhy is attenuation important?
Definitions:
Apparent (coda) Intrinsic (anelastic)
Radiative (parameter contrast)
true damping amplitude decay
• Needed to quantitatively link source and surface amplitudes.• Allows us to link signal characteristics, e.g. amplitude decay of the coda, to properties of the magma such as the viscosity
(Aki, 1984)
Seismometer
Quantifying amplitude losses
Trigger mechanism: brittle failure at conduit walls
Intrinsic attenuation in magma causes some damping of signal amplitude – but how much?
Contrast in elastic parameters causes some energy to be transmitted and some to be reflected
Qi
R (reflection coefficient)
T (transmission coefficient)
Q-1=Qi-1+Qr
-1
Q-1
Qr-1
Total amplitude decay is a combination of these contributions:
f
f
s
s
Further amplitude loss due to geometric spreading – signal travels to seismometer as surface wave: but DOES NOT contribute to apparent Q !
Amplitude decay of codaComparison of approaches:1. Kumagai & Chouet: used 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.
Figure from Kumagai & Chouet (1999)
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 intrinsic Q
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
ESC WG 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(taken from Chouet 1996)
Synthetic trace
Calculation of coda QCalculating Q using logarithms
Gradient of the line given by:
Hence Q is given by:
Unfiltered data
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)
Apparent Q value based on envelope maxima
Gradient of line =-0.10496
Q value from gradient = 31.5287
Linear Fit
Data
Results
Apparent (coda) Intrinsic (anelastic)
An amplitude battle: competing effects
Radiative (parameter contrast)
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
Results… in progress!
Apparent Q vs Reflection Coefficient: A Puzzle!
• Intuitively expect opposite behaviour to what is observed
• Due to difference between acoustic and interface waves?
Apparent Q vs. intrinsic Q for different parameter contrasts:
• Expect to shift curve vertically
• Needs further analysis!
Apparent (coda) Q vs. Reflection Coefficient
Reflection Coefficient (from parameter contrast)
App
aren
t Q fr
om c
oda
anal
ysis
Low R → low contrast → expect rapid decay of energy → low Q ??
High R → high contrast → expect slower decay of energy → high Q ??
R = 0.25
R = 0.50
R = 0.75
Future Work and developmentsShort-Term: Amplitudes• Quantitatively relate amplitudes at surface to slip at source → ‘magma flow meter’ idea. • Compare attenuation of acoustic waves with interface waves – aim to understand the variation with reflection coefficient !
Longer Term:
• Calculate apparent Q for real data? Can we constrain intrinsic Q or conduit properties?
• Wavefield models: refine to fit Q with frequency at each point. Look at other geometries?
• Magma flow modelling: work on including gas-loss and crystallisation processes. Simulate loading due to build up of extruded material (dome growth)
• Incorporating flow modelling results into wavefield models…
IUGG 2007
Quality Factor, Q• Widely used in seismology, inverse of attenuation• 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
Taken from Collier et al. (2006)