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

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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

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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

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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)

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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)

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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)

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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

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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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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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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

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

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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