low frequency coda decay: separating the different components of amplitude loss. patrick smith...

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

Propagation of seismic energy

P-wave

S-wave


ESC 2007

Interface waves

P-wave

S-wave


ESC 2007

Interface waves


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ESC 2007

reflections


ESC 2007


ESC 2007

Low frequencies

High frequencies

FAST MODE: I1NORMALDISPERSION

SLOW MODE: I2INVERSEDISPERSION

Low frequencies

High frequencies

Acoustic velocity of fluid


ESC 2007

I1

I2


ESC 2007

I1

I2

S


ESC 2007

S

I1

I2


ESC 2007

‘Secondary source’

I2


ESC 2007

Surface-wave



ESC 2007

Surface-wave


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I1R1


ESC 2007

I2

I1R1


ESC 2007

I2



ESC 2007



ESC 2007

Most of energystayswithin the conduit


ESC 2007


ESC 2007

R2


ESC 2007

R2

Events are recorded by

seismometers as surface

waves


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

Photo : R Herd, MVO

Vm/s

Towards a Magma Flow Meter

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…

Thanks for your attention!

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)

Seismometer at surface

AT

Seismometer at sourceASRC AR

Layer 1: solidss

Layer 2: fluid or solidff

4000 m

6000 m

500 m

2500 m

3000 m

ffss

ffssR

ffss

ffT

2

low frequency coda decay: separating the different components of amplitude loss. patrick smith...

Documents

brittle failure of melt

result of interface

lowfrequency seismicity

conduit walls

conduit act

lowfrequency earthquakes

harmonic standing waves

low frequency coda decay