Effects of magma compressibility

on volcano deformation and seismicity

Eleonora Rivalta

Outline

Interaction between magma-filled deformation sources:

1) Magma chamber ↔ dyking2) Magma chamber ↔ magma chamber3) Dyke ↔ faulting

and the role played by compressibility in the dynamics of these interactions.

1 -The 'missing magma' problem:the 1997 intrusion at Kilauea

(Owen et al., 2000)

= 3.8

Summit: -1.5 106 m3

Makahopuhi: -1.2 106 m3

Pu'u O'o: -12.7 106 m3

Dike: 23 106 m3

r V =V dyke

ΔV chamber

The 2007 'father's day' intrusion

(Montogomery-Brown et al., 2010, JGR)

rV = 3.0

Summit: -1.8 106 m3

Pu'u O'o: -0.02 106 m3

Dike 1: 0.8 106 m3

Dike 2: 15.8 106 m3

Pu'u O'o lake: -3.65 106 m3

The 2007 intrusion at Kilauea

(Montogomery-Brown et al., 2011)

The 'missing magma' problem:the 2005 intrusion in Afar

Wright et al., 2006

The 'missing magma' problem:the 2005 intrusion in Afar

Wright et al., 2006

r V =V dyke

ΔV chamber∼

∼ 2.5 km3

(0.25+0.25)km3=5

Interpretation

An additional source, too deep to be detected from deformation signals, fed the intrusion from below. → In general, difficult to test/falsify

Volume determinations are not reliable→ Not to the extent required to explain these discrepancies

Magma compressibility

Different source compliance

Effects of magma compressibilityon volcano deformation

Árnadóttir et al., 1998

Johnson et al., 2000

Johnson, 1992

Mastin et al., 2008

Magma compressibility and elastic responseof host rock mask the 'true volume' of the intrusionAppl. to volume budget of 1984 intrusion at Krafla

Tryggvason, 1981 Pressure variation and volume change at theKrafla magma reservoir

Considerations on the different volumes involved

Application to the relation between eruptedand deflation volumes at Mount St. Helens

Rivalta and Segall, 2008 'Mass conservation', volume budget during intrusion events

Rivalta, 2010 Dynamics of coupling between magma chambers and dikes

Physical model

dM=ρdV+V d ρ=(ρ dVdp

+Vd ρdp

)dp=ρV (βe+βm)dp

βe(spherical chamber )=3

4μ∼10−11−10−10Pa−1

βe(penny shaped crack )=1

pi−σ∼10−7Pa−1

(or much higher if magma contains bubbles)

βm=10−11−10−10Pa−1

Magma compressibility: Source compliance:

βm=1ρd ρdp

βe=1VdVdp

Physical model

If total mass is constant →

dM=ρdV+V d ρ=(ρ dVdp

+Vd ρdp

)dp=ρV (βe+βm)dp

r V=V i

ΔV c=1+βmβe

βe(spherical chamber )=3

4μ∼10−11−10−10Pa−1

βe(cigar−shaped chamber )=1μ

βe(ellipsoid ) depends on the aspect ratio

βe(penny shaped crack )=1

pi−σ∼10−7Pa−1(or much higher

if magma contains bubbles)

βm=10−11−10−10Pa−1

(Amoruso and Crescentini, 2009)

Rivalta and Segall, 2008

Physical model

Rivalta and Segall, 2008

The 'missing magma' problem:chronology

5 – 6 (Árnadóttir et al., 1998)1984 Krafla (Iceland)

1997 Kilauea (Hawaii) 3.8 (Owen et al., 2000)

2007 Kilauea (Hawaii) 3.0 (Montgomery-Brown et al., 2011)

2000 Miyakejima (Japan) 3.6 (Irwan et al., 2006)

2005 Manda-Harraro (Ethiopia) 5 - 2.2Grandin et al., 2009)

2007 Ferdinandina (Galapagos)

2004 Dallol (Ethiopia)

Year location rV

Ref

32 (Nobile et al., 2012, subm.)

2.6(Bagnardi and Amelung, 2012, subm.)2009 Ferdinandina (Galapagos) 2.0

(Wright et al., 2006,

Wright et al., 2012

The 2005 dike intrusion in Afar

Ayele et al., 2009

The 2005 dike intrusion in Afar

- 0.12 km3

ΔV Chambers:

ΔV Dike: +1.5 km^3

- 0.12 km3ΔV Chambers:

ΔV Dike: +2.0 km3

r_V = 2.2

ΔV Dike / ΔV Chambers =r_V = 2.8

- 0.42 km3

- 0.42 km3

- 0.37 km3

Grandin et al., 2009

Fernandina, Galapagos

rV = 2.6

Fernandina, Galapagos

rV = 2.0

Dallol, Ethiopia, 2004

(Nobile et al., 2011)

Dallol, Ethiopia

The 1997 intrusion at Kilauea

(Owen et al., 2000)

The 'missing magma' problem in volcano deformation

Einarsson and Brandsdottir, 1978

~ 2 km/h

~ 0.3 km/h

Izu Islands (Japan), 2000

Irwan et al., 2006

Physical model

dM i

dt=k pc−p i

dM c

dt=−k pc−p i dM

dt=ρV (βe+βm)dp

dt

On the other hand:On one hand:

k=ρmπR4

8ηLFor a cylindrical conduitL long and with radius R: (Pinel and Jaupart, 2003)

dp idt

=−p i−pc

, =

8L mV i em

mR4sphere=

8L r 314 m

3

R4

p.s.c.=641− La3

3R4

~ weeks to months

dM

Physical modeldp idt

= − 1i

p i−pc

dpcdt

= 1c

p i−pc

∫p1c

pc

dMOutc ∫

p i

dM i=0

Rivalta, 2010

The flow will stop when pc=pi=peq

V c=V 1c c p1

c−peqe− t

W=−V 1cc

W1W

pE 1−e− t

W

V i= b1W

pE 1−e− t

W

Chamber's volume loss:

Dike's volume:r V=

V i

V c=1mc

at any time!W=dike

sphere= bV 1c mc

i1W

=W c1W

≡W

Physical model

Rivalta, 2010

● Different timescales for dischargeand recharge

r V=V i

V c=1mc

at any time!

● Convexity upwards

● Strong dependence on βm, β

c

Validation: 2000 intrusion at Izu Islands

Rivalta, 2010

Validation: 2000 intrusion at Izu Islands

Rivalta, 2010

Pattern of induced seismicity

Keir et al., 2009

Belachew et al., 2011

'Vertical' dike propagation

(Bonforte et al., 2008, JGR)(Battaglia et al., 2011, JVGR)

Vertical propagation and stacked sills

(Sigmundsson et al., 2010)

Harrat Lunayyir, Saudi Arabia, 2009

(Pallister et al., 2011, Nature Geoscience)

2 - Interacting magma chambers

Interacting magma chambers

(Pascal et al., 2012, submitted)

Interacting magma chambers

Perspectives:

● Varying shapes ● Interacting sources (e.g. boundary elements)● Include magma properties (compressibility)● Dynamics of filling/emptying

3 - Magma compressibilityand dyke-faulting interaction

Magma compressibilityand dyke-faulting interaction

Δσ → ux

i

Δσ+ΔσF → ux

i + ∆ux

i

→ ∆V

Magma compressibilityand dyke-faulting interaction

MT fault=μ Af (0000

sin2 θ−cos2 θ

0− cos2 θ−sin2 θ )

MT Δdike=Ad ( λΔuμΔu j

0

μΔu j

(λ+2μ)ΔuμΔuk

μΔu k

0λΔu )

Magma compressibilityand dyke-faulting interaction

Magma compressibilityand dyke-faulting interaction

Induced earthquakes interact with dykes, which respond with a shearing and change of opening.

● Apparent rotation of the fault planes (up to ~27 degrees)● For low gas content & mass constant, pure DC● For higher gas content, significant isotropic and CLVD component● CLVD is physical: contraction/inflation of the dyke during the

earthquake

Perspectives

● Effects of compressibility are multifaceted and not intuitive● It helps thinking about 'mass' rather than volume● How much of the recurrent volume-multiplications observed

during dyking is due to magma compressibility and source compliance?

● More statistics will help us find/understand patterns: sill/dyke, magma composition, volatile content, depth of sources, geometry? → insight into plumbing at depth

● Dynamics of the plumbing● We need to understand more the influence of gas (bubble

nucleation, exsolution, type of degassing) on the observables (deformation, seismicity)

Acknowledgements

● Paul Segall● Maurizio Bonafede● Torsten Dahm● Emily Montgomery-Brown● Larry Mastin● Tim Wright● Derek Keir● Karen Pascal● Carolina Pagli● Adriano Nobile

● Francesco Maccaferri● Luigi Passarelli● Yosuke Aoki● Marco Bagnardi● Valerio Acocella