The use of earthquake rate changes as a stress meter at Kilauea volcano

Nature, V. 408, 2000

By J. Dietrich, V. Cayol, and P. Okubo

Presented by Celia Schiffman

Do changes in stress correlate with changes in earthquake

rates?• Stress changes and EQ rates are not linearly

correlated• EQ nucleation process is dependent on time and

stress (lab. observations)• Estimating stresses that drive EQ’s versus stress

changes resulting from EQ’s.• Kilauea:

– Frequent stressing events– Independent observations of deformation– High rates of seismic activity– Changes in seismicity/eruptions/subsurface magma

movement– Rift-zone magmatic expansion/detachment faulting

Formulas

R r

Sr

1) R r

Ý S rwhere d

1

Adt dS

state var iable [time /stress]

R earthquake rate (M1 M2)

r ss eq rate at Ý S rA dimensionless fault constitutive param (0.005 0.015)

normal stress min us pore fluid pressure, assume small stress changes

2) S S mod ified CS func

shear stress (pos in slip direction )

coeff of fault friction

constitutive param 0.25

Formulas

Stress step --> characteristic aftershock sequence (i.e. immediate jump in seismicity then decay according to Omori’s decay law [1/t])

1) R r

Ý S rwhere d

1

Adt dS

where ta A

Ý S

Two methods to estimate stress change from EQ rates

1) Stress as a function of time in a specific volume

-Calculate time series at grid points from earthquake rate data

-Calculate stress changes over succesive time intervals using stress steps at the midpoint of each time interval

(t) r

R(t) Ý S rwhere R(t) is observed, Ý S r is estimated

and r( Ý S r) from 1976 2000

Ý S Ata

d dt

A S

A

S A

dt

A d

S A dt AdAi

i1

S A lni

t

2Ai1

t

2A

S

time

t

(t1,1)

(t2,2)

S

Two methods to estimate stress change from EQ

rates2) Spatial distribution of stress changes for a stress event (EQ or intrusion)

-Use eq 1 to solve for constant stressing at Sr, take a stress step (corresponding to the stress event), then constant stressing at Sr again.

S

Ý S r exp(N2Ý S rt1

N1A ) 1

Ý S r exp(Ý S rt2

A ) 1

where N1 # eq's in t1N2 # eq's in t2

S depends on fault orientation and slip direction

-Eq counts are made for subregions sorted byfault orientation-6-13 km depths-Each volume needs at least 8 EQ’s-Grid nodes spaced 1 km apart

Timeline• Pre 1975:

– Eruptive activity• 1975:

– M7.2 EQ• 1975-1983:

– Intrusion (1977)– Rapid deformation (up to 25 cm/yr extension)– Intense seismicity– Aseismic creep on detachment– Rift opening at 40 cm/yr

• 1979-1983:

– 5 fold slowing of stressing rates• 1983:

– Eruption• Post 1983:

– Nearly continuous rift eruption– Deformation decreased to 4 cm/yr

Location

Observations

Deformation data sets

Number of earthquakes

-Eq rates are low-pass filtered-Assume Eq’s occur on faults that are optimally oriented in the stress field

-Artifacts from random fluctuations in EQ rate and possiblecatalog inconsistencies during swarm events-Slowing of stressing rates from 1981-83 (0.3->0.15)Next: Compare to BEM’s constructed from independent estimates of stress changes

Calculate stress changes based on eq’s

Model variables: depth, height, width, dip and opening of dikeDip and depth of detachment faultWidth of creeping portion of fault

Outputs:Predicted surface deformationsStress changes

Pick best fitting values for variablesbased on deformation data

Pre-1983 eruption

Post-1983 eruption

Boundary Element Models

Statistics:Slope=1.1Correlation=0.8

Problems•Non-linear relationship not clearly demonstrated•Is it really necessary?•Would a linear fit work just aswell?•Need geodetic data (GPS) to better constrainchanges in stress to see if step-function, or linear