Aseismic deformation transients in Aseismic deformation transients in subduction zone subduction zone

and the role of fault dilatancy and the role of fault dilatancy

---- Numerical simulation in the framework of Numerical simulation in the framework of rate and state frictionrate and state friction

Yajing LiuYajing LiuAllan M. RubinAllan M. Rubin

(Princeton)(Princeton)James R. RiceJames R. Rice

(Harvard)(Harvard)

September 25, 2008, SEIZE workshopSeptember 25, 2008, SEIZE workshop

Frictional strength is a function of sliding velocity (rate V) and the memory of asperity contacts (state θ). Observed in lab velocity jump tests (fixed normal stress) for a variety of natural and synthetic materials.

Rate and state friction (1)Rate and state friction (1)

[Dieterich, 1978, 1981; Ruina, 1983

Dieterich & Kilgore, 1996]

Rate and state friction (2)Rate and state friction (2) Rate-dependence a: No change in contact population, but contacts resist more because they are sheared faster. State-dependence b: No change in contact shear rate, but old (strong) contacts are destroyed and replaced with new (weak) ones. L = slip to renew asperity contact population (~ 10s m).

[ln( )]0 :0 :

( ) /.

ss

cr

cr cr

fa b

V

k b a Lk

k k k k

Stability parameters:

1.

s.s. velocity-weakening; s.s. velocity-strengthening.2. critical stiffness and system stiffness unstable; stable.

2*

(1 )( )Lhb a

Critical resolution size

00

0

( ) ln( ) ln( ) ;

1

ln( )

One-state-variable formulation:

Evolution law:

"ageing"

"slip"

VVp f a bV L

d Vdt Ld V Vdt L L

Geometry and model setupGeometry and model setup

[Liu and Rice., 2005]

Stability transition~ 60 km downdip

Lithostatic stress

Pore pressure p

Effective normal

stress p

simulated slow slip eventssimulated slow slip events

Several features comparable to observations:

Below locked zone, around friction stability transition.

Typical slip rate is 10 to 100 times of Vpl (~ 10-9 m/s).

Along-strike propagation speed is only 2-3 km/yr – increases as effective normal stress decreases (here 100 MPa is used).

Several lines of evidence suggest that pore Several lines of evidence suggest that pore pressure is high in the ETS source regions:pressure is high in the ETS source regions:

Dehydration conditions would be met, around ~350oC and above, for shallow-dipping subduction zones (Cascadia, SW Japan, S. Mexico), which exhibit short-period transients [Peacock et al., 2002; Wada et al., 2008].

Hypocenters of non-volcanic tremors in Cascadia sections mostly correspond to positive “unclamping” effective stress changes (<0.01MPa) on hypothesized vertical planes (fissures), due to transient slips [Kao et al., 2005; 2007; Liu and Rice, 2007].

Triggered tremors in Shikoku, Japan and Cascadia by passing surface waves from the 2004 Sumatra, and 2002 Denali earthquakes, respectively, and resonance-like response to tidal forcing, all suggest that “ETS” phenomena are sensitive to small stress changes, and indicate near-lithostatic fluid pressure in those source regions [e.g., Miyazaki and Mori, 2006; Rubinstein et al., 2007; Shelly et al., 2008].

Elastodynamic rupture: [Ida, 1973; Shibazaki and Shimamoto, 2007; Ampuero and Rubin, 2008]

max max/ '/ '/[ ln( / )]p rr plv V b V V

Analysis of response at high pore pressure Analysis of response at high pore pressure pp

Realistic situation: effective normal stress is high (finite) in the seismogenic zone, but much lower from stability transition and further downdip.

Simplified situation: most of the seismogenic zone is completely locked ( infinitely high) with width W extending up-dip of the stability transition and whole down-dip region at a much lower, uniform , due to dehydration.

Most of velocity-weakening zone lockedMost of velocity-weakening zone locked

Finite effective normal Finite effective normal stress in the stress in the

seismogenic zoneseismogenic zone

Features similar to observations can be produced:Interseismic period filled with aseismic transients.Average recurrence interval of ~ 2 yr. Slip rate 2-4 times of Vpl

Cumulative slip of ~ 1-2 cm

Dilatancy of fault gougeDilatancy of fault gouge

1 m/s 10 m/s 1m/s[Segall and Rice, 1995]

[Marone et al., 1990]

0 0

*

*0

*

0

ln( / ) [ ln( / )]

/ ( ) ( / ) /( )

1( )( ) ( ) ;

( ) 1.

/ ( ) :

membrane diffusion approximation

In the limit of low hydraulic diffusivity,

always s

ss

cr

V L V V

dp dt c p p d dt

fk p b a F c

L

F c

f b a

*0

0

( ) / ( );

/ :

table (small perturbation).

Frictional weakening v.s. dilatancy strengthening:

dilatancy dominates.

p r f b f F c

f b

4 4 1

0

1.0 10 , 5 100.6, 0.004, 0.03

30

MPaf b a b

MPa

In a subduction fault model, depth-variable friction In a subduction fault model, depth-variable friction parameters (gabbro), normal stressesparameters (gabbro), normal stresses

Gabbro is a better proxy for oceanic crust. Stability transition at around 510oC. ab < 0.01 up to ~600oC. Particularly, we use the data under supercritical water conditions.[He et al., 2007]

[He et al., 2007]

Pore pressure depth distribution is constrained by seismological observations where available, and by thermal and petrological models of northern Cascadia and SW Japan subduction zones. [Peacock et al., 2002; Hacker et al., 2003; Wada et al., 2008; Kodaira et al., 2004; Shelly et al., 2006]

Friction parameters (Friction parameters (aa, , aabb, , LL) and effective ) and effective normal stress depth distributionsnormal stress depth distributions

Without dilatancy, short-Without dilatancy, short-period spontaneous period spontaneous aseismic transients occur aseismic transients occur when when W/h*W/h* is within a is within a limited range. limited range.

*40 / 16.

2 , 0.16

50 , 13.7

W W h

MPa L mm

MPa L mm

km, Low: High:

Average slip ~ 2.4 cm.Average recurrence interval ~ 2.2 yr.

With dilatancy, short-With dilatancy, short-period spontaneous period spontaneous aseismic transients can aseismic transients can occur theoretically for occur theoretically for unlimited unlimited W/h*W/h*..

*40 / 16.

2 , 0.16/ 0.2 1.0.

W W h

MPa L mmT

km, Low:

MPa,

Average slip ~ 2.5 cm.Average recurrence interval ~ 3.5 yr.

indicator of drainageindicator of drainage

*/ssT V c L

dilatancy strengthening dilatancy strengthening v.s.v.s. frictional weakeningfrictional weakening

( / ) /( )ssE f b

Implications for seismogenic zone limits and Implications for seismogenic zone limits and depths of slow slip eventsdepths of slow slip events

?

[Dragert, Wang &

James, 2001]

No dilatancyNo dilatancy With dilatancyWith dilatancy/ 0.15 ( 1.0) MPa T

SummarySummary Short-period aseismic deformation transients emerge spontaneously Short-period aseismic deformation transients emerge spontaneously

when interstitial fluids are present and pore pressure is near-when interstitial fluids are present and pore pressure is near-lithostatic within certain depth range (limited W/h*).lithostatic within certain depth range (limited W/h*).

At low effective normal stress, fault stabilization by induced suction At low effective normal stress, fault stabilization by induced suction during dilatancy due to increased shear rates becomes important. during dilatancy due to increased shear rates becomes important.

Aseismic transients can appear for much larger W/h* (using lab values Aseismic transients can appear for much larger W/h* (using lab values of of LL). Both slip and recurrence interval (approximately) linearly increase ). Both slip and recurrence interval (approximately) linearly increase with W/h*. Maximum slip rate decreases as with W/h*. Maximum slip rate decreases as EE increases toward 1.0. increases toward 1.0.

““Coseismic” rupture can also be stabilized, with reduced rupture Coseismic” rupture can also be stabilized, with reduced rupture propagation speed and spatial extent. Fault can be frictionally unstable propagation speed and spatial extent. Fault can be frictionally unstable (a-b<0) but undergo no seismic slip. Implications for the relative depths (a-b<0) but undergo no seismic slip. Implications for the relative depths of thrust earthquakes and slow slip events?of thrust earthquakes and slow slip events?

Need more constraints on model parametersNeed more constraints on model parameters Fault gouge dilatancy coefficient :

Marone et al. [1990]: granite, 150MPa, Samuelson et al. [2007, 2008]:

Fine grain angular quartz, saturated. 0.8 to 30 MPa Westerly granite gouge (dry): 5 to 30 MPa Clay-rich ODP gouge (dry): 5 to 30 MPa

Dependence of on effective normal stress and temperature.

Hydraulic diffusivity: assumed nearly “undrained” in current earthquake simulations. a more complete analysis is necessary to examine effects of permeability, viscosity, and characteristic diffusion length d.

Rate and state friction parameters Significant differences in granite (dry and wet) and gabbro friction properties. [Blanpied et al., 1995, 1998; He et al., 2006, 2007] Dilatancy may also affect friction parameters a, b, and L. [Samuelson et al., 2008]

41.7 10

5 45.8 10 5.0 10 to 4 42.0 10 1.2 10 to

4 41.5 10 1.1 10 to

* 21/ /fc t d