interseismic deformation with aseismic stress-dependent fault slip

Eric A Hetland, Mark Simons, Ravi Kanda, Sue Owen

TO brown-bag – 03 April 2007

a very informal, and preliminary talk about how we are thinking about

Hsu et al., 2006

post-seismic slip following subduction ruptures:

fault rheology is not (explicitly) included in after-slip model

2005 Nias-Simeulue eq. (M8.7)

Pritchard & Simons, 2006

post-seismic slip following subduction ruptures:

fault rheology is not (explicitly) included in after-slip model

1995 Antofagasta eq. (M8.1)

post-seismic slip following subduction ruptures:

fault rheology is not included in after-slip model

2003 Tokachi-oki eq. (M8)

Baba et al., 2003

inter-seismic slip near regions of past subduction ruptures:

Suwa et al., 2006

model assumes fault slip during inter-seismic period is constant

Japan/southern Kurile trenches

we want an internally consistent model we want an internally consistent model that can describe observations of both that can describe observations of both inter-seismic and post-seismic inter-seismic and post-seismic deformation…deformation…

for now we are building subduction zone models that include repeated ruptures, on assumed asperities, with stress-dependent aseismic slip on the non-asperity portions of the subduction interface during the interseismic period…

Baba et al., 2003 Suwa et al., 2006

L

elastic half-space

long-termfault-slip

U’ cuts 1/2-space

with fault loading:

traction on the faultfinite fault plane in

1/2-space

slip on the fault(Burgers vector)

includes theoff-fault rheology

with fault loading:

=0

e.g.; Rice, 1993; Liu and Rice, 2005.

Note: no seismic radiation damping (e.g., Rice, 1993) - there are no seismic waves & no problems with unbounded slip velocities in our models…

“back-slip”introduced by J. Savage (Savage and Burford, 1973; Savage and Prescott, 1978; Savage, 1983) as a mathematically convenient fault loading mechanism in kinematic & quasi-kinematic models

+ =

Savage & Burford, 1973; Savage & Prescott, 1978

Suwa et al., 2006

red = lots of BSwhite = no BS

approximation only good approximation only good for spun-up systems:for spun-up systems:

rate of interseismic relaxation= rate of reloading

tractionon fault

part of faultthat is allowed to

slip interseismically

part of fault withcoseismic slip

part of faultthat slipssteadily

interseismicslip on fault

imposedruptures at

times Tp

long-termfault-slip

we impose ruptures - we do not solve for them:

locked

-

’-

tractionon fault

interseismicslip on fault

imposedruptures at

times Tp

part of faultthat is allowed to

slip interseismically

part of fault withcoseismic slip

part of faultthat slipssteadily

long-termfault-slip

we impose ruptures - we do not solve for them:

non-linear viscous(Montesi, 2004)

RS-friction(e.g. Marone et al., 1991)

linear viscous

need a fault rheology:

Dieterich, 1979; Ruina 1983; Rice and Gu, 1983 (figure from Ben-Zion, 2003)

rate- and state-friction

(a-b)<0 “ruptures”, (a-b)>0 “aseismic slip”

is a state variable, assume it is constant = L/v

= N

Ben-Zion, 2003

Lapusta et al., 2000

we impose ruptures - we only solve for aseismic slip:

fault rheology:

bulk rheology:

given by for now, assume elastic half-space and use Okada, 1992

model works for 3D, non-planar faults, with multiple asperities, arbitrary rheologic

parameters, we allow both dip- and strike-slip co- and inter-seismic slip, and irregular

(imposed) rupture sequencescurrently, we can impose coseismic slip in non-locked regions of the fault, but we do not allow interseismic slip in the locked regions…

use boundary elements…

= 30 GPa

’N = 300 MPa

D = 104 m

bo = 10 m

(a-b) = -1/10

-1 = 0.5 (a-b) = 0.05

-1 = 1.0 (a-b) = 0.10

10D

D/2

Dlockedsection

steady slip

at depth

“thrust fault” in an elastic half-space, dipping 45 degrees

modification of ubiquitous subduction back-slip model, by allowing interseismic slip here

10D

D/2

Dlockedsection

steady slip

at depth

“thrust fault” in an elastic half-space, dipping 45 degrees

interseismic surface

deformation is given by the locked

portions of the mega-thrust sliding as a normal fault at the plate rate (Savage, 1983)

a more realistic geometry

vert

ical

h

ori

zon

tal

back-slip model

10D

D/2

Dlockedsection

steady slip

at depth

“thrust fault” in an elastic half-space, dipping 45 degrees

does not include strains due to plate

bending, if incorporated, discrepancy

removed, total interseismic + coseismic =

subduction block motion…

a more realistic geometry

Ravi Kanda

vert

ical

h

ori

zon

tal

elastic slab model

“thrust fault” in an elastic half-space, dipping 45 degrees

10D

D/2

Dlockedsection

steady slip

at depth

in a spun-up model, total interseismic slip fills in the the areas above the co-seismic slip-profile

periodically impose this co-seismic slip

slip on the fault:

below the locked region

b>0 thrust slip

surface interseismic displacements:

xxxxxx

oo

surface interseismic displacements:

xxxxxx

ooo

surface interseismic displacements motivation:

2003 Tokachi-oki eq. (M8)

Baba et al., 2003

x

data from Sue Owen

slight curvaturetectonic?

surface interseismic displacements motivation:

2003 Tokachi-oki eq. (M8)

Baba et al., 2003

x

data from Sue Owen

determination of plate coupling:

Suwa et al., 2006

shown is back-slip rate vbs

invert GPS velocities for distributions of normal slip (vbs) on the mega-thrust

use back-slip model (Savage,

1983) to determine the “coupling coefficient”

• vbs = vT coupled (C=1)

• vbs = 0 uncoupled (C=0)

this assumes that the interseismic deformation is constant throughout the interseismic period

10D

D/2

Dlockedsection

steady slip

at depthinvert GPS velocities for distributions of normal slip (vbs) on the mega-thrust

use back-slip model (Savage,

1983) to determine the “coupling coefficient”

• vbs = vT coupled (C=1)

• vbs = 0 uncoupled (C=0)

slip is not constant through the cycle

determination of plate coupling:

this assumes that the interseismic deformation is constant throughout the interseismic period

variation of coupling through an interseismic period

xxxxxx

xxx

variation of coupling through an interseismic period

xxxxxx

variation of coupling through an interseismic period

xxxxxx

Lapusta et al., 2000

this model only contains co-seismic slip in the locked regions, no interseismic slip-allowed in the locked regions…

contrary to dynamic calculations…

two (of the many) remaining issues:

still learning to drive…

“lockedness” – we assume full slip in locked patches (asperities)

some directions currently aiming for:

include heterogeneous elastic structure by computing K(z;) from FE models…

include other bulk rheologies – K(z;): “simple” semi-analytic models & quite complicated FE models…

model the GPS data of inter- & post-seismic observations in Hokkaido (2D, 3D planar, respecting slab geometry, & …)

gOcad

1968

19732003

slip models from Yamanaka and Kikuchi (2002) vertically exaggerated