Numerical simulation of seismic cycles at a subduction zone with

a laboratory-derived friction law

Naoyuki Kato(1), Kazuro Hirahara(2), and Mikio Iizuka(3)

(1) Earthquake Research Institute, University of Tokyo(2) Graduate School of Environmental Sciences, Nagoya University (3) Research Organization for Information Science and Technology

Numerical simulation of seismic cycles at a subduction zone with a laboratory-derived friction law

Outline

1. Composite rate- and state-dependent friction law

2. Forecast models for the Tokai earthquake

3. Mechanism of episodic slip events

4. Historical earthquake sequence along the Nankai trough

- Future study -

Rate- and state-dependent friction law

= * + a ln(V/V*) + b ln(V*/L)

; friction coefficient

V; sliding velocity

; state variablea,b,L, *,V*; constants

d/dt = 1 - V/L; slowness law

d/dt = - (V/L) ln (V/L); slip law

d/dt = exp(-V/Vc) - (V/L) ln (V/L); composite law

Vc; constant Kato and Tullis (2001)

Simulation results of slide-hold-slide test

Simulation results of velocity stepping test

Stiffness independent higher healing rates for the slowness and composite laws explain laboratory data

Symmetric responses to velocity increases and decreases for the slip and composite laws explain laboratory data

Kato and Tullis (2001)

Kato and Tullis (2002)

Simulation of stick-slip cycle of a spring-block system

The recurrence interval and stress drop are the largest for the composite law.

Model for seismic cycle at the Tokai seismic gap along the Suruga trough, central Japan

Back slip distribution estimated from GPS data by Sagiya (1999)

2-D model for the Tokai earthquake Kato and Hirasawa (1999)

Seismic moment release of preseismic sliding

Kato and Tullis (2002)

seismic gap

Kuroki et al. (2002)

3-D model for the Tokai earthquake

Strain change (for one day before EQ)

Strain (1E-8)

Episodic strain event near the hypothesized source area of the Tokai earthquake detected by GPS

Data from Geographical Survey Institute(http://www.gsi.go.jp)

Hamamatsu

Hamamatsu

Saiki

Misho

Slow slip event beneath the Bungo channel, southwest Japan

Hirose et al. (1999)

Observed and model horizontal displacement

Distribution of estimated fault slip over 10 months

Moment magnitude = 6.6

SaikiMisho

Velocity changes for 3 years in southwest Japan(a) Apr. 1, 1996 - Apr. 1, 1997

(b) Apr. 1, 1997 - Apr. 1, 1998

(c) Apr. 1, 1998 - Apr. 1, 1999

Possible mechanism of episodic slip event on a plate interface

　

For a spring-block model, the ratio of spring stiffness to the

critical stiffness kc = (B-A)/L controls sliding mode.

(B-A = -dss/dlnV, L characteristic slip distance)

k >> kc → aseismic

　　 k ～ kc → episodic

　　 k << kc → seismic

For a finite fault in a uniform elastic medium, the critical fault

dimension rc = cGL/(B-A) may be defined, and r/rc controls

sliding mode. (c; constant ～ 1, G; rigidity)

r >> rc → seismic

　　 r ～ rc → episodic

　　 r << rc → aseismic

k

Simulation of slip on a flat fault in an infinite uniform elastic medium

A circular patch with negative A-B value is embedded in a uniform fault with positive A-B value.

stable

Possiblyunstable

The critical fault radius rc = 4.12 km.

The radius r of the negative A-B patch is 3.0 km.

r/rc = 0.73

Distribution of A-B (MPa)

Snapshot of distribution of slip velocity ln(V/Vpl)

(Vpl; the assumed plate velocity = 4 cm/yr)

The negative A-B patch is more strongly locked.

Snapshot of distribution of slip velocity ln(V/Vpl)

Time from the last slide = 5.7 years

Episodic slip starts in the negative A-B patch.

Snapshot of distribution of slip velocity ln(V/Vpl)

Time from the last slide = 13 hours

Episodic slip propagates in the negative A-B patch, but the slip is not significantly accelerated.

Snapshot of distribution of slip velocity ln(V/Vpl)

Time from the last slide = 32 days

Slip is decelerated because the rupture front enters the positive A-B region.

Snapshot of distribution of slip velocity ln(V/Vpl)

Time from the last slide = 150 days

Very slow slip propagates in the positive A-B region, while healing starts in the negative A-B patch.

Snapshot of distribution of slip velocity ln(V/Vpl)

Time from the last slide = 2.2 years

The negative A-B patch is strongly locked and the next cycle starts.

r = 3 km, rc = 4.12 km

A-B = 0.2 MPa at 1-6

A-B = -0.2 MPa at 7-8

Slip history during the entire cycle

r = 3 km, rc = 4.12 km

A-B = 0.2 MPa at 1-6

A-B = -0.2 MPa at 7-8

Slip history at the aseismic slip event

TIME (days)

Summary of simulation for episodic slip events

Aseismic episodic slip event may be simulated for a negative A-B patch with r/rc = 0.73.

Episodic events with various time duration may be simulated by varying r/rc-value. The duration of the event decreases with an increase in r/rc.

Episodic events may be simulated not only by nonuniform distribution of A-B but also by nonuniformity in the characteristic slip distance L or in the effective normal stress.

If the source size and duration of an episodic event are obtained, the value of (B-A)/L may be estimated.

Quasi-Static Modeling of Earthquake Cycle

Interaction on and between Faults

Dynamic Modeling of Earthquake Rupture Wave Propagation in Heterogeneous Media

Simulation and Prediction of Strong Motion

Interplate Earthquake FaultInland Active Fault

Viscoelastic Interaction

Frictional Law

Earthquake Generation and Strong Motion in 3-D Heterogeneous Media

Fault Constitutive Law

Plate Subduction

In the Earth Simulator Project, we take into consideration

heterogeneous viscoelastic structure,

a rate- and state-dependent friction, and

interactions of many segments of plate boundary

and inland active faults.

FEM; Iizuka, Poster

Solving friction problem; Prabhakar, Poster

CrustPlateUpper Mantle

Quasi-Static Earthquake Cycle Simulation with GeoFEM

3D-FEM Mesh

1100km900km

200km

200km

1150km750km

No. of Nodes ： 59400No. of Elements： 54752

No. of Nodes ： 11466No. of Elements： 10000

Northeast　 Japan

Southwest　 Japan