Institute of Geological & Nuclear Sciences Limited,Institute of Geological & Nuclear Sciences Limited,

P.O. Box 30368, Lower Hutt, New ZealandP.O. Box 30368, Lower Hutt, New Zealand

Ph: +64-4-5701444Ph: +64-4-5701444

Russell Robinson & Rafael Russell Robinson & Rafael Benites Benites

Synthetic Seismicity of

Multiple Interacting Faults

and its use for Modelling

Strong Ground Motion

AU S TR A L IANP LATE

PA C IFICP LATE

45 m m /aN orthIs land

S outhIs land

C hathamIs lands

New Zealand

tectonic and bathymetric

setting

Image from NIWANational Institute of Water and Atmospheric Research Ltd

Kerm

adec

Tre

nch

Hikurangi T

roug

h

Alpine

Fault

35 m m/a

Wellington regionWellington regiontopographytopography

Major faults of theMajor faults of theWellington regionWellington region

0

20

40

60

80

80 60 40 20 0 -20 -40 -60 -80

Dep

th (

km)

D is ta nc e fro m W elling to n (km )

Wellington Fault

P A C I F I C P L A T E

Earthquake Commission Earthquake Commission (EQC)(EQC)

A small fraction of fire insurance premiums is A small fraction of fire insurance premiums is used for earthquake insuranceused for earthquake insurance

They asked GNS:They asked GNS:

• What is the probability of two (or more ) large What is the probability of two (or more ) large earthquakes in the Wellington region within a earthquakes in the Wellington region within a few years of one another?few years of one another?

• What sort of shaking should we expect from a What sort of shaking should we expect from a large earthquake on the Wellington Fault?large earthquake on the Wellington Fault?

Synthetic Seismicity:• Computer model of a network of interacting

faults and a driving mechanism.• Generates long catalogues of seismicity so

that questions can be answered by statistical analysis.

• Computationally efficient but reasonably realistic.

• Fault properties are tuned to reproduce known slip rates/directions and other fault properties.

Features:

• Coulomb Failure Criterion.• Static/dynamic friction law, modified to

include healing.• Okada’s (1992) dislocation routines for

calculating induced stresses.• Stress propagation is at the shear wave

velocity.

Features:

• Induced changes in pore pressure are included.

• Mimics dynamic rupture effects to some degree.

• All interaction terms are kept in RAM.• The program has been “parallelized” to

run on a Beowulf PC cluster.

Fault InteractionsFault Interactions

Stress history of a single Stress history of a single cellcell

ModelModelfaultsfaults

Wellington FaultWellington FaultFault Length: 75 kmFault Width: 20 kmFault Dip: 90o

Cell Size: 1 x 1 kmCoefficient of Friction:

Asperity regions: Random between 0.65 and 0.95 Non-Asperity: Random between 0.40 and 0.70

Stress Drop: 25%Static/Dynamic Strength: 0.85Healing Time: 3.0 sDynamic Enhancement Factor: 1.2Pore Pressure: Initially ~ hydrostatic; varies with timeStress Propagation Velocity: 3.0 km/s

Typical ‘Characteristic’ EventTypical ‘Characteristic’ EventMoment: 1.41 x 1020 N-m; Mw 7.40

Model Sommerville (1999)Rupture Area 1500 km2 2810 km2

Average Slip 2.35 m 1.96 mArea of Asperities 345 km2 630 km2

Area of Largest Asperity 272 km2 458 km2

Radius of Largest Asperity ~9 km2 13 kmNum. of Asperities 2 + 1 very small 2.6Area Covered by Asperities 23% 22%Average Asperity Slip 1.67 2.01

ContrastCorner Spatial Wavenumber,

Along Strike 0.01 km-1 0.01 km-1

Along Dip 0.01 km-1 0.02 km-1

Slip Duration 3.0 s 2.55 sRupture Duration ~30 s -

Final slip distributionFinal slip distribution

Rupturing Rupturing ‘snapshots’‘snapshots’for a for a characteristiccharacteristicWellington Fault Wellington Fault eventevent

N o rth

E as t

S ta tio n

The w ho le rup ture o c cu rs in N tim e s teps .In each tim e s tep there are N sub fau lts b reakingn R

METHOD•Discrete wave number•Generalised reflection/transmission coefficients (Bouchon 1979, Kennet 1973, Chin and Aki 1991)

In the plane k-z

k ,k

k ,k

k ,k

yxSH

yxSV

yx

Ψ

Ψ

kky

kx

in which tn is the time shift corresponding to the time step n, XP and XS are the directivity correction factors for P and S waves, respectively, applied to each subfault m, and defined by:

θυυω

θυυω

rss

rpp

cos/2

LX

cos/2

LX

S

P

with r = average rupture velocity, L = length of the subfault m, and the angle between the point source corresponding to the subfault m and the station. The components of the wavefield contribution of each subfault in the k-z plane are rotated to the geographical coordinates.

)ωexp(X

Xsinψ Ψ

)ωexp( X

Xsin Φ

S

S

11

1 P

P

1

nm

myx

N r

mnm

N

nyx

n

N

n m

mN r

myxnmyx

ti

k,kk,k

ti

k,kK,k n

The complete wavefield in the source layer L is computed from:

SV

SV

τ

τ

kγ2μ lμ kγ2μ lμ

lμ kv2μ lμ kv2μ

ik vi ik vi

γ i ik iγ ik

u

u

LLLlLLLl

LlLLLlLL

LL

LL

zz

zx

z

x

for P-SV waves; and

Ψ

Ψ

SH

SH

LLLLzy

y

kγμ kγμ

ik ik-

τ

u

for SH waves, where:

The propagation through the layers is performed by applying the generalized reflection/transmission coefficients.

2

122

21

222

21

222

21

22

/2

/

/

βω kl

kβω

kωv

kkk

LL

LL

LL

yx

Ground displacement at x=5 km, y=70 km

Velocity and acceleration

Institute of Geological & Nuclear Sciences Limited,Institute of Geological & Nuclear Sciences Limited,

P.O. Box 30368, Lower Hutt, New ZealandP.O. Box 30368, Lower Hutt, New Zealand

Ph: +64-4-5701444Ph: +64-4-5701444

Russell Robinson & Rafael Russell Robinson & Rafael Benites Benites

www.gns.cri.nz