Transcript Synthetic Seismicity of Multiple Interacting Faults and its use for

Synthetic Seismicity of
Multiple Interacting Faults
and its use for Modelling
Strong Ground Motion
Russell Robinson & Rafael Benites
Institute of Geological & Nuclear Sciences Limited,
P.O. Box 30368, Lower Hutt, New Zealand
Ph: +64-4-5701444
New
Zealand
AUSTRALIAN
PLATE
45 mm/a
North
Island
tectonic and
bathymetric
setting
Chatham
Islands
/a
m
5m
3
Image from NIWA
National Institute of Water and Atmospheric Research Ltd
South
Island
PACIFIC
PLATE
Wellington region
topography
Major faults of the
Wellington region
Wellington
Fault
0
20
Depth (km)
40
60
PACIFIC PLATE
80
80
60
40
20
0
-20
Distance from Wellington (km)
-40
-60
-80
Earthquake Commission (EQC)
A small fraction of fire insurance premiums is
used for earthquake insurance
They asked GNS:
• What is the probability of two (or more ) large
earthquakes in the Wellington region within a
few years of one another?
• What sort of shaking should we expect from a
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 Interactions
Stress history of a single cell
Model
faults
Wellington Fault
Fault Length: 75 km
Fault Width:
20 km
Fault Dip:
90o
Cell Size: 1 x 1 km
Coefficient 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: 0.85
Healing Time: 3.0 s
Dynamic Enhancement Factor: 1.2
Pore Pressure: Initially ~ hydrostatic; varies with time
Stress Propagation Velocity: 3.0 km/s
Typical ‘Characteristic’ Event
Moment: 1.41 x 1020 N-m;
Rupture Area
Average Slip
Area of Asperities
Area of Largest Asperity
Radius of Largest Asperity
Num. of Asperities
Area Covered by Asperities
Average Asperity Slip
Contrast
Corner Spatial Wavenumber,
Along Strike
Along Dip
Slip Duration
Rupture Duration
Mw 7.40
Model
Sommerville (1999)
1500 km2
2810 km2
2.35 m
1.96 m
345 km2
630 km2
272 km2
458 km2
~9 km2
13 km
2 + 1 very small
2.6
23%
22%
1.67
2.01
0.01 km-1
0.01 km-1
3.0 s
~30 s
0.01 km-1
0.02 km-1
2.55 s
-
Final slip distribution
Rupturing
‘snapshots’
for a
characteristic
Wellington Fault
event
North
Station
East

The whole rupture occurs in N time steps.
In each time step n there are NR subfaults breaking
METHOD
•Discrete wave number
•Generalised reflection/transmission coefficients
(Bouchon 1979, Kennet 1973, Chin and Aki 1991)
In the plane k-z
ky
k
kx
  k x , k y 
Ψ SV k x , k y 

Ψ SH k x , k y 

 Nr 
sin X Pm 
Φ k x , K y      nm k x , k y 
 exp( iωt n )
n 1 m 1
X Pm 

Ψ

N
k x , k y   
N
n 1
n
 Nr 
sin XSm 
  ψ nmk x , k y 
exp( iωt n )
XSm 
m1
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:
XP 
ωL
υ p / υr  cos θ 
2 p
XS 
ωL
υs / υr  cos θ 
2 s
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.
The complete wavefield in the source layer L is computed from:
  ik
ux 

 
  i vL
uz 
   
  2μ L v L k
 τ zx 

 
 τ zz 
  μl l L
for P-SV waves; and
for SH waves, where:
 ik
iγL
 ik
i vL
 μl l L
2μL v L k
 2μL γ L k
 μl l L
u y 
 - ik
   
μ γ k
 τ zy 
 L L
 


 μL γ L k 
ik
k  k 2x  k 2y 
1
1


 2k  ω / β 
 L  ω /
2



 ik

 μl l L 

2μL γ L k 
  


  
 SV 
  


  
 SV 
 ΨSH 


  
 Ψ SH 
2
2
2
2
v L  ω /  L  k 
lL
 i γL
2
βL  k2
2
1
2
L
2
2
1
2
The propagation through the layers is performed by applying the generalized reflection/transmission coefficients.
Ground displacement at x=5 km, y=70 km
Velocity and acceleration
www.gns.cri.nz
Russell Robinson & Rafael Benites
Institute of Geological & Nuclear Sciences Limited,
P.O. Box 30368, Lower Hutt, New Zealand
Ph: +64-4-5701444