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Probabilistic Fault Displacement Hazard Analyses
Rui
ChenChris J. Wills
William A. BryantTim Dawson
Mark D. Petersen
Application to the Hayward Fault
Main Objective Develop a Probabilistic Fault
Displacement Hazard Map•
The idea of a fault displacement hazard map (PEER Lifelines, etc.)
•
PFDHA methodology and regressions (Mark Petersen et al.)
•
Fault displacement data (Tim Dawson, including some of Steve Wesnousky’s
2008 data)
•
Fortran code for PFDHA calculation (Tianqing
Cao
and Mark Petersen,
with modification)•
Detailed fault trace and fault branch activity (Bill Bryant)
•
Putting pieces together and developing the map
•
Calculating hazards at Highway 580 fault crossings
Methodology•
Mark Petersen et al. methodology (2004 –
2009). Regressions depend on: –
Accuracy of mapped fault trace–
Complexity of fault geometry–
Cell size (structure footprint size)
•
Fault specific application using detailed fault trace
•
A large number of cross-line profiles for map generation
After Tim Dawson (2004)
Partition of Fault Displacement
Displacement is partitioned among branches based on local geological evidence.
Without partition Partitioned
0
50
100
150
200
-500 -300 -100 100 300 500
Disp
lace
men
t (cm
)
Distance to Main Fault Trace (m)
Main Trace (70%)Branch 1 (20%)Branch 2 (10%)Combined
0
50
100
150
200
-500 -300 -100 100 300 500
Disp
lace
men
t (cm
)
Distance to Main Fault Trace (m)
Application to the Hayward Fault
•
Rupture of the Northern and Southern Hayward Fault segments
•
A characteristic, M 7.0 earthquake occurring once every 140 years
•
Modeled fault trace (in yellow) is defined by about 70 points selected in GIS based on:–
Alquist-Priolo
traces–
Jim Lienkaemper
traces
Fault Displacement Hazard Near Three 580 Crossings
Partition (Main Trace , Branch)
(90%, 10%)
(95%, 5%)
(100%, single trace)
0
50
100
150
200
-500 -300 -100 100 300 500 700
Disp
lace
men
t (cm
)
Distance to Main Fault Trace (m)
1st Crossing: Inferred Complex2nd Crossing: Inferred Complex3rd Crossing: Approximate
10% in 50 years25×25 m2 cell size
Fault Displacement Hazard Map Near Hayward
10% in 50 years25x25 m2
cell size
26 cross-line profiles
Partition of Displacement at
Selected LocationsMain Trace Branch 1 Branch 2
1 75% 5% 20% 2 90% 10% -3 95% 5% -4 90% 10% -5 85% 10% 5% 6 95% 5% -
580
238
Effect of Cell Size
3rd Highway 580 crossing10% in 50 years
Wells and Coppersmith (1993):
Modification:
)(
)(
1]|0[ bMa
bMa
eeMsrP +
+
+=≠
cellsofnumbertotalrupturewithcellratio =0
50
100
150
200
-200 -100 0 100 200
Dis
plac
emen
t (cm
)
Distance to Fault (m)
25x2550x50100x100150x150200x200Infinite
Cell Size (m2)0
0.2
0.4
0.6
0.8
1
4.5 5.5 6.5 7.5 8.5 9.5
Prob
abili
ty of
on-F
ault
Sufa
ce R
uptu
reEarthquake Magnitude
25x25 (0.74)50x50 (0.87)100x100 (0.90)150x150 (0.87)200x200 (0.93)Wells & Coppersmith (1993)
Estimate of On-Fault Displacement•
Wells and Coppersmith (1994)
•
Geological average or seismological average? What do they mean and how are they calculated?
MDave 9.032.6)(log10 +−=
)9.032.6(10)/(),( Mave ADDDlD +−×=
2004 data and regression:(normalized to seismological AD?)
0479.0)/(*9406.1)/(*4165.2/ 2 ++−= LlLlADD
2009 revision:(normalized to geological AD)
0.0
0.1
1.0
10.0
0.000 0.100 0.200 0.300 0.400 0.500
Norm
alize
d Av
erag
e Di
spal
cem
ent,
D/AD
Normalized distance, x/ L
D/AD = 1 x/ l ≥ 0.25D/AD = 3.8 (x/L)+0.05 x/L < 0.25σ =0.58
l/L
l/L
On-Fault Slip Distribution
Wesnousky
(2008):Asymmetric curves fit better than symmetric curves
Can we incorporate variation in the degree of asymmetry in PFDHA?
Probability Profiles
0%
10%
20%
30%
40%
-250 -200 -150 -100 -50 0 50 100 150 200 250
Prob
abili
ty of
D ≥
100 c
m
Distance to Fault (m)
25x25
50x50
100x100
150x150
200x200
Cell size (m2)3rd Highway 580 crossing
Multiple Probabilities
0
100
200
300
400
-200 -150 -100 -50 0 50 100 150 200
Disp
lace
men
t (cm
)
Distance to Fault (m)
10% (475 yrs)5% (975 yrs)2% (2475 yrs)
25x25 m2 cell50 yr probability
Summary
1.
Lateral extent of estimated zone of fault displacement increases with increasing uncertainty in fault location and increasing complexity of mapped fault traces
2.
Need continuous effort in augmenting fault displacement data and updating regression relations
3.
PFDHA is consistent with PSHA and may be a valuable tool in design