Common Problems in Estimation of Seismic Hazard Parameters and

UNIVERSITY OF PRETORIA
NATURAL HAZARD CENTRE, AFRICA
A Kijko, A Smit
Email: [email protected]
[email protected]
Common Problems
in Estimation of
Seismic Hazard Parameters
and their Solutions
The Schmidt Institute of Physics of the Earth
of the Russian Academy of Sciences,
1
Moscow, Russia
Seismic Hazard Assessment
Cornell-McGuire Procedure
(Cornell, 1968)
SITE
PARAMETERS
•activity rate λ
•b-value
•maximum magnitude mmax
SITE
2
Types of Problems Faced
3
Incompleteness of Seismic Catalogue
Combination of the largest earthquakes with complete data and
variable threshold magnitudes (Kijko and Sellevoll, 1992).
4
Incompleteness of Seismic Catalogue
(Kijko and Smit, 2012)
5
(Aki, 1965)
6
Previous Solutions for the Problem
7
Solution (Forgotten / Unknown)
8
Solution (Forgotten / Unknown)
9
Solution (Forgotten / Unknown)
10
(Kijko and Smit, 2012)
Aki (1965) estimator
11
12
Performance of Methods
Two complete catalogs simulation
1.4
Estimated b-value
"true" b-value = 1
+/- Standard error
Estimated b-value
1.3
1.2
1.1
1
0.9
0.8
0.7
100
150
200
250
300
350
400
Number of earthquakes
450
500
(Kijko and Smit,
2012)
13
Activity Rate of Estimation
(Kijko and Smit, 2012)
14
Estimation of Maximum Possible Magnitude
15
Approach 1: Based on Event Catalogue
16
Approach 1: Based on Event Catalogue
1. Pisarenko et al. (1996)
2. Cooke (1979)
17
Approach 1 : Based on Event Catalogue
18
Approach 1: Based on Event Catalogue
1. Pisarenko et al. (1996)
2. Cooke (1979)
19
Approach 2: Bayesian (combine event
catalogue with existing knowledge)
(1)
Courtesy Mark Petersen,
USGS
(2)
Cratons
Margins
20
Approach 2: Bayesian (combine event
catalogue with existing knowledge)
21
Flaw in Cornell’s Bayesian Procedure
Example of sample likelihod functions
0
Sample likelihood function
"true" mmax = 6.92
-0.2
ln(likelihood function)
mmax obs = 5.89
-0.4
-0.6
-0.8
-1
(Kijko, 2012)
-1.2
-1.4
5.5
6
6.5
7
7.5
Magnitude
8
8.5
9
22
Flaw in Cornell’s Bayesian Procedure
Effect of shift of sample likelihood function
7.1
Current EPRI Procedure
After correction by shift of Sample Likelihood Function
"true" mmax = 6.92
7
m
max
6.9
6.8
6.7
6.6
(Kijko, 2012)
6.5
0
100
200
300
400
500
600
Number of events
700
800
900
1000
23
Possible Correction for Procedure
24
Possible Correction for Procedure
25
Possible Correction for Procedure
Estimated mmax
400
Histogram of estimated m max
350
mean of estimated m max = 6.79 (error = -0.01)
"true" mmax = 6.8
Histogram of estimared mmax
300
250
200
150
100
50
0
6.4
6.5
6.6
6.7
mmax
6.8
6.9
7
7.1
26
Example: South Africa
•
Deterministic Seismic Hazard Analysis for Cape Town
•
Based on Milnerton (1809) earthquake of magnitude 6.3
•
Result ???
27
Example: South Africa
BUILDING CLASS #7: Reinforced Concrete Shear Wall
with Moment Resisting Frame, High Rise
80
Central Damage Factor
Central Damage Factor +/- SD
Central Damage Factor [%]
70
60
50
40
30
20
10
0
4
5
6
7
8
Intensity MMI
9
10
11
12
28
Example: South Africa
Expected Damage and Loss for Green Point Stadium
Building Class
Green Point Stadium
Expected
Damages
18%
Uncertainty
Interval
[11, -25]%
Estimated Loss due to ML = 6.87 earthquake
Building Cost
R4.4 billion
~US $600 million
Expected Monetary Loss
(@18%)
R792 million
~US $108 million
29
References
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Thank You
31

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