Deprem Tehlike Analizine Giriş: Türkiye’den Örnekler
Introduction to Seismic Hazard Analysis: Examples from
Turkey
Ali Osman Öncel, Turkey
Knowledge exists to be imparted. (R.W. Emerson(
Deprem Tehlike Analizi
• Erzincan ve Çevresi• Kuzey Anadolu Fay Zonu• Artçı Şokların Etkisi• Tehlike Haritaları• Mmax Estimation
Ali Osman Öncel, Turkey
Ali Osman Öncel, Turkey
Erzincan ve Çevresinin Sismotektoniği
Ali Osman Öncel, Turkey
Deprem Tehlike Analizi
• Erzincan ve Çevresi• Kuzey Anadolu Fay Zonu• Artçı Şokların Etkisi• Tehlike Haritaları• Mmax Estimation
Ali Osman Öncel, Turkey
Aktif Fay Haritaları
Ali Osman Öncel, Turkey
Türki’nin Depremleri
Ali Osman Öncel, Turkey
Depremlerin Yıllara Göre Değişimi
Ali Osman Öncel, Turkey
Türkiye ve Çevresinin Depremselliği
Deprem Tehlike Analizi
• Erzincan ve Çevresi• Kuzey Anadolu Fay Zonu• Artçı Şokların Etkisi• Tehlike Haritaları• Mmax Estimation
Ali Osman Öncel, Turkey
Artçı Şokların Etkisi
Ali Osman Öncel, Turkey
Tüm Şok ve Anaşok Deprem Verileri
Ali Osman Öncel, Turkey
Tekrarlanma Aralıkları Arasında ki Fark
Deprem Tehlike Analizi
• Erzincan ve Çevresi• Kuzey Anadolu Fay Zonu• Artçı Şokların Etkisi• Mmax Estimation
Ali Osman Öncel, Turkey
İvme Haritası
Ali Osman Öncel, Turkey
A. Kijko
Flaw in the EPRI Procedure for maximum earthquake magnitude estimation and
its correction
ESC 2010 6-10 September 2010 Montpeller, France
Andrzej Kijko, South Africa
Knowledge exists to be imparted. (R.W. Emerson(
Andrzej Kijko, South Africa
Contents
1. EPRI Bayesian Procedure for mmax
estimate
2. What is wrong with the procedure and
why?
3. How to cure it? Illustration
4. Conclusion and Remarks
Andrzej Kijko, South Africa
EPRI Procedure for mmax estimation (Cornell, 1994(
Splendid idea …
- combination of
observations with already
existing knowledge!
EPRI Procedure for mmax Estimation (Cornell, 1994)
Andrzej Kijko, South Africa
Prior mmax distribution for intraplate regions
Courtesy Mark Petersen, USGS
Cratons Margins
EPRI Procedure for mmax Estimation (Cornell, 1994)
Gaussian prior mmax distribution(e.g. M Ordaz, 2007)
Andrzej Kijko, South Africa
EPRI Procedure for mmax Estimation (Cornell, 1994)
Petersen's prior & Gaussian prior
Andrzej Kijko, South Africa
5 . 5 6 6 . 5 7 7 . 5 8 8 . 50
0 . 5
1
1 . 5
2
2 . 5
M a g n i t u d e mm a x
Prior
P r i o r D i s t r i b u t i o n s o f mm a x
G a u s s i a n p r i o r ( m e a n m
m a x= 6 . 9 2 S D = 0 . 5 )
P r i o r f o r i n t r a p l e t e r e g i o n s b y M . P e t e r s e n ( U S G S )M e a n o f p r i o r m
m a x
EPRI Procedure for mmax estimation, (Cornell, 1994)
Andrzej Kijko, South Africa
⋅=
maxmaxmax mof
yprobabilitprior
mgiven
likelihoodsampleconst
samplethegiven
mof
yprobabilitPosterior
Andrzej Kijko, South Africa
)()|()( maxmaxmax mpmLkmp priorposterior ⋅⋅= x
5 . 5 6 6 . 5 7 7 . 5 8 8 . 5 9- 1 . 4
- 1 . 2
- 1
- 0 . 8
- 0 . 6
- 0 . 4
- 0 . 2
0E x a m p le o f s a m p le l i k e l i h o d f u n c t i o n s
M a g n i t u d e
ln(like
lihoo
d fun
ction)
S a m p l e l i k e l i h o o d f u n c t i o n
" t r u e " mm a x
= 6 . 9 2
mm a x
o b s = 5 . 8 9
EPRI Procedure for mmax estimation, (Cornell, 1994)
5 . 5 6 6 . 5 7 7 . 5 8 8 . 50
0 . 5
1
1 . 5
2
2 . 5
M a g n i t u d e mm a x
Prior P
DFP r i o r D i s t r i b u t i o n s o f m
m a x
G a u s s i a n p r i o r ( m e a n m
m a x= 6 . 9 2 S D = 0 . 5 )
P r i o r f o r i n t r a p l e t e r e g i o n s b y M . P e t e r s e n ( U S G S )M e a n o f p r i o r m
m a x
Flow in EPRI Procedure
Andrzej Kijko, South Africa
• For the sample likelihood function,
the range of observations
(magnitudes) depends on the
unknown parameters.
• This dependence violates the
fundamental rules of application of
maximum likelihood estimation
procedure.
• EPRI Bayesian procedure by default will underestimate value
of mmax !
• EPRI Bayesian procedure will locate mmax somewhere between maximum observed magnitude
and “true” mmax
Andrzej Kijko, South Africa
Flow in EPRI Procedure
Confirmation 1: Prior Distribution for Intraplate Regions (by M. Petersen, USGS)
Andrzej Kijko, South Africa
1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 06 . 1
6 . 2
6 . 3
6 . 4
6 . 5
6 . 6
6 . 7
6 . 8
6 . 9
7
7 . 1
E s t i m a t e d mm a x
w i t h p r i o r o f mm a x
f o r i n t r a p la t e r e g i o n s
A c t i v i t y r a t e L a m b d a * T i m e s p a n o f c a t a lo g u e [ Y ]
mm
ax
mm a x
e s t i m a t e d
mm a x
o b s e r v e d
" t r u e " mm a x
= 6 . 9 2
Andrzej Kijko, South Africa
Confirmation 2: Gaussian Prior (by Cornell, 1994)
1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 06 . 1
6 . 2
6 . 3
6 . 4
6 . 5
6 . 6
6 . 7
6 . 8
6 . 9
7
7 . 1
E s t i m a t e d mm a x
w i t h G a u s s i a n P r i o r
A c t i v i t y r a t e L a m b d a * T i m e s p a n o f c a t a lo g u e [ Y ]
mm
ax
mm a x
e s t i m a t e d
mm a x
o b s e r v e d
" t r u e " mm a x
= 6 . 9 2
How to Correct the Flaw in the EPRI Procedure?
Andrzej Kijko, South Africa
• Eliminate effect
• Eliminate cause
Approach #1: Eliminate Effect
Andrzej Kijko, South Africa
Shift the Likelihood Function from
maximum observed magnitude to
maximum expected mmax
Δmm̂ obsmaxmax +=
[ ]∫=∆max
min
d)(m
m
nM mmF
Approach #1: Eliminate EffectCorrection by Shift of Sample Likelihood Function
Approach #1: Correction by shift of Sample
Likelihood Function
0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 06 . 5
6 . 6
6 . 7
6 . 8
6 . 9
7
7 . 1E f f e c t o f s h i f t o f s a m p le l i k e l i h o o d f u n c t i o n
N u m b e r o f e v e n t s
mm
ax
C u r r e n t E P R I P r o c e d u r eA f t e r c o r r e c t i o n b y s h i f t o f S a m p l e L i k e l i h o o d F u n c t i o n
" t r u e " mm a x
= 6 . 9 2
Andrzej Kijko, South Africa
Our Problem: For the sample likelihood function, the range of observations (magnitudes) depends on the unknown parameters
Approach #2: Eliminate CauseCorrection by Account of Magnitude Uncertainty
4 4 . 5 5 5 . 5 6 6 . 5 7 7 . 5 8 8 . 5 9
1 0- 6
1 0- 4
1 0- 2
1 00
M a g n i t u d e
G R
G R - a p p a r e n t
mmax
Andrzej Kijko, South Africa
0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 06 . 5
6 . 6
6 . 7
6 . 8
6 . 9
7
7 . 1E f f e c t o f a c c o u n t o f m a g n i t u d e u n c e r t a i n t y
N u m b e r o f e v e n t s
mm
ax
C u r r e n t E P R I P r o c e d u r eA f t e r c o r r e c t i o n b y a c c o u n t o f m a g n i t u d e u n c e r t a i n t y
" t r u e " mm a x
= 6 . 9 2
Andrzej Kijko, South Africa
Approach #2: Eliminate CauseCorrection by Account of Magnitude Uncertainty
Comparison of Two Correction Procedures
0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 06 . 5
6 . 6
6 . 7
6 . 8
6 . 9
7
7 . 1
C o m p a r i s o n o f mm a x
e s t i m a t i o n p r o c e d u r e s
N u m b e r o f e v e n t s
mm
ax
C u r r e n t E P R I P r o c e d u r e
A f t e r c o r r e c t i o n b y a c c o u n t o f m a g n i t u d e u n c e r t a i n t yA f t e r c o r r e c t i o n b y s h i f t o f S a m p l e L i k e l i h o o d F u n c t i o n
" t r u e " mm a x
= 6 . 9 2
Andrzej Kijko, South Africa
Andrzej Kijko, South Africa
Conclusions and Remarks
•Current EPRI Bayesian procedure by default underestimates value of mmax and locates mmax somewhere between maximum observed magnitude and “true” mmax.
•Underestimation of mmax can reach value of ½ a unit of magnitude.
•Two ways to correct the flaw of the procedure are presented.
Thank You