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

PDF

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