Deprem Tehlike Analizine Giriş

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



Erzincan ve Çevresinin Sismotektoniği





Aktif Fay Haritaları


Türki’nin Depremleri


Depremlerin Yıllara Göre Değişimi


Türkiye ve Çevresinin Depremselliği




Artçı Şokların Etkisi


Tüm Şok ve Anaşok Deprem Verileri


Tekrarlanma Aralıkları Arasında ki Fark


• Erzincan ve Çevresi• Kuzey Anadolu Fay Zonu• Artçı Şokların Etkisi• Mmax Estimation


İvme Haritası


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(


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


EPRI Procedure for mmax estimation (Cornell, 1994(

Splendid idea …

- combination of

observations with already

existing knowledge!

EPRI Procedure for mmax Estimation (Cornell, 1994)


Prior mmax distribution for intraplate regions

Courtesy Mark Petersen, USGS

Cratons Margins


Gaussian prior mmax distribution(e.g. M Ordaz, 2007)



Petersen's prior & Gaussian prior


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)


⋅=

maxmaxmax mof

yprobabilitprior

mgiven

likelihoodsampleconst

samplethegiven

mof

yprobabilitPosterior


)()|()( 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


• 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


Flow in EPRI Procedure

Confirmation 1: Prior Distribution for Intraplate Regions (by M. Petersen, USGS)


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


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?


• Eliminate effect

• Eliminate cause

Approach #1: Eliminate Effect


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


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


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


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


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


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



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

Education

Deprem Tehlike Analizine Giriş