earhquake statistics

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Department of Earth SciencesKFUPM

Introduction to Seismology

Earthquake Statistics (pp. 371-396)

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Ali [email protected]

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STUDENT PRESENTATION DAYEarthquake Seismology-May 9, 2007

Magnitude Occurrence

log10 Nc(m) = a - bm

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3

2

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4 5 6 7 8

log10 Nc

Magnitude m

This is a whole process distribution, that means we use allthe earthquakes in the data set or catalogue (nota f t e r s h o c k s ) … … … … … … … … … … … … … … … …

The magnitude of the quake expected to be largest in a year is:………………………

m1 = a/b [i.e. Nc = 1]

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The Gutenberg and Richter (1944) cumulative frequency-magnitude law. The number of earthquakes in a region decreases exponentially with magnitude or:……………..

Charles F. Richter(source:Michigan Technological University)

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Frequency-Magnitude Statistics

Worldwide Worldwide bb--valuevalue is is are between 2/3 and 1are between 2/3 and 1

Magnitude-Frequency Relationship1918-2005

Log N = -1.0M + 8.4

-0.5

1.5

3.5

5.5

7.5

2.5 3.5 4.5 5.5 6.5 7.5 8.5

Magnitude

Log

(N

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Log

(N)

Earthquake Earthquake Number Magnitude Classification per year

>8 Great 37-7.9 Major 206-6.9 Strong 1805-5.9 Moderate 1800

4-4.9 Light 100003-3.9 Minor 900002-2.9 Very Minor 1000000

The b value is a coefficient describing the ratio of small to large earthquakes within a given area and time period. It is often shown to be the same over a wide range or magnitudes. It is the slope of the curve in the Gutenberg-Richter recurrence relationship (Source, Bullen and Bolt, 1987).… … … … … … … … … … . .

Source: Fowler, 2005

N= Number of earthquakesM= Magnitude

Magnitude Versus Energy

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Comparison of frequency, magnitude, and energy released of earthquakes and other phenomena. The magnitude used here is moment magnitude, Mw (After Incorporated Research Institutions for S e i s m o l o g y ) … … … … … … … … … … … … … … … … … … … . .

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PM Seismic Moment and Fault Length

Seismic moment is a measure of earthquake size related to the leverage of the forces (couples) across the area of the fault slip. It is equal to the rigidity of the rock times the area of faulting times the amount of slip. The dimensions of seismic moment are dyne-cm (or Newton-meters).

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PM Frequency-Seismic Moment Statistics

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PM Frequency-Magnitude Statistics

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PM Frequency-Magnitude Statistics

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PM Time Variation of Seismic Moment

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Oncel and Wyss, 2000

Variation in b value along the Fault Zones

Calavaras Fault

North Anatolian Fault Zone




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http://geology.about.com/library/bl/blquakestats.htmIllustration courtesy IRIS Consortium

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Previous Lecture

Magnitude Occurrence The Gutenberg-Richter Law

Beno GutenbergCharles Richter

Magnitude versus Energy Seismic Moment and Fault Length Frequency-Seismic Moment StatisticsFrequency-Magnitude StatisticsSpatial-variation of b-value along the Fault

Zones

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Oncel and Wyss, 2000

Calavaras Fault

North Anatolian Fault Zone

How to find the asperities by b-value?

Source Characterization Source Characterization for Simulating Strong Ground Motionfor Simulating Strong Ground Motion

Source: Kojiro Irikura, AGU 2003

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Relation between Relation between Rupture Area and MRupture Area and M00

Outer Fault Parameters

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10

100

1000

10000

1.00E+24 1.00E+25 1.00E+26 1.00E+27 1.00E+28Seismic Moment(dyne-cm)

Rup

ture

Are

a (k

m^2

)

Kagoshima(3/26) YamaguchiIwate (Miyakoshi et al., 2000)Kobe (Sekiguchi et al, 2000)Kocaeli (Sekiguchi and Iwata, 2000)Chichi (Iwata and Sekiguchi, 2000)Tottori (Sekiguchi and Iwata, 2000)

Somervill et al. (1999)

Somerville et al. (1999) and Miyakoshi et al. (2001)

Relation between Relation between Combined Area of Combined Area of Asperities and MAsperities and M00

Inner Fault Parameters1

10

100

1000

10000

1.00E+24 1.00E+25 1.00E+26 1.00E+27 1.00E+28Seimic Moment(dyne-cm)

Com

bine

d A

rea

ofA

sper

ities

(km

^2)

Kagoshima(3/26) YamaguchiIwate (Miyakoshi et al., 2000)Kobe (Sekiguchi et al, 2000)Kocaeli (Sekiguchi and Iwata, 2000)Chichi (Iwata and Sekiguchi, 2000)Tottori (Sekiguchi and Iwata, 2000)

Somervill et al. (1999)

Source: Kojiro Irikura, AGU 2003

What is Asperity?How to find the asperities ?

Spatial Distribution of Moment Releases during 1968 Tokachi-oki Earthquakeand 1994 Sanriku-okiEarthquake

(Nagai et al., 2001)

Repetition of Asperities

1944

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What is Annual Mean? HOMEWORK Due to May 12: Make it under EXCEL and prove SOLUTION?

Difficulties

(1) Often observe non-linearity or roll-off at large magni tude…………………………………………..

(2) Largest earthquake “catastrophe”………………….(3) Often observe roll-off at lower magnitudes

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Magnitude

(3)

(1)(2)

Log

N

Why (1), (2) and (3)? Reasons?

Knopoff, 2000Southern California

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Causing Deviation From a Linear Frequency-Magn i tude Re la t ion

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http://geology.about.com/library/bl/blquakestats.htmIllustration courtesy IRIS Consortium

Previous Lecture

Asperity based Source CharacterizationRelation between Rupture Area and Seismic MomentRepetition of Asperities

Frequency of Earthquakes in California: Firs Paper on Earthquake Statistics

Roll-off pattern in Magnitude distribution: Possible Reasons

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Incompleteness in Data

(1) Often observe non-linearity or roll-off at large magni tude…………………………………………..

(2) Largest earthquake “catastrophe”………………….(3) Often observe roll-off at lower magnitudes

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Magnitude

(3)

(1)(2)

Log

N

Why (1), (2) and (3)? Reasons?

Mc Threshold Magnitude, which indicates data c o m p l e t e n e s s

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Earthquake Completeness

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Oncel and Wilson, 2007

What is Time- or Space Variation in Earthquake Completeness?

Time-space analysis of e a r t h q u a k e completeness indicates the best value of Mc, which is 2.9, resulted a n a l y s e d d a t a o f consecu t ive moving w i n d o w … … … … … …

Significance?

Long-term Earthquake

Completeness

0111/1800 - 12/19927.5 - 8.0

2481/1850 - 12/19927.0 - 7.5

1661/1890 - 12/19926.5 - 7.0

1591/1915 - 12/19926.0 - 6.5

610111/1930 - 12/19925.5 - 6.0

1514231/1950 - 12/19925.0 - 5.5

2827621/1965 - 12/19924.5 - 5.0

10241191/1976 - 12/19924.0 - 4.5

EasternZone

Central Zone

Western Zone

Number of EarthquakesCompletenessPeriod

Magnitude Range

0111/1800 - 12/19927.5 - 8.0

2481/1850 - 12/19927.0 - 7.5

1661/1890 - 12/19926.5 - 7.0

1591/1915 - 12/19926.0 - 6.5

610111/1930 - 12/19925.5 - 6.0

1514231/1950 - 12/19925.0 - 5.5

2827621/1965 - 12/19924.5 - 5.0

10241191/1976 - 12/19924.0 - 4.5

EasternZone

Central Zone

Western Zone

Number of EarthquakesCompletenessPeriod

Magnitude Range

Oncel and LaForge, 1998

This method takes into a c c o u n t u n e q u a l completeness periods for d i f f e r e n t m a g n i t u d e r a n g e s ( W e i c h e r t , 1 9 8 0 ) … … … …

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BLACK SEA

AFRICAN PLATE

EURASIAN PLATE

ARABIAN PLATE

ANATOLIAN

AGEANSEA

33

36

39

42

45

23 28 33 38 43 48

A:WesternB:Central

C:EasternNAFZ

Mainshocks for Turkey: 1900 and 1997

DESIRABLE PROPERTIES OF EARTHQUAKE CATALOGUES

Homogeneity: if parameters are redetermined then uniform redetermination magnitudes determined uniformly or calibrated against each other intensity values on same scale all parameters to known accuracy, e.g. hypocentresComplete: ideally complete down to small magnitudes, but certainly of known completeness…………………..Duration: catalogue to cover a long time span, ideally greater than the largest return periods……………….Source material: known and referenced if there are multiple sources for some earthquakes and parameters are not uniformly re-determined then a stated hierarchy of pre ferences amongst sources……………………..Computer readable: simple format………………….

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http://neic.usgs.gov/neis/epic/epic_rect.htmlUse rectangular coordinates of your term project and make a small program under EXCELL for tabulating earthquakes through th e c a ta logue “S ign i f i can t Wor lwide Ear thquakes” for d i f f e ren t magn i tude range “∆M=0.5” as done for North Anatolian Fault Zone. Add an explanation regarding longer-term of earthquake occurrence “4000 t h o u s a n d ye a r s ” ? F i n a l l y , determine Magnitude-Frequency Re la t ion? . . . . . . . . . . . . . . . . . . . . . . . . .

Homework Due to May 19

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P is typically about 1.

Source: Stein and Wysession, 2003

EARTHQUAKE OCCURRENCE

S i m p le P o iss o n p ro cess or random mode l :Assume that an earthquake or event in a given magnitude range and a given volume of the Earth’s crust is assumed to be found equally in any unit time interval, and it is independent of any other earthquake………………………..

( )!nt nλ

P (n, λt) = e -λt

Probability Density

n: number events in time t ifλ: the mean rate of occurrence

Then, Poissonian probability :

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P(T) = λ e-λTThe d i s t r i bu t i on o f t ime intervals T between quakes:

Assumptions are:

The probability of a quake is identical for any interval along the time axis

Stationarity (the mean rate λ is not a function of time)

iii)

Lim P {[N (t, t + ∆t)] > 1} = 0∆t → 0

Orderly events (probability of simultaneous events is zero)

ii)

N(t, t + ∆) independent of N (τ, τ + ∆τ)Independent eventsi)

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Earthquake Statistics: Example from regions of low seismic areas


Introduction to SeismologySource: Fenton, Adams and Halchuk, 2006

Previous Lecture

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Earthquake Completeness: Threshold Magnitude (Mc)Spatial-Temporal detection of Mc for Modern Catalogue

(1992-1999): Example from North Anatolian Fault ZoneLong-term detection of Mc: Example from NAFZ based on

approach of unequal observation periods for different magnitudes

Earthquake Catalogues: Desirable Properties

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Recall: MAGNITUDE OCCURRENCEThe Gutenberg and Richter (1944) cumulative frequency-magnitude law. The number of earthquakes in a region decreases exponentially with magnitude or:………………….log10 Nc(m>M) = a - bm

4

3

2

1

4 5 6 7 8

log10 Nc

Magnitude m

This is a whole process distribution, that means we use allthe earthquakes in the data set or catalogue (notaftershocks)………………………………………………….

The magnitude of the quake expected to be largest in a year is:………………………..

m1 = a/b [i.e. Nc = 1]

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b=βx log e log e=0.4343

Seismicity of Stable Cratonic Cores (SCC)

Modified after Fenton, Adams, Halchuk, 2006

N. America

S. America

Africa

Australia

India

Arabia

Greenland

Siberia

Antarctica

Earthquake catalogue completeness

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Magnitude-Frequency (per 50.7 x 106 km2) plot for the worldwideSCC seismicity data set

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Stable Craton

Once a decade a M6.5

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log10 Nc(m) = 3.68 – 0.947 m

Worldwide rates of stable cratonic core seismicity

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2002Plattsburgh

NY

stablewest east

stablewest

east

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Source: Al-Amri., 2005

Seismicity of Saudi Arabia

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Total Slip in the M7.3 Landers EarthquakeTotal Slip in the M7.3 Landers Earthquake

Rupture on a Fault

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DepthInto the

earth

Surface of the earth

Distance along the fault plane100 km (60 miles)

Slip on an earthquake faultSlip on an earthquake fault

START

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Slip on an earthquake faultSecond 2.0Slip on an earthquake faultSecond 2.0

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Bigger Faults Make Bigger EarthquakesBigger Faults Make Bigger Earthquakes

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5.5 6 6.5 7 7.5Magnitude

Kilo

met

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Bigger Earthquakes Last a Longer TimeBigger Earthquakes Last a Longer Time

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5.5 6 6.5 7 7.5 8

Magnitude

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earhquake statistics

Technology

seismology introduction

faultzones introduction

seismologykfupmseismic

magnitude classification

ismoment magnitude

fault lengthseismic

fault slip

energy seismic moment