Earhquake Statistics
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Transcript of Earhquake Statistics
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Department of Earth SciencesKFUPM
Introduction to Seismology
Earthquake Statistics (pp. 371-396)
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STUDENT PRESENTATION DAYEarthquake Seismology-May 9, 2007
Magnitude Occurrence
log10 Nc(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 (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
Department of Earth SciencesKFUPM
Introduction to Seismology
Earthquake Statistics (pp. 371-396)
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mol
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KFU
PM
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
1
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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Department of Earth SciencesKFUPM
Introduction to Seismology
Earthquake Statistics (pp. 371-396)
Intr
oduc
tion
to
Seis
mol
ogy-
KFU
PM
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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Department of Earth SciencesKFUPM
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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Slip on an earthquake faultSecond 4.0Slip on an earthquake faultSecond 4.0
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Slip on an earthquake faultSecond 6.0Slip on an earthquake faultSecond 6.0
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Slip on an earthquake faultSecond 8.0Slip on an earthquake faultSecond 8.0
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Slip on an earthquake faultSecond 10.0Slip on an earthquake faultSecond 10.0
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Slip on an earthquake faultSecond 12.0Slip on an earthquake faultSecond 12.0
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Slip on an earthquake faultSecond 14.0Slip on an earthquake faultSecond 14.0
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Slip on an earthquake faultSecond 16.0Slip on an earthquake faultSecond 16.0
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Slip on an earthquake faultSecond 18.0Slip on an earthquake faultSecond 18.0
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Slip on an earthquake faultSecond 20.0Slip on an earthquake faultSecond 20.0
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Slip on an earthquake faultSecond 22.0Slip on an earthquake faultSecond 22.0
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Slip on an earthquake faultSecond 24.0Slip on an earthquake faultSecond 24.0
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Bigger Faults Make Bigger EarthquakesBigger Faults Make Bigger Earthquakes
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1
10
100
1000
5.5 6 6.5 7 7.5Magnitude
Kilo
met
ers
8
21
Bigger Earthquakes Last a Longer TimeBigger Earthquakes Last a Longer Time
1
10
100
5.5 6 6.5 7 7.5 8
Magnitude
Sec
onds
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