Introduction to Seismology: Earthquake Statistics and Magnitude-Frequency Relationships

Introduction to Seismology
Introduction to Seismology-KFUPM

Earthquake Statistics
(pp. 371-396)
Ali Oncel
oncel@kfupm.edu.sa
Department of Earth Sciences
KFUPM

STUDENT PRESENTATION DAY
Earthquake Seismology-May 9, 2007

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

log10 Nc(m) = a - bm Charles F. Richter
(source:Michigan Technological
University)

4

log10 Nc 3 The magnitude of the quake
2 expected to be largest in a
1
year is:………………………
4 5 6 7 8
m m1 = a/b [i.e. Nc = 1]
Magnitude
This is a whole process distribution, that means we use all
the earthquakes in the data set or catalogue (not
aftershocks)…………………………………………

1


Frequency-Magnitude Statistics
Magnitude-Frequency Relationship Earthquake Earthquake Number
1918-2005 Magnitude Classification per year
>8 Great 3
(N)

7.5
7-7.9 Major 20
Log (N

5.5 Log N = -1.0M + 8.4
Log

3.5 6-6.9 Strong 180
1.5 5-5.9 Moderate 1800
-0.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 4-4.9 Light 10000
Magnitude 3-3.9 Minor 90000
Source: Fowler, 2005 2-2.9 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).
… … … … … … … … … … . .
N= Number of earthquakes
M= Magnitude Worldwide b-value is
are between 2/3 and 1

Magnitude Versus Energy

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
Seismology)…………………………………………………..

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).

2


Frequency-Seismic Moment Statistics



3


Time Variation of Seismic Moment

Variation in b value along the Fault Zones

Calavaras Fault

North Anatolian Fault Zone
Oncel and Wyss, 2000


Illustration courtesy IRIS Consortium
http://geology.about.com/library/bl/blquakestats.htm
(pp. 371-396)
Ali Oncel
oncel@kfupm.edu.sa
KFUPM

4


Previous Lecture

Magnitude Occurrence
The Gutenberg-Richter Law
Beno Gutenberg
Charles Richter
Magnitude versus Energy
Seismic Moment and Fault Length
Frequency-Seismic Moment Statistics
Spatial-variation of b-value along the Fault
Zones

How to find the asperities by b-value?

Calavaras Fault

North Anatolian Fault Zone
Oncel and Wyss, 2000

Source Characterization
for Simulating Strong Ground Motion

Source: Kojiro Irikura, AGU 2003

5

10000

Relation between
Rupture Area (km^2)

1000
Rupture Area and M0
100
Outer Fault Parameters
Somervill et al. (1999)

What is Asperity?
Kagoshima(3/26) Yamaguchi
Iwate (Miyakoshi et al., 2000)
10 Kobe (Sekiguchi et al, 2000)
Kocaeli (Sekiguchi and Iwata, 2000)

How to find the asperities ?
Chichi (Iwata and Sekiguchi, 2000)
Tottori (Sekiguchi and Iwata, 2000)

1
1.00E+24 1.00E+25 1.00E+26 1.00E+27 1.00E+28
Seismic Moment(dyne-cm) 10000
Somervill et al. (1999)
Kagoshima(3/26) Yamaguchi
Iwate (Miyakoshi et al., 2000)
Combined Area of
Asperities (km^2)

Kobe (Sekiguchi et al, 2000)
Kocaeli (Sekiguchi and Iwata, 2000)
1000 Chichi (Iwata and Sekiguchi, 2000)

Relation between Tottori (Sekiguchi and Iwata, 2000)

Combined Area of 100

Asperities and M0 10

Inner Fault Parameters 1
1.00E+24 1.00E+25 1.00E+26 1.00E+27 1.00E+28
Seimic Moment(dyne-cm)
Somerville et al. (1999) and Miyakoshi et al. (2001)
Source: Kojiro Irikura, AGU 2003

Repetition of Asperities

Spatial Distribution of
Moment Releases during
1968 Tokachi-oki Earthquake
and 1994 Sanriku-oki
Earthquake

(Nagai et al., 2001)

1944

6

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

Difficulties Knopoff, 2000
Southern California

(3)
Log N

(2)
(1)
Magnitude

(1) Often observe non-linearity or roll-off at large
magnitude…………………………………………..
(2) Largest earthquake “catastrophe”………………….
(3) Often observe roll-off at lower magnitudes
Why (1), (2) and (3)? Reasons?

Inadequate
Sample Size

Causing Deviation From
a L in ea r Frequency-
Magnitude Relation

7


Illustration courtesy IRIS Consortium
http://geology.about.com/library/bl/blquakestats.htm
(pp. 371-396)
Ali Oncel
oncel@kfupm.edu.sa
KFUPM

Previous Lecture

Asperity based Source Characterization
Relation between Rupture Area and Seismic Moment
Repetition of Asperities
Frequency of Earthquakes in California: Firs
Paper on Earthquake Statistics
Roll-off pattern in Magnitude distribution:
Possible Reasons

Incompleteness in Data
Mc Threshold Magnitude,
(3) which indicates data
completeness
Log N

(2)
(1)
Magnitude
(1) Often observe non-linearity or roll-off at large
magnitude…………………………………………..
(2) Largest earthquake “catastrophe”………………….
(3) Often observe roll-off at lower magnitudes
Why (1), (2) and (3)? Reasons?

8


Earthquake Completeness
Significance? 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
analysed data of
consecutive moving
window………………

Oncel and Wilson, 2007

Mainshocks for Turkey: 1900 and 1997
45
EURASIAN PLATE
Long-term
BLACK SEA
B:Central
Earthquake
42
A:Western NAFZ
C:Eastern
Completeness
39
ANATOLIAN

AGEAN This method takes into
SEA

36
account unequal
completeness periods for
different magnitude
33 AFRICAN PLATE ARABIAN PLATE
ranges (Weichert,
23 28 33 38 43 48

Magnitude
1 9 8 0 ) … … … …
Completeness Number of Earthquakes
Range Period
Western Central Eastern
Zone Zone Zone
4.0 - 4.5 1/1976 - 12/1992 119 24 10
4.5 - 5.0 1/1965 - 12/1992 62 27 28
Oncel and
5.0 - 5.5 1/1950 - 12/1992 23 14 15 LaForge, 1998
5.5 - 6.0 1/1930 - 12/1992 11 10 6
6.0 - 6.5 1/1915 - 12/1992 9 5 1
6.5 - 7.0 1/1890 - 12/1992 6 6 1
7.0 - 7.5 1/1850 - 12/1992 8 4 2
7.5 - 8.0 1/1800 - 12/1992 1 1 0

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. hypocentres
Complete: 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
preferences amongst sources……………………..
Computer readable: simple format………………….

9


http://neic.usgs.gov/neis/epic/epic_rect.html
Use rectangular coordinates of
your term project and make a
small program under EXCELL for
tabulating earthquakes through
the catalogue “Significant
Worlwide Earthquakes” for
different magnitude range
“∆M=0.5” as done for North
Anatolian Fault Zone. Add an
explanation regarding longer-term
of earthquake occurrence “4000
thousand years”? Finally,
determine Magnitude-Frequency
Relation?.........................

Homework
Due to May 19

Source: Stein and Wysession, 2003

P is typically about 1.

EARTHQUAKE OCCURRENCE

Simple Poisson process or random model:
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………………………..

n: number events in time t if
λ: the mean rate of occurrence (λ t ) n

P (n, λt) = e -λt
n!
Then, Poissonian probability :
Probability Density

10


The distribution of time
intervals T between quakes: P(T) = λ e-λT
Assumptions are:
i) Independent events N(t, t + ∆) independent of N (τ, τ + ∆τ)

ii) Orderly events (probability Lim P {[N (t, t + ∆t)] > 1} = 0
of simultaneous events is ∆t → 0
zero)

iii) Stationarity (the mean rate The probability of a quake is identical for
λ is not a function of time) any interval along the time axis


Source: Fenton, Adams and Halchuk, 2006

Earthquake Statistics: Example from
regions of low seismic areas

Ali Oncel
oncel@kfupm.edu.sa
KFUPM

Previous Lecture

Earthquake Completeness: Threshold Magnitude (Mc)
Spatial-Temporal detection of Mc for Modern Catalogue
(1992-1999): Example from North Anatolian Fault Zone
Long-term detection of Mc: Example from NAFZ based on
approach of unequal observation periods for different
magnitudes
Earthquake Catalogues: Desirable Properties

11

Recall: MAGNITUDE OCCURRENCE

The 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 b=βx log e log e=0.4343

4 The magnitude of the quake
log10 Nc 3 expected to be largest in a
2 year is:………………………..
1
m1 = a/b [i.e. Nc = 1]
4 5 6 7 8
m
Magnitude

This is a whole process distribution, that means we use all
the earthquakes in the data set or catalogue (not
aftershocks)………………………………………………….

Seismicity of Stable Cratonic Cores (SCC)
Greenland

Siberia

Arabia
N. America

India
Africa

S. America
Australia

Antarctica
Modified after Fenton, Adams, Halchuk, 2006

Earthquake catalogue completeness

12


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

Stable Craton

Once a decade
a M6.5

log10 Nc(m) = 3.68 – 0.947 m

Worldwide rates of stable cratonic core
seismicity

13

Introduction to Seismology-KFUPM Introduction to Seismology-KFUPM Introduction to Seismology-KFUPM

14

west east
stable

Plattsburgh
2002 NY

Seismicity of east
Saudi Arabia west
stable

Source: Al-Amri., 2005

15

Rupture on a

Fault

Total Slip in the M7.3 Landers Earthquake

Slip on an earthquake fault

START

Surface of the earth

Depth
Into
the
earth 100 km (60 miles)
Distance along the fault plane

Second 2.0

16


Second 4.0

Second 6.0

Second 8.0

17


Second 10.0

Second 12.0

Second 14.0

18


Second 16.0

Second 18.0

Second 20.0

19


Second 22.0

Second 24.0

Bigger Faults Make Bigger
Earthquakes
1000

100
Kilometers

10

1
5.5 6 6.5 7 7.5 8
Magnitude

20


Bigger Earthquakes Last a Longer
Time

100
Seconds

10

1
5.5 6 6.5 7 7.5 8
Magnitude

21

Introduction to Seismology: Earthquake Statistics and Magnitude-Frequency Relationships

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