Earthquake Magnitudes and Seismic Measurements
FUNDAMENTALS of
ENGINEERING SEISMOLOGY
EARTHQUAKE
MAGNITUDES
Earthquake source characterization
•
Magnitude
•
Fault dimensions (covered before)
•
Slip distribution (kinematics)
•
Fourier transform refresher
•
Point source representation
–
Spectral shape
–
Corner frequency
–
Stress parameter
Earthquake Magnitude
•
Earthquake magnitude scales originated
because of
–
the desire for an
objective
measure of
earthquake size
–
Technological advances -> seismometers
Earthquake Magnitudes
•
In the 1930’s, Wadati in Japan and Richter
in California noticed that although the
peak
amplitudes
on seismograms from different
events differed, the
peak amplitudes
decreased with distance in a similar manner
for different quakes.
Seismogram Peak Amplitude
F
The
peak amplitude
is the size of the largest
deflection from the zero line.
Richter’s Observations
Richter’s Local Magnitude
•
Richter used these observations to
construct the first magnitude scale, M
L
(Richter’s Local Magnitude for Southern
California).
•
He based his formula for calculating the
magnitude on the astronomical brightness
scale - which was
logarithmic
.
Logarithmic Scales
•
In a logarithmic scale such as magnitude
•
A change in one magnitude unit means a
change of a factor of 10 in the amplitude of
ground shaking (
wait! This is an often used
wait! This is an often used
statement, but it is too simplistic, and I
statement, but it is too simplistic, and I
hope you will know why by the end of the
hope you will know why by the end of the
course
course
).
In a logarithmic scale such as magnitude:
A change in one magnitude unit means a
change of a factor of 10 in the amplitude of
motion that defines the magnitude. This could
be the response of a particular type of
instrument, or it could be ground motions at
very long periods or ground motions at periods
near 1 sec, etc.
F
o
r
p
e
a
k
g
r
o
u
n
d
m
o
t
i
o
n
s
a
n
d
r
e
s
p
o
n
s
e
s
p
e
c
t
r
a
,
t
h
e
s
c
a
l
i
n
g
i
s
u
s
u
a
l
l
y
l
e
s
s
t
h
a
n
1
0
M
/
2
w
h
e
r
e
M
i
s
t
h
e
m
o
m
e
n
t
m
a
g
n
i
t
u
d
e
,
d
e
f
i
n
e
d
s
h
o
r
t
l
y
,
r
a
t
h
e
r
t
h
a
n
1
0
M
.
The proper statement
Richter’s Magnitude Scale
•
Defined for specific attenuation conditions valid
for southern California
•
Only valid for one specific type of seismometer
•
Can be used elsewhere if local attenuation
correction is used and simulated Wood-Anderson
response is computed
•
Not often used now, although it IS a measure of
ground shaking at frequencies of engineering
interest
Richter tied his formula to a specific instrument, the Wood-Anderson
torsion seismograph
He assumed a reference motion at a reference distance. To compute the
magnitude at different distances, he calibrated the attenuation function
Ml=Log A
max
-Log A
0
-
logA
0
changes from region to region
. The calibration of a local magnitude scale for
a given region implies the determination of the empirical attenuation correction for
that region (and the magnitude station corrections
)
The W-A seismometers are not still used. The W-A recording is computed numerically
(by convolving the ground displacement with the W-A transfer function)
Richter fixed the scale assuming that a
M
L
=3 earthquake produces 1mm of
maximum amplitude on a Wood-Anderson
seismometer at 100 km
In many studies, the attenuation function is determined by a parametric
approach
where the reference distance and the reference magnitude are fixed
In agreement with the Richter scale.
In contrast to the general magnitude formula, M
L
considers only the maximum
displacement amplitudes but not their periods. Reason: WA instruments are short-
period and their traditional analog recorders had a limited paper speed. Proper
reading of the period of high-frequency waves from local events was rather
difficult. It was assumed, therefore, that the maximum amplitude phase (which in
the case of local events generally corresponds to Sg, Lg or Rg) always had roughly
the same dominant period.
The smallest events recorded in local microearthquake studies have negative values
of M
L
while the largest M
L
is about 7 , i.e., the M
L
scale also suffers saturation (see
later).
Despite these limitations, M
L
estimates of earthquake size are relevant for
earthquake engineers and risk assessment since they are closely related to
earthquake damage. The main reason is that many structures have natural periods
close to that of the WA seismometer (0.8s) or are within the range of its pass-band
(about 0.1 - 1 s).
A review of the development and use of the Richter scale for determining
earthquake source parameters is given by Boore (1989).
From the IASPEI New Manual Seismological Observatory Practice
Modern Seismic Magnitudes
•
Today seismologists use different seismic
waves to compute magnitudes
•
These waves generally have lower
frequencies than those used by Richter
•
These waves are generally recorded at
distances of 1000s of kilometers instead of
the 100s of kilometers for the Richter scale
(this is important because most earthquakes
occur in remote places, such as under the
oceans, without instruments within 100s of
kilometers)
Teleseismic M
S
and m
b
•
Two commonly used modern magnitude
scales are:
•
M
S
, Surface-wave magnitude (Rayleigh Wave)
•
m
b
, Body-wave magnitude (P-wave)
Note: also Ms suffers of saturation (see later…)
Collaboration between research teams in Prague, Moscow and Sofia resulted
in the proposal of a new Ms scale and calibration function, termed Moscow-
Prague formula, by Karnik et al. (1962):
for epicentral distances 2° < Δ < 160° and source depth h < 50 km. The
IASPEI Committee on Magnitudes recommended at its Zürich meeting in
1967 the use of this formula as standard for Ms determination for shallow
seismic events (h ≤ 50 km)
Work started by Gutenberg developed a magnitude scale based on surface wave
recordings at teleseismic distances. The measure of amplitude is the maximum
velocity (A/T)max. This allowed not only to link the scale to the energy, but also
to account for the large variability of periods T corresponding to the maximum
amplitude of surface waves, depending on distance and crustal structure.
Surface wave magnitude
Gutenberg (1945b and c) developed a magnitude relationship for
teleseismic body waves such as P, PP and S in the period range 0.5
s to 12 s. It is based on theoretical amplitude calculations corrected
for geometric spreading and (only distance-dependent!) attenuation
and then adjusted to empirical observations from shallow and deep-
focus earthquakes, mostly in
intermediate-period records
:
mB = log (A/T)
max
+ Q(Δ, h)
Gutenberg and Richter (1956a) published a table with Q(Δ) values
for P-, PP- and S-wave observations in vertical (V=Z) and
horizontal (H) components for shallow shocks, complemented by
diagrams Q(Δ, h) for PV, PPV and SH which enable also magnitude
determinations for intermediate and deep earthquakes. These
calibration functions are correct when ground displacement
amplitudes are measured in intermediate-period records and given
in micrometers (1 μm = 10
-6
m).
Body wave magnitude
Later, with the introduction of the WWSSN short-period 1s-seismometers (see
Fig. 3.11, type A2) it became common practice at the NEIC to use the calibration
function Q(Δ, h) for
short-period PV only
. In addition, it was recommended that
the largest amplitude be taken
within the first few cycles
(see Willmore, 1979)
instead of measuring the maximum amplitude in the whole P-wave train. One
should be aware that this practice was due to the focused interest on
discriminating between earthquakes and underground nuclear explosions. The
resulting
short-period mb
values strongly underestimated the
body-wave
magnitudes for mB
> 5 and, as a consequence, overestimated the annual
frequency of small earthquakes in the magnitude range of kt-explosions. Also, mb
saturated much earlier than the original Gutenberg-Richter mB for intermediate-
period body waves or Ms for long-period surface waves Therefore, the IASPEI
Commission on Practice issued a revised recommendation in 1978 according to
which the maximum P-wave amplitude for earthquakes of small to medium size
should be measured within 20 s from the time of the first onset and for very large
earthquakes even up to 60 s (see Willmore, 1979, p. 85). This somewhat reduced
the discrepancy between mB and mb but in any event both are differently scaled
to Ms and the short-period mb necessarily saturates earlier than medium-period
mB.
However, some of the national and international agencies have only
much later or not even now changed their practice of measuring
(A/T)max for mb determination in a very limited time-window, e.g.,
the International Data Centre for the monitoring of the CTBTO still
uses a time window of only 6 s (5.5s after the P onset), regardless of
the event size.
24
Why is it called “moment”?
Radiation from a shear dislocation with slip S over area A
in material with rigidity
μ
is identical to that from a double
couple with strength
μ
U
A (units stress*displacement*area,
but stress = force/area, so units = force*displacement = a
couple = work = energy)
25
Nomenclature
•
M
w
–
Defined by Kanamori as an energy magnitude
(includes a parameter in addition to moment), but
he clearly had in mind the present mapping of
moment and magnitude but setting the additional
parameter to a constant value
•
M
–
T
h
e
f
i
r
s
t
e
x
p
l
i
c
i
t
m
a
p
p
i
n
g
o
f
m
o
m
e
n
t
(
M
0
)
a
n
d
m
o
m
e
n
t
m
a
g
n
i
t
u
d
e
(
M
)
–
T
o
d
a
y
p
e
o
p
l
e
b
y
-
a
n
d
-
l
a
r
g
e
u
s
e
M
w
(
c
a
n
w
r
i
t
e
i
t
i
n
e
m
a
i
l
)
;
o
n
l
y
p
u
r
i
s
t
s
s
u
c
h
a
s
D
M
B
u
s
e
M
.
What is the proper equation?
•
M
= 2/3 log M
0
– 10.7?
•
M
= 2/3 log M
0
– 10.73 ?
•
The former is correct, it corresponds to
Log M
0
= 1.5
M
+ 16.05 (not 16.0 or 16.1)
•
Hanks (personal commun.) chose 16.05 to average
relations with constant terms of 16.0 and 16.1
Why use moment magnitude?
•
It is the best single measure of overall
earthquake size
•
It does not saturate (discussed later)
•
It can be estimated from geological
observations
•
It can be estimated from paleoseismology
studies
•
It can be tied to plate motions and recurrence
relations
Empirical relations can be
used to estimate moment
magnitude based on size of
felt area – eg. Johnston et
al., 1996 relations for mid-
plate areas
Moment Magnitude is the Best
Measure of Earthquake Size
“the big one”
Moment
Physical units (dyne-cm)
10
26
: Northridge, 1994
10
30
: Sumatra, 2004
Big range!
No saturation:
bigger rupture
bigger moment
31
USGS - SUSAN HOUGH
The Largest Earthquakes
M
i
s
t
h
e
a
p
p
r
o
p
r
i
a
t
e
c
h
o
i
c
e
f
o
r
c
o
m
p
a
r
i
n
g
t
h
e
l
a
r
g
e
s
t
e
v
e
n
t
s
,
i
t
d
o
e
s
n
o
t
s
a
t
u
r
a
t
e
.
1960 Chile
9.5
2004 Sumatra 9.3
1964 Alaska
9.2
1952 Kamchatka
9.1
1965 Aleutians
9.0
(This pie chart needs to be revised to include the 2004 Sumatra
earthquake, but the chart serves to emphasize that 0.1 M units
corresponds to a factor of 1.4 increase in moment.)
•
Why are the largest earthquakes along subduction
zones?
•
For crustal earthquakes the width is limited by the
thickness of the superficial crust brittle layer (~20
km). The thickness of the brittle layer is
controlled by temperature, which increases with
depth
•
Width is often considered smaller than the length
even for small earthquake
O
R
D
E
R
S
O
F
M
A
G
N
I
T
U
D
E
F
a
u
l
t
w
i
d
t
h
20 km
surface
brittle
plastic
O
R
D
E
R
S
O
F
M
A
G
N
I
T
U
D
E
F
a
u
l
t
w
i
d
t
h
20 km
surface
brittle
plastic
faults
O
R
D
E
R
S
O
F
M
A
G
N
I
T
U
D
E
F
a
u
l
t
w
i
d
t
h
20 km
surface
brittle
plastic
faults
O
R
D
E
R
S
O
F
M
A
G
N
I
T
U
D
E
F
a
u
l
t
w
i
d
t
h
Converting between magnitude scales:
Empirical relations (or sometimes
theoretical relations) can be used to
convert between magnitude scales. This
is important in deriving magnitude
recurrence statistics for a region or
source zone, as all magnitudes should be
first reported on the same scale before
characterizing their statistics
Surface wave magnitude is a close approximation
to Moment M for Ms 6 to 8 events
Body-wave magnitude is not a good measure of moment M,
especially for large events
Relations between magnitude scales
Magnitude Discrepancies
•
Ideally, you want the same value of
magnitude for any one earthquake from each
scale you develop, i.e.
–
M
S
= m
b
= M
L
=
M
•
But this does not always happen:
–
San Francisco 1906: M
S
= 8.3,
M
= 7.8
–
Chile 1960: M
S
= 8.3,
M
= 9.6
Why Don’t Magnitude Scales
Agree?
•
Simplest Answer:
–
Earthquakes are complicated physical
phenomena that are not well described by a
single number
.
–
Can a thunderstorm be well described by one
number ? (No. It takes wind speed, rainfall,
lightning strikes, spatial area, etc.)
Why Don’t Magnitude Scales Agree?
•
More Complicated Answers:
•
The distance correction for amplitudes depends on
geology.
•
Deep earthquakes do not generate large surface waves -
M
S
is biased low for deep earthquakes.
•
Some earthquakes last longer than others, even though
the peak amplitude is the same.
•
Variations in stress release along fault, for same
moment.
•
Not all earthquakes are self similar (that is, the relative
radiation at different frequencies can differ--- examples:
1999 Chi-Chi compared to “standard” California
earthquake).
Why Don’t Magnitude Scales Agree?
•
Most complicated reason:
–
Magnitude scales
saturate
–
This means there is an upper limit to magnitude
no matter how “large” the earthquake is
–
For instance M
s
(surface wave
magnitude)
seldom gets above 8.2-8.3
Example: m
b
“Saturation”
F
m
b
seldom gives
values above 6.7 - it
“saturates”.
F
m
b
must be
measured in the first
5 seconds - that’s
the (old) rule.
What Causes Saturation?
•
The rupture process
.
–
Small earthquakes rupture small areas and are relatively
depleted in long-period signals
.
–
Large earthquakes rupture large areas and are rich in
long-period motions (we’ll study this later, when we
discuss source scaling)
What Causes Saturation?
The relative size of the fault and the wavelength of the
motion used to determine the magnitude is a key part of
the explanation.
•
Small fault compared to the wavelength: the
magnitude will be a good measure of overall
earthquake size.
•
Large fault compared to the wavelength: the
magnitude will be determined by radiation from only a
portion of the fault, and the magnitude will not be a
good measure of overall fault size
47
Saturation (cartoon)
Relations between Magnitude Scales
N
o
t
e
s
a
t
u
r
a
t
i
o
n
49
Are m
b
and M
s
still useful?
•
YES!
–
Many (most) earthquakes are small enough that
saturation does not occur
–
Empirical relations between energy release and
m
b
and M
s
exist
–
The
ratio
of m
b
to M
s
can
indicate whether a
given seismogram is from an earthquake or a
nuclear explosion (
verification seismology
)
(Whoops, this uses moment. Oh well, a plot of M
s
vs. m
b
is similar)
Magnitude Summary
M
a
g
n
i
t
u
d
e
S
y
m
b
o
l
W
a
v
e
P
e
r
i
o
d
Local (Richter)
M
L
S or Surface Wave*
0.8 s
Body-Wave
m
b
P
1 s
Surface-Wave
M
s
Rayleigh
20 s
M
o
m
e
n
t
M
w
,
M
R
u
p
t
u
r
e
A
r
e
a
,
S
l
i
p
1
0
0
’
s
-
1
0
0
0
’
s
•
Magnitude is a measure of ground shaking amplitude.
•
More than one magnitude scale is used to study
earthquakes.
•
All magnitude scales have the same logarithmic form.
•
Since different scales use different waves and
different period vibrations, they do not always give the
same value
.
Energy magnitude Me
Energy magnitude Me
M
e
=
2
/
3
(
l
o
g
E
s
–
4
.
4
)
H
o
w
e
v
e
r
,
t
h
i
s
r
a
t
i
o
d
e
p
e
n
d
s
o
n
t
h
e
s
t
r
e
s
s
d
r
o
p
Δ
σ
w
h
i
c
h
v
a
r
i
e
s
b
y
a
b
o
u
t
t
h
r
e
e
o
r
d
e
r
s
o
f
m
a
g
n
i
t
u
d
e
P. Bormann
F
o
r
s
h
a
l
l
o
w
E
Q
s
C
h
o
y
a
n
d
B
o
a
t
w
r
i
g
h
t
(
1
9
9
5
)
f
o
u
n
d
B
o
a
t
w
r
i
g
h
t
&
C
h
o
y
(
1
9
8
5
)
C
h
o
y
&
B
o
a
t
w
r
i
g
h
t
(
1
9
9
5
)
w
i
t
h
M
e
=
M
w
+
0
.
2
7
f
o
r
K
a
n
a
m
o
r
i
´
s
a
v
e
r
a
g
e
c
o
n
d
i
t
i
o
n
:
E
s
/
M
0
=
5
X
1
0
-
5
.
F
o
r
s
o
m
e
d
e
e
p
E
Q
´
s
Δ
σ
u
p
t
o
a
b
o
u
t
1
0
0
M
P
a
h
a
s
b
e
e
n
d
e
t
e
r
m
i
n
e
d
!
Mw and Me may differ significantly !
Mw and Me may differ significantly !
•
M
w
i
s
r
e
l
a
t
e
d
t
o
a
v
e
r
a
g
e
d
i
s
p
l
a
c
e
m
e
n
t
a
n
d
r
u
p
t
u
r
e
a
r
e
a
a
n
d
t
h
u
s
t
o
=
>
t
e
c
t
o
n
i
c
e
f
f
e
c
t
s
o
f
E
Q
Reprinted from Choy et al., 2001
P. Bormann
•
M
e
i
s
m
o
r
e
c
l
o
s
e
l
y
r
e
l
a
t
e
d
t
o
t
h
e
e
x
i
t
a
t
i
o
n
o
f
h
i
g
h
e
r
f
r
e
q
u
e
n
c
i
e
s
a
n
d
t
h
u
s
t
o
=
>
d
a
m
a
g
e
p
o
t
e
n
t
i
a
l
o
f
E
Q
Conclusions
P. Bormann
•
M
w
a
n
d
M
e
a
r
e
t
h
e
o
n
l
y
p
h
y
s
i
c
a
l
l
y
w
e
l
l
-
d
e
f
i
n
e
d
a
n
d
n
o
n
-
s
a
t
u
r
a
t
i
n
g
m
a
g
n
i
t
u
d
e
s
,
h
o
w
e
v
e
r
,
t
h
e
y
m
e
a
n
d
i
f
f
e
r
e
n
t
t
h
i
n
g
s
.
•
D
e
t
e
r
m
i
n
a
t
i
o
n
o
f
M
w
a
n
d
M
e
h
a
s
t
o
b
e
b
a
s
e
d
o
n
(
V
)
B
B
,
d
i
g
i
t
a
l
r
e
c
o
r
d
s
(
b
a
n
d
w
i
d
t
h
:
2
t
o
4
d
e
c
a
d
e
s
o
r
6
t
o
1
3
o
c
t
a
v
e
s
)
.
•
A
l
l
c
l
a
s
s
i
c
a
l
b
a
n
d
-
l
i
m
i
t
e
d
m
a
g
n
i
t
u
d
e
s
(
t
y
p
i
c
a
l
l
y
1
t
o
3
o
c
t
a
v
e
s
)
,
s
a
t
u
r
a
t
e
(
e
.
g
.
;
M
l
,
m
b
,
m
B
a
n
d
M
s
)
.
•
B
a
n
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Magnitude-frequency distribution
57
58
Recurrence Rate
59
Slip Rate
Recurrence Rate
•
Slip rate = N mm/year
•
M
max
event = X meters (average) slip
•
Characteristic model: T
r
= X/N
•
e.g
Sagaing fault: ? mm/yr
60
Slip Rate
Recurrence Rate
•
Slip rate = N mm/year
•
M
max
event = X meters (average) slip
•
Characteristic model: T
r
= X/N
•
e.g
Sagaing fault: 20 mm/year
M
max
= ?
61
Slip Rate
Recurrence Rate
•
Slip rate = N mm/year
•
M
max
event = X meters (average) slip
•
Characteristic model: T
r
= X/N
•
e.g
Sagaing fault: 20 mm/year
M
max
= 8, X = ?
62
Slip Rate
Recurrence Rate
•
Slip rate = N mm/year
•
M
max
event = X meters (average) slip
•
Characteristic model: T
r
= X/N
•
e.g
Sagaing fault: 20 mm/year
M
max
= 8, X = 6 m
T
r
= ?
63
Slip Rate
Recurrence Rate
•
Slip rate = N mm/year
•
M
max
event = X meters (average) slip
•
Characteristic model: T
r
= X/N
•
e.g
Sagaing fault: 20 mm/year
M
max
= 8, X = 6 m
T
r
= 6/(.02) = 300 yrs
64
Slip Rate
Recurrence Rate
•
Slip rate = N mm/year
•
M
max
event = X meters (average) slip
•
Characteristic model: T
r
= X/N
•
e.g
Sagaing fault: 20 mm/year
M
max
= 7.5, X = ?
65
Slip Rate
Recurrence Rate
•
Slip rate = N mm/year
•
M
max
event = X meters (average) slip
•
Characteristic model: T
r
= X/N
•
e.g
Sagaing fault: 20 mm/year
M
max
= 7.5, X = 3 m
T
r
= ?
66
Slip Rate
Recurrence Rate
•
Gutenberg-Richter distribution:
~10% of moment released in M<M
max
events
•
e.g
Sagaing fault: 20 mm/year
M
max
= 8, X = 6 m
T
r
= 6/(.018) = 333 yrs
M
max
= 7.5, X = 3 m
T
r
= 3/(.018) = 167 yrs
67
If time remains, proceed to
ROSE_2013_W1D4L1_Fourier_spectra.pptx
End
Delve into the fundamentals of engineering seismology and earthquake magnitudes, exploring topics such as fault dimensions, slip distribution, spectral shapes, Richter's observations, and logarithmic scales. Gain insights into how seismic measurements are characterized and understand the significance of peak amplitudes in seismograms. Learn about the development of magnitude scales and the logarithmic nature of earthquake measurements.
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Presentation Transcript
FUNDAMENTALS of FUNDAMENTALS of ENGINEERING SEISMOLOGY ENGINEERING SEISMOLOGY EARTHQUAKE MAGNITUDES
Earthquake source characterization Magnitude Fault dimensions (covered before) Slip distribution (kinematics) Fourier transform refresher Point source representation Spectral shape Corner frequency Stress parameter
Earthquake Magnitude Earthquake magnitude scales originated because of the desire for an objective measure of earthquake size Technological advances -> seismometers
Earthquake Magnitudes In the 1930 s, Wadati in Japan and Richter in California noticed that although the peak amplitudes on seismograms from different events differed, the peak amplitudes decreased with distance in a similar manner for different quakes.
Seismogram Peak Amplitude F The peak amplitude is the size of the largest deflection from the zero line.
Richters Local Magnitude Richter used these observations to construct the first magnitude scale, ML (Richter s Local Magnitude for Southern California). He based his formula for calculating the magnitude on the astronomical brightness scale - which was logarithmic.
Logarithmic Scales In a logarithmic scale such as magnitude A change in one magnitude unit means a change of a factor of 10 in the amplitude of ground shaking (wait! This is an often used statement, but it is too simplistic, and I hope you will know why by the end of the course).
The proper statement In a logarithmic scale such as magnitude: A change in one magnitude unit means a change of a factor of 10 in the amplitude of motion that defines the magnitude. This could be the response of a particular type of instrument, or it could be ground motions at very long periods or ground motions at periods near 1 sec, etc. For peak ground motions and response spectra, the scaling is usually less than 10M/2 where M is the moment magnitude, defined shortly, rather than 10M.
Richters Magnitude Scale Defined for specific attenuation conditions valid for southern California Only valid for one specific type of seismometer Can be used elsewhere if local attenuation correction is used and simulated Wood-Anderson response is computed Not often used now, although it IS a measure of ground shaking at frequencies of engineering interest
Richter tied his formula to a specific instrument, the Wood-Anderson torsion seismograph He assumed a reference motion at a reference distance. To compute the magnitude at different distances, he calibrated the attenuation function
Richter fixed the scale assuming that a ML=3 earthquake produces 1mm of maximum amplitude on a Wood-Anderson seismometer at 100 km Ml=Log Amax-Log A0 -logA0 changes from region to region. The calibration of a local magnitude scale for a given region implies the determination of the empirical attenuation correction for that region (and the magnitude station corrections) The W-A seismometers are not still used. The W-A recording is computed numerically (by convolving the ground displacement with the W-A transfer function)
In many studies, the attenuation function is determined by a parametric approach = + + log( / ) ( ) LogA n R R k R R M 0 ref ref ref where the reference distance and the reference magnitude are fixed In agreement with the Richter scale.
In contrast to the general magnitude formula, ML considers only the maximum displacement amplitudes but not their periods. Reason: WA instruments are short- period and their traditional analog recorders had a limited paper speed. Proper reading of the period of high-frequency waves from local events was rather difficult. It was assumed, therefore, that the maximum amplitude phase (which in the case of local events generally corresponds to Sg, Lg or Rg) always had roughly the same dominant period. The smallest events recorded in local microearthquake studies have negative values of ML while the largest ML is about 7 , i.e., the ML scale also suffers saturation (see later). Despite these limitations, ML estimates of earthquake size are relevant for earthquake engineers and risk assessment since they are closely related to earthquake damage. The main reason is that many structures have natural periods close to that of the WA seismometer (0.8s) or are within the range of its pass-band (about 0.1 - 1 s). A review of the development and use of the Richter scale for determining earthquake source parameters is given by Boore (1989). From the IASPEI New Manual Seismological Observatory Practice
Modern Seismic Magnitudes Today seismologists use different seismic waves to compute magnitudes These waves generally have lower frequencies than those used by Richter These waves are generally recorded at distances of 1000s of kilometers instead of the 100s of kilometers for the Richter scale (this is important because most earthquakes occur in remote places, such as under the oceans, without instruments within 100s of kilometers)
Teleseismic MS and mb Two commonly used modern magnitude scales are: MS, Surface-wave magnitude (Rayleigh Wave) mb, Body-wave magnitude (P-wave)
Surface wave magnitude Work started by Gutenberg developed a magnitude scale based on surface wave recordings at teleseismic distances. The measure of amplitude is the maximum velocity (A/T)max. This allowed not only to link the scale to the energy, but also to account for the large variability of periods T corresponding to the maximum amplitude of surface waves, depending on distance and crustal structure. Collaboration between research teams in Prague, Moscow and Sofia resulted in the proposal of a new Ms scale and calibration function, termed Moscow- Prague formula, by Karnik et al. (1962): A A = + = . 1 + 3 . 3 + log ( ) log 66 log Ms s T T max max for epicentral distances 2 < < 160 and source depth h < 50 km. The IASPEI Committee on Magnitudes recommended at its Z rich meeting in 1967 the use of this formula as standard for Ms determination for shallow seismic events (h 50 km) Note: also Ms suffers of saturation (see later )
Body wave magnitude Gutenberg (1945b and c) developed a magnitude relationship for teleseismic body waves such as P, PP and S in the period range 0.5 s to 12 s. It is based on theoretical amplitude calculations corrected for geometric spreading and (only distance-dependent!) attenuation and then adjusted to empirical observations from shallow and deep- focus earthquakes, mostly in intermediate-period records: mB = log (A/T)max+ Q( , h) Gutenberg and Richter (1956a) published a table with Q( ) values for P-, PP- and S-wave observations in vertical (V=Z) and horizontal (H) components for shallow shocks, complemented by diagrams Q( , h) for PV, PPV and SH which enable also magnitude determinations for intermediate and deep earthquakes. These calibration functions are correct when ground displacement amplitudes are measured in intermediate-period records and given in micrometers (1 m = 10-6 m).
Later, with the introduction of the WWSSN short-period 1s-seismometers (see Fig. 3.11, type A2) it became common practice at the NEIC to use the calibration function Q( , h) for short-period PV only. In addition, it was recommended that the largest amplitude be taken within the first few cycles (see Willmore, 1979) instead of measuring the maximum amplitude in the whole P-wave train. One should be aware that this practice was due to the focused interest on discriminating between earthquakes and underground nuclear explosions. The resulting short-period mb values strongly underestimated the body-wave magnitudes for mB > 5 and, as a consequence, overestimated the annual frequency of small earthquakes in the magnitude range of kt-explosions. Also, mb saturated much earlier than the original Gutenberg-Richter mB for intermediate- period body waves or Ms for long-period surface waves Therefore, the IASPEI Commission on Practice issued a revised recommendation in 1978 according to which the maximum P-wave amplitude for earthquakes of small to medium size should be measured within 20 s from the time of the first onset and for very large earthquakes even up to 60 s (see Willmore, 1979, p. 85). This somewhat reduced the discrepancy between mB and mb but in any event both are differently scaled to Ms and the short-period mb necessarily saturates earlier than medium-period mB.
However, some of the national and international agencies have only much later or not even now changed their practice of measuring (A/T)max for mb determination in a very limited time-window, e.g., the International Data Centre for the monitoring of the CTBTO still uses a time window of only 6 s (5.5s after the P onset), regardless of the event size.
The modern standard magnitude measure: MOMENT MAGNITUDE It is defined in terms of seismic moment, M , by the equation: 0 2log 3 M 10.7 M 0 Seismic moment can be measured from seismograms or calculated by the defining equation M SA 0 Where is the modulus of rigidity in the vicinity of the source, S is average slip over the ruptured area A of the fault. 24
Why is it called moment? Radiation from a shear dislocation with slip S over area A in material with rigidity is identical to that from a double couple with strength UA (units stress*displacement*area, but stress = force/area, so units = force*displacement = a couple = work = energy) 25
Nomenclature Mw Defined by Kanamori as an energy magnitude (includes a parameter in addition to moment), but he clearly had in mind the present mapping of moment and magnitude but setting the additional parameter to a constant value M The first explicit mapping of moment (M0) and moment magnitude (M) Today people by-and-large use Mw (can write it in email); only purists such as DMB use M.
What is the proper equation? M = 2/3 log M0 10.7? M = 2/3 log M0 10.73 ? The former is correct, it corresponds to Log M0 = 1.5M + 16.05 (not 16.0 or 16.1) Hanks (personal commun.) chose 16.05 to average relations with constant terms of 16.0 and 16.1
Why use moment magnitude? It is the best single measure of overall earthquake size It does not saturate (discussed later) It can be estimated from geological observations It can be estimated from paleoseismology studies It can be tied to plate motions and recurrence relations
Empirical relations can be used to estimate moment magnitude based on size of felt area eg. Johnston et al., 1996 relations for mid- plate areas
Moment Magnitude is the Best Measure of Earthquake Size Quake 1906 San Francisco 1960 Chile Ms M 8.3 8.3 7.8 9.5
Moment Physical units (dyne-cm) 1026: Northridge, 1994 1030: Sumatra, 2004 Big range! No saturation: bigger rupture bigger moment 31 the big one USGS - SUSAN HOUGH
The Largest Earthquakes M is the appropriate choice for comparing the largest events, it does not saturate. 1960 Chile 9.5 2004 Sumatra 9.3 1964 Alaska 9.2 1952 Kamchatka 9.1 1965 Aleutians 9.0 (This pie chart needs to be revised to include the 2004 Sumatra earthquake, but the chart serves to emphasize that 0.1 M units corresponds to a factor of 1.4 increase in moment.)
ORDERS OF MAGNITUDE Fault width Why are the largest earthquakes along subduction zones? For crustal earthquakes the width is limited by the thickness of the superficial crust brittle layer (~20 km). The thickness of the brittle layer is controlled by temperature, which increases with depth Width is often considered smaller than the length even for small earthquake
ORDERS OF MAGNITUDE Fault width surface brittle 20 km plastic
ORDERS OF MAGNITUDE Fault width surface faults brittle 20 km plastic
ORDERS OF MAGNITUDE Fault width surface faults brittle 20 km plastic
Converting between magnitude scales: Empirical relations (or sometimes theoretical relations) can be used to convert between magnitude scales. This is important in deriving magnitude recurrence statistics for a region or source zone, as all magnitudes should be first reported on the same scale before characterizing their statistics
Surface wave magnitude is a close approximation to Moment M for Ms 6 to 8 events
Body-wave magnitude is not a good measure of moment M, especially for large events
Relations between magnitude scales Ms(Ekstrom) Ms(Ambraseys et al., 1996) ML(Hutton and Boore, 1984) mbLg (Atkinson and Boore, 1987) MS mbLg ML 8 Time: 20:51:43 Date: 2003-09-05; Other Magnitude File: C:\metu_03\regress\MLMSMN_M.draw; 6 4 4 6 8 Moment Magnitude
Magnitude Discrepancies Ideally, you want the same value of magnitude for any one earthquake from each scale you develop, i.e. MS = mb = ML = M But this does not always happen: San Francisco 1906: MS = 8.3, M = 7.8 Chile 1960: MS = 8.3, M = 9.6
Why Dont Magnitude Scales Agree? Simplest Answer: Earthquakes are complicated physical phenomena that are not well described by a single number. Can a thunderstorm be well described by one number ? (No. It takes wind speed, rainfall, lightning strikes, spatial area, etc.)
Why Dont Magnitude Scales Agree? More Complicated Answers: The distance correction for amplitudes depends on geology. Deep earthquakes do not generate large surface waves - MS is biased low for deep earthquakes. Some earthquakes last longer than others, even though the peak amplitude is the same. Variations in stress release along fault, for same moment. Not all earthquakes are self similar (that is, the relative radiation at different frequencies can differ--- examples: 1999 Chi-Chi compared to standard California earthquake).
Why Dont Magnitude Scales Agree? Most complicated reason: Magnitude scales saturate This means there is an upper limit to magnitude no matter how large the earthquake is For instance Ms (surface wavemagnitude) seldom gets above 8.2-8.3
Example: mbSaturation F mb seldom gives values above 6.7 - it saturates . F mb must be measured in the first 5 seconds - that s the (old) rule.
What Causes Saturation? The rupture process. Small earthquakes rupture small areas and are relatively depleted in long-period signals. Large earthquakes rupture large areas and are rich in long-period motions (we ll study this later, when we discuss source scaling)
What Causes Saturation? The relative size of the fault and the wavelength of the motion used to determine the magnitude is a key part of the explanation. Small fault compared to the wavelength: the magnitude will be a good measure of overall earthquake size. Large fault compared to the wavelength: the magnitude will be determined by radiation from only a portion of the fault, and the magnitude will not be a good measure of overall fault size 47
Relations between Magnitude Scales Note saturation 49
Are mb and Ms still useful? YES! Many (most) earthquakes are small enough that saturation does not occur Empirical relations between energy release and mb and Ms exist The ratio of mb to Ms canindicate whether a given seismogram is from an earthquake or a nuclear explosion (verification seismology)
