The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
The Size of an Earthquake (& Explosion)
Won-Young Kim
Lamont-Doherty Earth Observatory of Columbia University
Palisades, NY 10964, USA
How do we measure the size of an earthquake or an explosion?
rupture length? surface break?, fault slip?, intensity & duration of shaking?
Richter’s scale: some people asks, “Where is the Richter Scale?”
Intensity – severity of shaking, historical events
Magnitude – instrumental measure of relative size of earthquakes
Seismic Moment (M0) – work done, fault geometry and slip
Radiated Energy – dynamic rupture
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Seismic Intensity
Intensity measures the severity of shaking and indicates the local effects and potential
for damage produced by an earthquake. It does not measure the size of an earthquake
source. MMI (Modified Mercalli; 10 point scale), and Japan Meteorological Agency
seismic intensity scale (a seven-point scale widely used in Northeastern Asia).
• Macroseismic
observations (isoseismal
map) of historical events
are still useful to evaluate
earthquake hazard, due to
longevity of observations,
especially in SCR with low
seismicity.
• ShakeMaps (Instrumental
Intensity Map) generated
by using observed ground
motions and near surface S
wave velocities (Vs30m)
became very useful.
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
(left panel) CIIM (Community Internet Intensity Map) – felt reports are filed in using
postal ZIP codes for location by the public.
(right panel) Instrumental Intensity Map: Observed ground motions are mapped into
a modern form of isoseismal map – ShakeMap.
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Instrumental Intensity Map (ShakeMap)
Regression relationships between Modified Mercalli intensity and PGA, PGV are
used to calculate ShakeMaps of PGA, PGV, and PSA (0.3s, 1s, 3s) in near real-time.
The ShakeMap is very useful for emergency response after a strong earthquake.
Imm = 3.66 log(PGA) – 1.66
(for MM V – VIII; Wald et al.,1999);
INSTRUMENTAL INTENSITY SCALE
(MODIFIED MERCALLI INTENSITY SCALE, MMI)
ESTIMATED INTENSITY PERCEIVED SHAKING
--------------------------------- ------------------------------I
Not Felt
II-III
Weak
IV
Light
V
Moderate
VI
Strong
VII
Very Strong
VIII
Severe
IX
Violent
X
Extreme
---------------------------------- --------------------------------
POTENTIAL DAMAGE
--------------None
None
None
Very Light
Light
Moderate
Moderate/Heavy
Heavy
Very Heavy
----------------
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Magnitude
Earthquake magnitude scales in general do not directly represent any physical
parameters of the source. Magnitude scales can be used to represent relative size
of earthquakes.
•
•
•
Simplicity of magnitude scales allows us to process large number of events in a
very short time.
Providing the public with quick information on the size of an earthquake.
Fundamental data to be included in earthquake catalogs, which are the basis for a
variety of scientific research projects.
The magnitude scales currently used for measuring relative sizes of earthquakes are
based on empirical formulas, which give results that depend on the wave types
and frequency band used.
We will review several magnitude scales: ML, MS, mB, mb(P), mb(Lg), and Mw.
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Simulation of traditional short– and long–period seismograms from digital, broadband
record. We determine mb(P) from WWSSN-SP (World Wide Standardized
Seismographic Network) short-period record, mB and Ms from WWSSN-LP record.
mb(P)
Ms
mB
mB
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Frequency band used for various magnitude determination
Various instruments used
world wide and their
instrument response.
WOODAND= WoodAnderson torsion
seismograph, T0=0.8s
WWSSN-SP=WorldWide Standardized
Seismographic Network
(T0=1s)
WWSSN-LP (T0=15s)
KIRNOS= long-period
SKD seismometer,
SRO = Seismic Research
Observatory borehole
seismometer with T0=30s
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Amplitude and period measurements
B = zero-to-peak amplitude
2B = peak-to-peak amplitude
B ~ ½ (2B)
T = period
a) & b) Teleseismic body-wave
c) Regional P- or S-wave train
d) Regional S or Rayleigh wave
e) Surface wave
A – [Amax] - ML (Richter scale)
A/T – [Amax / T] (Ms, mB, mb(P))
(A/T)max – mb(Lg)
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Richter’s (1935) local magnitude, ML, (or Richter scale),
“The magnitude of any shock is taken as the logarithms of the maximum trace
amplitude, expressed in microns, with which the standard short period torsion
seismometer (T0 = 0.8 sec., V=2800, h=0.8) would register that shock at an epicentral
distance of 100 kilometers.” Richter found a formula for amplitude attenuation as,
log A0 = 3.37 – 3 log D
(200 < D < 600 km)
Following the method originally used by Richter (1935, 1958), ML is given by,
ML = log10A(D) – log10A0(D) + C
Where:
A(D) = the maximum zero-to-peak trace amplitude in millimeters measured from a
Wood-Anderson seismogram at an epicentral distance D,
log10A0(D) = the empirically derived attenuation curve,
D = the epicentral distance in kilometers and,
C = the station correction.
Richter, Charles F., An instrumental earthquake magnitude scale, Bulletin of the
Seismological Society of America, 25, 1-32, 1935.
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Attenuation curves for
Southern California and
Eastern North America.
(ENA).
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Eastern North America (ENA)
•
Observed horizontal–
component Wood-Anderson
peak amplitudes are plotted
against distance. Each
amplitude is corrected for
station magnitude correction
and is normalized by mean
network magnitude. The thick
line shows a slope of -1.55.
(b) Observed vertical–component
Wood-Anderson peak
amplitudes are plotted against
distance. The thick line shows
a slope of -1.45.
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
(a) Group velocity of observed Wood-Anderson
peak amplitudes are plotted against distance.
Over 90% fall 3.7-3.2 km/s with a mean 3.42
km/s +/-0.25 km/s, predominantly Lg waves.
.
(b) Period of each peak amplitude on WoodAnderson records are plotted against
distance.
Eastern North America (ENA), Kim (1998)
ML= log10A(D)(in mm) + 1.55 log10D – 0.22 + C
(for 100 < D < 800 km; horizontal)
ML= log10A(D)(in mm) + 1.45 log10D + 0.11 + C
(for 100 < D < 800 km; vertical)
Where D=epicentral distance in km, C=station
correction.
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Teleseismic Surface wave magnitude, Ms
A magnitude scale based on teleseismic surface waves was described by Gentenberg &
Richter (1936) and developed more extensively by Gutenberg (1945). For shallow
earthquakes at distance 15˚ <D<130˚,
Ms = log10 A + 1.656 log10D + 1.818,
where:
A = max. ground displacement amplitude in microns due to surface wave of 20s period,
measured on a horizontal component;
D = epicentral distance in degrees.
Karnik et al. (1962) proposed the formula (adopted officially by IASPEI)
Ms = log10(A/T)max + 1.66 log10D + 3.3,
(20˚ < D < 160˚)
where:
A = ground amplitude in microns measured on a vertical component seismograph;
T = period in seconds;
D = epicentral distance in degrees.
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Teleseismic, intermediate-period body-wave magnitude, mB
mB = log (A/T) + Q (D, h)
(Gutenberg & Richter, 1956)
where,
A / T = maximum in the wave group of either P, PP, or SH-wave, with separate tables and charts
of Q for each phase.
Q(D, h) = attenuation function for PZ established by Gutenberg and Richter (1956),
D = epicentral distance in degrees, 21˚  D  100;
h = focal depth.
Gutenberg was able to use body waves of period between 0.2 – 30s due to Benioff 190 seismometer which was really a broadband seismograph (T0=1s, Tg=90s).
Alternatives to Q(D, h) have been proposed that fit global sets of log10(A/T) with lower
variance, that are more consistent with recent velocity models of the earth, or that
better preserve the ratio of mb to seismic moment over the entire range of earthquake
focal depths.
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Q(D, h) = attenuation function for PZ established by Gutenberg and Richter (1956)
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Q(D, h) = attenuation function for SH, Gutenberg and Richter (1956)
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Teleseismic, short-period body-wave magnitude, mb(P)
mb(P) = log (A/T) + Q (D, h) (Gutenberg & Richter, 1956)
where,
A = P-wave amplitude in microns, the maximum trace-amplitude in the entire P-phase train
(time spanned by P, pP, sP, and possibly PcP and their codas, but ending before PP);
T = period in seconds, T < 3s;
Q(D, h) = attenuation function for PZ established by Gutenberg and Richter (1956);
D = epicentral distance in degrees, 21˚  D  100;
h = focal depth.
After deployment of WWSSN stations with short- and long-period seismographs, mB
procedure was applied to shorter period P waves amplitude measurements. So,
mb or mb(P) is determined in the frequency band of the WWSSN short-period,
vertical-component and widely used by U.S. Geological Survey on their PDE bulletin.
Later, the digital data is filtered so that the frequency response of the seismograph/filter
system replicates that of a WWSSN short-period seismograph
Veith & Clawson (1972) proposed a mb(P) magnitude scale that has been used in
nuclear test ban verification research community and later by IDC of CTBTO.
mb(P) tends to saturate at about mb(P)=6.5.
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Frequency band used for various magnitude determination
Various instruments used
world wide and their
instrument response.
WWSSN-SP=WorldWide Standardized
Seismographic Network
(T0=1s)
WWSSN-LP (T0=15s)
KIRNOS= long-period
SKD seismometer,
SRO = Seismic Research
Observatory borehole
seismometer with T0=30s
WOODAND= WoodAnderson torsion
seismograph, T0=0.8s
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Simulation of traditional short– and long–period seismograms from digital, broadband
record. We determine mb(P) from WWSSN-SP (World Wide Standardized
Seismographic Network) short-period record, mB and Ms from WWSSN-LP record.
mb(P)
Ms
mB
mB
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Regional magnitude measured using 1-sec period Lg wave, mb(Lg)
Nuttli’s (1973) short-period magnitude scale was derived for use with the verticalcomponent for the sustained max. amplitude of the 1-sec period Lg wave for
earthquakes within the magnitude mb = 3.0 to 5.5.
For central United States,
mb(Lg)= 3.75 + 0.90 log10 D + log10(A/T)max
for 0.5o < D <4o
mb(Lg)= 3.30 + 1.66 log10 D + log10(A/T)max
for 4o < D < 30o
A=zero-to-peak amplitude in microns,
D= distance in degrees,
(A/T)max = value of 1-sec period Lg wave recorded by short-period vertical
seismograph. In practice, it is measured as the third largest amplitude in the time
window corresponding to group velocities of 3.6 to 3.2 km/s, in the period-range 0.7
to 1.3s.
It is very useful for events in the distance ranges not covered by mb(P), or Ms.
The size of an Earthquake
Local magnitude, ML, and
mb(Lg) comparsion in
eastern North America.
mb(Lg) is slightly higher
than ML, about 0.15 m.u.,
but both magnitudes are
quite consistent.
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Seismic Moment (M0)
Introduced in seismology by K. Aki in 1966, the scalar seismic moment is,
M0 = m A u
Where m = shear modulus, A=fault area, and u= average final slip. Since the
broadband seismometers with high-dynamic range dataloggers were deployed in
early 1990’s, the seismic moment became reliable measured quantity from
seismograms.
Seismic moment is the best earthquake parameter to measure the size of an
earthquake.
For great earthquakes with surface breaks, the seismic moment of those earthquakes
can be determined from above formula.
It measures kinematic rupture of earthquakes.
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Seismic moment determination from waveform modeling, Mw > ~4.0
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Seismic moment determination from Lg
wave spectra:
M0 = W0 / (F Rqf) 4pr Vs3 R, (for R<R0)
= W0 / (F Rqf) 4pr Vs3 R0(R/R0)1/2
(for R>R0)
Where:
W0 = low-frequency spectral level,
F = free-surface amplification,
Rqf = shear wave radiation pattern
= 0.63 rms value,
r = mass density at the source,
Vs= shear wave speed,
R = epicentral distance,
R0= reference distance, marking transition
from geometrical spreading for simple body
waves to geometrical spreading forLg
waves.
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Mw – moment magnitude
The standard formula for Mw derives from Kanamori (1977), via Hanks and
Kanamori (1979):
Mw = (2/3) (log10M0 – 9.1)
where M0 = scalar moment in N·m, determined from waveform modeling or from the
long-period asymptote of spectra.
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Usage of various Magnitude Scales, a summary table
Source type Distance /
Wave type
Magnitude
depth
Local
Distance range/
Frequency band
P, Pg, S, Lg
ML, mb(Lg)
0 < D <1000 km
0.8-20 Hz
Regional
Earthquake
Explosion
Lg, Reyleigh mb(Lg), Ms
wave, Rg
4 <D <20
Teleseismic,
shallow
P, Surface
wave
Ms, mb(P),
mB
20 < D < 180
Teleseismic,
deep
P, PP, SH
mb(P), mB,
20 < D < 160
High-yield
P, Lg,
Rayleigh (Z)
mb(P), Ms,
mb(Lg)
4 < D< 180
P, Lg, Rg,
coda
mb(Lg), ML,
mb(P), Ms
0 < D < 20
Y > 1 kton
Low-yield
Y < 1 kton
Note
0.6 – 5 Hz, 2-13s
0.6-5 Hz / 20sec
0.6-5 Hz, 2-30 sec
0.8-10 Hz, 20sec
0.8-20 Hz, 2-3sec
Mw
Works
for all
cases.
(CMT,
Spectral)
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Magnitude and Yield of Underground Nuclear Explosions
The size of explosions such as, underground nuclear explosions and large industrial
chemical explosions are usually represented by their “yield” in metric tons. For large
explosions that generate significant seismic waves, mb(P) – short-period body-wave
magnitude, has been the most widely used measure of their seismic size.
• Use appropriate seismic magnitude – yield relations.
• Variations in seismic source coupling: Geologic emplacement medium, depth of
burial and yield.
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
magnitude – yield relations
0.75 log (Yield in kilotons) = mb – 4.45 (for hardrock, fully coupled; Murphy, 1996)
Yield determination from surface wave:
0.97 log (Yield in kilotons) = Ms – 2.16 (for Yield > 62 kt and hardrock site;
Sykes & Cifuentes,
1984).
For North Korean
nuclear test on
10/09/2006, yield was
approx. 0.6 kiloton
based on mb(P)=4.3
(10 obs.) and assuming
a fully coupled
explosion.
Nuclear explosions
with 1 kton yield have
mb(P) = ~4.0
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
North Korean nuclear test on Oct. 09,
2006.
What is the best magnitude scale to
estimate yield of the test?
3-component seismic records
(Vertical = Z; North-South = NS; and
East-West = EW) at MDJ. (a) the
nuclear test on 9 October 2006, (b) an
earthquake on 16 December 2004,
and (c) a chemical explosion on 19
August 1998.
Traces are aligned on P arrivals. The
event id (UNT= underground nuclear
test and Chemex= chemical
explosion), component, peak
amplitude of trace in micrometer/s,
origin time and magnitude are
indicated.
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Consistency of measurements is important for magnitude.
To study seismicity and earthquake hazards, we need earthquake catalog with long
time window and homogeneous magnitudes.
Must follow protocol (proposed methodology) as closely as possible,
Problems have occurred over the years when transition from old to new technology
Transition from Analog to Digital Seismology in early 1970’s.
Mostly short-period seismometers with low-dynamic range digital seismographs were
deployed.
Mn (Nuttli’s mb(Lg)) scale was used at the Geological Survey of Canada using Lg
wave amplitudes measured on a new digital data with frequency contents dominantly
~5 Hz, consequently Mn underestimated about 0.4 m.u. when compared with
mb(Lg). Discrepancy can be as high as 0.7 m.u. for larger earthquakes with M > 4.0.
Either filter the data to generate 1–s Lg wave or apply appropriate attenuation curve
for the new measurements. Mn is still determined incorrectly, under the argument
that the changes will introduce discontinuity of their earthquake catalog.
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Amplitude and period measurements
B = zero-to-peak amplitude
2B = peak-to-peak amplitude
B ~ ½ (2B)
T = period
a) & b) Teleseismic body-wave
c) Regional P- or S-wave train
d) Regional S or Rayleigh wave
e) Surface wave
A – [Amax] - ML (Richter scale)
A/T – [Amax / T] (Ms, mB, mb(P))
(A/T)max – (mb(Lg), Ms)
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Transition from narrow bands, LP and SP, to broadband seismology
mb(P) on WWSSN-SP or equivalent records with dominant period ~0.6s (1.67 Hz)
were used at NEIC for PDE monthly listing, and ISC has also taken those
measurements when compiling a comprehensive global earthquake bulletin.
Starting in 1995, when CTBT passed United Nations and open for signing and entry
into force, US Government supported to create pIDC (prototype IDC) in Washington
D.C, pIDC began very good job to acquire data and process in real time.
Event detection, location, identification and attribution (assigning magnitude etc.).
pIDC measured amplitudes and periods information were submitted to ISC and soon
seismologists started to see some inconsistent pattern of earthquake magnitude. For
example, comparision between mb(ISC) vs mb(PDE), mb(REB) vs mb(PDE),
showed discrepancies.
[mb(REB) – reviewed event bulletin by pIDC]
mb(ISC) was slightly biased toward smaller magnitude as well.
Why?
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
pIDC established mb(P) determination procedure slightly different from traditional
mb(P) methodology.
1. Higher frequency band is used: 0.8-5 Hz (cf. ~0.6-3 Hz; WWSSN-SP),
2. Amplitude was measured within the first 5.5 sec after the onset P arrival,
instead of conventional 15-20s window.
3. Veith & Clawson (1972) short-period P-wave magnitude scale is used
mp = log (A/T) + P, where the P factors are function of distance and focal depth
and A=vertical, short-period P-wave peak-to-peak amplitude in micron/sec.
mb(REB) started to underestimate mb(P) when compared to mb(PDE). The
discrepancy is not linear, and hence could not be easily corrected.
Upper limit of the various magnitude scales due to saturation.
mb(P) = 6.5
Ms = ~8.5
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Scaling law of earthquake source spectra.
w–square model of the source
displacement amplitude spectra for Ms=1
to Ms=8 are plotted against seismic
moment. Dashed line indicates locations
of the corner frequencies.
This figure shows dependence of
magnitude measurements on earthquake
source spectra. Surface magnitude
saturate at about Ms ~8.5, whereas
teleseismic body-wave magnitude, mb(P),
measurements saturate at mb(P) ~6.5.
Ms is good for Ms 5.5 – 8.5, whereas mb
is good for mb 4.0 - 6.5.
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Unusual Seismic Events and Their Size
Extended use of magnitude and event information:
Airplane impacts and building collapses at WTC, NYC during 09/11/2001 disaster
Bombing of American Embassy in Nairobi, Kenya; yield
Russian submarine Kursk disaster off the coast of Barent Sea
Landslide, submarine slumping,
..
Seismic data provided accurate time, location and relative size of these events.
We measured amplitudes of seismic signals generated by such exotic sources and
assigned equivalent magnitudes (e.g., magnitude 3.0 Richter scale equivalent)
Public want to know, how to relate such information into unfolding disaster.
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
References
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Boatwright, J., and Choy, G. (1986). Teleseismic estimates of the energy radiated by shallow
earthquakes. J. Geophys. Res., 91, 2095-2112.
Gutenberg, B. (1945). Amplitudes of surface waves and magnitudes of shallow earthquakes. Bull. Seism. Soc.
Am., 35, 3-12.
Gutenberg, B. (1945b). Amplitudes of P, PP, and S and magnitude of shallow earthquakes. Bull.
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Kanamori, H. (1977). The energy release in great earthquakes. J. Geophys. Res. 82, 2981-2987.
The size of an Earthquake
LCSN Operators Workshop, Oct. 2007
Won-Young Kim
Karnik, V., Kondorskaya, N.V., Riznichenko, Yu.V., Savarensky, Ye.F., Soloviev, S.L., Shebalin,
N.V., Vanek, J., and Zatopek, A. (1962). Standardization of the earthquake magnitude
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Academic Publishers, 247-293.
Nuttli, O.W. (1973). Seismic wave attenuation and magnitude relations for eastern North
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Richter, Charles F. (1935), An instrumental earthquake magnitude scale, Bulletin of the
Seismological Society of America, 25, 1-32, 1935.
Richter, C.F. (1958). Elementary Seismology, W.H. Freeman, San Francisco, Calf., 578 pp.
Sykes, L.R. and I.L. Cifuentes (1984). Yield of Soviet underground nuclear tests from seismic
surface waves: Compliance with the Threshold Test Ban Treaty, Proc. Natl. Acad. Sci., USA
81, 1922-1925.
Veith, K. F., and Clawson, G. E. (1972). Magnitude from short-period P-wave data. Bull. Seism.
Soc. Am., 62, 2, 435-452.
Wald, D. J., V. Quitoriano, T. Heaton, and H. Kanamori (1999). Relationships between Peak
Ground Acceleration, Peak Ground Velocity and Modified Mercalli Intensity in California,
Earthquake Spectra, 15.