the size of an earthquake lcsn operators workshop, oct. 2007won-young kim the size of an earthquake...

The size of an Earthquake LCSN Operators Workshop, Oct. 2007 Won-Young Kim

The Size of an Earthquake (& Explosion)

Won-Young KimLamont-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


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.


(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.


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 POTENTIAL DAMAGE --------------------------------- ------------------------------- ---------------

I Not Felt NoneII-III Weak NoneIV Light NoneV Moderate Very LightVI Strong LightVII Very Strong ModerateVIII Severe Moderate/HeavyIX Violent HeavyX Extreme Very Heavy

---------------------------------- -------------------------------- ----------------


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.


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)

mB mB

Ms


Various instruments used world wide and their instrument response.

WOODAND= Wood-Anderson torsion seismograph, T0=0.8s

WWSSN-SP=World-Wide Standardized Seismographic Network (T0=1s)WWSSN-LP (T0=15s)

KIRNOS= long-period SKD seismometer,

SRO = Seismic Research Observatory borehole seismometer with T0=30s

Frequency band used for various magnitude determination


Amplitude and period measurements

B = zero-to-peak amplitude2B = peak-to-peak amplitudeB ~ ½ (2B)T = period

a) & b) Teleseismic body-wavec) Regional P- or S-wave traind) Regional S or Rayleigh wavee) Surface wave

A – [Amax] - ML (Richter scale)

A/T – [Amax / T] (Ms, mB, mb(P))

(A/T)max – mb(Lg)


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 km

Following the method originally used by Richter (1935, 1958), ML is given by,

ML = log10A() – log10A0() + C

Where:A() = the maximum zero-to-peak trace amplitude in millimeters measured from a

Wood-Anderson seismogram at an epicentral distance , log10A0() = the empirically derived attenuation curve, = 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.


Attenuation curves for Southern California and Eastern North America.(ENA).


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.


(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 Wood-

Anderson records are plotted against distance.

Eastern North America (ENA), Kim (1998)

ML= log10A()(in mm) + 1.55 log10– 0.22 + C

(for 100 < < 800 km; horizontal)

ML= log10A()(in mm) + 1.45 log10+ 0.11 + C

(for 100 < < 800 km; vertical)

Where =epicentral distance in km, C=station correction.


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˚ <<130˚,

Ms = log10 A + 1.656 log10+ 1.818,

where:A = max. ground displacement amplitude in microns due to surface wave of 20s period, measured on a horizontal component;= epicentral distance in degrees.

Karnik et al. (1962) proposed the formula (adopted officially by IASPEI)

Ms = log10(A/T)max + 1.66 log10 + 3.3, (20˚ < < 160˚)

where:A = ground amplitude in microns measured on a vertical component seismograph;T = period in seconds; = epicentral distance in degrees.


Teleseismic, intermediate-period body-wave magnitude, mB

mB = log (A/T) + Q (, 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(, h) = attenuation function for PZ established by Gutenberg and Richter (1956), = epicentral distance in degrees, 21˚ 100;h = focal depth.

Gutenberg was able to use body waves of period between 0.2 – 30s due to Benioff 1-

90 seismometer which was really a broadband seismograph (T0=1s, Tg=90s).

Alternatives to Q(, 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.


Q(, h) = attenuation function for PZ established by Gutenberg and Richter (1956)


Q(, h) = attenuation function for SH, Gutenberg and Richter (1956)


Teleseismic, short-period body-wave magnitude, mb(P)

mb(P) = log (A/T) + Q (, 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(, h) = attenuation function for PZ established by Gutenberg and Richter (1956);= epicentral distance in degrees, 21˚ 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 seismographVeith & 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.


Various instruments used world wide and their instrument response.

WWSSN-SP=World-Wide Standardized Seismographic Network (T0=1s)

WWSSN-LP (T0=15s)

KIRNOS= long-period SKD seismometer,

SRO = Seismic Research Observatory borehole seismometer with T0=30s

WOODAND= Wood-Anderson torsion seismograph, T0=0.8s

Frequency band used for various magnitude determination


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)

mB mB

Ms


Regional magnitude measured using 1-sec period Lg wave, mb(Lg)

Nuttli’s (1973) short-period magnitude scale was derived for use with the vertical-component 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 + log10(A/T)max for 0.5o < <4o

mb(Lg)= 3.30 + 1.66 log10 + log10(A/T)max for 4o < < 30o

A=zero-to-peak amplitude in microns,= 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.


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.


Seismic Moment (M0)

Introduced in seismology by K. Aki in 1966, the scalar seismic moment is,

M0 = A u

Where = 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.


Seismic moment determination from waveform modeling, Mw > ~4.0


Seismic moment determination from Lg wave spectra:

M0 = FRVsR, (for

R<R0)

= 0 / (F R) 4Vs3 R0(R/R0)1/2

(for R>R0)Where:0 = low-frequency spectral level,F = free-surface amplification,R = shear wave radiation pattern = 0.63 rms value,= 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.


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.


Usage of various Magnitude Scales, a summary table

Source type Distance /

depth

Wave type Magnitude Distance range/

Frequency band

Note

Earthquake

Local P, Pg, S, Lg ML, mb(Lg) 0 < <1000 km

0.8-20 HzMwWorks for all cases.

(CMT, Spectral)

Regional Lg, Reyleigh wave, Rg

mb(Lg), Ms 4 < <200.6 – 5 Hz, 2-13s

Teleseismic, shallow

P, Surface wave

Ms, mb(P), mB

20 < < 1800.6-5 Hz / 20sec

Teleseismic, deep

P, PP, SH mb(P), mB, 20 < < 1600.6-5 Hz, 2-30 sec

Explosion

High-yield

Y > 1 kton

P, Lg, Rayleigh (Z)

mb(P), Ms, mb(Lg)

4 < < 1800.8-10 Hz, 20sec

Low-yield

Y < 1 kton

P, Lg, Rg, coda

mb(Lg), ML, mb(P), Ms

0 < < 200.8-20 Hz, 2-3sec


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.


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


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.


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.


Amplitude and period measurements

B = zero-to-peak amplitude2B = peak-to-peak amplitudeB ~ ½ (2B)T = period

a) & b) Teleseismic body-wavec) Regional P- or S-wave traind) Regional S or Rayleigh wavee) Surface wave

A – [Amax] - ML (Richter scale)

A/T – [Amax / T] (Ms, mB, mb(P))

(A/T)max – (mb(Lg), Ms)


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?


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 depthand 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) = 6.5Ms = ~8.5


Scaling law of earthquake source spectra.

–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.


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 disasterBombing of American Embassy in Nairobi, Kenya; yield Russian submarine Kursk disaster off the coast of Barent SeaLandslide, 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.


ReferencesAki, K. (1966). Generation and propagation of G waves from the Niigata earthquake of June 16, 1964. 2.

Estimation of earthquake moment, released energy, and stress-strain drop from G wave spectrum, Bull. Earthquake Res. Inst., Tokyo Univ., 44, 23-88.

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. Seism. Soc. Am., 35, 57-69.

Gutenberg, B., and Richter, C.F. (1936). Magnitude and energy of earthquakes, Science, 83, 183-185.

Gutenberg, B., and Richter, C.F. (1954). Seismicity of the Earth. Princeton University Press, 2nd ed., 310 pp.Gutenberg, B., and Richter, C.F. (1956a). Magnitude and energy of earthquakes. Annali di Geofisica, 9, 1-15.Gutenberg, B., and Richter, C.F. (1956b). Earthquake magnitude, intensity, energy and acceleration. Bull.

Seism. Soc. Am., 46, 105-145.Hanks, T.C. and Kanamori, H. (1979). A moment magnitude scale, J. Geophys. Res. 84, 2348-

2350. Kanamori, H. (1977). The energy release in great earthquakes. J. Geophys. Res. 82, 2981-2987.


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 scales. Studia Geophysica et Geodaetica, 6, 41-48.

Kim, W.-Y. (1998). The ML scale in Eastern North America. Bull. Seism. Soc. Am. 88, 4, 935-951.

Murphy, J. R. (1996). Type of seismic events and their source descriptions, in Monitoring a Comprehensive Test Ban Treaty, E. Husebye and A. M. Dainty (eds.), Kluwer Academic Publishers, 247-293.

Nuttli, O.W. (1973). Seismic wave attenuation and magnitude relations for eastern North America. J. Geophys. Res., 78, 876-885.

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.

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