LECTURE 4

MEASURING

EARTHQ UAKE SIZE

© Northwestern University, 2007

EARLY I DEAS

• Describe damage inflicted by earthquake

→→ "INTENSITY Scales"

Always written with roman numerals (IV, VII, XI, etc.) Dynamic connection: Intensityshould express

ground accelerationBUT...

Modified Mer calli Intensity Scale, 1931

(" MMI ")Fr. G. Mercalli at Vesuvius

ca. 1910

Shortcomings of Intensity Scales

• Not directly related to earthquakesource

• Damage obviously distance-depen-dent

• Needs population to report damage

• Affected by site response

Example of Intensity maps for1886 Charleston, USA, earthquake.

EARTHQ UAKE MAGNITUDES

• An essentially empirical concept, intr-oduced byRichter [1935], long beforeany physical understanding of earth-quake sources

• To this day, measurements haveremained largely ad hoc, especially atshort distances.

[Bolt, 1987]

→→ To this day,measurements haveremained largely

ad hoc,

especially atshort distances.

PROGRESS in the 1940s

• Apply worldwide

• Try (!!) to justify theoretically

→→ Leads to first worldwide quantifiedcatalogue of earthquakes

"Seismicity of the Earth"

Gutenberg and Richter[1944; 1954]

B. Gutenberg, 1958

"MODERN" MA GNITUDES

Standardized at Prague meeting of the IUGG (1961)

• Use Body (P) Wav es to define short period magnitude,mbaround a period of 1 second

mb = log10A

T+ Q(∆; h)

• Use Surface (Rayleigh) wav eto define "Long"-period magnitude,Ms, at T = 20 s.

Ms = log10A

T+ 1. 66log10 ∆ + 3. 3

Still largely empirical; Constants not justified [Okal,1989]

∆

h

Q(∆, h)

BODY-WAVE MAGNITUDE mbFrom first-arriving wa ve trains (" P " W av es)

* Should be measured at period close to 1 second

Station CTA (Charter Towers, Queensland, Australia);∆ = 55°

• Remove instrument response

• Band-pass filter between 0.3 and 3 seconds

• Select window of 80 seconds duration aroundP wave

• Apply Body-wav eMagnitude formula

mb = log10A

T+ Q(∆; h) (A in microns)

mb = 7. 2mb = 7. 2

SUMATRA−ANDAMAN, 26 DEC 2004

SURFACE-WAVE MAGNITUDE MsFrom later Surface-wave train (" Rayleigh" W av es)* Should be measured at Period of 20 seconds

Station CTA (Charter Towers, Queensland, Australia);∆ = 55°

• Remove instrument response

• Band-pass filter between 15 and 25 seconds

• Select window of 11 minutes duration around Rayleigh wav e

• Apply Surface-wav eMagnitude formula

Ms = log10A

T+ 1. 66log10 ∆ + 3. 3 (A in microns)

Ms = 8. 19Ms = 8. 19

SUMATRA−ANDAMAN, 26 DEC 2004

EARTHQ UAKES TAKE TIME T O OCCUR

• The larger the earthquake, the longer the source("Scaling Law").

• Measuring large earthquakes at small periods simply misses their true size.

• In the case of Sumatra, full size available only from normal modes.

mb Ms

TSUNAMITSUNAMI

GPS

EARTHQ UAKE SOURCE GEOMETRY

Fr om Single Force to Double-Couple

The physical representation of an earthquake source is a system of forces known as aDouble-Couple, the direction of the forces in each couple being the direction of slipon the fault and the direction of the normal to the fault plane.

Mathematically, the system of forces is described by aSecond-Order Symmetric Deviatoric TENSOR

(3 angles and a scalar).

Single Force

Double Couple

Direction of Slip

Normal to the Fault

[Stein and Wysession,2002]

The scalar is the commonmomentof the 2 couples.It is called theseismic momentseismic momentof the earthquake (M0M0)It represents its source intrue physical units(dyn*cm or N*m ).

SEISMIC MOMENT

The double-couple representing a seismic source is quanti-fied through itsmoment, which represents the commontorque of the opposing couples.

It is a real physical quantity, called the seismic moment andits expression is:

M0 = ∫Σ µ ∆u dS

whereµ is the rigidity of the medium,∆u the slip betweenthe fault walls at each point of the fault, and the integral istaken over the surface of faulting.

In particular, for a rectangular fault of lengthL andwidth W,

M0 = µ ⋅ L W ⋅ ∆u

M0 is measured in dyn*cm (or N*m).

Note that Kanamori [1977] has introduced a so-called

"moment magnitude"Mw given by

Mw =2

3log10 M0 − 16. 1

The retrieval of the seismic momentM0 from seismologicaldata is a relatively complex procedure.

While the equations relating the double-couple to theobservable seismic wav eforms are indeed linear, theyinvolve not only the scalar momentM0, but rather the vari-ous elements of the double-couple, which make up the com-ponents of a

Second-Order Symmetric Deviatoric Singular Tensor.

Historically, the first measurements ofM0 from seismograms were performedby forward modeling (involving sometrial-and-error).The first M0 (3 × 1027

dyn*cm) was published for the 1964Niigata earthquake by Aki [1966].

Around 1970,Gilbert and Dziewonski[1970] laid the theo-retical ground for the directinversion of the seismicmoment from seismograms.

K. Aki (1964)

Second-Order Symmetric Deviatoric Singular Tensor

Normal to fault plane

Direction of slip

Representation of double-couple involves aMoment Ten-sor M = { Mij } w ith components (of amplitudeM0) in thedirections of slipu and normal to faultn:

M = M0 ⋅ [ u n + n u ] ( u ⊥ n )

(In tensor notation:Mij = M0 (ui n j + u j ni ) ; ui ni = 0).

In the {x1 , x2 , x3} f rame,

M =

0

0

M0

0

0

0

M0

0

0

NOTE: Zero trace ("Deviatoric") (Mii = 0).

Eigenvaluesof M are: { −M0 ; 0, M0 }

Eigenvectors arex2 and bisectors ofu, n

("Principal stress axes").

→→ An additional complexity stems from the fact that the4−parameterrepresentation of the double-couple isless gen-eral than a 6−dimensional symmetric tensor, or even than a5−dimensional deviatoric symmetric tensor (Mii = 0).

• The deviatoric constraint is expressed as alinear function ofthe components {Mij }, and thus simply reduces the modelspace to a 5−dimensionalvector space. EASY !

• By contrast, the further constraint (a vanishing intermediateeigenvalue)

→→ cannot be expressed as a linear combination of the {Mij }.THUS, one usually

INVERTS for all 5 components,in the hope that the inver-sion will yield a small intermediate eigenvalue, and then

INTERPRETS the solution as the"best fitting [4−parame-ter] double-couple"among those 5 components...

but also

→→ brings a predictableinstability into the inversion, as thematrix sought is inherently singular....

As such, Moment Tensor Inversion is a difficult problem in theo-retical seismology, which requires, at the minimum,a very largedataset.

** This is why it may be interesting to develop and applymethodologies which explore the low-frequency part of theseismic spectrum, while at the same time keeping the conceptof a single number, namely the philosophy of a

magnitude scale.

CENTROID-MOMENT-TENSOR SOLUTIONGCMT EVENT: C200708020321A DATA: II IU CU IC GE L.P.BODY WAVES: 64S, 165C, T= 50MANTLE WAVES: 62S, 138C, T=125SURFACE WAVES: 64S, 172C, T= 50TIMESTAMP: Q-20070802104412CENTROID LOCATION:ORIGIN TIME: 03:21:51.2 0.1LAT:51.11N 0.00;LON:179.66W 0.01DEP: 32.2 0.2;TRIANG HDUR: 5.6MOMENT TENSOR: SCALE 10**26 D-CMRR= 1.010 0.006; TT=-1.050 0.005PP= 0.031 0.005; RT= 0.740 0.010RP= 0.716 0.010; TP=-0.403 0.004PRINCIPAL AXES:1.(T) VAL= 1.484;PLG=64;AZM=2972.(N) 0.045; 15; 603.(P) -1.538; 21; 156BEST DBLE.COUPLE:M0= 1.51*10**26NP1: STRIKE=271;DIP=27;SLIP= 123NP2: STRIKE= 54;DIP=67;SLIP= 74

----------- ------------------- ---------#####--------- -----#################----- ---#######################-## --############################# -######## ##############----# -######### T #############------# ########## ###########--------- #######################---------- ####################------------- #################-------------- ##############----------------- #########-------------------- ----------------- ------- --------------- P ----- ------------- --- -----------

Example of Global CMT(ex-Harvard) Inversion

More than 25,000 CMT solutions havebeen performed and catalogued under theGlobal-CMT project.

• Algorithm canin principle run automati-cally.

08 JULY 2007, AleutianIslands

Note that intermediateeigenvalue isnot exactly zero...

M0 = 1. 5× 1026 dyn*cm

J.F. Gilbert

A.M. Dziewon´ski

J.H. Woodhouse

G. Ekstro m

TSUNAMI WARNING: THE CHALLENGE

• Upon detection of a teleseismic earthquake, assess in real-timeits tsunami potential.

• HINT: Tsunami being low frequency is generated by longestperiods in seismic source ("static momentM0").

• PROBLEM:Most popular measure of seismic source size, sur-face wav emagnitudeMs , saturates for large earthquakes.

EXTREME

PROBABLE

LOW

NIL

FAR-FIELDTSUNAMI DANGER

[Geller,1976]

Ms SATURATES AROUND 8.2

MmMm and TREMORS

[Okal and Talandier,1989]

• DesignNEWMagnitude Scale,Mm ,using mantle Rayleigh wav es,with variablevariableperiod

• Directly related to seismic momentM0

• All constants justified theoretically

• Incorporate into Detection Algorithms to

AUTOMATE PROCESS

* I mplemented,Papeete, Tahiti (1991),PTWC (1999)

ORIGIN of MANTLE MA GNITUDE Mm

• Now possible to make measurement in Fourier space (frequency domain)

• Spectral amplitude of Rayleigh wav econtrolled bySource, Propagation:

X(ω) = a√ π2

⋅e

−ωa∆2UQ

√ sin∆⋅

1

U

sR l −1/2 K0 − i qR l 1/2K1 − pR l 3/2 K2

⋅ M0

→→ TheKi depend only on frequency and source depth;

→→ Trigonometric factorssR, qR, pR depend only on the geometry of focal mechanism and source-receiver layout.

Conversely, one can extractM0 from

Mm = log10 M0 − 20 = log10 X(ω) + CD + CS + C0

where

• CD =1

2log10 sin∆ + log10 e ⋅

aω ∆2UQ

(distance correction)

• CS is aSource correctionwhich, at each frequency, can be built theoretically byav eraging the source terms over many geometries and source depths.

• C0 is a locking constant, predicted theoretically (depends only onπ and Earthradiusa).

TREMORSSingle-Station Algorithm for Automated Detection and

Evaluation of Far-Field Tsunami Risk

Jacques Talandier, Emile A. Okal, Dominique Reymond,1991

• Automatic detection of distant earthquake

• Automatic Location of Epicenter

• Automatic computation of the event’s Mantle Magnitude

Mm = log10 X(ω) + CD + CS − 0. 90

from spectral amplitudeX(ω) of surface (Rayleigh) seismic wav es atthe longest possible periods (250 to 300 seconds)

AV OIDS MAGNITUDE SATURATION

• Allows quasi-real time estimation of tsunami risk

• Operational at Laboratoire de Ge´ophysique, Tahiti since 1991.

• Also in use at Pacific Tsunami Warning Center, Ewa Beach; Chile.

RECALL...

T = 55 s; Mm = 8. 78

T = 80 s; Mm = 8. 71

T = 120 s; Mm = 8. 60T = 150 s; Mm = 8. 55T = 200 s; Mm = 8. 49× 3

T = 250 s;Mm = 8. 40× 7

TREMORS: EXAMPLE OF APPLICATIONKurile Is. Earthquake,04 OCT 1994,Station: TKK (Chuuk, Micronesia)

• Detection: Analyse signal levelcompared to previous minute.

• Location :S − P gives distance(36° or 4000 km).

Geometry ofP wave giv es azimuth.

• Estimate seismic moment

→ Fourier-transform Rayleighwave(highlighted)

→ At each period, computespectral amplitude, correct forexcitation and distance;obtainMm

→ Conclusion: AverageMm = 8. 60

(M0 = 4 × 1028 dyn-cm).

Harvard solution (obtained later):

M0 = 3 × 1028 dyn-cm (Mm = 8. 48)

TREMORS -- Operational Aspects

• Performance against subsequently published values ofM0

CONFIRMED: A VOIDS SATURATION

TREMORS -- Operational Aspects

• Response Time of TREMORS algorithm

A TREMORS station at an epicentral distance of 15°can issue a useful warning for a shore located 400 kmfrom the event.

MMm CAN WORK at SHORT DISTANCES

Tested by Okal and Talandier [1992] down to

∆ = 1. 5° (165 km).

MMm WORKS for GIGANTIC EVENTS

Chile, 1960

Works even on sev erely clipped records obtained on instru-ments with poor dynamic.

[Okal and Talandier,1991]

MMm CAN WORK for HISTORICAL EVENTS

Important for reassessment of old events, based onvery sparse datasets.

17 AUGUST 1906 -- Aleutian Islands

Wiechert mechanical seismometer, Strasbourg

Mm = 8. 58; M0 = 3. 8× 1028 dyn*cm

THE INFAMOUS "TSUN AMI EAR THQUAKES"

• A particular class of earthquakes defying seismic source scaling laws.

Their tsunamis are much larger than expected from their seismic magni-tudes (even Mm).

• Example: Nicaragua, 02 September 1992.

THE EARTHQUAKE WAS NOT FELT AT SOME BEACH COMMUNITIES,

WHICH WERE DESTROYED BY THEWAVE 40 MINUTES LATER

170 killed, all by the tsunami, none by the earthquake

El Transito, NicaraguaEl Popoyo, Nicaragua

"TSUNAMI EAR THQUAKES"

• The Cause:Earthquake has exceedingly slowrupture process releasing very little energy intohigh frequencies felt by humans and contributingto damage[Tanioka, 1997; Polet and Kanamori,2000].

• The Challenge: Can we recognize them fromtheir seismic wav es in [quasi-]real time?

• The Solution:The Θ parameter [Newman andOkal, 1998] compares the "size" of the earth-quake in two different frequency bands.

→ Use generalized−P wavetrain (P, pP, sP).

→ Compute Energy Flux at station[Boatwright and

Choy, 1986]

→ IGNORE Focal mechanism and exact depthtoeffect source and distance corrections (keep the"quick and dirty"magnitude"philosophy).

→ Add representative contribution ofS waves.

1994 Jav a"Tsunami Earthquake"

Station: TAU(Hobart, Tasmania)

→ DefineEstimated Energy, EE

EE = (1 + q)16

5

[a/g(15;∆)]2

(Fest)2ρ α

ωmax

ωmin

∫ ω2 u(ω) 2 eω t* (ω) ⋅ dω

→ Scale to Moment throughΘ = log10EE

M0

→ Scaling laws predictΘ = −4. 92.

• Tsunami earthquakes characterized byDeficientΘ (as much as 1.5 units).

Now being implemented at Papeete and PTWC

••• Nicaragua, 1992

Java, 1994

Chimbote,Peru, 1996

.5

EXAMPLE of COMPUT ATION of PARAMETER Θ

JAPAN

RED Events are SLOW (Θ ≤ − 5. 8)

Note that this event had a trend towards being FAST

(Outer ridge event NOT at SUBDUCTION INTERFACE)

PROBLEM with Θ for V ERY L ARGE EVENTS

• The duration of the source (and hence of theP-wave train may be so long that thePwave interferes with subsequent phases (PP, even S)

Example: Sumatra-AndamanEvent, 26 DEC 2004

Duration of Source: 500 to 600 seconds (8 to 10 minutes)

Station MSEY (Mahe, Seychelles;∆ = 41°).

P

S

OTHER APROACHES

• MwP [Tsuboi,1996]

Idea: Try to recover the full moment information from thePwaves which arrive faster than the Rayleigh wav es.

• Note that formula forP waves inv olves

TIME DERIV ATIVE of MOMENT FUNCTION , XX

Idea is to computeTIME INTEGRALof P wave deformation torecover X, and hence static momentM0.

Problems: Instrument records velocity, so double integrationneeded; noisy at long periods;NOT tested on large earthquakes.

MwpMwp : EXAMPLE of COMPUT ATION

OKUSHIRI, J apan EARTHQUAKE, 12 JULY 1993

Harvard CMT: M0 = 4. 7× 1027M0 = 4. 7× 1027 dyn-cmStation PFO (∆ = 77. 1°) Station NWAO (∆ = 78. 1°)

Raw(∼ Velocity)

Raw(∼ Velocity)

Ground Motion Ground Motion

Integratedground motion

Integratedground motion

M0 = 5. 3× 1027M0 = 5. 3× 1027 dyn-cm M0 = 3. 3× 1027M0 = 3. 3× 1027 dyn-cm[J. Hebden,Northwestern Univ., 2006]

Σ mbΣ mb: A new, promising development

[Bormann and Wylegalla,2005]

• Idea: Make standard measurements ofmb but keep adding their contributions throughout theP wavetrain, as long as enough energy is present.

• Seems to work fine, even for large earthquakes

• Drawbacks: Operational aspects of algorithmstill largelyad hoc.

Lacks theoretical justification.

Same problems asΘ, Mwp (duration of window).

A simple [trivial ?], robust measurement[Ni et al.,2005]

• Duration of source from High-Frequency (2−4 Hz)

TeleseismicP wavetrain

26 DEC 2004

t = 559 s

28 MAR 2005

t = 177s

DEVELOP ALGORITHM T O MEASURE

HIGH-FREQUENCY P−WAVE DURATION

TONGA, 3 May 2006 — Charter Towers (CTA)

∆ = 37 °

P SPcP PP Rayleigh

ORIGINAL

FILTERED 2 ≤ f ≤ 4 Hz

COMPUTE ENVELOPE

τ 1/3 (at 1/3 Maximum)= 17.3 secondsτ 1/4 (at 1/4 Maximum)= 26.7 seconds

[Reymond and Okal,2006]

PRELIMINAR Y DAT ASET (τ 1/3)

52 earthquakes; 1072records

→→ 2004 Sumatra event recognized as very long

→→ "Tsunami Earthquakes" also identified

(τ 1/3 = 167 s;τ 1/4 = 291 s)

(Java, 2006; Nicaragua, 1992)

→→ By contrast, the 2006 Kuriles earthquake is notfound to exhibit slowness.This confirms its character as weak and late, butnot slow.

SUMATRA 2004

JAVA 2006NICARAGU A 1992

KURILES 2006

WWPhase: The Origin[Kanamori,1993]

WMmWMm :

A " QUICK-and-DIR TY" MAGNITUDE APPR OACH

to QUANTIFYING the WW PHASE

Emile A. OKAL

What IS the WW Phase ?

A combination of multiply-reflected body phases sam-pling the upper mantle at very low frequencies (1 to5 mHz) and arriving betweenP andRayleighwaves.

→→ It can also be regarded as a superposition of Rayleighovertones, i.e., of spheroidal modes of the relevant fre-quencies, with high group velocities (5. 5< U < 9 km/s).

0Sl 1Sl 2Sl 3Sl 4Sl 5Sl 6Sl 7Sl

WW PHASE as COMBINATION of SPHEROIDAL MODES

EARLY I NVESTIGATIONS (1993−94)

Attempt to retrieve long-period behavior ofM0 fromW phase under themagnitudeconcept

RECENT DEVELOPMENTS

• In the wake of the 2004 Sumatra event, Lockwood andKanamori [2006] showed that theW phase was promi-nently recorded world-wide and that its spectral amplitudecould be quantified.

→→ Rivera and Kanamori[2007, 2008] later showed thatWphase signals could be inverted to obtained the ultra-longperiod focal mechanism of the event.

WMm: A NEW LOOK

• In this framework, we re-open the question of therapidrapidquantification of theW phase, in the spirit of amagnitudemeasurement:

→→ "quick-and-dirty";

→→ paying no attention to details such as focal mechanismand exact depth;

→→ but reconstructing reliably the behavior of the seismicmoment at ultra-long periods.

• Based on our experience with the mantle magnitudeMm,we seek to make a mesaurement, from the spectral ampli-tude of theW phase, of the seismic momentM0 through aW−magnitude:

WMm = log10 M0 − 20.

DESIGNING WMm

We recall the formula for the standard mantle magnitudeMm

Mm = log10 X(ω) + CD + CS + C0

for Rayleigh wav es, whereX is the spectral amplitude at angluar fre-quencyω, CD a distance correction,Cs a source correction dependingonly onω, andC0 a locking constant, justifiable theoretically.

This formula is generally applicable to all wav es expressing the super-position of normal modes of the Earth alonga single continuousbranch, and as such was succesfully applied to Love wav es, 1stRayleigh overtones, and even tsunamis [Okal and Titov, 2007].

• The challenge regarding the W phase comes from its nature as asuperpositionof several overtone branchesfeaturing widely differ-ent excitation functions as well as attenuation coefficients.

• In particular, the latter preclude the easy definition of a universal distance correctionCD.

DESIGNING WMm (II)

Rather, we proceed by building a large database of syntheticW phasesfor many focal mechanisms (6480 geometries varying three angles) andepicentral distances (from 20 to 130 degrees).

Each synthetic is then Fourier-transformed, and the resulting 1321920spectral amplitudesX at 17 frequencies between 1 and 5 mHz keptinto a database.

For each of the 204 combinations of distance∆ and angular frequencyω, the 6480 spectral amplitudes are geometrically averaged [over focalgeometry] to obtain anad hocbut theoretically derived correction:

C(∆, ω) = −1

6480 focalgeometries

(φ,δ , λ )

Σ log10 X(∆,ω; φ,δ , λ )

Correction C(∆, ω)

WMm: EXAMPLE OF COMPUT ATION

BENGKULU , Sumatra, 12 SEP 2007

M0 (CMT) = 5. 05× 1028 dyn*cm

Station: HNR (Honiara, Solomon Is.), ∆ = 58°

P S

W

Rayl.→→

Instrument Deconvolved (1≤ f ≤ 20mHz)

U = 9 km/s + 15 minutes→→

• DeconvolveInstrument

• WindowRecord

• F.F.T.

• Then, at eachFrequency:

→→ ReadC(∆; ω)

→→ Apply : WMm = log10 X(ω) + C + 7. 0

Av erage Residual: r = 0. 09r = 0. 09 log. units

EXAMPLE: BENGKULU 2007 (ctd.) Results on 26 Stations(338 values)

Residualsr = WMm − (log10 M0 − 20 )

Our results suggest the elimination of the longest period (T = 819. 2s);and of stations at distances∆ < 40°.

→→ The average moment fromWMm then becomesM0 = 6. 35× 1028 dyn*cm,compared to apublished CMTof M0 = 5. 05× 1028 dyn*cm

→→ The resulting residuals have an average r = 0. 10± 0. 27r = 0. 10± 0. 27 logarithmic units.

Published CMT

APPLICATION to 61 EVENTS

Av erage Residual r = 0. 40± 0. 29

Best Regression:WMm = 0. 75 log10 M0 − 12. 65

Note: Slope influenced by outliers at both low and highmoment values.

ANALYZING and REMOVING the OUTLIERS

04361Sumatra:Undersampled, even at 800 s.

91112Costa Rica:Too few stations, all in same azimuth (early days of IRIS).

07256Bengkulu III:Follows previous, larger event;Contaminated by multipleR from latter.

06360Taiwan: Double event, followed 8 minutes laterby second shock, leading to contamination.

07353 Aleutian:???

After removal of outliers

Av erage residual: r = 0. 37± 0. 22

Best Regression:WMm = 0. 83 log10 M0 − 15. 03

APPLICATION to CHALLENGING CASES

Tsunami EarthquakesTsunami Earthquakes

94153 Java96052 Chimbote, Peru06198 Java

ALL MOMENTS CORRECTLYASSESSED USINGWMmWMm

92246 NicaraguaOverestimated; Too few Stations (early days of IRIS)

Difficult ("Late") Earthquakes

01174 Peru06319 Kuriles

ALL MOMENTS CORRECTLYASSESSED USINGWMmWMm

WMmWMm NOT AFFECTED by SLOWNESS

Residualr = WMm − (log10 M0 − 20)

plotted as a function of the

slowness parameterΘ = log10(EE / M0).

Correlation Coefficient:52%

without Sumatra 2004 :47%

Θ = log10(EE / M0)

r=

WM

m−

(log 1

0M

0−

20)

CONCLUSIONS

• The mantle magnitude formalism can be successfullyapplied to theW phase, using a single distance/frequencycorrection, which remains fully justifiable theoretically.

• Distances less than 40° and periods longer than 800 s arebetter avoided.

• An adequate number of stations (> 10), well distributed inazimuth, is necessary.

• On the average, WMm slightly overestimates publishedCMT moments, raising the question of the possible exis-tence of ultra-low-frequency components to the source ofvery large earthquakes.

• Most importantly , WMm faithfully assesses tsunamiearthquakes and other challenging events.

• The phase can be processed on the average about 20 min-utes before Rayleigh wav es.