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EARTHQUAKES (2):

WAVEFORM MODELING, MOMENT TENSORS, & SOURCEPARAMETERS

Kikuchi and Kanamori, 1991

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SOMETIMES FIRST MOTIONS DONT

CONSTRAIN FOCAL MECHANISM

Especially likely when

- Few nearby stations, as in the oceans, so

arrivals are near center of focal sphere

- Mechanism hassignificant dip-slip

components, so planes dont cross nearcenter of focal sphere

Additional information is obtained by

comparing the observed body and surface

wavesto theoretical, orsynthetic waveforms

computed for varioussourceparameters,

and finding a model that best fitsthe data,

either by forward modeling or inversion.

Waveform analysis also gives information

aboutearthquake depths and rupture

processesthat cant beextracted from first

motions.

?

? ?

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Regard ground motion

recorded on seismogram

as a combination offactors:

- earthquake source

- earth structure throughwhich the waves

propagated

- seismometer

Create syntheticseismogram as Fourier

domain convolution of

these effects

SYNTHETIC SEISMOGRAM AS CONVOLUTION

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SOURCE TIME FUNCTION DURATION PROPORTIONAL TO FAULT LENGTH LAND

THUS CONSTRAINS IT

Also depends on seismic velocity V and rupture velocity Vr

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SOURCE TIME FUNCTION DURATION ALSO VARIES WITH STATION AZIMUTH FROM

FAULT, AND THUS CAN CONSTRAIN WHICH NODAL PLANE IS THE FAULT PLANE

Analogouseffect:thunder igenerated by sudden heating of air along a lightning channel in

the atmosphere. Observers in positionsperpendicularto the channel hear a brief, loud,

thunder clap, whereas observers in the channel direction hear a prolonged rumble.

Directivity similar to Doppler Shift,but differs in requiring finite source

dimensionStein & Wysession, 2003

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BODY WAVE MODELING

FOR SHALLOW

EARTHQUAKEInitial portion of seismogram

includes direct P wave and surface

reflections pP and sP

Hence result depends crucially on

earthquake depth and thus delaytimes

Powerful for depth determination

Stein & Wysession, 2003

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SYNTHETIC BODY

WAVE

SEISMOGRAMS

Focal depth determines the

time separation between

arrivals

Mechanism determines relative

amplitudes of

the arrivals

Source time function

determines

pulse shape & duration

IMPULSES

WITH SEISMOMETER AND

ATTENUATION

Okal, 1992

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BODY WAVE MODELING FOR DEPTH

DETERMINATION

Earthquake mechanism reasonably well

constrained by first motions.

To check mechanism and estimate depth,

synthetic seismograms computed for various

depths.

Data fit well by depth ~30 km.

Depths from body modeling often better than

from location programs using arrival times

International Seismological Center gave depth of

0 17 km: Modeling shows this is too shallow

Depth constrains thermomechanical structure of

lithosphere

Stein and Wiens, 1986

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MORE COMPLEX STRUCTURE CAN BE INCLUDED

Stein and Kroeger, 1980

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High frequencies determining pulseshapepreferentially removed by attenuation.

Seismogram smoothed by both attenuation and seismometer.

Pulses atteleseismic distances can look similar for differentsourcetime functions

ofsimilar duration.

Best resolution for details ofsourcetime functions from strong motion records

closeto earthquake.

EARTH & SEISMOMETER

FILTER OUT HIGH

FREQUENCY DETAILS

Stein and Kroeger, 1980

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MODEL

COMPLEX

EVENTB

YSUMMING

SUBEVENTS

1976 Guatemala

Earthquake

Ms 7.5 on Motagua fault,

transform segment of

Caribbean- North

American plate boundary

Caused enormousdamage and

22,000 deaths

Kikuchi and Kanamori, 1991

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SYNTHESIZE SURFACE WAVES IN FREQUENCY DOMAIN

SOURCEGEOMETRY

EARTH

STRUCTURE

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Amplitude radiation patterns for Love and

Rayleigh waves corresponding to several focal

mechanisms, all with a fault plane strikingNorth.

Show amplitude of surface waves in

different directions

Can be generated for any fault geometry and

compared to observations to find the best

fitting source geometry

SURFACE WAVE AMPLITUDE

RADIATION PATTERNS

Stein & Wysession, 2003

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SURFACE WAVE

MECHANISM

CONSTRAINT

Normal faulting

earthquake in diffuse

plate boundary zone of

Indian Ocean

First motions constrainonly E-W striking,

north-dipping, nodal

plane

Second plane derived

by matchingtheoretical surface

wave amplitude

radiation patterns

(smooth line)to

equalized data.

Stein, 1978

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SURFACE WAVE CONSTRAINT ON DEPTH

How well waves of different periods are generated depends on depth

DEPTH (km)

Tsai & Aki,

1970

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SURFACE WAVE

DIRECTIVITY

CONSTRAINT

1964 Mw 9.1 Alaska

earthquake

7m slip

include finite fault

area (500 km long)directivity to match

surface wave

radiation pattern

Pacific subducts

beneath North

America

Kanamori, 1970

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SEISMIC MOMENT TENSOR

Represents other types of seismic sources as well as slip on a fault

Gives additional insight into the rupture process

Simplifies inverting (rather than forward modeling ) seismograms to estimate source

parameters

Used to produce global data set of great value for tectonics

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FORCES REPRESENTING SEISMIC SOURCES

SINGLE FORCE -Landslide (Grand Banks

slump) or Explosion (Mt. St.

Helens)

SINGLE COUPLE - add 3for isotropic explosion

DOUBLE COUPLE - slip on

fault

Stein & Wysession, 2003

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SEISMIC MOMENT

TENSOR

General representationof seismic source using

9 force couples

Stein & Wysession, 2003

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EXPLOSION

IMPLOSION

EARTHQUAKES

(DOUBLE COUPLE)

OTHER SOURCES

(CLVD)

Dahlen and Tromp, 1998

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MOMENT TENSOR ADVANTAGES

FOR SOURCE STUDIES:

Analyze seismograms without assuming that they result from slip on a fault. In someapplications, such as deep earthquakes or volcanic earthquakes, we would like to identify

possible isotropic or CLVD components.

Makes it easier to invert seismograms to find source parameters, because seismograms are

linear functions of components of the moment tensor, but are complicated products of

trigonometric functions of the fault strike, dip, and slip angles. This is not a problem in forward

modeling, but makes it hard to invert the seismograms to find the fault angles.

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MOMENT TENSOR DATA FOR TECTONIC STUDIES

Globally-distributed broadband digital seismometers permit reliable focal mechanisms to be

generated within minutes after most earthquakes with Ms > 5.5 and made available through the

Internet.

Several organizations carry out this service, including the Harvard CMT (centroid moment tensor)

project.

CMT inversion yields both a moment tensor and a centroid time and location. This location often

differs from that in earthquake bulletins, such as that of the International Seismological Centre(ISC), because the two locations tell different things. Bulletins based upon arrival times of body

wave phases like P and S give the hypocenter: the point in space and time where rupture began.

CMT solutions, using full waveforms, give the centroid or average location in space and time of the

seismic energy release.

The availability of large numbers of high-quality mechanisms (Harvard project has produced over17,000 solutions since 1976) is of great value in many applications, especially tectonic studies.

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SEISMOLOGY GIVES FOCAL MECHANISMS, SEISMIC MOMENTS, SOMEINFORMATION ABOUT FAULT DIMENSIONS

Our goal is to use these to understand tectonics

LomaPrieta

1989

Ms 7.1

Davidson

et al., 2002

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THREE EARTHQUAKES IN

NORTH AMERICA - PACIFIC

PLATE BOUNDARY ZONE

Tectonic setting affects

earthquakesize

San Fernando earthquake on buried thrust fault

in the LosAngeles area, similarto Northridge

earthquake. Short faults arepart of an oblique

trend in the boundary zone, so fault areas are

roughly rectangular. The down-dip width seems

controlled by the factthat rocks deeperthan

~20 km are weak and undergo stablesliding

ratherthan accumulatestrain for future

earthquakes.

San Francisco earthquake ruptured a long

segment oftheSanAndreas with significantlylargerslip, but becausethe fault is vertical, still

had a narrow width. Thisearthquake illustrates

approximately the maximum size of continental

transform earthquakes.

Alaska earthquake had much larger rupturearea because it occurred on shallow-dipping

subduction thrust interface. The larger fault

dimensions give riseto greaterslip, so the

combined effects of larger fault area and more

slip cause largestearthquakesto occur at

subduction zones ratherthan transforms.Stein & Wysession, 2003

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EARTHQUAKE SOURCE PARAMETER ESTIMATES HAVE CONSIDERABLE UNCERTAINTIES

FOR SEVERAL REASONS:

- Uncertainties due to earth's variability and deviations from the mathematical simplifications used.Even with high-quality modern data, seismic moment estimates for the Loma Prieta earthquake vary

by about 25%, and Ms values

vary by about 0.2 units.

- Uncertainties for historic earthquakes are large. Fault length estimates for the San Francisco

earthquake vary from 300-500 km, Ms was estimated at 8.3 but now thought to be ~7.8, and faultwidth is essentially unknown and inferred from the depths of more recent earthquakes and geodetic

data.

- Different techniques (body waves, surface waves, geodesy, geology) can yield

different estimates.

- Fault dimensions and dislocations shown are average values for quantities that can vary significantly

along the fault

Hence different studies yield varying and sometimes inconsistent values. Even so, data are sufficient

to show effects of interest.

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LARGER EARTHQUAKES GENERALLY HAVE LONGER FAULTS AND LARGER

SLIP

M7, ~ 100 km long, 1 m slip; M6, ~ 10 km long, ~ 20 cm slip Important for tectonics,

earthquake source physics, hazard estimation

Wells andCoppersmith, 1994

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IF STRESS DROP IN EARTHQUAKES IS APPROX IMATELY CONSTANT

LONGER FAULTS (L LARGER) HAVE LARGER SLIP D

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IF STRESS DROP IN EARTHQUAKES IS APPROX IMATELY CONSTANT

LINEAR DIMENSION3 OR FAULT AREA3/2 INCREASES WITH MOMENT M0

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EARTHQUAKE STRESS DROPS TYPICALLY 10s TO 100s OF BARS

Estimate from fault area if known

Kanamori, 1970

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ESTIMATING STRESS DROP FROM BODY WAVE MODELING

-- HARDER

Stein and

Kroeger,

1980

Inferring source

dimension from time

function requires

assuming rupture

velocity & fault

geometry

Estimated stress

drop ~1 / L3 , so

uncertainty in fault

dimension causeslarge uncertainty in

W

Small differences in

time function

duration correspondto larger differences

in stress drop, even

for assumed

rupture velocity &

fault geometry

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ESTIMATE STRESS DROP FROM

SOURCE SPECTRA

Infer corner frequency reflecting fault

dimensions

Challenging

Results depend on assumed fault

geometry & rupture velocity

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INTRAPLATE EARTHQUAKES THOUGHT TO HAVE HIGHER STRESS DROP (?)

Kanamori andAnderson, 1975

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WHY?

- Only a small fraction of stress released ?

- Lab values apply to contact area, only a fraction of total fault surface ?

-Lab values dont scale correctly ?

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DIFFERENT MAGNITUDES REFLECT ENERGY RELEASE AT DIFFERENT

PERIODS

1 s - Body wave

magnitude mb

20 s - Surface wave

magnitude Ms

Long period - moment

magnitude Mw derived

from moment M0

Geller, 1976

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Compared to ridgeearthquakes, transform earthquakes often have large

Ms relativeto mb and large Mw relativeto Ms suggesting thatseismic

waveenergy is relatively greater at longerperiods.

Earthquakesthatpreferentially radiate at longerperiods are called "slow"

earthquakes.

Underlying physics unclear

SLOW EARTHQUAKES

Stein and Pelayo, 1991

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5

ENERGY & MAGNITUDE

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SUMMARY

Body & surface waveform modeling improve estimates of focal mechanism &depth

CMT data provides large mechanism dataset

Some generalizations can be made about earthquake source parameters

Results facilitate tectonic studies of plate motions, plate boundary zone andintraplate deformation, and thermo-mechanical structure of the lithosphere