EARTHQUAKES (2):

WAVEFORM MODELING, MOMENT TENSORS, & SOURCE PARAMETERS

Kikuchi and Kanamori, 1991

SOMETIMES FIRST MOTIONS DON’T

CONSTRAIN FOCAL MECHANISM Especially likely when

- Few nearby stations, as in the oceans, so arrivals are near center of focal sphere

- Mechanism has significant dip-slip components, so planes don’t cross near

center of focal sphere

Additional information is obtained by comparing the observed body and surface waves to theoretical, or synthetic waveforms computed for various source parameters, and finding a model that best fits the data, either by forward modeling or inversion.

Waveform analysis also gives information about earthquake depths and rupture processes that can’t be extracted from first motions.

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Regard ground motion recorded on seismogram as a combination offactors:

- earthquake source

- earth structure through which the waves propagated

- seismometer

Create synthetic seismogram as Fourier domain convolution of these effects

SYNTHETIC SEISMOGRAM AS CONVOLUTION

SOURCE TIME FUNCTION DURATION PROPORTIONAL TO FAULT LENGTH L AND THUS CONSTRAINS IT

Also depends on seismic velocity V and rupture velocity Vr

SOURCE TIME FUNCTION DURATION ALSO VARIES WITH STATION AZIMUTH FROM FAULT, AND THUS CAN CONSTRAIN WHICH

NODAL PLANE IS THE FAULT PLANE

Analogous effect: thunder igenerated by sudden heating of air along a lightning channel in the atmosphere. Observers in positions perpendicular to 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 dimension Stein & Wysession,

2003

BODY WAVE MODELING FOR

SHALLOW EARTHQUAKE

Initial portion of seismogram includes

direct P wave and surface reflections pP and sP

Hence result depends crucially on earthquake

depth and thus delay times

Powerful for depth determination

Stein & Wysession, 2003

SYNTHETIC BODY WAVE

SEISMOGRAMS

Focal depth determines the time separation between arrivals

Mechanism determines relative amplitudes ofthe arrivals

Source time function determinespulse shape & duration

IMPULSES

WITH SEISMOMETER AND ATTENUATION

Okal, 1992

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

MORE COMPLEX STRUCTURE CAN BE INCLUDED

Stein and Kroeger, 1980

High frequencies determining pulse shape preferentially removed by attenuation.

Seismogram smoothed by both attenuation and seismometer.

Pulses at teleseismic distances can look similar for different source time functions of similar duration.

Best resolution for details of source time functions from strong motion records close to earthquake.

EARTH & SEISMOMETER

FILTER OUT HIGH FREQUENCY

DETAILS

Stein and Kroeger, 1980

MODEL COMPLEX EVENT BY SUMMING

SUBEVENTS

1976 Guatemala Earthquake

Ms 7.5 on Motagua fault, transform segment of Caribbean- North American plate boundary

Caused enormous damage and22,000 deaths

Kikuchi and Kanamori, 1991

SYNTHESIZE SURFACE WAVES IN FREQUENCY DOMAIN

SOURCE GEOMETRY

EARTH STRUCTURE

Amplitude radiation patterns for Love and Rayleigh waves corresponding to several focal mechanisms, all with a fault plane striking North.

Show amplitude of surface waves indifferent directions

Can be generated for any fault geometry and compared to observations to find the bestfitting source geometry

SURFACE WAVE AMPLITUDE

RADIATION PATTERNS

Stein & Wysession, 2003

SURFACE WAVE MECHANISM CONSTRAINT

Normal faulting earthquake in diffuse plate boundary zone of Indian Ocean

First motions constrain only E-W striking, north-dipping, nodal plane

Second plane derived by matching theoretical surfacewave amplitude radiation patterns (smooth line) to equalized data. Stein, 1978

SURFACE WAVE CONSTRAINT ON DEPTH

How well waves of different periods are generated depends on depth

DEPTH (km)

Tsai & Aki, 1970

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

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

FORCES REPRESENTING SEISMIC SOURCES

SINGLE FORCE - Landslide (Grand Banks slump) or Explosion (Mt. St. Helens)

SINGLE COUPLE - add 3 for isotropic explosion

DOUBLE COUPLE - slip on fault

Stein & Wysession, 2003

SEISMIC MOMENT TENSOR

General representation of seismic source using 9 force couples

Stein & Wysession, 2003

REPRESENTING EARTHQUAKE WITH MOMENT TENSOR

Simple representation yields seismic waves produced by a complex rupture involving displacements varying in space and time on irregular fault

First, approximate rupture with a constant average displacement D over a rectangular fault

Approximate further as a set of force couples.

Approximations are surprisingly successful at matching observed seismograms.

Stein & Wysession, 2003

FOR FAULT ORIENTED NORMAL TO COORDINATE AXIS, MOMENT TENSOR IS

Mo is scalar moment

EXPLOSION IMPLOSION

EARTHQUAKES

(DOUBLE COUPLE)

OTHER SOURCES (CLVD)

Dahlen and Tromp, 1998

Nettles and Ekstrom, 1998

MOMENT TENSOR ADVANTAGES FOR SOURCE STUDIES:

Analyze seismograms without assuming that they result from slip on a fault. In some applications, 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.

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 over 17,000 solutions since 1976) is of great value in many applications, especially tectonic studies.

SEISMOLOGY GIVES FOCAL MECHANISMS, SEISMIC MOMENTS, SOME INFORMATION ABOUT FAULT DIMENSIONS

Our goal is to use these to understand tectonics

Loma Prieta

1989

Ms 7.1Davidson et al., 2002

THREE EARTHQUAKES IN NORTH AMERICA - PACIFIC PLATE BOUNDARY ZONE

Tectonic setting affectsearthquake size

San Fernando earthquake on buried thrust fault in the Los Angeles area, similar to Northridge earthquake. Short faults are part of an oblique trend in the boundary zone, so fault areas are roughly rectangular. The down-dip width seems controlled by the fact that rocks deeper than ~20 km are weak and undergo stable sliding rather than accumulate strain for future earthquakes.

San Francisco earthquake ruptured a long segment of the San Andreas with significantly larger slip, but because the fault is vertical, still had a narrow width. This earthquake illustrates approximately the maximum size of continental transform earthquakes.

Alaska earthquake had much larger rupture area because it occurred on shallow-dipping subduction thrust interface. The larger fault dimensions give rise to greater slip, so the combined effects of larger fault area and more slip cause largest earthquakes to occur at subduction zones rather than transforms.Stein & Wysession, 2003

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 valuesvary 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 fault width is essentially unknown and inferred from the depths of more recent earthquakes and geodetic data.

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

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 and Coppersmith, 1994

IF STRESS DROP IN EARTHQUAKES IS APPROX IMATELY CONSTANT

LONGER FAULTS (L LARGER) HAVE LARGER SLIP D

IF STRESS DROP IN EARTHQUAKES IS APPROX IMATELY CONSTANT

LINEAR DIMENSION3 OR FAULT AREA3/2 INCREASES WITH MOMENT M0

EARTHQUAKE STRESS DROPS TYPICALLY 10s TO 100s OF BARS

Estimate from fault area if known

Kanamori, 1970

ESTIMATING STRESS DROP FROM BODY WAVE MODELING -- HARDER

Stein and Kroeger, 1980

Inferring source dimension from time function requiresassuming rupture velocity & fault geometry

Estimated stress drop ~1 / L3 , so uncertainty in faultdimension causes large uncertainty in ∆

Small differences in time function duration correspondto larger differences in stress drop, even for assumedrupture velocity & fault geometry

ESTIMATE STRESS DROP FROM SOURCE SPECTRA

Infer corner frequency reflecting fault dimensions

Challenging

Results depend on assumed fault geometry & rupture velocity

INTRAPLATE EARTHQUAKES THOUGHT TO HAVE HIGHER STRESS DROP (?)

Kanamori and Anderson, 1975

WHY?

- Only a small fraction of stress released ?

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

-Lab values don’t scale correctly ?

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

Compared to ridge earthquakes, transform earthquakes often have large Ms relative to mb and large Mw relative to Ms suggesting that seismic wave energy is relatively greater at longer periods.

Earthquakes that preferentially radiate at longer periods are called "slow" earthquakes.

Underlying physics unclear

SLOW EARTHQUAKES

Stein and Pelayo, 1991

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ENERGY & MAGNITUDE

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 and intraplate deformation, and thermo-mechanical structure of the lithosphere