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5 EARTHQUAKES WAVEFORM MODELING

SW 4.3-11

- 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 has significant dip-slip components,

so planes dont 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

cant be extracted from first motions.

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SYNTHETIC SEISMOGRAM AS CONVOLUTION

Regard ground motion recorded on seismogram as a

combination of factors - earthquake source -

earth structure through which the waves

propagated - seismometer Create synthetic

seismogram as Fourier domain convolution of these

effects

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SOURCE TIME FUNCTION DURATION PROPORTIONAL TO

FAULT LENGTH L AND 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. THIS DIRECTIVITY CAN

CONSTRAIN WHICH NODAL PLANE IS THE FAULT PLANE

Directivity similar to Doppler Shift, but differs

in requiring finite source dimension

Stein Wysession, 2003

For earthquake, V/VR 1.2 for shear waves and 2.2

for P waves. Maximum duration is 180 from the

rupture direction, and the minimum is in the

rupture direction. Analogous effect thunder

generated by sudden heating of air along a

lightning channel in the atmosphere. Here V/VR

0, so observers perpendicular to the channel

hear a brief, loud, thunder clap, whereas

observers in the channel direction hear a

prolonged rumble.

A fault can seem finite for body waves but not

surface waves. A 10-km long fault, which we

might expect for a magnitude 6 earthquake, is

comparable to the wavelength of a 1 s body wave

propagating at 8 km/s, but small compared to the

200-km wavelength of a 50 s surface wave

propagating at 4 km/s. On the other hand, a

300-km long fault for a magnitude 8 earthquake

would be a finite source for both waves.

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

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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

BODY WAVE MODELING FOR DEPTH DETERMINATION Earthq

uake 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

EARTH SEISMOMETER FILTER OUT HIGH FREQUENCY

DETAILS

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.

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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

and 22,000 deaths

SW 4.3-11

ACTUAL EARTHQUAKE FAULT GEOMETRIES CAN BE MUCH

MORE COMPLICATED THAN A RECTANGLE

Fault may curve, and require 3D-description.

Rupture can consist of sub-events on different

parts of the fault with different orientations.

Can be treated as superposition of simple

events.

1992 Landers, California Mw 7.3

SCEC Website

Generally seismograms are dominated by large

longer-period waves that arrive after the P and S

waves. These are surface waves whose energy is

concentrated near the earth's surface.

As a result of geometric spreading, their energy

spreads two-dimensionally and decays with

distance r from the source approximately as r -1

, whereas the energy of body waves spreads

three-dimensionally and decays approximately as r

-2. Thus at large distances from the source,

surface waves are prominent on seismograms.

Love waves result from SH waves trapped near the

surface. Rayleigh waves are a combination of P

and SV motions.

Figure 2.7-3 Multiple surface waves circle the

earth.

From geometric spreading alone, expect minimum at

?90º, and maxima at 0º and 180º Also have

effects of anelasticity

SYNTHESIZE SURFACE WAVES IN FREQUENCY DOMAIN

EARTH STRUCTURE

SOURCE GEOMETRY

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SURFACE WAVE AMPLITUDE RADIATION PATTERNS

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

in different directions at same distance Can be

generated for any fault geometry and compared to

observations - after data equalized to same

distance - to find the best fitting source

geometry

Stein Wysession, 2003

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SURFACE WAVE MECHANISM CONSTRAINTNormal

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 surface wave amplitude radiation

patterns (smooth line) to equalized data.

S W 4.3-13

SURFACE WAVE CONSTRAINT ON DEPTH How well waves

of different periods are excited depends on depth

S W 4.3-14

For fundamental mode Rayleigh waves, excitation

at given period decreases with source depth

h For a given depth, longer periods better

excited

Reciprocity principle states that under

appropriate conditions the same displacement

occurs if the positions of the source and

receiver are interchanged Thus if surface wave

displacement decreases with depth, deeper

earthquakes dont excite them as well Longer

period waves see deeper, so better excited for

source at given depth

SURFACE WAVE CONSTRAINT ON DEPTH How well waves

of different periods are generated depends on

depth

DEPTH (km)

S W 4.3-14

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