5: EARTHQUAKES

WAVEFORM MODELING

S&W 4.3-11

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. THIS DIRECTIVITY CAN CONSTRAIN WHICH

NODAL PLANE IS THE FAULT PLANE

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.

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

Stein & Wysession, 2003

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

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

S&W 4.3-11

Fault may curve, and require 3D-description.

Rupture can consist of sub-events on different partsof the fault with different orientations.

Can be treated as superposition of simple events.

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are needed to see this picture.

ACTUAL EARTHQUAKE FAULT GEOMETRIES CAN BE MUCH MORE COMPLICATED THAN A RECTANGLE

1992 Landers, California Mw 7.3 SCEC Website

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.

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.

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

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 at same distance

Can be generated for any fault geometry and compared to observations - after data equalized to same distance - 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. S & W 4.3-13

SURFACE WAVE CONSTRAINT ON DEPTH

How well waves of different periods are excited depends on depth

For fundamental mode Rayleigh waves, excitation at given period decreases with source depth h

For a given depth, longer periods better excited

S & W 4.3-14

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 don’t 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