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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

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Presentation Transcript
slide1

5: EARTHQUAKES

WAVEFORM MODELING

S&W 4.3-11

slide2

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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slide3

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

slide5

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

Also depends on seismic velocity V and rupture velocity VR

slide7

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.

slide8

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.

slide9

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

slide12

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

slide13

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

slide15

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.

slide17

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

S&W 4.3-11

slide18

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

slide19

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.

slide20

Love waves result from SH waves trapped near the surface.

Rayleigh waves are a combination of P and SV motions.

slide22

From geometric spreading alone, expect minimum at =90º, and maxima at 0º and 180º

Also have effects of anelasticity

slide23

SYNTHESIZE SURFACE WAVES IN FREQUENCY DOMAIN

EARTH STRUCTURE

SOURCE GEOMETRY

slide25

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

slide27

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

slide28

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

slide29

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

slide30

SURFACE WAVE CONSTRAINT ON DEPTH

How well waves of different periods are generated depends on depth

DEPTH (km)

S & W 4.3-14

slide31

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