5: EARTHQUAKES

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5 EARTHQUAKES WAVEFORM MODELING
SW 4.3-11
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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 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.
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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.
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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
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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
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MORE COMPLEX STRUCTURE CAN BE INCLUDED
Stein and Kroeger, 1980
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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
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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
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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.
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Love waves result from SH waves trapped near the
surface. Rayleigh waves are a combination of P
and SV motions.
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Figure 2.7-3 Multiple surface waves circle the
earth.
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From geometric spreading alone, expect minimum at
?90º, and maxima at 0º and 180º Also have
effects of anelasticity
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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
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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
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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

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SURFACE WAVE CONSTRAINT ON DEPTH How well waves
of different periods are generated depends on
depth
DEPTH (km)
S W 4.3-14
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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