8: EARTHQUAKE SOURCE PARAMETERS

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8 EARTHQUAKE SOURCE PARAMETERS Magnitude, fault
area, fault slip, stress drop, energy release
the big one
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EARTHQUAKE MAGNITUDE
Earliest measure of earthquake size Dimensionless
number measured various ways, including ML
local magnitude mb body wave magnitude Ms surface
wave magnitude Mw moment magnitude Easy to
measure Empirical - except for Mw, no direct tie
to physics of faulting
Note not dimensionally correct
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COMPARE EARTHQUAKES USING SEISMIC MOMENT M0
Magnitudes, moments (dyn-cm), fault areas, and
fault slips for several earthquakes Alaska San
Francisco differ much more than Ms implies M0
more useful measure Units dyne-cm or
Nt-M Directly tied to fault physics Doesnt
saturate
Stein Wysession, 2003
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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
values vary 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 yield different
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.
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Moment magnitude Mw Magnitudes saturate No
matter how big the earthquake mb never exceeds
6.4 Ms never exceeds 8.4 Mw defined from moment
so never saturates
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SOURCE PULSE FROM EARTHQUAKE
TIME DURATION rupture time T R needed to
propagate along fault
rise time TD for full slip at any point
TR fault length / rupture velocity
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SPECTRUM OF SOURCE TIME FUNCTION
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SOURCE SPECTRUM is flat and equal to seismic
moment at periods longer than corner frequency
2/TR Decays below corner frequency Corner
frequency shifts to left (lower frequency) for
larger earthquakes with longer faults
Seismic moment
HIGH
LOW
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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
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DIFFERENT MAGNITUDE SCALES REFLECT AMPLITUDE AT
DIFFERENT PERIODS
Body surface wave magnitudes saturate - remain
constant once earthquake exceeds a certain size -
because added energy release in very large
earthquakes is at periods gt 20 s
20 s
1 s
No matter how big an earthquake is, body and
surface wave magnitudes
do not exceed 6.5 and 8.4, respectively.
For very large earthquakes only low period
moment magnitude reflects earthquakes size.
This issue is crucial for tsunami warning because
long periods excite tsunami,
but are harder to study in real time
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E. Okal
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SCALING RELATIONS BETWEEN SOURCE PARAMETERS
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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.
THREE EARTHQUAKES IN NORTH AMERICA - PACIFIC
PLATE BOUNDARY ZONE Tectonic setting
affects earthquake size
Stein Wysession, 2003
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STRAIN STRESS CHANGES
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EARTHQUAKE STRESS DROPS TYPICALLY 10s TO 100s OF
BARS Estimate from fault area if known
Kanamori, 1970
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SPECTRAL CORNER FREQUENCY APPROACH
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Problem for shallow earthquakes P, pP, and sP
often overlap, yielding a combined spectrum quite
different from the source pulse. Spectra differ
between stations due to the variation in
amplitude between direct and reflected arrivals,
and cannot be used to corner frequencies or
seismic moment. Difficulty can be addressed by
modeling the body waves, including the free
surface reflections, and estimating the source
time function duration by matching the observed
waveforms. Given a duration estimate and an
assumed fault geometry, the fault length and
stress drop are estimated as in corner frequency
analysis.
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ESTIMATING STRESS DROP FROM BODY WAVE MODELING --
HARDER
Inferring source dimension from time function
requires assuming rupture velocity fault
geometry Estimated stress drop 1 / L3 , so
uncertainty in fault dimension causes large
uncertainty in ?? Small differences in time
function duration correspond to larger
differences in stress drop, even for
assumed rupture velocity fault geometry
Stein and Kroeger, 1980
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INTRAPLATE EARTHQUAKES THOUGHT TO HAVE HIGHER
STRESS DROP (?)
(the slope is 3/2)
4.6-11
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IF STRESS DROP IN EARTHQUAKES IS APPROX IMATELY
CONSTANT LONGER FAULTS (L LARGER) HAVE LARGER
SLIP D
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IF STRESS DROP IN EARTHQUAKES IS APPROX IMATELY
CONSTANT LINEAR DIMENSION3 OR FAULT AREA3/2
INCREASES WITH MOMENT M0
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LARGER EARTHQUAKES GENERALLY HAVE LONGER FAULTS
AND LARGER SLIP
Wells and Coppersmith, 1994
M7, 100 km long, 1 m slip M6, 10 km long,
20 cm slip Important for
tectonics, earthquake source physics, hazard
estimation
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SLOW EARTHQUAKES
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
Stein and Pelayo, 1991
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For a given moment and fault shape, lower stress
drop corresponds to larger fault dimensions, and
hence longer time functions and smaller corner
frequencies. Given two earthquakes with the same
rupture velocity, one with lower stress drop will
have less high frequency radiation, and thus
lower Ms and mb. Similar effects can result
from a slower rupture velocity, which also gives
a longer time function for a given fault
dimension.
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ENERGY RADIATED BY EARTHQUAKE
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ENERGY MAGNITUDE
5
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Earthquakes of a given magnitude are 10 times
less frequent than those one magnitude smaller.
An M7 earthquake occurs approximately monthly,
and an earthquake of Mgt 6 about every three days.
Hence although earthquake predictor I. Browning
claimed to have predicted the 1989 Loma Prieta
earthquake, he said that near a date there would
be an M6 earthquake somewhere, a prediction
virtually guaranteed to be true. Magnitude is
proportional to the logarithm of the energy
released, so most energy released seismically is
in the largest earthquakes. An M 8.5 event
releases more energy than all other earthquakes
in a year combined. Hence the hazard from
earthquakes is due primarily to large (typically
magnitude gt 6.5) earthquakes.
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• WHY?
• Only a small fraction of stress released ?
• Lab values apply to contact area, only a
  fraction of total fault surface ?
• -Lab values dont scale correctly ?