toward a source spectral model for ets heidi houston university of washington
Post on 21-Dec-2015
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Toward a source spectral model for ETS
Heidi Houston
University of Washington
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• Constructing spectral source models for ETS– Important tool for understanding physics
and scaling - e.g., -2 models for earthquakes
– Serve as reference to compare– - variability of ETS’s– - short- and long-period character of ETS– - different sizes of events - ETS, SSE, VLF, etc
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Indications that high frequency spectrum falls off as f-1
• Displacement spectra -
• strong tremor day
• Spectral slope near f-1
• Instrument removed
Spectra of 20-min intervals on Sept. 10 2005
10-1 1 10
Frequency (Hz)
Mo
men
t-ra
te s
pe
ctru
m (
N-m
)
slope f -1
101
21
014
101
6
low -> high tremor moment
tre
mo
r m
om
ent
tre
mo
r m
om
ent
noisenoise
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Spectra of different duration tremor events on 9/8/2005
• Pieces of tremor 40 s to 1 hr
• Spectral slopes near f-1
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Ide et al.’s proposed scaling law for
duration vs moment: duration ~ M01
• They used– LFE - low frequency eqs– VLF - very low
frequency eqs– SSE - slow slip events– ETS - episodic tremor
and slip– Silent earthquakes
• Contrast with regular earthquakes (Houston, 2001)– duration ~ M0
1/3
Ide, Beroza, Shelly, Uchida, Nature, 2007Log M0
Log
dura
tion
Cascadian LFEs
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Assume that high-frequency spectral amplitudes ~ duration1/2
• Tremor signal incoherent at high frequency
• High-frequency amplitude spectrum ~ duration1/2 ~ M0
1/2 (from Ide et al. 2007)
• => faster increase w/M0 than for earthquakes which have h.f. amplitude spectrum ~ M0
1/3
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1 100.01
10^19
10^16
10^13
Frequency (Hz)
Mom
ent
rate
spe
ctru
m (
Nm
/s/H
z)
ETS spectral model
• Enforce high-frequency ampl. ~ M0
1/2
• then c ~ M0-1/2
• If c = c vR (/M0)1/3
• must have vR 1/3 ~ M0
-1/6
• h.f. amplitude increases faster than for earthquakes
regular w-2 model
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For -1 model with h.f. spect. amp. ~ M01/2
• need M() = M0 c /(c+) for spectral slope
• needc = c vR (/M0)1/3 to get units right
• impliesc ~ M0-1/2
• Then vR 1/3 ~ M0-1/6
• If constant, vR ~ M0-1/6
• If vR constant, ~ M0-1/2
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Start to compare data to model
• GPS moment• Get moment rate-spectrum at 1-10 Hz
from tremor• Assumption: tremor consists mainly of
direct S waves• Levels calibrated empirically by small
earthquakes
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Estimate band-limited moment-rate from tremor
• displacement at station => tremor moment-rate
• assume signal consists mostly of direct far-field S-waves– PA array in Olympic Mountains, almost directly over region of
high slip
• assume average radiation pattern – or assume shear slip in subduction direction
• assume Q (~200), beta, distance to source
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Empirical calibration - compare network moment to band-limited ‘tremor moment’
• 4 small quakes– M1.5 - M 2.9
• M2.9 on 20050913– 60 km from array
• Applying processing and assumptions (e.g., direct S-waves) obtain M4.0– factor of ~40 overestimation of moment– probably due to reverberations at the site
• Adjust band-limited moment estimate accordingly
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Scaling of high-frequency spectral amplitudes
• Tremor signal incoherent at high frequency
• High-frequency amp spectrum ~ duration1/2 ~ M0
1/2
• High-frequency amplitude spectrum of N days ~ N1/2 amplitude spectrum of 1 day
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• Estimates for 2005 Cascadia ETS
• Spectral amplitudes corrected for 14-day duration
• Tremor spectral amps corrected w/empirical calibration
1 100.01
10^19
10^16
10^13
Frequency (Hz)
Mom
ent
rate
spe
ctru
m (
Nm
/s/H
z)
GPS moment
0.0000001
VLFs from Japan
Tremor from Cascadia
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1 100.01
10^19
10^16
10^13
Frequency (Hz)
Mom
ent
rate
spe
ctru
m (
Nm
/s/H
z)
ETS spectral model
• 2005 ETS =>• vR ~ 0.1 m/s ~ 0.1MPa• still underpredicts
data– spectral bumps– shorter duration
process (tides?)– calibration
preliminary
• gather data• compare data
GPS moment
VLFs from Japan
Tremor from Cascadia
0.0000001
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1 100.01
10^19
10^16
10^13
Frequency (Hz)
Mom
ent
rate
spe
ctru
m (
Nm
/s/H
z)
Possibility that real spectrum is more complex
GPS moment
VLFs
Tremor
0.0000001
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Summary
• Constructing spectral source models for ETS• understand physics• for reference in comparison
• Underway: data comparison - spectral models provide reference
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Useful things
• More studies should provide info about tremor amplitude
• Test assumptions of• f-1 falloff• M0 ~ duration1
• Collect data on• vR vs M0
• vs M0
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TremorTremor
EarthquakeEarthquake
seconds
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Strong tremor (black) and LFEs (red) at BS01 2-8 Hz
M1.7 earthquake
LFEs much smaller than tremor
Time (s)
Co
unt
s
Amplitudes not same
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VLFs:Very low
frequency events
• Not common• Occur during some, not all, tremor events
• 30 minute record• red traces filtered at 0.02 to 0.05 Hz • black traces filtered at 2 to 8 Hz
VLF
Ito et al., Science, 2007
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Ito et al., Science 2006
Tremor, VLF’s, and tilt migrate together in space and time
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VLFtime
functionsfrom Ide
et al.
Ide et al., GRL, 2008Ide et al., GRL, 2008
• onset and termination not abrupt
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M0 - durationX relation for VLFs
• Slope of 1/3 to 1/2, not 1
• Is M0 ~ duration1 really true?
Ide et al., GRL 2008
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Menagerie of slow events
• LFE - low frequency eqs ~.3 s, M1• VLF - very low frequency eqs ~50 s, M4• SSE - slow slip events ~4 days, M6• ETS - episodic tremor and slip ~14 days,
M6.6• Silent earthquakes ~1 yr, M7
• All shear slip*, longer duration, less seismic energy• Ide et al.’s philosophy: lump all together, seek scaling
relation
tilt
GPS
GPS
*a bit controversial
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Moment-duration scaling for earthquakes:duration ~ M0
1/3
• M0 = D L W
• Quasi-constant aspect ratio => L ~ W• Quasi-constant stress drop => D ~ W
• So M0 ~ L3 ~ (vRT)3 ~ T3
• T ~ M01/3
Constant rupture velocity vR
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• Estimate spectral amp for 14 days of tremor
• Assume N days of tremor have N times energy as 1 day so spectral amp ~ N1/2
Spectra of 20-min intervals on 20050910
10-1 1 10
Frequency (Hz)
Mom
ent-
rate
spe
ctru
m (
N-m
)slope f -1
101
21
014
101
6
low -> high tremor moment
tre
mo
r m
om
ent
tre
mo
r m
om
ent
noisenoise
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Spectra of different duration tremor events on 9/8/2005
• Pieces of tremor 40 s to 1 hr
• Large variation in spectral ampl.
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Suggested time functions of slow slip processes
• Duration ~ moment1
• implies time function’s mean amplitude doesn’t grow with moment or time
• Source time functions like boxcars
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Suggested time functions of slow slip processes
• Duration ~ moment1
• implies time function’s mean amplitude doesn’t grow with moment or time
• Source time functions like boxcars
• High frequencies generated only at beginning and end– would allow small and large events to have same high-
frequency content
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Ide et al. proposed f-
1 model
• Solid: f-2 model for reference
• Dashed: f-1 model
Ide et al., Nature, 2007
1s
3s
10s
33s
0.1s
100s
3s
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• standard -2 model• M() =• M0 c
2 /(c
2 + 2)
• corner freq c = c (/M0)1/3
-1 model• M() =• M0 c
1 /(c
1 + 1) c = 2/T
• Goal: compare model, high- and low frequency data
Similar smooth -1 spectral model
1 100.01
10^19
10^16
10^13
Frequency (Hz)
Mom
ent
rate
spe
ctru
m (
Nm
/s/H
z)
0.0000001
.
.
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Can this “slow slip” source model be
correct?• Only for boxcar time
functions
• Not for realistic t.f.s – 1 sec LFE does not have same
spectral amplitude at high frequencies as slow-slip event lasting days
– Real onsets and terminations not sufficiently abrupt
Ide et al., Nature, 2007
1s
3s
10s
33s
0.1s
100s
3s
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• duration ~ M01 & f-1 spectrum => boxcar t.f.s
– implies “events” have abrupt onset and termination so that all/most high frequencies generated then
• consider onsets and terminations of actual VLFs, tremor, and ETS
• Not abrupt.
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• Further implication of model: LFEs have same amplitude (moment-rate) as VLFs or ETS tremor
• Not realistic.
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20050911
24 hours of tremor from Sept 2005
• Stack of 12 envelopes of – horizontal displacement– 6 array stations– 1-8 Hz
• Gradual onsets and terminations
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• July 2004 Sequim array
• Sept 2005 Port Angeles array
• January 2007 Price Lake array - near initiation of ETS
15 days
3 Cascadia ETSshow gradual onsets
Creager and colleaguesCreager and colleagues
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Tremor “events” Sept 8, 2005
24 hours
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Other implications of f-1 spectral model
• energy/moment ratio varies greatly with moment
• does not apply above some frequency– need falloff faster than f-1.5 to
avert energy catastrophe– implies a smallest LFE because
above some f spectral falloff must exceed 1.5
Ide et al., Nature, 2007
1s
3s
10s
33s
0.1s
100s
3s
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20050911
24 hours of tremor from Sept 2005 ETS
• Stack of 12 envelopes of – horizontal displacement– 6 array stations– 1-8 Hz
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VLFtime
functionsfrom Ide
et al.
Ide et al., GRL, 2008Ide et al., GRL, 2008
• 2-3 SSEs / yr
• Estimate total moment found in active day
• VLF moment in each SSE
– ~1-5 e15 Nm
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Possible pitfalls
• Lumping together and comparing LFEs, VLFs, SSEs, ETSs, silent earthquakes, afterslip– amounts to the conflation of an event with a
series of events– like comparing a mainshock to the subevents in it
• Moment ~ duration1 may not hold
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What spectral model could work for “slow-slip processes”?
• 1 to 10 Hz tremor has spectral fall-off near -1
• Is there a simple f-1 source model that fits tremor, VLFs and ETS?
• In what sense can these slow-slip processes be self-similar?– e.g. LFE, VLF, SSE, ETS?
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Thank you!
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Are stations in near- or far-field of tremor radiation?
• Pujol (eq 9.5.20) implies if /r >> 1 near-field terms dominate– = 2 c/ =c / f
• c could be P or S wave velocity 3 - 6 km/s• f could be 1 to 8 Hz• r ranges from 25 to 80 km• Therefore, /r at most about 6/25 ~ .25• => near-field terms not important• However, at periods > 3 s, near-field could become
important!
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Comparison of original (green) and alternate (cyan) spectral models for slow slip
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Alternate end-member spectral model
1 100.01
10^19
10^16
10^13
Frequency (Hz)
Mom
ent
rate
spe
ctru
m (
Nm
/s/H
z)• Enforce high-frequency ampl. ~ M0
1/2
• then c ~ M0-2
• OK fit leads to stress drop ~3000Pac ~ c (/M0)1/2
• compared to 40,000Pa for entire ETS
• need more data
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2005 Cascadia ETS
• Need larger corner freq, shorter time
• Tides modulate tremor in Cascadia and Japan (Rubenstein et al, 2007; Nakada etal, 2008)
• Dashed green line with c appropriate for 12 hours duration 1 100.01
10^19
10^16
10^13
Frequency (Hz)
Mom
ent
rate
spe
ctru
m (
Nm
/s/H
z)
0.0000001
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high-frequency spectral behavior
• Regular earthquakes w/ -2 model– M0 = DLW & quasi-const vR=> dur ~ M0
1/3
– h.f. spectral amp ~ dur ~ M01/3
• Slow-slip phenomena– M0 ~ dur (really??)– h.f. spectral amp ~ dur1/2 ~ M0
1/2
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• LFE (red), VLF (orange), and SSE (green) occur in the Nankai trough while ETS (light blue) occur in the Cascadia subduction zone. These follow a scaling relation of M0 ~ t, for slow earthquakes. Purple circles are silent earthquakes. Black symbols are slow events listed in the bottom half of Table 1. a, Slow slip in Italy23, 24, representing a typical event (circle) and proposed scaling (line). b, VLF earthquakes in the accretionary prism of the Nankai trough26. c, Slow slip and creep in the San Andreas Fault21, 22. d, Slow slip beneath Kilauea volcano25. e, Afterslip of the 1992 Sanriku earthquake27. Typical scaling relation for shallow interplate earthquakes is also shown by a thick blue line.
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Slow events on/near plate interface below locked zone
Ito et al., Science, 2007
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Spatial relationship of slow earthquake phenomena in Japan
red LFEs ~1sorange VLFs ~20-100sgreen SSEs ~3-4 dayspurple 1946 Nankai earthquake (M8) Ide et al., Nature 2007
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Locations of Cascadia 2007 tremor (Wech and Creager) and slip (Melbourne)
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Creager and colleagues65 LFEs vary in amplitude and duration
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• Can duration ~ M0 and quasi-continuous h.f. radiation be consistent with a self-similar source model?
• No.
• Example - if you add some high frequency to above t.f.s to make f-1 you still have unreasonable result that LFE has same amplitude as ETS even though there are many LFEs occurring at same time to make ETS
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Why do earthquakes scale?• Earthquake follow scaling law because ruptures grow
– on quasi 2-D plane– At quasi-constant rate near shear-wave speed dynamic
rupture propagation
• In contrast, slow slip phenomena (ETS, SSE, VLF, LFE) propagate at various speeds– slow speeds, quasi-static processes
• So what is physical reason for slow slip to follow scaling law over wide moment range???
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• Like comparing apples to cells of apples?
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Slow SlipSlow Slip
‘‘slow slip event’slow slip event’
long-termlong-term motionmotion
inter-slipinter-slipmotionmotion
Rogers and Dragert, 2003
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Subduction zone earthquakes are the Big Ones, occurring where the downgoing plate is usually
stuck. About 10% chance of M9+ each 50 years.
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Juan de Fuca Plate
North American Plate
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Scaling for high-frequency spectral amplitudes
• assume N days of tremor has N times energy of 1 day of tremor
• amplitude spectrum ~ power spectrum1/2
• amplitude spectrum of N days ~ N1/2 amplitude spectrum of 1 day
• => h. f. amp ~ duration1/2 ~ M01/2
• faster increase w/M0 than for earthquakes
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High-frequency spectral amplitudes
• assume N days of tremor has N times energy of 1 day of tremor
• amplitude spectrum ~ power spectrum1/2
• amplitude spectrum of N days ~ N1/2 amplitude spectrum of 1 day
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Does model work if “slow-slip process” portion is per sec?
• Not as shown. – Long period portion is
inconsistent w/ dur~M0
– Consider M02 = 33 M01 and t2 = 33 t1
Ide et al., Nature, 2007
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Time functions of slow slip processes
• Duration ~ moment1
• implies time function’s mean amplitude doesn’t grow with moment or time
• This case has high frequencies generated only at beginning and end
• Duration ~ moment0.85
• implies time function’s mean amplitude grows much less with moment or time than for regular earthquakes
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Scaling and the relation Scaling and the relation
between tremor and slow slipbetween tremor and slow slip
Heidi Houston,Univ of Washington
with thanks to Ken Creager, Aaron Wech
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Things to learn from tremor amplitude levels
• Duration-moment scaling of tremor events– contrast with earthquakes
• How much moment is needed to generate tremor? – what fraction of GPS slow-slip moment?
• Is tremor the sum of many small regular earthquakes?
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• Define ‘tremor moment’ as moment needed to generate 1-10 Hz tremor– band-limited– Duration-moment scaling of tremor “events”
• Tremor moment much less than moment of slow slip from GPS
• Tremor moment greater than predicted by -1 model
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• How does the duration of NV tremor events scale with moment?
• Ide et al. (2007) suggest for “slow-slip events” duration ~ M0
1
– but scaling relation was produced by lumping several different types of phenomena together (e.g. SSE, LPE)
• Here I define and extract events systematically from one data stream
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Ide et al.’s data
for duration-moment scaling
• They used– LFE - low frequency
eqs– VLF - very low
frequency eqs– SSE - slow slip events– ETS - episodic tremor
and slip– Silent earthquakes
Ide et al., Nature, 2007
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How to define tremor “event”?
• Straightforward - amplitude (of envelope) above threshold defines event
• Ideally an “event” should be separated from other events– by say at least the duration of the “event”
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20050911
One day of tremor from Sept 2005
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Processing
• Use horizontal records• From short-period and broadband stations of Port
Angeles array (thanks to Ken Creager and Aaron Wech)– sensitivity to 20 s (sp), 50 s (bb)
• Remove instrument response• Filter for tremor
– 1 to 8 Hz
• Take envelopes using Hilbert transform• Stack 10 to 12 envelopes
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Port Angeles array
• 11 stations– 6 short period – 5 broadband
• Ken Creager and colleagues, NSF-EarthScope
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Envelopes from 6 stations on 9/11/2005
24 hours
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Envelope -> events• Filter envelope (stack) further
– Lowpass • tried 30 to 200 s
• Define event as any piece of envelope – longer than 4* filtering period, and – above an amplitude threshold
• 0.06 to 0.25 of envelope max
• amount of record that comprises tremor events is 40 to 90% depending on threshold and filtering– typically 70-80%, – also depends on day in ETS
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20050909
20050908
20050910 Saturday
3 days of tremor
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20050911 Sunday
20050912
20050913
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Can we define a moment from envelope of tremor?
• Requires assumptions about nature of radiation– Direct far-field S waves
• Then tremor moment-rate can be defined and obtained from envelopes,
• Tremor moment is area under tremor moment-rate (tremor event ~ time function)
• Tremor moment - moment associated with tremor radiation – band-limited, not a true moment
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Shearer, Intro to Seismology
• Displacement
• Velocity
Near-field Far-field SpectrumFar-Field
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Smooth vs jerky slip
displacement (near-field) displacement (far-field)
MM00 MM00
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• ~2 week duration• Mw 6.7 from
inversion of GPS motions– 3.1 cm slip– near PA array
Sept 2005 tremor and slip
Tremor locations fromCreager, Wech, Sweet(posters)
Slip map from Melbourne
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Dur
atio
n (s
)
Tremor Moment (area under tremor envelope)
Thus tremor moment in a tremor event is the area under tremor moment rate ~ the envelope of displacement
1.7 hours1.7 hours
2 min2 min
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Duration vs Tremor Moment• Dur ~ MTr
0.85
• For range of reasonable parameters, exponent ~ 0.82 to 0.90
• Highest amplitudes associated with longer episodes
Tremor Moment (area under tremor envelope)
Dur
atio
n (s
)
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Threshold = 8%, Smoothing frequency = 0.02
Day #events Exp p:
Dur ~ MTrp
0908 49 68% 0.86
0909 43 52% 0.86
0910 42 75% 0.85
0911 25 88% 0.83
0912 15 88% 0.86
0913 45 67% 0.83
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Implications for event “time functions”
• Duration ~ moment1
• implies time function’s mean amplitude doesn’t grow with moment or time
• Duration ~ moment0.85
• implies time function’s mean amplitude grows much less with moment or time than for regular earthquakes
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Empirical calibration
• M2.9 earthquake– on 20050913– 60 km from array
• Applying processing and assumptions (e.g., direct S-waves) obtain M4.0– factor of ~40 overestimation of moment– probably due to reverberations at the site
• Moment - duration relation adjusted
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How does this fit in with Ide et al.’s scaling?
• Less tremor moment than predicted from slow slip– but consistent w/ San
Andreas tremor?– Liu & Rice result is also
to left of Ide’s scaling
• Covers 2 to 3 orders of magnitude
• Slow slip not just composed of tremor?
after calibrationafter calibration
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Tremor moment -> Mw for most active days
Day Total “tremor
Mw”
0908 5.5
0909 5.0
0910 5.5
0911 5.0
0912 5.45
0913 5.3
Total slow slip in 2005 ETS <=> Mw 6.7 (Melbourne)
Would need 63 days of Mw 5.5’s to make Mw 6.7
Only ~15 days available
Tremor moment << 25% of GPS moment
How much “tremor moment” is released during ETS?
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• Comparison between total slip needed to generate tremor and GPS slip in slow-slip events– Tremor fleas ride on back of large slow-slip
elephants
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Slow slip vs tremor
• Total ETS moment of 2005 ~ 1.1-1.4 1019 Nm ~ Mw6.7
• 2 weeks ~ 1.2 106 sec– need 1013 Nm/sec for 14 days– need 1 M2.7/sec for 14 days– 10 M2 /sec– 100 M1.3/sec
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Is tremor the sum of many small regular earthquakes?
• Sum 108 Mw 1.3 earthquakes– 100 eqs/sec needed for 14
days– 105 for 1000 sec
• Spectral sums too high• Spectral slope flat• Summing regular
earthquakes doesn’t match data
~ 3MPa~ 3MPa
Mw 1.3Mw 1.3
Mw 2.0Mw 2.0
Frequency (Hz)Frequency (Hz)
11 1010 100100
10101111
10101212
10101616
Displacement Spectra for 1000 sec Displacement Spectra for 1000 sec
Mom
ent
rate
Mom
ent
rate
Typical spectralTypical spectrallevel for 1000 seclevel for 1000 secon strong tremor dayon strong tremor day
Sums of 100000 M1.3’sSums of 100000 M1.3’s
Sums of 10000 M 2.0’sSums of 10000 M 2.0’s
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Summation details
• To simulate 1000 sec of tremor (~M4.7)– summed 10000 M2’s– summed 100000 M1.3’s
• Small events follow omega-squared model
– A() = M0 c2 / (c
2 + c
2) where corner frequency
c = 2 0.49 (/M0)0.333
• Random phase shifts– also tried more regular phase shifts
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• Variation in tremor absent for T>2 sec
• Potential longer-period phenomena not perfectly correlated w/ tremor
• Makes sense to define “tremor moment”
Spectra of 20-min intervals on 20050910
10-1 1 10
Frequency (Hz)
Mom
ent-
rate
spe
ctru
m (
N-m
)slope f -1
101
21
014
101
6
low -> high tremor moment
- because tremor itself is band-limited
tre
mo
r m
om
ent
tre
mo
r m
om
ent
noisenoise
Guralp 40T 1 Hz seismometersGuralp 40T 1 Hz seismometers
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Spectra of 20-min intervals on 20050911
10-1 1 10Frequency (Hz)
Mom
ent-
rate
spe
ctru
m (
N-m
)
slope f -1
101
21
014
101
6
• Variation in tremor spectral amplitude collapses for periods longer than 2 s– reappears ~10 s but does not correlate to
amplitude variations from 1 to 8 Hz
• Spectral slope of 1-8 Hz tremor ~ -1.2
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-2-2 modelmodel
• A() = M0 c2 / (2
+ c2)
c = 2 0.49 (/M0)0.333
-1-1 modelmodel
• A() = M0 c1 / (1
+ c1)
c = 2 (/M0)1
Spectral models: Spectral models: -2-2 and and -1-1
Mw 1.3Mw 1.3
Mw 2.0Mw 2.0
Frequency (Hz)Frequency (Hz)11 1010 100100
10101111
10101212
10101616
Mom
ent
rate
Mom
ent
rate
10101919 Mw 6.7Mw 6.7
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Spectral models: Spectral models: -2-2, , -1.18-1.18, and , and -1-1
Mw 1.3Mw 1.3
Mw 2.0Mw 2.0
Frequency (Hz)Frequency (Hz)11 1010 100100
10101111
10101212
10101616
Mom
ent
rate
Mom
ent
rate
10101919
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• Consistent with tremor spectra
• Possible that tremor and slow slip involve different physical processes
Slow slipSlow slip
Tremor bumpTremor bump
Mw 6.7Mw 6.7
Mw 2.0Mw 2.0
11 1010
Mw 1.3Mw 1.3
Mw 2.7Mw 2.7
10101111
10101212
10101616
10101919
100100
??
Need falloff faster than Need falloff faster than -1.5-1.5 to avert energy catastrosphe to avert energy catastrosphe
Possible source spectrum for ETS?
10101414
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Ide et al., GRL, 2008Ide et al., GRL, 2008
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Kii Peninsula, Japan Sept 29, 1999station KIS ~30 km distance
Ide et al., GRL, 2008Ide et al., GRL, 2008
2 - 8 Hz2 - 8 Hz
.02 - .05.02 - .05
.002 -. 02.002 -. 02
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Ide et al., GRL, 2008Ide et al., GRL, 2008
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Ide et al., GRL, 2008Ide et al., GRL, 2008
• 2-3 ETS several times/yr
• Estimate total moment found in active day
• VLF moment in each ETS
– ~1-5 e15 Nm
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• Are VLFs in Cascadia?
• ETS process may have shorter corner period than ~10 days– need shorter
timescale - e.g. tidal forcing periods?
Slow slipSlow slip
Tremor bumpTremor bump
Mw 6.7Mw 6.7
Mw 2.0Mw 2.0
11 1010
Mw 1.3Mw 1.3
Mw 2.7Mw 2.7
10101111
10101212
10101616
10101919
100100
??
Need falloff faster than Need falloff faster than -1.5-1.5 to avert energy catastrosphe to avert energy catastrosphe
Possible source spectrum for ETS?
.01.01
from VLFs in Japanfrom VLFs in Japan
10101414
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Conclusions
• Automatic approach to define tremor events and tremor moment-rate (proportional to envelope) to obtain scaling relation
• Duration scales as tremor moment~0.85
– supports scaling law under development for slow-slip processes
• some aspect
– reflection of amplitude-limited nature
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Conclusions, cont.• Spectra suggest tremor is band limited
– so tremor moment can be sensibly defined
• Total tremor moment << true moment associated with slow slip in ETS– most ETS slip is aseismic or outside 1 to 10 Hz (probably
longer period)
• => as tremor amplitude waxes and wanes over time-scales of minutes to hours, longer-period radiation (e.g. VLFs) does not always vary in tandem
• => slow slip not ‘simply’ the sum of tremor
during Sept 2005 ETS
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‘Crustal’ earthquakes occur because the crust is deforming, as well as the subduction zone slipping and the plate flexing. In a 50-year window, the chances are 5% & 15% of an M6.5+ earthquake on the Seattle fault & in the crust anywhere
in the Puget Sound region, respectively.
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‘Intraplate’ (deep) earthquakes have been moderate in size & deep, occurring as the plate flexes on its way down. In a
50-year window, there’s an 84% chance of an M6.5+ interplate earthquake.
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ETS in our backyard
ETS in our backyard