Toward a source spectral model for ETS

Heidi Houston

University of Washington

• 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

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

Spectra of different duration tremor events on 9/8/2005

• Pieces of tremor 40 s to 1 hr

• Spectral slopes near f-1

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

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

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

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

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

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

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

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

• 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

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

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

Summary

• Constructing spectral source models for ETS• understand physics• for reference in comparison

• Underway: data comparison - spectral models provide reference

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

TremorTremor

EarthquakeEarthquake

seconds

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

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

Ito et al., Science 2006

Tremor, VLF’s, and tilt migrate together in space and time

VLFtime

functionsfrom Ide

et al.

Ide et al., GRL, 2008Ide et al., GRL, 2008

• onset and termination not abrupt

M0 - durationX relation for VLFs

• Slope of 1/3 to 1/2, not 1

• Is M0 ~ duration1 really true?

Ide et al., GRL 2008

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

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

• 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

Spectra of different duration tremor events on 9/8/2005

• Pieces of tremor 40 s to 1 hr

• Large variation in spectral ampl.

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

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

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

• 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

.

.

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

• 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.

• Further implication of model: LFEs have same amplitude (moment-rate) as VLFs or ETS tremor

• Not realistic.

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

• 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

Tremor “events” Sept 8, 2005

24 hours

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

20050911

24 hours of tremor from Sept 2005 ETS

• Stack of 12 envelopes of – horizontal displacement– 6 array stations– 1-8 Hz

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

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

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?

Thank you!

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!

Comparison of original (green) and alternate (cyan) spectral models for slow slip

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

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

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

• 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.

Slow events on/near plate interface below locked zone

Ito et al., Science, 2007

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

Locations of Cascadia 2007 tremor (Wech and Creager) and slip (Melbourne)

Creager and colleagues65 LFEs vary in amplitude and duration

• 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

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???

• Like comparing apples to cells of apples?

Slow SlipSlow Slip

‘‘slow slip event’slow slip event’

long-termlong-term motionmotion

inter-slipinter-slipmotionmotion

Rogers and Dragert, 2003

Subduction zone earthquakes are the Big Ones, occurring where the downgoing plate is usually

stuck. About 10% chance of M9+ each 50 years.

Juan de Fuca Plate

North American Plate

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

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

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

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

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

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?

• 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

• 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

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

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”

20050911

One day of tremor from Sept 2005

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

Port Angeles array

• 11 stations– 6 short period – 5 broadband

• Ken Creager and colleagues, NSF-EarthScope

Envelopes from 6 stations on 9/11/2005

24 hours

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

20050909

20050908

20050910 Saturday

3 days of tremor

20050911 Sunday

20050912

20050913

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

Shearer, Intro to Seismology

• Displacement

• Velocity

Near-field Far-field SpectrumFar-Field

Smooth vs jerky slip

displacement (near-field) displacement (far-field)

MM00 MM00

• ~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

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

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

)

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

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

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

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

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?

• 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

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

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

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

• 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

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

-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

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

• 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

Ide et al., GRL, 2008Ide et al., GRL, 2008

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

Ide et al., GRL, 2008Ide et al., GRL, 2008

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

• 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

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

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

‘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.

‘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.

ETS in our backyard

ETS in our backyard