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Earthquake triggering Properties of aftershocks and foreshocks

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Earthquake triggering

Properties of aftershocks and foreshocks

and implications for earthquake forecasting

AgnèsHelmstetter, ISTerre, CNRS, University Grenoble 1

Outline

Aftershocks

when? where? scaling with mainshock size?

why? : static, dynamic, or postseismic stress change?

model? : ETAS or rate & state

Foreshocks

Earthquakes that trigger by chance a larger event

… or part of the nucleation process?

Distribution in time, space and magnitude and comparison with ETAS

1yr### Foreshocks and aftershocks of Landers, California

1 day

M=7.3

M=6.5

1992/4/23

Joshua-Tree

m6.1

Foreshocks a

few hrs before

Landersm≤3.6

1992/6/28

Landers

m7.3

Japan M=9.1### Temporal decay of aftershocks

Sumatra M=9.0

m=7

California

m=2

Omori

p=0.9

- stacks for California and rate following the Sumatra and Tohoku M=9 EQs
- aftershock rate ~1/tp with p≈0.9 (Omori’s law)
- duration ≈ yrs indep of M

Japan M=9.1### Scaling with mainshock magnitude

Sumatra M=9.0

N(M)~10M

California

2

- Aftershock rate N(M)~10M ~ rupture area
- Magnitude distribution P(M)~10-M (GR law)
- Small and large EQs have the same influence on EQ triggering !

Seismicity remotely triggered by M7.3 Landers EQ [Hill et al 1993]### Dynamic triggering

Long Valley

Geysers

Parkfield

unfiltered

filtered 5-30 Hz

- Mostly in geothermal or volcanic areas
- Dynamic stress change ≈ 1 bar >> static
- During seismic wave propagation
- but also in the following days
- Transient deformation at Long-Valley :
- change in fluid pressure ?

Summary of observations about aftershocks

- aftershock rate decays as N~1/t, for t between a few sec and several yrs, independently of M
- + short-term remote dynamic triggering by seismic waves
- number of aftershocks increases as N ~10M~ L2, for 0
- small EQs collectively as important as larger ones for triggering
- the size of a triggered EQ is not constrained by M
- typical triggering distance ≈ L ≈ 0.01x10m/2 km,
- max distance for t<1day ≈ 7L

Triggered seismicity : not only aftershocks!

- Other evidences of triggered seismicity, natural and human-induced
- rainfall (pore pressure changes due to diffusing rain water) [Hainzl et al 2006]
- CO2 degassing [Chiodini et al 2004; Cappa et al 2009]
- slow slip events [Segall et al 2006; Lohman & McGuire 2007, Ozawa et al 2007]
- tides (hydrothermal, volcanic areas or shallow thrust EQs, ∆≈10 kPa, ∆R=10%)[Tolstoy et al 2002 ; Cochran et al 2004]
- migration of underground water or magma [Hainzl & Fisher 2002]
- nuclear explosions [Parsons & Velasco 2009]
- mining (stress concentrations due to the excavation)[McGarr et al., 1975]
- dams (filling of water reservoirs)[Simpson et al 1988, Gupta 2002]
- fluid injections or extraction (geothermal power plants, hydraulic fracturing, for oil and gas production, injection of wastewater, extraction of groundwater) [McGarr et al., 2002; Gonzales et al 2012; Ellsworth 2013]
- … any process that modifies the stress or the pore pressure

≈yrs### What triggers aftershocks?

time

time

time

seismicity rate

after a mainshock

R

Aftershocks triggered by

Static stress changes? postseismic? dynamic?

Coseismic, permanent afterslip, fluids seismic waves

σ

σ

σ

≈yrs

time

≈sec

Static stress change### Mechanisms of aftershocktriggering

permanent change⇒easy to explain long-time triggering

fast decay with distance ~ 1/r3⇒how to explain distant aftershocks?

Dynamic stress change

short duration⇒how to explain long time triggering?

slower decay with distance ~ 1/r⇒better explains distant aftershocks

Postseismic relaxation

afterslip, fluid flow, viscoelastic relaxation

slow decay with time, ~ seismicity rate ⇒ easy to explain Omori law

but smaller amplitude than coseismic stress change

Statistical model : ETAS### Modellingtriggeredseismicity

seismicity rate = background+ triggered seismicity[Kagan, 1981, Ogata 1988…]

R(t,r) = µ(r) + ∑ti

Physical model : coulomb stress change calculations + rate & state model

A ≈ 0.01 parameter of R&S friction law, increase of friction with V

σ: normal stress ; τ: coulomb stress change ;τr’tectonic stressing rate

r : background seismicity rate for τ’=τr’ ; N : cumulated number∫R(t)dt

[Dieterich 1994]

space

time

space

time

ETAS model

Input : proba that an EQ (t,r,m) triggers another EQ(t’,r’,m’)

Results : multiple interaction between EQs

R(t)

Aftershocks

« direct » Omorilaw

Rd(t) ~1/tp

t

mainshock

t

mainshock

ETAS : aftershocks and foreshocks (t)

- Assumptions:
- Results

Aftershocks +aft. of aft. + …

« global » Omorilaw

Rg(t) » Rd(t)

Rg(t) ≈ 1/tpgwthpg

Foreshocks

Inverse Omori law

R(t) ~1/tpf

pf

Foreshocks### “Foreshocks”, “mainshocks”, “aftershocks”

inverse Omori law

N(t)~1/(t+c)pfwith pf≤ p

Aftershocks, Omori law

N(t)~1/(t+c)p

seismicity rate

background rate

time

mainshock

average over many sequences

---- a typical sequence

ETAS model : main results

- Aftershocks
- “Global” Omori law with a pglobal≤ pdirect
- Bath’s law : largest aftershock average magnitude = M-1.2
- Diffusion of aftershocks
- Foreshocks
- Inverse Omori law with pforeshocks≤pdirect
- Rate of foreshocks independent of mainshock magnitude (if any EQ is a mainshock)
- Deviation from GR law bforeshocks≤b
- Migration toward mainshock

τ(t)

R(t)

T» ta

R(t)

T«ta

Rate-and-state : periodic stress changes

- stress : τ(t) = cos(2πt/T) + τ’r t
- T« ta or T»ta
- ta : nucleation time ≈ yrs

slow

short-times regime

for T«ta

R~R0exp(τ/Aσ)

tides, seismic waves

long-times regime

for T»ta

R~dτ/dt

tectonic loading

fast

Rate-and-state : triggering by a stress step

- Reproduces Omori law withp=1for a positive stress change
- Requires a very large ∆ : c=10-4 ta=100 days Aσ=1 MPa⇒∆=15 MPa !

triggering

quiescence

Heterogeneity of EQ source and aftershocks

- Planar fault with uniform stress drop

slip∆ EQ rate

- Real faults : heterogeneous slip and rough faults
- >hetergoneousstress change in the rupture zone
- > most aftershocks on or very close to the rupture zone

slip

∆

EQ rate

[Marsan, 2006; Helmstetter & Shaw, 2006]

mean stress τ0Slip and shear stress heterogeneity, aftershocks

Modified « k2 » slip model: U(k) ~ 1/(k+1/L)2.3 [Herrero & Bernard, 1994]

aftershock map

synthetic catalog

R&S model

shear stress

stress drop τ0 =3 MPa

slip

∆(MPa)

x(km)

R&S model, stress heterogeneity, and aftershock decay with timeAftershock rate

heterogeneous ∆

∆/As=10

∆/As=-10

Heterogeneous

- triggering at short-timet«ta : Omori law with p<1
- quiescence at long time (t≈ta≈yrs)
- [Marsan, 2006; Helmstetter and Shaw, 2006]

Modified k2 slip model, off-fault stress change

- fast attenuation of high frequency τ perturbations with distance

d

L

coseismic shear

stress change (MPa)

Modified k2 slip model, off-fault aftershocks

- seismicity rate and stress change as a function of d/L
- quiescence for d >0.1L

d

L

standard deviation

average stress change

R&S and aftershock time decay

- stacked A.S. for 82 M.S. with 3
- triggering following Omori law decay for 10 s

[Peng et al 2007]

Data

Fit by rate-state model with a Gaussian stress pdf

<∆τ> =0

std(∆τ)/An = 11

ta= 0.9 yrs

p=1

ta

Modeling aftershock rate with R&S model and heterogeneous static stress change

Sequence pτ* (MPa)ta (yrs)

Morgan Hill M=6.2, 1984 0.68 6.2 78.

Parkfield M=6.0, 2004 0.88 11. 10.

Stack, 3

San Simeon M=6.5 2003 0.93 18. 348.

Landers M=7.3, 1992 1.08** 52.

Northridge M=6.7, 1994 1.09** 94.

Hector Mine M=7.1, 1999 1.16** 80.

Superstition-Hills, M=6.6,1987 1.30 ** **

*[Peng et al., 2007]

**we can’t estimate τ* becausep>1

R(t)

τ(t)

time

time

R&S : triggering by afterslip

Mainshock ⇒ coseismic stress change

⇒ afterslip

⇒ postseismicreloading

⇒ aftershocks?

AfterslipPostseismic Aftershock rate stress change

V(t)

time

R&S : triggering by afterslip

We assume stressing rate due to afterslipdτ/dt~ τ’0/(1+t/t*)qwithq=1.3

seismicity rate

stressing rate

- Apparent Omoriexponent p(t) decreasesfrom 1.3 to 1

R&S model and Omori’s law

Deviations from Omori law with p=1 can be explained by :

Coseismictriggering with heterogeneous stress step

- short-time triggering p≤1, p↘ with t and with stress heterogeneity
- long-time quiescence

Postseismic triggering by afterslip

- Omori law decay with p< or >1

τ(x,y)

τ(t)

τ(t)

p=1

log R

log R

r

r

p=1

log t

log t

EQ triggering and EQ forecasting

- seismicity rate increases a lot (≈104) after a large EQ
- … but the proba of another large EQ is still very low !
- limited use for EQ forecasting ?
- Methods : statistical (ETAS, STEP, kernel smoothing …) or physical models (R&S + Coulomb stress change)
- ETAS generally provides the best forecasts [Woessner et al 2011; Segou et al 2013]
- Very simple to use (requires only t,x,y,z,m)
- Bad modeling of early A.S. spatial distribution
- … but can be corrected (kernel smoothing of early A.S.) [Helmstetter et al 2006]
- Coulomb-stress change with R&S
- Good fit in the far-field, but bad near the rupture (∆ is not accurate)
- … but can be corrected by assuming a pdf of ∆[Hainzl et al 2009]
- Usually include only M>6 M.S. (with known slip)

Increase of seismic activity before mainshock ### And before the mainshock?

- … on average
- Part of the nucleation process ?
- Or cascading triggering process ?

Example : seismicity rate before each M>7 mainshock in California and stack for all M>5 (for R<20 km)### Seismicity rate before mainshock

Stacks for California and ETAS for mainshock with 2### Seismicity rate before a mainshock

- Mainshock : any EQ not preceded by a larger EQ for T=100 days and r<10 km
- Foreshocks : EQs within 100 days before and 10 km
- Power-law ↗ of seismicity : inverse Omori law
- Number of foreshocks ↗ with M because of mainshock selection rules

p=0.8

p=0.8

Stacks for California and ETAS for mainshocks with 2 (SHLK catalog) ### Spatial distribution of foreshocks (M)

- small d : similar pdf(d) for all M, but ! location error ↗ with M
- large d : increase in pdf(d) for all M due to selection rule MF.S. < MM.S.

Stacks for California and ETAS for mainshocks with M>4### Spatial distribution of foreshocks (time)

- California ETAS

timebefore M.S. (day).

- apparent migration towardmainshock.

Swarms sometimes detected before mainshocks (not explained by ETAS) ex : M=9 Tohoku [Marsan et al, 2013]### Foreshocks = asesimic loading ?

- «Repeating» EQs (triggered by aseimic slip?) and low-frequency noise
- ex : m=7.6 Izmit[Bouchon et al 2011] or M=9 Tohoku [Kato et al 2012]
- Slow slip event
- Ex : M=8.1 Iquique [Ruiz et al, 2014]
- Accelerating foreshock sequences followed by enhanced aftershock rate
- Stack of M>6.5 mainshocks worldwide [Marsan et al 2014]
- Foreshock / aftershock ratio istoo large
- Stack for 2.5
- Foreshocks do not promote the mainshock (∆<0)
- Landers M=7.3 and other EQs in California M4.7-6.4 [Dodge et al 1995,1996]
- Accelerating slip predicted by R&S friction law and lab friction experiments … but very small slip (≈ Dc) and difficult to detect [Dieterich 1992]

but in most cases nothing special occurs before mainshocks### Asesimic loading before mainshocks?

- and most slow EQs, repeating EQs or swarms are not followed by mainshocks !
- need to consider whole seismicity (not only before mainshocks) to check that these patterns are really unusual !

fitting seismicity with ETAS with variable background µ(t,r) to detect deviations = transient [Marsan et al, 2013]### Swarms before mainshocks

- Transient before
- Tohoku, Jan-Feb/2011
- ≈30 days, 40 km
- ●all EQs
- ●transient
- but several other swarms detected not related to large EQs …

accelerating repeating EQs with very similar waveforms during the last 44 mn before M=7.6 1999 Izmit EQ [Bouchon et al 2011]### Repeating EQs before mainshocks

- 18 events with 0.3

Normalized waveforms, chronological order

Waveforms of the 1st and 2nd ev.

Top : filter <3 Hz

migrating foreshocks and repeating EQs before M9.0 Tohoku [Kato et al 2012]### Repeating EQs before mainshocks

- repeating EQs : large correlation -> same exact location?

Intense foreshock activity and a SSE before M=8.1 Iquique [Ruiz et al 2014]### Slow slip events before mainshocks

M8.1

M6.7

SSE with slip≈1m following the largest M6.7 foreshock 15 days before mainshock (or unusually large afterslip?)

Stacked seismicity rate with M>4 before and after M>6.5 mainshocks in the worldwide ANSS catalog [Marsan et al 2014]### Foreshock activity related to enhanced aftershocks

- Population A :
- Significant precursory
- acceleration
- Population B :
- No significant precursory
- acceleration
- This pattern cannot be explained by ETAS, incompleteness, or # in M.S. M
- episodic creep that preceded the M.S. and lasted during the A.S. sequence?

M7.3 mainshock### Foreshocks did not trigger each other and did not trigger the mainshock?

Stress change due to the Landers foreshocks did not trigger the mainshock (∆<0)… but results depend on relocation method

M7.3 mainshock

M3.6

foreshock

M3.6

foreshock

[Marsan 2014]

SHLK catalog

M3.6 foreshock

In SHLK catalog

[Dodge et al 1995]

Conclusion

- earthquake triggering explains most properties of EQ catalogs
- triggering mechanism : static? dynamic? postseismic?
- but some discrepancies : swarms, heterogeneity, excess of foreshocks …
- need to model accurately «normal» seismicity to detect deviations
- deviations from normal seismicity ⇒ aseismic loading?
- detection of “aseismic loading” : from EQ catalogs? Geodesy?
- aseismic loading = precursor (part of nucleation)?
- or aseismic loading = potential triggering factor (like foreshocks)?
- implication for EQ forecasting :
- ↗ in seismicity rate ⇒ ↗ in the proba of a future large event?
- Or can we do better?

Tutorial : statistical analyses of EQ catalogs to reveal nucleation and triggering patterns

- distribution of aftershocks and foreshocks in time, space and magnitude
- transient increase in catalog incompleteness after a large EQ, implication for the temporal decay of aftershocks
- how to identify foreshocks, mainshock and aftershocks?
- comparison of foreshocks and aftershocks properties in ETAS model or in the R&S model
- can we estimate ETAS model parameters (p, c, α, µ, b …) from stacked aftershock sequences?
- how dependent are the results on : parameter choices (windows in time, space, magnitude …), location errors, catalog incompleteness …?

Tutorial

- download and unzip
- ftp://ist-ftp.ujf-grenoble.fr/users/helmstea/CARGESE.zip
- Archive with EQ catalogs, matlab codes, ETAS program
- You alsoneedmatlab and a fortran compiler to use the ETAS simulator

Tutorial : earthquake catalogs

- ANSS catalog for California
- M≥1 ; 31≦ lat ≦ 43°N ; -127 ≦ lon ≦ -110°
- Relocated SHLK catalog for California
- M≥0 ; 31.4 ≦ lat ≦ 37°N ; -121.5≦ lon ≦ -114°
- Worldwide ANSS catalog
- M≥4
- ETAS catalog :
- GR law : b=1, M0=0, md=2
- Aftershock : productivity K(m)~10αmwithα=1
- Omori law : p=1.1, c=0.001 day
- Aftershock spatial distribution : Φ(r,M)~1/(r+d010M/2)1+µ
- with d0=0.01 km and µ=1
- Uniform background, R=1000 km, Zmax=50 km, 2 M≥2 EQs / day

Tutorial : codes

- demo.m :
- plots of earthquakes in space and time to illustrate clustering
- aftershock rate following a large EQ and fit by Omori's law using MLE
- transient changes in completeness magnitude mc after large Eqs
- estimation of mc for different time and space windows (by fitting the magpdf by the product of a GR law and an erf function)
- stack_aft.m
- stack of aftershocks sequences for different classes of mainshock magnitude
- simple selection rules (time, space and magnitude windows, following [Helmstetter et al 2005]
- aftershock rate as a function of time, distance and magnitude including correction for time-dependent completeness
- scaling of aftershock productivity with mainshock magnitude
- comparison of California or worlwide seismicity and an ETAS catalog

Tutorial : codes

- stack_for.m :
- stack of foreshock sequences for different classes of mainshock magnitude
- foreshock rate as a function of time, distance and magnitude
- comparison of California or worldwide seismicity and an ETAS catalog
- aft_RS
- aftershock rate due to a static stress change using the rate-and-state model, as a function of time and space [Dieterich 1994]

Tutorial : codes

- Toolbox :
- omori_synt_cat : generates a EQ times following Omori’s law
- Omori_fit : fit aftershock time decay by Omori’ law using Max. Likelihood
- get_pm_erfGR : estimation of mc and b by fitting a magnitude distribution by the product of a GR law and an erf function
- get_for, get_aft : selection of F.S., M.S. and A.S. using windows in t, r, and m. Computes rates of EQs in t, r and m.
- get_mc : compute completeness magnitude for each EQ due to increase in etection threshold following large EQs[Helmstetter et al 2006]

R&S : triggering by a stress step

L

r

R(r) for t

Stress change for a dislocation of length L: τ(r)~(1-(L/r)3)-1/2 -1

- Very few events for r>2L
- «diffusion» of aftershocks with time
- Shape of R(r) depends on time, very # from τ(r)
- Difficult to guess triggering mechanisms from the decrease of R(r)

τ

L

r

R(r) for t>ta

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