Earthquake triggeringProperties of aftershocks and foreshocks

and implications for earthquake forecastingAgnès Helmstetter, ISTerre, CNRS, University Grenoble 1

Earthquake triggering

When? Where? What size?

Scaling with mainshock size?

How?…

OutlineAftershocks

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

Foreshocks and aftershocks of Landers, California

1yr 1 day

1992/4/23Joshua-Treem6.1

1992/6/28Landersm7.3

Foreshocks a few hrs before Landers m≤3.6

M=7.3M=6.5

Temporal decay of aftershocks

> 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

m=2

m=7

Omori p=0.9

Japan M=9.1Sumatra M=9.0

Calif

orn

ia

Scaling with mainshock magnitude

> 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 !

N(M)~10M

California2<M<7.5

Japan M=9.1

Sumatra M=9.0

Aftershocks : Where?

> relocated catalog for

Southern California[Shearer et al., 2004]

> average distance

≈ rupture length L

<d> ≈ 0.01x10m/2 km

> max distance ‘+’

dmax ≈ 7 L

≈ 0.07x10m/2 km

7<m<7.5- aftershocks 1 day after

-- background1 day before

2<m<2.5

num

ber o

f afte

rsho

cks

distance from mainshock hypocenter (km)

mainshocks 7<m<7.5

mainshock 2<m<2.5

b=1

> aftershocks magnitude distribution = GR law

> aftershock size does not depend on the mainshock magnitude !

Aftershocks : What size?

Dynamic triggeringSeismicity remotely triggered by M7.3 Landers EQ [Hill et al 1993]

Long Valley

Geysers

Parkfieldunfiltered

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 ?

> 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<M<9.

> 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

Summary of observations about 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

Triggered seismicity : not only aftershocks!

What triggers aftershocks?

seismicity rateafter a mainshock

Aftershocks triggered by

Static stress changes? postseismic? dynamic?Coseismic, permanent afterslip, fluids seismic waves

R

σ

timetime

time≈yrs

≈yrs

≈sectime

σ σ

Mechanisms of aftershock triggering

Static stress change

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

Modelling triggered seismicity

Statistical model : ETAS

seismicity rate = background + triggered seismicity [Kagan, 1981, Ogata

1988…]

R(t,r) = µ(r) + ∑ti<t ϕ(t-ti, |r-ri|, mi)

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]

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

Results : multiple interaction between EQs

ETAS model

time

spa

ce

time

s

pace

ETAS : aftershocks and foreshocks (t)

Assumptions:

Results Aftershocks + aft. of aft. + …« global » Omori law Rg(t) » Rd(t)

Rg(t) ≈ 1/tpg

wth pg<p

ForeshocksInverse Omori law

R(t) ~ 1 / t p

f

pf<p

<R(t)>

mainshock t

t

Aftershocks« direct » Omori law Rd(t) ~1/tp

R(t)

mainshock

“Foreshocks”, “mainshocks”, “aftershocks”

Foreshocks inverse Omori law N(t)~1/(t+c)pf with pf≤ p

Aftershocks, Omori lawN(t)~1/(t+c)p

seismicity rate

mainshock

background rate

time

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

> stress : τ(t) = cos(2πt/T) + τ’r t

> T« ta or T»ta

> ta : nucleation time ≈ yrs

T» ta

T«ta

τ(t)

R(t)

R(t)

slow

fast

Rate-and-state : periodic stress changes

long-times

regime

for T»ta

R~dτ/dt

tectonic loading

short-times

regime

for T«ta

R~R0exp(τ/Aσ)

tides, seismic waves

Rate-and-state : triggering by a stress step

triggeringquiescence

> Reproduces Omori law with p=1for a positive stress change

> Requires a very large ∆ : c=10-4 ta=100 days Aσ=1 MPa ⇒ ∆=15 MPa !

Heterogeneity of EQ source and aftershocks

Planar fault with uniform stress drop

slip ∆ EQ rate

Real faults : heterogeneous slip and rough faults

> hetergoneous stress change in the rupture zone

> most aftershocks on or very close to the rupture zone

∆slip

[Marsan, 2006; Helmstetter & Shaw, 2006]

EQ rate

mean stress τ0

Slip and shear stress heterogeneity, aftershocks

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

slipshear stressstress drop τ0 =3 MPa

aftershock mapsynthetic catalog R&S model

R&S model, stress heterogeneity, and aftershock decay with time

heterogeneous ∆

x(km)

∆(M

Pa)

Aftershock rate

∆/ =As 10∆/As=-10Heterogeneous

> triggering at short-time t«ta : Omori law with p<1

> quiescence at long time (t≈ta≈yrs)

[Marsan, 2006; Helmstetter and Shaw, 2006]

• fast attenuation of high frequency τ perturbations with distance

Modified k2 slip model, off-fault stress change

Ld

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

average stress change

standard deviation

dL

[Peng et al 2007]

p=1

ta

R&S and aftershock time decay > stacked A.S. for 82 M.S. with 3<M<5 z<50 km in Japan

> triggering following Omori law decay for 10 s <t<1 yr with p

increasing slightly with time

Data

Fit by rate-state model

with a Gaussian stress

pdf

<∆τ> =0

std(∆τ)/An = 11

ta = 0.9 yrs

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

Sequence p

τ* (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<M<5, Japan* 0.89 12. 1.1

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* because p>1

Mainshock ⇒ coseismic stress change

⇒ afterslip

⇒ postseismic reloading

⇒ aftershocks?

R&S : triggering by afterslip

τ(t)

time

R(t)

time

V(t)

time

Afterslip Postseismic Aftershock rate

stress change

We assume stressing rate due to afterslip dτ/dt ~ τ’0/(1+t/t*)q with q=1.3

> Apparent Omori exponent p(t) decreases from 1.3 to 1

seismicity ratestressing rate

R&S : triggering by afterslip

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

R&S model and Omori’s law

τ(t)

log R

log t

r

p=1

τ(x,y)

τ(t)

log R

log t

r p=1

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)

And before the mainshock?

> Increase of seismic activity before mainshock

… on average

> Part of the nucleation process ?

> Or cascading triggering process ?

Seismicity rate before mainshock

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

Seismicity rate before a mainshock

> Stacks for California and ETAS for mainshock with 2<M<7.5

> 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

CaliforniaETAS

p=0.8 p=0.8

Magnitude pdf of foreshocks

> Stacks for California and ETAS for mainshock with 2<M<7.5

> For small mainshocks : roll-off Mforeshock<Mmainshock

> For large mainshocks : increase in the rate of large EQs

> ETAS theory : P(m)= GR(m,b) + GR(m,b-α) [Helmstetter et al 2003]

CaliforniaETAS

Spatial distribution of foreshocks (M)

> Stacks for California and ETAS for mainshocks with 2<M<7.5 (SHLK catalog)

CaliforniaETAS

> 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.

Spatial distribution of foreshocks (time)

> Stacks for California and ETAS for mainshocks with M>4

CaliforniaETAS

> apparent migration toward mainshock.

time before M.S.

(day).

Foreshocks = asesimic loading ?

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

> «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 is too large

Stack for 2.5<M<5.5 mainshocks in California [Shearer 2012]

> 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]

Asesimic loading before mainshocks?

> but in most cases nothing special occurs 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 !

Swarms before mainshocks

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

Transient before

Tohoku, Jan-Feb/2011

≈30 days, 40 km

● all EQs

● transient

> but several other swarms detected not related to large EQs …

Repeating EQs before mainshocks

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

> 18 events with 0.3<M<2.7, distant by <20 m

Normalized waveforms, chronological order Waveforms of the 1st and 2nd ev.Top : filter <3 Hz

Repeating EQs before mainshocks

> migrating foreshocks and repeating EQs before M9.0 Tohoku [Kato et al

2012]

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

M8.1

M6.7

Slow slip events before mainshocks

Intense foreshock activity and a SSE before M=8.1 Iquique [Ruiz et al 2014]

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

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

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?

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

[Marsan 2014]

SHLK catalog

M3.6 foreshock

M7.3 mainshock

M7.3 mainshock

M3.6 foreshock

[Dodge et al 1995]

M3.6 foreshockIn SHLK catalog

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 also need matlab 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)~10αm with α=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 mag pdf 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]

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)

R(r) for t>ta

R(r) for t<ta

rL

r

Lτ

R&S : triggering by a stress step