Transcript Earthquake triggering, foreshocks and aftershocks

Earthquake triggering
Properties of aftershocks and foreshocks
and implications for earthquake forecasting
Agnès Helmstetter, ISTerre, CNRS, University Grenoble 1
Earthquake triggering
When? Where? What size?
Scaling with mainshock size?
How?…
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
Foreshocks and aftershocks of Landers, California
1yr
1 day
M=7.3
1992/4/23
Joshua-Tree
m6.1
1992/6/28
Landers
m7.3
M=6.5
Foreshocks a
few hrs before
Landers m≤3.6
Temporal decay of aftershocks
Japan M=9.1
Sumatra M=9.0
m=7
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
Scaling with mainshock magnitude
Japan M=9.1
Sumatra M=9.0
N(M)~10M
California
2<M<7.5
> 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 !
Aftershocks : Where?
- aftershocks
1 day after
7<m<7.5
-- background
1 day before
> relocated catalog for
number of aftershocks
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
2<m<2.5
distance from mainshock hypocenter (km)
Aftershocks : What size?
>
aftershocks magnitude distribution = GR law
>
aftershock size does not depend on the mainshock magnitude !
mainshocks 7<m<7.5
b=1
mainshock 2<m<2.5
Dynamic triggering
Seismicity remotely triggered by M7.3 Landers EQ [Hill et al 1993]
Long Valley
Geysers
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 ?
Parkfield
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<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
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
>
mining (stress concentrations due to the excavation) [McGarr et al., 1975]
>
dams (filling of water reservoirs) [Simpson et al 1988, Gupta 2002]
[Parsons & Velasco 2009]
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
What triggers aftershocks?
seismicity rate
after a mainshock
R
≈yrs
time
Aftershocks triggered by
Static stress changes?
postseismic?
Coseismic, permanent afterslip, fluids
σ
dynamic?
seismic waves
σ
σ
≈yrs
time
time
time
≈sec
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]
ETAS model
space
Input : proba that an EQ (t,r,m) triggers another EQ(t’,r’,m’)
space
time
Results : multiple interaction between EQs
time
ETAS : aftershocks and foreshocks (t)
Assumptions:
R(t)
Aftershocks
« direct » Omori law
Rd(t) ~1/tp
t
mainshock
Results
<R(t)>
Foreshocks
Inverse Omori law
R(t) ~ 1 / t pf
pf<p
Aftershocks + aft. of aft. + …
« global » Omori law
Rg(t) » Rd(t)
Rg(t) ≈ 1/tpg wth pg<p
mainshock
t
“Foreshocks”, “mainshocks”, “aftershocks”
seismicity rate
Foreshocks
inverse Omori law
N(t)~1/(t+c)pf with pf≤ p
Aftershocks, Omori law
N(t)~1/(t+c)p
background rate
mainshock
 average over many sequences
---- a typical sequence
time
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
Rate-and-state : periodic stress changes
>
stress : τ(t) = cos(2πt/T) + τ’r t
>
T« ta or T»ta
> ta :
τ(t)
nucleation time ≈ yrs
short-times regime
long-times regime
for T«ta
for T»ta
R~R0exp(τ/Aσ)
R~dτ/dt
tides, seismic waves
tectonic loading
R(t)
T» ta
slow
R(t)
T«ta
fast
Rate-and-state : triggering by a stress step
triggering
quiescence
>
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
Slip and shear stress heterogeneity, aftershocks
Modified « k2 » slip model: U(k) ~ 1/(k+1/L)2.3 [Herrero & Bernard, 1994]
slip
shear stress
stress drop τ0 =3 MPa
mean stress τ0
aftershock map
synthetic catalog
R&S model
R&S model, stress heterogeneity, and aftershock
decay with time
Aftershock rate
heterogeneous ∆
∆(MPa)
x(km)
>
triggering at short-time t«ta : Omori law with p<1
>
quiescence at long time (t≈ta≈yrs)
[Marsan, 2006; Helmstetter and Shaw, 2006]
∆/As=10
∆/As=-10
Heterogeneous 
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<M<5 z<50 km in Japan
>
triggering following Omori law decay for 10 s <t<1 yr with p increasing slightly
with time
[Peng et al 2007]
Data
Fit by rate-state model with a
Gaussian stress pdf
<∆τ> =0
std(∆τ)/Asn = 11
ta = 0.9 yrs
p=1
ta
Modeling aftershock rate with R&S model and
heterogeneous static stress change
Sequence
Morgan Hill M=6.2, 1984
τ* (MPa)
p
0.68
Parkfield M=6.0, 2004
6.2
0.88
78.
11.
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
**
ta (yrs)
**
10.
R&S : triggering by afterslip
Mainshock ⇒ coseismic stress change
⇒ afterslip
⇒ postseismic reloading
⇒ aftershocks?
Afterslip
Postseismic
stress change
V(t)
Aftershock rate
R(t)
τ(t)
time
time
time
R&S : triggering by afterslip
We assume stressing rate due to afterslip dτ/dt ~ τ’0/(1+t/t*)q with q=1.3
seismicity rate
stressing rate
>
Apparent Omori exponent p(t) decreases from 1.3 to 1
R&S model and Omori’s law
Deviations from Omori law with p=1 can be explained by :
Coseismic triggering with heterogeneous stress step
τ(x,y)
log R
τ(t)
r
log t
>
>
short-time triggering p≤1, p↘ with t and with stress heterogeneity
long-time quiescence
τ(t)
log R
Postseismic triggering by afterslip
r
log t
>
Omori law decay with p< or >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
California
p=0.8
ETAS
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]
California
ETAS
Spatial distribution of foreshocks (M)
> Stacks for California and ETAS for mainshocks with 2<M<7.5 (SHLK catalog)
California
ETAS
> 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
California
ETAS
time
before
M.S.
(day).
> apparent migration toward mainshock.
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?
Slow slip events before mainshocks
Intense foreshock activity and a SSE before M=8.1 Iquique [Ruiz et al 2014]
M8.1
M6.7
SSE with slip≈1m following the largest M6.7 foreshock 15 days before mainshock
(or unusually large afterslip?)
Foreshock activity related to enhanced aftershocks
Stacked 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
M7.3 mainshock
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]
M3.6 foreshock
In SHLK catalog
[Dodge et al 1995]
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]
R&S : triggering by a stress step
Stress change for a dislocation of length L: τ(r)~(1-(L/r)3)-1/2 -1
R(r) for t<ta
L
r
τ
L
R(r) for t>ta
r
>
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)