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Title: Earthquake triggering, stress changes


1
Earthquake triggering, stress changes
2
Outline
Seismicity in Southern California
3
Earthquake clustering
  • Seismicity in Southern California with m2
  • Symbol size rupture area 10m
  • Color represents longitude -120 -116

Northridge M6.7
Joshua- Tree, M6.1
Hector Mine M7.1
Landers M7.3
4
Earthquake clustering
  • Seismicity in Southern California with m2
  • Symbol size rupture area 10m
  • Color represents longitude -120 -116

Joshua- Tree, M6.1
Landers M7.3
5
Foreshocks, mainshocks, aftershocks
? average over many sequences ---- 1 typical
sequence
6
!! Non-conventional definition of
mainshocksand aftershocks
  • Mainshock any isolated EQ
  • Aftershock EQ within the influence zone
    (T,R) of the mainshock
  • can be LARGER than the mainshock
  • Motivation can we explain the triggering of a
    large EQ by a smaller one using the same laws
    as for a small EQ triggered by a larger one?

7
When Relaxation of number of aftershocks with
timeand scaling with mainshock magnitude M
P(m) GR law
  • Aftershock rate decays with time as N1/t0.9 for
    all M (Omori law)
  • Only the number of aftershocks increases with M,
    N rupture area 10M

8
How are large EQs from smaller ones?
  • theyre larger L100.5m
  • but same stress drop
  • static coulomb stress change ?(r/L,?)
  • so the number of aftershocks fault area L2
    10m as observed
  • small and large EQS collectively as important
    for triggering and for stress transfers between
    EQS if P(m)10m (GR law)

M5, L3 km
9
How big are triggered events Distribution of
aftershocks magnitudes for different mainshock
size M
Southern California 1980-2005
  • Same mag distribution for all M
  • Only the number of aft increases with M

10
Where Spatial distribution of aftershocks
mainshocks M7-7.5
? aftershocks --- background
  • relocated catalog for Southern Califorina
  • Shearer et al., 2004
  • Triggering distance increases with M
  • Max triggering distance
  • R 2 rupture length
  • 0.02x10m/2 km

Number of aftershocks
mainshock M2-2.5
Distance from mainshock (km)
11
Where Triggering distance as a function M
  • triggering distance d(m) 0.01x100.5m km
    rupture length

12
Summary earthquake triggering, observations
  • Aftershock rate decays as N1/t0.9, for t
    between a few sec and several yrs, independently
    of the mainshock magnitude M.
  • The number of aftershocks increases as N 10M
    L2 , for 0ltMlt9.
  • Small EQs collectively as important as larger
    ones for EQ triggering
  • The size of a triggered event is not constrained
    by the mainshock size
  • The typical triggering distance L 0.01x10M/2
    km.
  • The maximum triggering distance is 2L
  • These observations can be explained by several
    models of earthquake triggering by static stress
    changes, such as the rate-and-state model of
    Dieterich 1994.

13
How
  • static (permanent) coseismic stress change
    stress weakening
  • - rate-and-state friction Dieterich, 1994
  • subcritical crack growth Das Scholz, 1981
    Shaw, 1993
  • damage rheology Ben-Zion Lyakhovsky, 2005
  • or stress relaxation with time
  • - fluid diffusion Nur Booker, 1972
  • - postseismic slip asperities Schaff et al.,
    1998
  • - viscous relaxation (?) Mikumo and Miyatake,
    1979
  • dynamic stress changes (seismic waves) ?
  • - does not explain long-time triggering
  • Gomberg, 1997 Brodsky et al., 1998, 2003

14
Models for EQ triggering and forecasting
  • Epidemic Type EQ Sequence (ETES)
  • Kagan and Knopoff, 1981 Ogata, 1988
  • Empirical model, based on Omori law GR law
  • Seismicity rate depends on time, location and
    mag of past EQs
  • Rate-and-State
  • Dieterich, 1994
  • Physical model based on rate-and-state friction
    law
  • Seismicity rate as a function of stress history
    rate-and-state friction

15
Epidemic Type Earthquake Sequence (ETES) model
  • Input
  • Probability that an EQ (t,x,m) triggers another
    (t,x,m)
  • Results
  • Multiple interactions between EQs

16
Definition of ETES model
  • Seismicity rate "background"
    "aftershocks"
  • Magnitude distribution G.R. law
  • Aftershocks Omori law and increase of
    aftershock with magnitude

17
ETES model, foreshocks and aftershocks
  • Input
  • Results

Aftershocks Aftershocks of aftershocks
 global Omori law Rg(t) 1 / t p
with p p Rg(t) Rl(t)
Foreshocks Inverse Omori law R(t) 1 / t p
with p p
18
Foreshock, mainshocks , aftershocks
LM

X
X
LF
x
X
X
  • same properties F?M and M?A
  • - in time Omori, aftershock duration and p
    exponent indep. of mM
  • - in space rM-rF LF rA-rM LM
  • - in magnitude P(mA) G.R. law indep. of mM
  • NA(mM) 10?m
  • same physical mechanisms for F?M and M?A
  • from nucleation, critical point model, or
    rupture experiments

19
Rate-and-state friction law
  • Friction law Dieterich, 1979 Ruina, 1983
  • ? ?0 A ln (V) B ln(?)
  • d?/dt 1 - ?V/Dc
  • steady state
  • ? const. (A-B) ln (V)
  • stable if AgtB EQs AltB

Dieterich Kilgore, 1996
20
Rate-and-state friction law and EQ triggering
by a static stress change
  • without perturbation V1/(tc-t)
  • (nucleation phase)
  • Initial population of faults with uniform pdf of
    rupture time
  • ?? increases V and moves the fault closer to
    failure
  • Clock change ?tc depends on initial state
  • Increase of seismicity rate and Omori law decay

Dieterich, 1994
?tc
21
Rate-and-state model of seismicity Dieterich
1994
  • Relation between seismicity rate R and (Coulomb)
    stress history
  • and
  • For a static stress change constant tectonic
    loading rate

22
Coseismsic slip, stress change, and aftershocks
Planar fault, uniform stress drop
Slip Shear stress Seismicity rate RS
model
23
Spatial distribution of aftershocks
Map aftershocks Landers, 1992, M7.3 S.
California tlt1yr
Aftershocks within 1 km from the fault plane
24
Spatial distribution of aftershocks
  • Most aftershocks occur on or close to the
    fault plane, where the shear stress change
    decreases on average
  • Shear stress change must be very heterogeneous
    to explain on fault aftershock triggering with
    the rate-and-state model
  • - fault roughness Dieterich, 2005
  • - slip heterogeneity

25
Shear stress heterogeneity due to fault geometry
  • Dieterich, 2005

26
Slip and shear stress heterogeneity
  • Stochastic scale-invariant kinematic slip model
    Herrero and Bernard, 1994
  • Large kgt1/L U(k) 1/k2
  • Large EQ sum of small ones
  • Small klt1/L U(k) const.
  • Random phase
  • Reproduces the 1/f2 power spectrum seismogramms
    (displacement) for fgtfc
  • Shear stress power-spectrum ?(k) 1/k for kgt1/L
  • - infinite standard deviation!
  • - small scale cutoff
  • - or U(k) 1/kn with ngt2

U(k)1/k2
27
Slip and shear stress heterogeneity
  • Modified  k2  slip model U(k) 1/(k1/L)2.3
  • Stress drop ?0 3 MPa

?0
28
Slip and shear stress heterogeneity RS model
  • Synthetic aftershock catalog generated using
    Dieterich 1994 model
  • (without multiple interactions between
    aftershocks)

29
Stress heterogeneity and aftershock decay with
time
  • Aftershock rate from RS model with modified k2
    slip model
  • R(t) ?fault R(t,?) P(?) d?
  • assuming A?n 1 MPa

Stress distribution Gaussian
30
Modified k2 slip model, Off-fault aftershocks
  • On fault
  • - for kgt1/L
  • - slip
  • U(k) 1/k2.3
  • - shear stress change
  • ?(k) 1/k1.3
  • Distance dltL
  • from the fault
  • ?(k) exp(-kd)/k1.3

Distance from the fault d/L
31
Stress heterogeneity and aftershock decay with
time
  • RS model produces Omori law with p1 for an
    exponential pdf P(?)
  • P(?) exp(- ?/?o)
  • R(t) ? R(t,?) P(?) d? 1/tp for tta
    with p 1- A?n/?o

32
Stress heterogeneity and aftershock decay with
time
  • Aftershock rate for P(?) exp(-?/?o)
  • p 1- A?n/?o for t ta
  • p decreases if  heterogeneity 
  • ?o increases

p0.9 Stacked aft sequences in S. California
33
Aftershock decay for a Gaussian stress
distribution
  • stress distribution
  • P(?) exp-(?-?0)2 /2?2
  • aftershock rate close to Omori law
  • with effective exponent
  • p 1- A ?n?0 - A2?n2 log(t/ta) /?2

Omori law with p0.80
34
Inversion of stress changes from aftershock rate
  • Deviations from Omori law with p1 due to
  • stress decrease / increase with time
  • Dieterich, JGR 1994 Nature 2000
  • or heterogeneity of coseismic stress change, due
    to
  • - fault geometry Dieterich, 2005
  • - heterogeneity of coseismic slip
  • hard to distinguish between small scale stress
    heterogeneity and temporal variation
  • We invert for P(?) from aftershocks rate R(t)
  • Solve R(t) ? R(t,?) P(?) d?
  • assuming stress does not change with time
  • problem RS model with instantaneous stress
    change cant explain pgt1

35
Inversion of stress pdf from aftershock rate
Test on synthetic RS catalogs
modified k2 model
slip
Shear stress change
Rate State Dieterich, 1994
Aftershock rate (model)
EQ catalog ti , i1,..,N tminltt lttmax
Aftershock rate (simul)
36
Inversion of stress pdf from aftershock rate
  • Complete distribution P(?)
  • - solution of R(t) ? R(t,?) P(?) d?
  • - fixed ta, Rr, A?n
  • Gaussian P(?)
  • - fixed A?n, Rr
  • - invert for ?, ?0 and ta

37
Inversion of stress pdf from aftershock rate
Synthetic RS catalog - input P(?) N150000 -
inverted P(?), fixed A?n , Rr and ta A?n1
MPa - Gaussian P(?) ?0 3 MPa ?20 MPa
fixed A?n and Rr , invert for ta , ?0 and ?
p0.93
38
Inversion of stress pdf from aftershock rate
Synthetic RS catalog - input P(?) N230 -
inverted P(?), fixed A?n , Rr and ta A?n1 MPa -
Gaussian P(?), fixed A?n and Rr , invert for ta,
?0 and ? ?0 3 MPa ?20 MPa - Gaussian
P(?), fixed A?n , ?0 and Rr , invert for ta and ?
p0.93
39
Inversion of stress pdf from aftershock rate
Synthetic RS catalog - input P(?) N3857 -
inverted P(?) not constrained A?n0.1 MPa -
Gaussian P(?), fixed A?n and Rr , invert for ta,
?0 and ? ?0 3 MPa ?20 MPa - Gaussian
P(?), fixed A?n , ?0 and Rr , invert for ta and ?
Omori p0.993
40
Parkfield 2005 m6 aftershock sequence
  • Fixed
  • A?n 1 MPa
  • ?0 3 Mpa
  • Inverted
  • ? 11 MPa
  • ta 10 yrs
  • Loading rate
  • d?/dt A?n / ta
  • 0.1 MPa/yr
  •  Recurrence time 
  • tr ta ?0/A?n
  • 30 yrs

Data, aftershocks Fit RS model Gaussian P(?) Fit
Omori law p0.88
ta
foreshock
Rr
41
Stacked aftershock sequences, Japan (80, 3ltMlt5,
zlt30)
Data, aftershocks Fit RS model Gaussian P(?) Fit
Omori law p0.89
  • Fixed
  • A?n 1 MPa
  • ?0 3 Mpa
  • Inverted
  • ? 12 MPa
  • ta 1.1 yrs
  • Loading rate
  • d?/dt A?n / ta
  • 0.9 MPa/yr
  • Recurrence time
  • tr ta ?0/A?n
  • 3.4 yrs

foreshocks
ta
Rr
42
Landers, 1992, M7.3, aftershock sequence
  • Fixed
  • A?n 1 MPa
  • ?0 3 Mpa
  • Inverted
  • ? 2350 MPa
  • ta 52 yrs
  • Loading rate
  • d?/dt A?n / ta
  • 0.02 MPa/yr
  •  Recurrence time 
  • tr ta ?0/A?n
  • 156 yrs

Data, aftershocks Fit RS model Gaussian P(?) Fit
Omori law p1.08
foreshocks
ta
Rr
43
Hector Mine 1999 M7.1 aftershock sequence
  • Fixed
  • A?n 1 MPa
  • ?0 3 MPa
  • Inverted
  • ? 438 MPa
  • ta 80 yrs
  • Loading rate
  • d?/dt A?n / ta
  • 0.012 MPa/yr
  •  Recurrence time 
  • tr ta ?0/A?n
  • 240 yrs

Data, aftershocks Fit RS model Gaussian P(?) Fit
Omori law p1.16
ta
foreshocks
Rr
44
Morgan Hill, 1984 M6.2, aftershock sequence
  • Fixed
  • A?n 1 MPa
  • ?0 3 Mpa
  • Inverted
  • ? 6.2 MPa
  • ta 26 yrs
  • Loading rate
  • d?/dt A?n / ta
  • 0.04 MPa/yr
  • Recurrence time
  • tr ta ?0/A?n
  • 78 yrs

data, aftershocks Fit RS model Gaussian P(?) Fit
Omori law p0.68
foreshocks
ta
Rr
45
Inversion of stress - Conclusion
  • Stress drop not constrained if catalog too short
  • We can estimate ? (width of P(?)) for a
    limited catalog if plt1
  • And if we know A?n
  • - A?n 1 MPa ? A0.01 (Lab experiments,
    Dieterich and Kilgore 1996)
  • ?n100 MPa (lithostatic pressure at
    5km)
  • - A?n 0.1 MPa ? (relation between ta and
    recurrence time Dieterich, 1994)
  • Effect of secondary aftershocks?
  • - increase ref EQ rate Rr Ziv and Rubin, 2003,
    but does not change p or ? ?
  • Heterogeneity of A?n? (does not change R(t) if
    A?n less heterogeneous than ??)
  • Post-seismic stress relaxation?
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