Interaction and loading of non-repeating multiplets.

Pascal Bernard Maxime Godano Pierre Dublanchet Clara Duverger IPGP

seismicity

Cross-trigger

creep pore pressure

REPEATERS Nadeau et al 1995 Nadeau & Johson 1998

REPEATERS: repeated rupture of the same mechanical asperity creep Creep  slip, stress drop, length Slip, stress drop, length  creep Parkfield: Location uncertainty: 5-10 m Covariance Tr Covariance Mo Cumulative Mo Nadeau & Johson 1998

Repeat time (Tr ) can vary: detection of transient creep Aftershocks of the 1989 Loma Prieta earthquake, Schaff et al., 1998 1/Tr ~ dN/dt repeater rate Repeater rate ~ 1/t = Omori law Creep velocity ~ 1/t , slow slip transient log(t) Typical response to coseismic stress step For a velocity strengtening fault surface

Can we quantify creep from repeaters, and check this creep with independent measurements?

Soultz –geothermal field – 1993 experiment

water injection: 0 to 100 bars, 17 days

multiplet

Slip =4 cm When? Why?

Acceleration spectra of multiplet Large Source overlap of multiplet: repeater Accurate relocation and precise estimate of source radius from corner frequency Bourouis and Bernard, 2006

Soultz - 1996

cumulative slip (cm) 4 0 2800 time 16 days

Repeaters

3400 0 depth (m)

Aseismic : M=3.5

Bourouis and Bernard, 2006

Soultz - 1996 creep creep

Cumulative slip

creeping faults with decelerating slip: Velocity weakening

Log(t) 1/t

Seismicity rate Omori law

Bourouis and Bernard, 2006

t t

-

Slow Pore pressure diffusion

v=100 m/day -

Fast propagation of creep front

v = 1 – 10 m /minute -

Slow Creep relaxation, triggering sesmic repeaters

-

seismic moment of slow slip : M=3.5 >> seismic moment of earthquake ruptures

t Loading of seismic asperities: Creep,… t or pore pressure P ?

asperity s t

P

t Coulomb failure stress Loading with shear stress s eff

=

s

-P

Loading with pore pressure s eff

=

s

-P

Loading with shear stress + pore pressure s eff

=

s

-P

Isolated asperities – assume creep around…: Slip of the asperity necessarely catches up creep around it allows to quantify slow transient or steady slip on creeping faults But: Not so simple!…

Parkfield repeaters Nadeau & Johnson 1998 Repeat time Mo 1/6 Simple repeater model with constant stress drop T ~ Mo 1/3 Coseismic slip D u = C ( Ds /m) R Coseismic Seismic moment Mo = m D u S = C p Ds hence : D u ~ 1 /m Ds 2/3 Mo 1/3 Repeat time Tr = D u/vl , R 3 vl = seismic loading velocity = average seismic slip rate Hence, prediction for constant Ds and vl: Tr ~Mo 1/3 Observation: Tr ~ Mo 1/6 creep

Coseismic slip Mo = m D u S = C D u = C ( Ds /m) R p Ds R 3 and D u = C ( Ds /m) R hence : D u ~ 1 /m Ds 2/3 Mo 1/3 Repeat time Tr = D u/vl , hence Ds 2/3 Mo 1/3 1/vl ~ Mo 1/6

Assume vl = constant (independent of scale)

This implies Ds

~ Mo -1/4 vl

3/2 i.e., small magnitude have very large stress drops (small dimension) Assume average slip rate given by geodesy: 2.3 cm/yr, Nadeau & Johnson 1998 Mo -1/4 Very high stress drop, small sizes and large slip for small Mo

- Highly controversial: very large stress drop! nonetheless, the N&J1998 relationship: log(d) = 0.17 log(Mo) - 2.36 was used (mostly in Japan) to quantify creep on the subduction interplate (Igarashi 2003 , Uchida 2009, Igarashi 2010, Uchida & Matsizawa 2011…)

Igarashi 2003 M>3 ,L=0.2-1.5 km 1-4 Hz, C>0.95 at 2 st.

Large slip rates

Preseismic slip from repeaters in Japan Uchida et al.2004

Preseismic 10 days 1989, M=7.1

Repeaters M>2.5 2211 in 561 sequences Postseismic 100 days - Evidence for a nucleation phase - Uncertain quantification of slip

Can we trust the quantitative estimates of creep?

How strongly is it model-dependent?

Observation: Tr ~ Mo 1/6 Prediction for constant Ds and vl: Tr ~Mo 1/3 Ds 2/3 Mo 1/3 1/vl ~ Mo 1/6

MODEL WITH CONSTANT LOADING VELOCITY

vl = constant implies Ds ~ Mo -1/4 vl 3/2 (Nadeau&Johnson, 1998) i.e.,

small magnitudes have very large stress drops

(small dimension)

MODEL WITH CONSTANT STRESS DROP

Ds = constant implies : vl ~ Mo 1/6 and

vl ~ R 1/2

Which means that

small magnitudes have smaller loading rates

-

partial aseismic slip

of small seismic asperities (Beeler, 2001; Chen & Lapusta, 2009) -

clamping

from neighboring locked areas (Sammis and Rice, 2001)

Sammis & Rice, 2001 on the border of a locked area Weak asperity with radius a At distance a , stressing rate ~ a 1/2 Local creep rate ~ a 1/2

R=83 m produces slip rate=1 cm/s smallest patch « seismically » active Cumulative slip

postseismic coseismic preseismic

R = 124 m x R = 150 m R = 350 m Chen & Lapusta, 2003

Constant stress drop Mo seismic/Mo total

Universal slope, position depending on : - local loading rate - characteristic slip L of R&S friction law Chen et al. 2007

Lengliné et al. 2009 Dublanchet et al., 2013 Repeaters in Parkfield Assumption: Ds =3 MPa Source radius R from Mo = 16/7p Ds R 3 Repeaters in Parkfield: may be not so much isolated on a creeping fault requires independent evaluation of source source size

In Japan: a M=4.8 repeater and its neighbouring multiplets Uchida et al., 2007 P& S Spectral ratio between 2 events eliminates propagation effects Average over stations, find fc1 and fc2 fc~0.3v/r (Sato and Hiroswa 1973)

Seismicity of the western rift of Corinth, Greece

Rigo et al. 1996; Avallone et al. 2004 - low angle dip of microseismicity - NS localized gradient of strain rate from GPS

normal faults rooting on a major detachment

1.5 cm/yr

LOCKED

detachment

CREEPING

Bernard et al. , 2007

Creeping zone: numerous multiplets identified – any repeaters?

Relocation with double-difference (HYPO-DD) Lambotte et al. , 2013

Seismic layer:

-Thick layer, irregular geometry, complex internal structure with inbedded smaller faults

Hence, the seismic « layer » is unlikely to be a mature detachment Would the multiplet seismicity inform us on the style and amount of creep?

Western rift of Corinth, 2004 seismic swarm :

Migrating along faults

Normal fault Weak layer Godano et al., 2013 Fasouleika fault: green Aigion fault :black

2004 swarm -

Global picture: diffusion 10 km, 200 days : 50m /day + internal diffusion velocity within multiplets

Normal fault Weak layer Migration of pore pressure pulse?

D=0.022 m 2 /s D=0.4 m 2 /s R=(4 p D t) 1/2 30 days Variability of diffusivity D within multiplets Normal fault 1.6 days Duverger, 2014 Weak layer Diffusivity increases with length/width of the multiplet Pore pressure pulse migrating in the permeable zone at the intersection of the faults and the weak layer

Duverger, 2014 Aigion f.

Fasouleika f.

In the seismic « layer » the diffusivities decrease outwards More damaged/more permeable rock in the core of the layer Diffusivity (m/s2) Not determined 0.1

1 0.01

0.001

Latorre, 2004; Gautier et al. 2006 5 km Weak, brittle layer Z

Diversity of Internal space-time structure of the multiplets Source size estimate from corner frequencies Duverger, 2014 - diversity of spatial clustering / source area overlap - a few repeaters -large uncertainties in source size

Distribution of interevent time T : caracterizes clustering Hainzl, 2006 Gamma distribution To = average interevent time g = 0.3

Strong mechanical interactions between ruptures at short times Mix between transient forcing of the system and cascade (cross tirgger) effect Duverger et al., 2014

2004 seismic swarm : multiscale process

-Diffusion of seismicity – 10 km main fault + weak, permeable layer - diffusion within small faults, 1 km (multiplets) - strong seismic Interaction at short time/short distances (100 m) - only a few repeaters (colocated)

forcing by pore pressure transient + cross-triggering

Normal fault Godano et al., 2014 Fasouleika fault: green Aigion fault :black

Analysis of a persistent multiplet: response to a steady creep? Godano et al. 2014 1995 rupture 1995 rupture

2000-2007 One or a few repeaters?

Overlapping source areas?

What is forcing the multiplet?

What is around the multiplet?

HypoDD relocation: +- 10m

requires an accurate determination of source size

~Mo Adjust a spectral source model w -square: Mo, corner frequancy fc + attenuation (Q, d ,..) + site effect - estimate fc - infer: source duration source dimension Site effect fc Attenuation

Displacement source spectrum g

=2 gives an

w

-square model

Brune 1971 : n=1, Boatwright 1976: n=2 (sharper fc, better fit ; Abercrombie 1995) Use the source spectral ratio ratio f1 f2

spectral ratio

: estimate likelihood of fc1 and fc2 10:03 Spectral ratio 23:18 23:18/10:03 10:03 noise level 23:18 noise level fc1 Marginal pdf S spectra fc2

Earthquakes a and b 1 ratio gives 2 corner frequencies (for a specific station) fa fb Marginal Pdf for all EQ pairs including a (or b) Product of pdf: find maximum a posteriori variance from maxima distribution Result: pdf of

corner frequencies

for each earthquake and each station

corner frequency and directivity Expanding crack model With late stopping phases Madariaga 1976 t D u R q azimut Brune 1971 n Average: f c (S)=0.21 b /r (for vr/ b =0.9) for unidirectional rupture fc ~ C d /T with Cd= 1/(1-cos (q) vr/c) T source duration

Corner frequencies versus dip and azimuth angles Modeling with an expanding circular crack (Madariaga 1976) fc(P)/fc(S)=1 Excludes an expanding circular crack at high rupture velocity ( fcP/fcS=1.5) q n

For a unilateral rupture : f c =1/(1-cos (q) vr/c) .1/T q depends on azimut and distance of station Hence f c depends on azimuth of station q N Fit to azimuth N215 °, hence updip rupture; vr ~ 0.5 vs

corner frequency and directivity Expanding crack model With late stopping phases Madariaga 1976 C d =1/(1-cos (q) vr/c) k-square slip model, with narrow slip pulse Ruiz et al , 2011 f c ~ C d /T Brune 1971 f c (S)=0.21 b /r azimut Acceleration spectrum Cd 2 Cd 1 f

For one EQ, likelyhood estimate: pdf of corner frequency seismic moment * choose a simple source rupture mode: unilateral, bilateral * choose a rupture velocity : ~0.3- 0.7 vs Provides a pdf of source radii, stress drops, and coseismic slip

Unilateral vr=0.5 .vs

Random sampling: vr=(0.5+-0.2) vs Uni & bilateral; Mo+-uncertainty % overlap depends on vr and fc(T) Slip is maximum near the center can we say something about the creep on the fault around?

3 D elastic modeling:with Rate and State friction on a planar fault Heterogeneous distribution of (a-b), accounting for dynamic radiation Dublanchet et al. 2013, 2014 Velocity weakening, circular asperities, with same (a-b)<0 Velocity strengthening around them (a-b>0) Velocity weakening, square asperities, with heterogeneous (a-b)<0 No space between asperities

Interacting Mechanical asperities (R&S): threshold for system stability Critical density of asperities, function of (a-b) Delayed interaction Effective Friction parameters Dublanchet, 2013 Dynamic rupture Stability threshold depends on:

asperity density

and

strength of inter-asperity

« barriers » Dublanchet et al., 2013

Creep around asperity cluster locked around asperity cluster

Dublanchet et al. 2013 Average cumulative slip in Corinth multiplet

Inferring the loading process of planar multiplets

Observation:

Cumulative coseismic slip

creeping 2 end-models locked

x

Corinth swarm

Probability > 80%

= Locked around the cluster

Dublanchet et al., 2014

Faulting context of the Corinth multplet 866

Take advantage of highly correlated waveforms of multiplets for: -

accurate relative location

with double difference techniques using correlations -- stable spectral ratios allowing

better estimate of corner frequencies fc

-- need of statistical (bayesian, pdf) approach for estimating

fc and source size

(play with realistic kinematic/dynamic models, infer directivity) -- loading mechanisms:

creep, yes, …………………but also pore pressure!

-- evidence for

multi-scale space-time dynamics

- analyze the collective behaviour of multiplets (

diffusion, cumulative slip

distribution, ..) - distinguish between creep and pore pressure loading - knowing the loading process,

infer the time dependent hazard

fault(s): cross triggering, nucleation phase, … on the surrounding --

direct measurement of strain

: GPS, tiltmeters, strainmeters…