IV. The seismic cycle IV. 1 Conceptual and kinematic models IV.2 Comparison with observations IV.3 Interseismic strain IV.4 Postseismic deformation IV.5 Dynamic models

Source Model of Nias Earthquake Source duration: 100s, Rupture velocity: km/s; Rise time: 15 sec (Konca et al, 2007)

Postseismic deformation over 11 months

(Hsu et al, 2006) - Afterslip occurred both updip and downdip of the ruptured area. - The geodetic moment accrued by 30% in the first few months following the mainshock.

V o interseismic slip rate on the megathrust, 4 cm/yr t r the relaxation time, ~ 8 year d the coseismic jump ~ 900 (Hsu et al, 2006) The observed time evolution is consistent with frictional afterslip modeled form a velocity strengthening friction law (Perfettini and Avouac, 2004)

Time evolution of postseismic slip -The spatial distribution of afterslip is approximately stationary. - Slip increases in proportion to the logarithm of time ~ (Hsu et al, 2006)

1995 Antofagasta earthquake, N. Chile (M w = 8.0) Displacements (dominated by co-seismic) Velocities (2 years after earthquake) Data from Klotz et al. (1999) and Khazaradze and Klotz (2003) (From Kelin Wang, SEIZE meeting, 2008)

Alaska: ~ 40 years after a great earthquake M = 9.2, 1964 Freymueller et al. (2008) The plate interface has partially or completely relocked in the rupture area. Some stations on land still move seaward!

GPS data: Green: Klotz et al. (2001) Red: Wang et al. (2007) Chile: ~ 40 years after a great earthquake M = 9.5, 1960 (From Kelin Wang, SEIZE meeting, 2008; Wang, 2007)

Cascadia: ~ 300 years after a great earthquake Wells and Simpson (2001) (From Kelin Wang, SEIZE meeting, 2008; Wang, 2007)

Rupture Stress relaxation Stress relaxation Afterslip Locking Afterslip and transient slow slip: short-lived, fault friction Stress relaxation: long-lived, mantle rheology (From Kelin Wang, SEIZE meeting, 2008; Wang, 2007)

Inter-seismic (Cascadia) Post-seismic 2 (Alaska, Chile) Co-seismic Coast line Post-seismic1 (Sumatra)

References Hsu, Y. J., M. Simons, J. P. Avouac, J. Galetzka, K. Sieh, M. Chlieh, D. Natawidjaja, L. Prawirodirdjo, and Y. Bock (2006), Frictional afterslip following the 2005 Nias-Simeulue earthquake, Sumatra, Science, 312(5782), Wang, K, Elastic and Viscoelastic Models of Crustal Deformation in Subduction Earthquake Cycles, In The Seismogenic Zone of Subduction Thrust Faults, edited by T. Dixon and J. C. Moore, Columbia University Press, 2007.

IV. The seismic cycle IV. 1 Conceptual and kinematic models IV.2 Comparison with EQ observations IV.3 Learning from interseismic strain IV.4 Dynamic models

Kinematic model : the model is parametrised in term of the slip history on the fault (earthquakes, interseismic defornation, postseismic deformation….) Dynamic model: Deformation, including slip history on faults is deduced from the rheology and boundary conditions.

Is this model consistent with our understanding of the mechanics of crustal deformation? What is the reason for transition to the Locked Fault one to the Creeping zone?

Crustal Rheology (Kohlstedt et al., 1995) ‘brittle’ ‘ductile’

(Mackwell et al., 1998) In all plots solid lines are linear least squares fit to the data. Dotted lines represent fit to data of the flow-law at the bottom of each plot

Static Friction is generally of the order of 0.6 for most rock types (Byerlee, 1978) The shear stress at frictional yield depends linearly on normal stress

-unstable slip is possible if the decrease of friction is more rapid than elastic unloading during slip (‘slip weakening’) - The fault needs to restrength with time afetr slip event (‘healing’). Condition for ‘stick-slip’ sliding Stick-slip motion requires weakening during seismic sliding, hence static friction > dynamic friction (Scholz, 1990)

(Marone, 1998) DcDc Dynamic friction decreases with slip rate Static friction depends on hold time

Previous figure (a) Measurements of the relative variation in static friction with hold time for initially bare rock surfaces (solid symbols) and granular fault gouge (open symbols). The data have been offset to  s = 0.6 at 1 s and thus represent relative changes in static friction. (b) Friction data versus displacement, showing measurements of static friction and s in slide-hold-slide experiments. Hold times are given below. In this case the loading velocity before and after holding Vs/r was 3 m/s (data from Marone 1998). (c) The relative dynamic coefficient of friction is shown versus slip velocity for initially bare rock surfaces (solid symbols) and granular fault gouge (open symbols). The data have been offset to d = 0.6 at 1 m/s. (d) Data showing the transient and steady-state effect on friction of a change in loading velocity for a 3-mm-thick layer of quartz gouge sheared under nominally dry conditions at 25-MPa normal stress (data from J Johnson & C Marone). (Marone, 1998)

Rate-and-State Friction  =  * (T)+a ln(V/V * )+b ln(  * ) d  /dt=1-V  /D c (Dieterich 1981; Ruina 1983) (Scholz, 1990) Generally a and b are of the order of ~ (e.g., Blanpied et al, 1998; Marone, 1998)

Rate-and-State Friction  =  * (T)+a ln(V/V * )+b ln(  * ) d  /dt=1-V  /D c (Dieterich 1981; Ruina 1983) (Scholz, 1990) At steady state:  ss = D c /V   ss  * +(a-b) ln(V/V * )

Effect of temperature and normal stress on friction A, Dependence of (a - b) on temperature for granite. B, Dependence of (a - b) on pressure for granulated granite. This effect, due to lithification, should be augmented with temperature. Laboratory experiments show that stable frictional sliding is promoted at temperatures higher than about 300°C, and possibly at low temperatures.

Rate strengthening (a-b>0) : – quartzo-feldspathic rocks :T 300C –poorly cohesive fault-gouge –Some clays at low temperature (T<100C), –serpentine (T<400C). (Marone, 1998)

Condition for ‘stick-slip’ Stick-slip motion requires weakening during seismic sliding, hence static friction > dynamic friction - unstable slip is possible if the decrease of friction is more rapid than elastic unloading during slip (‘slip weakening’)

Condition for ‘stick-slip’ At steady state: The system is rate-strengthening if a-b>0, only stable sliding is permitted The system is rate-weakening if a-b<0,  ss  * +(a-b) ln(V/V * )  F/  u>K, i.e. (  s -  d ) σ n /D c >K - stick-slip slip is possible if the decrease of friction is more rapid than elastic unloading during slip: - The system undergoes stable frictional sliding (conditional stability) if (Rice and Ruina 1983; Sholz, 1990)  F/  u<K, i.e. (  s -  d ) σ n /D c <K

 ss=  * +(a-b) ln(V/V * ) a-b > 0 stable sliding a-b < 0 slip is potentially unstable Correspond to T~300 °C For Quartzo- Feldspathic rocks Stationary State Frictional Sliding (Blanpied et al, 1991) (Rice and Ruina 1983) a-b

T inter = 96.2 ans Seismic Cycle Modeling (Perfettini et al, 2003) Slip as a function of depth. Each line represents the slip distribution at a given time. Every 5 yr in the interseismic period. For velocity change of 10% durin dynamic rupture. Maximum sliding velocity on the fault as a function of time.

Slip as a function of depth over the seismic cycle of a strike–slip fault, using a frictional model containing a transition from unstable to stable friction at 11 km depth (Tse and Rice, 1981; Shloz, 1992)

Aseismic stable frictional becomes dominant for temperatures above ~ 300°C-400°C. This is consistent with laboratory experiments which show that stable frictional sliding (a-b>0) is promoted at temperatures higher than about 300°C for Quartzo-felspathic rocks. Fluids may play a role too (cf MT results). From Blanpied et al, (1991) (Avouac, 2003)

Frictional sliding (rate-and-state friction)  =  * +a ln(V/V * )+b ln(  * ) d  /dt=1-V  /D c Ductile Flow dε/dt = A f H 2 O m σ n ℮ -Q/RT Constitutive laws used to model crustal deformation and the seismic cycle

FEM code: ADELI (Hassani, Jongmans and Chery 1997) Rheology: Brittle failure (Drucker-Prager criterion) Non linear, temperature dependent creep law Surface processes: Linear diffusion + flat deposition in the foreland Boundary conditions: Hydrostatic fundation, 20 mm/yr horizontal shortening (Cattin and Avouac, JGR, 2000)

Mechanical model - FEM ADELI (Hassani, Jongmans and Chery 1997) - Rheology: Coulomb brittle failure + Non linear creep law depending on local temperature. - Surface processes: linear diffusion and flat deposition in the foreland - Boundary conditions: Hydrostatic fundation, 18mm/yr horizontal shortening

(Cattin and Avouac, JGR, 2000) Due to the thermally activated flow law the model predicts a localized ductile shear zone that coincides with the creeping zone of the MHT.

21 +/-1.5 mm/yr The effective friction on the MHT needs to be low (<0.1)

Provided that effective friction on MHT is low (<0.1), the model reconciles geodetic and holocene deformation Seismicity falls in the zone of enhanced Coulomb stress in the interseismic period Modeling Interseismic Deformation (Cattin and Avouac, 2000)

Modeling postseismic Deformation

Viscoelastic stress relaxation model for Chile, viscosity 2.5  Pa s (c) (Hu et al, 2004)

(hu et Earthquake followed by locking (Hu et al, 2004)

Different along-strike rupture lengths and slip magnitudes (surface velocities 35 years after an earthquake; mantle viscosity 2.5 x Pa s) (Hu et al, 2004)

A simple Fault Model Locked Fault Zone Brittle Creeping Fault Zone: Ductile Shear Zone

Frictional sliding Ductile Shear F: Driving Force (assumed constant) F fr : Frictional resistance F  : Viscous resistance to A simplified springs and sliders model F F = F fr + F  F < F fr No slip F > F fr Stick-slip a-b<0 (Perfettini and Avouac, 2004b) a-b>0

Stress transfer during the seismic cycle F : Driving Force (assumed constant)  F fr : Co-seismic drop of frictional resistance F  : Viscous resistance F  >>  F fr F    F fr (Perfettini and Avouac, 2004b) Two characteristic times are governing the temporal evolution of deformation - Brittle creep relaxation time tr - Maxell time T M

(Perfettini et al, 2005) Interseismic displacement at AREQ relative to stable South America is landward. The persistent seaward motion of AREQ after the earthquake is due to postseismic relaxation. The modeling suggest that may be interseismic is never really stationary Displacement at AREQ relative to stable South America before and after the Mw 8.1, 2001, Arequipa earthquake.

References Cohen, S. C. (1999), Numerical models of crustal deformation in seismic zones, Adv. Geophys., 41, Wang, K, Elastic and Viscoelastic Models of Crustal Deformation in Subduction Earthquake Cycles, In The Seismogenic Zone of Subduction Thrust Faults, edited by T. Dixon and J. C. Moore, Columbia University Press, Cattin, R., and J. P. Avouac (2000), Modeling mountain building and the seismic cycle in the Himalaya of Nepal, Journal of Geophysical Research-Solid Earth, 105(B6), Wang, K. L., J. H. He, H. Dragert, and T. S. James (2001), Three-dimensional viscoelastic interseismic deformation model for the Cascadia subduction zone, Earth Planets and Space, 53(4), Hu, Y., K. Wang, J. He, J. Klotz, and G. Khazaradze (2004), Three-dimensional viscoelastic finite element model for postseismic deformation of the great 1960 Chile earthquake, Journal of Geophysical Research-Solid Earth, 109(B12). Perfettini, H., and J. P. Avouac (2004), Stress transfer and strain rate variations during the seismic cycle, Journal of Geophysical Research-Solid Earth, 109(B6).