1. interseismic deformation with aseismic stress-dependent fault slip Eric A Hetland, Mark Simons, Ravi Kanda, Sue Owen TO brown-bag – 03 April 2007 a very informal, and preliminary talk about how we are thinking about

2. Hsu et al., 2006 post-seismic slip following subduction ruptures: fault rheology is not (explicitly) included in after-slip model 2005 Nias-Simeulue eq. (M8.7)

3. Pritchard & Simons, 2006 post-seismic slip following subduction ruptures: fault rheology is not (explicitly) included in after-slip model 1995 Antofagasta eq. (M8.1)

4. post-seismic slip following subduction ruptures: fault rheology is not included in after-slip model 2003 Tokachi-oki eq. (M8) Baba et al., 2003

5. inter-seismic slip near regions of past subduction ruptures: Suwa et al., 2006 model assumes fault slip during inter-seismic period is constant Japan/southern Kurile trenches

6. we want an internally consistent model that can describe observations of both inter-seismic and post-seismic deformation… for now we are building subduction zone models that include repeated ruptures, on assumed asperities, with stress-dependent aseismic slip on the non-asperity portions of the subduction interface during the interseismic period… Baba et al., 2003 Suwa et al., 2006

7. L elastic half-space long-term fault-slip  U  ’ cuts 1/2-space with fault loading: traction on the fault finite fault plane in 1/2- space slip on the fault (Burgers vector) includes the off-fault rheology

8. with fault loading:  =0 e.g.; Rice, 1993; Liu and Rice, 2005. Note: no seismic radiation damping (e.g., Rice, 1993) - there are no seismic waves & no problems with unbounded slip velocities in our models…

9. “back-slip” introduced by J. Savage (Savage and Burford, 1973; Savage and Prescott, 1978; Savage, 1983) as a mathematically convenient fault loading mechanism in kinematic & quasi-kinematic models + = Savage & Burford, 1973; Savage & Prescott, 1978 Suwa et al., 2006 red = lots of BS white = no BS approximation only good for spun-up systems: rate of interseismic relaxation = rate of reloading

10. traction on fault part of fault that is allowed to slip interseismically part of fault with coseismic slip part of fault that slips steadily interseismic slip on fault imposed ruptures at times T p long-term fault-slip we impose ruptures - we do not solve for them:  locked   - ’’ -

11. traction on fault interseismic slip on fault imposed ruptures at times T p part of fault that is allowed to slip interseismically part of fault with coseismic slip part of fault that slips steadily long-term fault-slip we impose ruptures - we do not solve for them: non-linear viscous (Montesi, 2004) RS-friction (e.g. Marone et al., 1991) linear viscous need a fault rheology:

12. Dieterich, 1979; Ruina 1983; Rice and Gu, 1983 (figure from Ben-Zion, 2003) rate- and state-friction (a-b) 0  “aseismic slip”  is a state variable, assume it is constant   = L/v  =   N

17. Ben-Zion, 2003 Lapusta et al., 2000

18. we impose ruptures - we only solve for aseismic slip: fault rheology: bulk rheology: given by for now, assume elastic half- space and use Okada, 1992 model works for 3D, non-planar faults, with multiple asperities, arbitrary rheologic parameters, we allow both dip- and strike-slip co- and inter-seismic slip, and irregular (imposed) rupture sequences currently, we can impose coseismic slip in non- locked regions of the fault, but we do not allow interseismic slip in the locked regions… use boundary elements…

19.  = 30 GPa  ’ N = 300 MPa D = 10 4 m b o = 10 m  (a-b) = -1 /10 -1 = 0.5  (a-b) = 0.05 -1 = 1.0  (a-b) = 0.10

20. 10D D/2 D locked section steady slip at depth “thrust fault” in an elastic half-space, dipping 45 degrees modification of ubiquitous subduction back-slip model, by allowing interseismic slip here

21. 10D D/2 D locked section steady slip at depth “thrust fault” in an elastic half-space, dipping 45 degrees interseismic surface deformation is given by the locked portions of the mega-thrust sliding as a normal fault at the plate rate (Savage, 1983) a more realistic geometry vertical horizontal back-slip model

22. 10D D/2 D locked section steady slip at depth “thrust fault” in an elastic half-space, dipping 45 degrees does not include strains due to plate bending, if incorporated, discrepancy removed, total interseismic + coseismic = subduction block motion… a more realistic geometry Ravi Kanda vertical horizontal elastic slab model

23. “thrust fault” in an elastic half-space, dipping 45 degrees 10D D/2 D locked section steady slip at depth in a spun-up model, total interseismic slip fills in the the areas above the co-seismic slip-profile periodically impose this co-seismic slip

24. slip on the fault: below the locked region b>0  thrust slip

25. surface interseismic displacements: xxxxxx oo

26. surface interseismic displacements: xxxxxx o oo

27. surface interseismic displacements motivation: 2003 Tokachi-oki eq. (M8) Baba et al., 2003 x data from Sue Owen slight curvature tectonic?

28. surface interseismic displacements motivation: 2003 Tokachi-oki eq. (M8) Baba et al., 2003 x data from Sue Owen

29. determination of plate coupling: Suwa et al., 2006 shown is back-slip rate v bs invert GPS velocities for distributions of normal slip (v bs ) on the mega-thrust use back-slip model (Savage, 1983) to determine the “coupling coefficient” v bs = v T  coupled (C=1) v bs = 0  uncoupled (C=0) this assumes that the interseismic deformation is constant throughout the interseismic period

30. 10D D/2 D locked section steady slip at depth invert GPS velocities for distributions of normal slip (v bs ) on the mega-thrust use back-slip model (Savage, 1983) to determine the “coupling coefficient” v bs = v T  coupled (C=1) v bs = 0  uncoupled (C=0) slip is not constant through the cycle determination of plate coupling: this assumes that the interseismic deformation is constant throughout the interseismic period

31. variation of coupling through an interseismic period xxxxxx xxx

32. variation of coupling through an interseismic period xxxxxx

33. variation of coupling through an interseismic period xxxxxx

34. Lapusta et al., 2000 this model only contains co-seismic slip in the locked regions, no interseismic slip-allowed in the locked regions… contrary to dynamic calculations…

35. two (of the many) remaining issues: still learning to drive… “lockedness” – we assume full slip in locked patches (asperities) some directions currently aiming for: include heterogeneous elastic structure by computing K(z;  ) from FE models… include other bulk rheologies – K(z;  ): “simple” semi-analytic models & quite complicated FE models… model the GPS data of inter- & post-seismic observations in Hokkaido (2D, 3D planar, respecting slab geometry, & …)

36. gOcad 1968 1973 2003 slip models from Yamanaka and Kikuchi (2002) vertically exaggerated