1. Elizabeth H. Hearn, UBC, Vancouver, CANADA in collaboration with Semih Ergintav, Marmara Research Centre, Gebze, TURKEY Robert Reilinger, MIT, Cambridge MA, USA Simon McClusky, MIT, Cambridge MA, USA Roland Bürgmann, UC Berkeley, Berkeley CA, USA Elizabeth H. Hearn, UBC, Vancouver, CANADA in collaboration with Semih Ergintav, Marmara Research Centre, Gebze, TURKEY Robert Reilinger, MIT, Cambridge MA, USA Simon McClusky, MIT, Cambridge MA, USA Roland Bürgmann, UC Berkeley, Berkeley CA, USA Numerical models of the North Anatolian Fault Zone in Turkey University of Southern California - March 5, 2007

2. The North Anatolian Fault Zone in Turkey: Continental transform plate boundary 1999

3. Slip rates are averaged over many earthquake cycles. They match predictions of plate motion models. Regional Tectonics and the North Anatolian Fault Zone Reilinger et al., 2006

4. ‘rigid’ down to asthenosphere with localized shear zones? creeping below mid-crust? How does the aseismic relative motion of plates occur? Are plates thick or thin? e.g., Jimenez-Munt and Sabadini, 2002 e.g., Provost et al. 2003 block figure courtesy Michael Rymer

5. This slip rate does not necessarily match the geologic slip rate. Deformation around faults may vary between earthquakes. This slip rate does not necessarily match the geologic slip rate. Deformation around faults may vary between earthquakes. coseismic // postseismic “interseismic” Snapshots: GPS slip rates Within an individual earthquake cycle Deformation around a plate boundary varies between earthquakes

6. Vauchez et al., 1998...or a hybrid?

7. Today: What do models of postseismic and interseismic deformation tell us about the NAFZ plate boundary? Postseismic deformation: perturbation to GPS velocities caused by the 1999 Mw = 7.5 and 7.2 Izmit and Düzce earthquakes Interseismic deformation: GPS velocities around central NAFZ segments that last failed from 1700’s to the early 1940’s coseismic // postseismic interseismic Snapshots: GPS

8. Today: What do models of postseismic and interseismic deformation tell us about the NAFZ plate boundary? Postseismic deformation: perturbation to GPS velocities caused by the 1999 Mw = 7.5 and 7.2 Izmit and Düzce earthquakes Interseismic deformation: GPS velocities around central NAFZ segments that last failed from 1700’s to the early 1940’s Simple models can explain each, but not both!

9. episodic earthquakes elastic upper crust transient lower crust? transient upper mantle transient upper mantle (mantle asthenosphere) LC UM RS friction or (at greater depths) viscous shear zone RS friction or (at greater depths) viscous shear zone Today: What do models of postseismic and interseismic deformation tell us about the NAFZ plate boundary?

10. Postseismic deformation modeling approach GPS site epicentre modeled ruptures 1000 x 1000 x 300 km Free surface, fixed sides and base Free surface, fixed sides and base 3D viscoelastic finite-element model Izmit and Düzce earthquake slip are imposed Izmit and Düzce earthquake slip are imposed Model calculates stresses and velocities at requested time intervals

11. Postseismic deformation modeling approach GPS site epicentre modeled ruptures We are less sure about rheology of aseismically deforming material (i.e. viscosity) and its distribution: vary these parameters We are less sure about rheology of aseismically deforming material (i.e. viscosity) and its distribution: vary these parameters We think we know elastic structure, coseismic slip

12. WRSS at a particular time is WRSS* Find parameters that minimize misfit of modeled GPS site velocities to observations Find parameters that minimize misfit of modeled GPS site velocities to observations

13. viscoelastic relaxation: lower crust (Newtonian) afterslip: viscous creep along shear zone (Newtonian) Izmit postseismic deformation prior to the Düzce earthquake: three hypotheses afterslip: velocity-strengthening friction (earlier study: Hearn et al., 2002)      

14. viscoelastic relaxation: lower crust (Newtonian) afterslip: viscous creep along shear zone (Newtonian) Izmit postseismic deformation prior to the Düzce earthquake: three hypotheses afterslip: velocity-strengthening friction (earlier study: Hearn et al., 2002)

15. viscoelastic relaxation: lower crust (Newtonian) afterslip: viscous creep along shear zone (Newtonian) x x x x afterslip: velocity-strengthening friction strong lower crust and upper mantle strong lower crust and upper mantle Izmit postseismic deformation prior to the Düzce earthquake (earlier study: Hearn et al., 2002)

16. Velocity-strengthening friction primer equation applies after some small threshold slip distance (a-b) = velocity-strengthening parameter this leads to stable sliding along the fault instead of earthquakes, and accelerated postseismic slip this leads to stable sliding along the fault instead of earthquakes, and accelerated postseismic slip at some depths (~0 to 2 and 10+ km), the friction coefficient increases with sliding velocity V

17. 34 mm/yr (model) vs. 28 mm/yr (GPS and 1000-yr paleoseismic; Titus et al. 2006) vs. 28 mm/yr (GPS and 1000-yr paleoseismic; Titus et al. 2006) increasing t/T Creeping sections of NAFZ and SAFZ may also be explained with velocity-strengthening friction

18. From C. Scholz, 2005 Depth distribution and rate of NAFZ fault slip varies between earthquakes

19. Which parameters worked best? A-B = about 0.5 MPa in mid-crust: small A-B = about 0.5 MPa in mid-crust: small Small A-B is consistent with: deep Izmit earthquake rupture high pore pressures Small A-B is consistent with: deep Izmit earthquake rupture high pore pressures

20. What about the later postseismic deformation?

21. New GPS postseismic data* 7 years of postseismic GPS site velocity data 50+ GPS sites with at least 6 occupations during that time Displacements are fit to functions of time, so velocities may be calculated at any time Can this rich dataset be fit with afterslip alone? *Ergintav et al., 2007, to be submitted this summer

22. No! Afterslip is insufficient to explain the GPS site velocities after 3 months Total modeled afterslip after a year Distance along fault (km) Depth (km) slip (m) 0 0 1.2 M = 1.07 x 10 Nm M = 1.07 x 10 Nm 20 o o Not enough! About twice this slip would be required. But all coseismic shear stress on the fault has been spent. Not enough! About twice this slip would be required. But all coseismic shear stress on the fault has been spent.

23. Afterslip model : GPS velocities too slow at some sites, especially after several months ULUT Data FE Model east (mm/yr) north (mm/yr) time post-Izmit (days) ULUT - zoomed Data FE Model Kinematic inversion east (mm/yr) north (mm/yr) time post-Izmit (days)

24. Simplest hybrid model: Afterslip plus Maxwell viscoelastic relaxation (A-B): 0 to 2 km and 10+ km intervals held constant (A-B): 0 to 2 km and 10+ km intervals held constant : lower crust - vary upper crust lower crust upper mantle (mantle asthenosphere) : upper mantle - vary LC UM LC UM

25. Geophysical evidence for mantle flow? Hearn et al. 1994: (not me!) Slow Pn beneath Anatolia Several seismic studies suggest high T and/or melt This is consistent with moderate viscosities Several seismic studies suggest high T and/or melt This is consistent with moderate viscosities Sandvol et al., 2001: attenuated Sn (regional seismic phase) beneath Anatolia Sandvol et al., 2001: attenuated Sn (regional seismic phase) beneath Anatolia

26. Broad backarc with young ‘tectonic age’? Currie and Hyndman, 2006 Anatolia: 13 Ma? and 70-100 mW/m2 Anatolia: 13 Ma? and 70-100 mW/m2 Anatolia: 20 km ? Anatolia? Black Sea?

27. Which parameters worked best? Afterslip + viscoelastic relaxation models Normalized WRSS, t = 0 to 900 days Fit improves for lower crust or upper mantle viscosities of 2 - 5 x 10 Pa s Fit improves for lower crust or upper mantle viscosities of 2 - 5 x 10 Pa s 19

28. Best afterslip + viscoelastic model: 1 yr Dynamic model WRSS* = 2250 (70% reduction) September, 2000 1080 (85% reduction)

29. Best afterslip + viscoelastic model: 3 yrs Dynamic model WRSS* = no reduction (50% reduction)

30. Blue = pre-Izmit GPS velocities, 1-sigma errors Pink = block model velocities (Reilinger et al., 2006) Is this model compatible with interseismic GPS velocities?

31. D D D’ Blue = pre-Izmit GPS velocities, 1-sigma errors Pink = block model velocities (Reilinger et al., 2006) Is this model compatible with interseismic GPS velocities?

32. D D D’ Reilinger et al., 2006 localized strain around NAFZ: like a 20 km locking depth insensitive to time since previous major earthquake (profiles across other NAFZ segments look similar) localized strain around NAFZ: like a 20 km locking depth insensitive to time since previous major earthquake (profiles across other NAFZ segments look similar) Interseismic GPS velocities Can lower crust or upper mantle with a viscosity of 5 x 10 Pa s produce this? 19

33. Interseismic GPS velocities and slip rate estimate Slip rate of 27-29 mm/yr Slip rate of 27-29 mm/yr ‘locking depth’ = 16-20 km Reilinger et al. 2006 Can a linear viscoelastic model produce something like this? Not really.

34. Can the postseismic deformation model explain the observed interseismic deformation? Earthquake cycle modeling is required UM LC impose periodic earthquakes and velocity boundary conditions on 3D finite-element model of NAFZ and lithosphere model several cycles, until cycle invariant status attained compare absolute velocities at appropriate time in the earthquake cycle to GPS velocities

35. periodic coseismic slip frictional afterslip: all models to 24 km (some to 32 km) frictional afterslip: all models to 24 km (some to 32 km) viscoelastic layers: linear nonlinear transient viscoelastic layers: linear nonlinear transient Earthquake cycle models 0 km 24 km 32 km to 300 km

36. Depth distribution and rate of aseismic slip

37. Afterslip velocity (mm/yr) Afterslip velocity (mm/yr) Shear stress perturbation (MPa, relative to 20 MPa background stress) Shear stress perturbation (MPa, relative to 20 MPa background stress) 3 y 9 y 16 y 42 y 140 y Aseismic slip rate and shear stress fluctuations over the interseismic interval

38. Meanwhile, viscoelastic relaxation is occurring in the upper mantle, and together these processes control interseismic velocities around the fault.

39. Best postseismic model is incompatible with interseismic GPS velocities around the NAFZ Reilinger et al. 2006 interseismic GPS data No variation with time in EQ cycle! Reilinger et al. 2006 interseismic GPS data No variation with time in EQ cycle! Model prediction for 1940’s rupture segment Model prediction for 1940’s rupture segment Modeled velocities around fault are very sensitive to time since the last earthquake

40. Explore other mantle rheologies: nonlinearly stress-dependent viscosity Explore other mantle rheologies: nonlinearly stress-dependent viscosity

41. interseismic GPS interseismic GPS This is a bit better...

42. Problem Differential stress is too low for dislocation creep (nonlinear flow with n > 3) Problem Differential stress is too low for dislocation creep (nonlinear flow with n > 3)

43. Explore other mantle rheologies: Burgers Body rheology (two viscosities) see also Hetland (2005) for 2D analytical models of the NAFZ with transient mantle rheology depends on time since a step in stress rate depend on change in stress rate and on temperature (for dunite, Chopra, 1997) depend on change in stress rate and on temperature (for dunite, Chopra, 1997) and

44. interseismic GPS = 10 = 2 to 5 x 10 Pa s = 10 years 19 This is good - little variation in strain rates for most of the interseismic interval

45. upper crust trans. lower crust? transient upper mantle transient upper mantle (mantle asthenosphere) LC UM episodic earthquakes RS friction or (at greater depths) viscous shear zone RS friction or (at greater depths) viscous shear zone What do models of postseismic and interseismic deformation tell us about the NAFZ plate boundary?

46. Could the NAFZ model work for the SAF? no M 7.5’s in the GPS era: if there is a transient or nonlinear response, it could be hard to see. from Parkfield: shallow frictional afterslip occurs first (Johnson et al. 2006). rich history of earthquake cycle models. -- Rate-and-state frictional or viscous fault plus Maxwell substrate (Johnson et al., 2004; Li and Rice, 1986, and more). ---Models with nonlinear lower crust (Reches et al., 1993) --- Many earlier / classic models (e.g. Savage and Prescott, 1978; Segall 2002, Thatcher 1983) rich history of earthquake cycle models. -- Rate-and-state frictional or viscous fault plus Maxwell substrate (Johnson et al., 2004; Li and Rice, 1986, and more). ---Models with nonlinear lower crust (Reches et al., 1993) --- Many earlier / classic models (e.g. Savage and Prescott, 1978; Segall 2002, Thatcher 1983)

47. Creeping section of the San Andreas Fault: GPS rate < long-term rate? Creeping section of the San Andreas Fault: GPS rate < long-term rate? could this also be addressed with non-uniform interevent times? 34 mm/yr (model) vs. 28 mm/yr (GPS and 1000-yr paleoseismic; Titus et al. 2006) vs. 28 mm/yr (GPS and 1000-yr paleoseismic; Titus et al. 2006) increasing t/T

48. Work in progress - improved EQ cycle models (A) irregular interevent times (B) finite rupture segments (C) transient effect superimposed on nonlinear rheology as Chopra intended (D) biviscous rheology (Ivins and Sammis 1996) in lower crust models, if admissible (E) 3D viscoelastic structure: contrast in effective plate thickness across the NAFZ? Tethyside accretionary complexes? (A) irregular interevent times (B) finite rupture segments (C) transient effect superimposed on nonlinear rheology as Chopra intended (D) biviscous rheology (Ivins and Sammis 1996) in lower crust models, if admissible (E) 3D viscoelastic structure: contrast in effective plate thickness across the NAFZ? Tethyside accretionary complexes? Sengor, 2005 Sandvol et al., 2001

49. Summary “Later” postseismic and interseismic deformation suggest viscoelastic relaxation of upper mantle or lower crust, but a transient rheology is required Early postseismic deformation is compatible with velocity-strengthening afterslip along the NAFZ, driven by coseismic stresses. (At depth the NAFZ could be a viscous shear zone.) Istanbul, August 2006

50. Bonus slide: What about nonlinear lower crust? can obtain decent fit to GPS velocities (n = 3) can obtain decent fit to GPS velocities (n = 3) for realistic lithologies, very low interseismic strain rate required

51. Postseismic strain (and stressing) rates in the Marmara Sea coseismic 900 days