Hiroyuki Noda Nadia Lapusta Caltech

1. 3D simulations of seismic and aseismic fault slip with evolving temperature and pore pressure: Interaction of two fault segments and low interseismic shear stress Hiroyuki Noda Nadia Lapusta Caltech Summary: Dynamic weakening at coseismically high slip rate dramatically decreases the long-term fault strength ! 18. Dec. 2009 hnoda@caltech.edu

2. Hydrothermal effects on frictional resistance Pore pressure variations change frictional resistance by changing effective normal stress. Effective stress law Elastodynamic normal stress (positive in compression) Pore pressure Effective normal stress Shear traction Friction coefficient Thermal pressurization Since the thermal expansivity of water is much larger than that of rocks, frictional heating can increase p if the surrounding medium is not very permeable. First introduced in considering catastrophic landslides [Hibab, 1967], with many application to earthquakes: Sibson [1973], Lachenbruch [1980]; Mase & Smith [1985,1987]; Segall & Rice [1995]; Andrews [2002]; Garagash & Rudnicki [2003a,b]; Rice [2006]; Noda, Dunham, & Rice [2009]; among many others.

3. Aim of this work • To develop a methodology for long-term, earthquake sequence simulations fully accounting for the inertial and hydrothermal effects. • To see how the frictional and hydraulic properties affect earthquake cycles: stress state, spatio-temporal slip distribution, and characteristics of each dynamic event. • To see if it is possible to produce differences in frequency content of seismic radiation from different parts of the fault, as observed in the 1999 Chi-Chi, Taiwan, earthquake. Details skipped I’ll concentrate on “strength of a fault” today. Details skipped

4. 1999 (Mw 7.6) Chi-Chi, Taiwan, earthquake • The long-period component is dominant in the northern region where the fault slip is larger than the southern region [e.g. Ma et al., 2003]. • The long-period component in the strong motion data increases when thermal pressurization is introduced locally in a dynamic rupture propagation calculation [Andrews, 2005]. Figure from Ma et al. [2001] • Temperature measurements at bore holes in the North showed that the frictional resistance is only ~0.1×snduring the earthquake[Tanaka et al., 2006; Kano et al., 2006]. We reproduced those features in earthquake sequence calculation. (Though not today’s topic) Figure from Ma et al. [2003]

5. Problem settings Inertial effect is included. Two patches (15 km x 15 km) Patch I at negative x Rate-weakening friction High hydraulic diffusivity Patch II at positive x Rate-weakening friction Potentially low hydraulic diffusivity (susceptible to thermal pressurization)

6. Friction law on the fault (y = 0, x and z vary) Friction law with effective normal stress f θ σn p V : Friction coefficient : State variable (slowness) : Total normal stress on the fault : Fluid pressure : |V| Rate- and state-dependent friction coefficient a b V0 f0 : Parameter representing direct effect : Parameter representing evolution effect : Reference slip rate : Reference friction coefficient State evolution law (aging law or slowness law) L θss : Characteristic evolution length (slip) : State variable at the stead state

7. Temperature and fluid pressure evolution Diffusion of temperature normal to the fault T αth ω ρ c : Temperature : Thermal diffusivity : Heat generation per unit volume : Density : Heat capacity per unit mass Diffusion of fluid pressure normal to the fault αhy Λ : Hydraulic diffusivity : Fluid pressure change / temperature change Heat source distribution w : Half width of the shear zone

8. Patch I Patch II

9. Heterogeneity in the hydraulic diffusivity Slip distribution at z = 0, black lines every 1 sec during EQs and gray ones every 10 years The region more susceptible to thermal pressurization has larger displacements in model-spanning events. The slip deficit in the other region is filled with smaller and more frequent events.

10. Effect of heterogeneity in the hydraulic diffusivity on temperature distribution Temperature and effective normal stressevery 1 sec in a large event at z = 0 Fault temperature is highest not in the region of the largest slip. The fault area of highest temperature has intermediate level of slip, but high frictional resistance.

11. Interseismic shear stress Shear stress at xz = 0. In the region of efficient thermal pressurization, shear stress is lower interseismically due to larger stress drop. That is why events that occur early in the cycle may not propagate through that region.

12. Nucleation locations on faults with heterogeneous hydraulic diffusivities - Theoretical estimate of the nucleation length is smaller if TP is more efficient [Segall and Rice, 2006]. - However, our simulations show that such areas may actually be unfavorable for earthquake nucleation due to interseismically lower shear stress. This point highlights the importance of considering the effects of variation in the physical properties in the context of earthquake sequences.

13. Work in progress 2D earthquake cycle simulation with a strong rate-weakening Collaboration with N. Lapusta and J. R. Rice Crustal-plane model [Lehner et al., 1981; Kaneko and Lapusta, 2008] “Flash heating” embedded in the regularized Dieterich-Ruina (aging) law A weak patch at the end to nucleate ruptures frequently.

14. Result: sequence of pulse-like ruptures every 2 seconds • We produced a sequence of pulse-like ruptures.

15. Stress history during an event • Ruptures can propagate at a very low pre-stress producing a reasonable value of stress-drop although the peak shear stress is high.

16. Long-term shear stress (Normal stress) x (Averaged f0) (Spatially averaged shear stress) (Time-averaged heat production) • Averaged shear stress and the long-term heat generation rate is much lower than the frictional strength to be measured at low slip rates.

17. Conclusions • We have developed a methodology for simulating earthquake cycles that accounts for the evolution of temperature and pore pressure on the fault and their 1D diffusion off the fault. • The region of more efficient thermal pressurization (TP) has larger slipwhen it ruptures. Hence it does not rupture in every event. • The highest temperature does not occur in the area of largest slip. • Efficient TP decreases interseismic shear stress. This is why a rupture is not nucleated there though a theoretical nucleation size is smaller. • With the extreme rate-weakening, we obtain a sequence of pulse-like ruptures with reasonable value of slip and stress drop, low interseismic shear stress, and low heat generation. High velocity friction plays a very important role in determining the long-term shear stress (strength).

19. Combined effect of rate-hardening and T.P. Less negative a-b in a patch at x > 0

20. Frequency contrast in the coseismic fault motion Large slip, but depleted in high frequencies

22. The resulting complexity in EQ magnitude distribution Magnitude of the events as a function of time Without heterogeneity, the model produces characteristic events. Heterogeneity causes long earthquake cycles that contain events of different sizes.

23. Slip rate distribution at z = 0, every 1 sec The maximum slip velocity does not change much. The “tail” becomes longer as thermal pressurization becomes effective.

24. Problem setting Revise to smaller table Two patches (15 km x 15 km) with gradual margins. Starting from b-a = 0.004 and αhy = 10-2 m2/s in both patches, they are decreases in the patch at x > 0.

25. Lab-measured physical propertiesrate- and state- parameters Samples are collected from bore holes in the northern and southern regions from a fault zone which ruptured 1999 at 200 – 300 m depth. North: Rate-hardening South: Rate-weakening Tanikawa and Shimamoto, 2009

26. Stress-reduction curves and low heat generation Shear stress as a function of slip at x = -10 km (black) and 10 km (gray). Apparent stress weakening distance is determined by rate- and state-law in the permeable region, and by T.P. in the less permeable region.

27. Lab-measured physical propertiespermeability North: Less permeable South: More permeable Tanikawa and Shimamoto, 2009

28. Summary of measured physical properties [Tanikawa and Shimamoto, 2009] South : Rate-weakening Susceptible to nucleation More permeable North : Rate-hardening Less permeable Susceptible to thermal pressurization This data serves as motivation for exploring heterogeneities in rate dependence and permeability (hydraulic diffusivity) along the faults. We caution that the data is based on only two points at shallow depths (~ 200-300 m).