Hiroyuki Noda *1 , Nadia Lapusta *1*2 , and James R. Rice *3

1. Earthquake Sequence Calculations with Dynamic Weakening Mechanisms: Statically Strong but Dynamically Weak Fault and Low Interseismic Shear Stress Hiroyuki Noda*1, Nadia Lapusta*1*2, and James R. Rice*3 *1 Division of Geological and Planetary Sciences, California Institute of Technology *2 Division of Engineering and Applied Science, California Institute of Technology *3 Department f Earth and Planetary Sciences and School of Engineering and Applied Sciences, Harvard University

2. Are major well-developed faults strong or weak? Definition based on average shear stress level Statically, we expect t = 200 MPa × 0.6 ~ 100 MPa at typical seismogenic depths. Well-established fact: Average static stress drop is  1 to 10 MPa (Typical average stress change in a large earthquake)

3. Observational evidence for “weak” major faults The outflow of heat observed for the San Andreas fault implies that shear stresses acting during sliding are of the order of 10 MPa or less (Brune et al., 1969; Henyey and Wassenburg, 1971; Lachenbruch and Sass, 1973, 1980). Steep angle between the principal stress direction and the fault trace inferred for some major strike-slip faults (e.g., Townend and Zoback, 2004; Hickman and Zoback, 2005) Significant rotations of principal stress directions(e.g., Wesson and Boyd, 2007). Geometry of thrust-belt wedges (Suppe, 2007).

4. Why would faults be “weak” on average? Fault is CLOSE to static failure before large events, small dynamic stress variations, nucleation can occur anywhere Fault is FAR from static failure before large events, large dynamic stress variations, nucleation in special places

5. Friction experiments for rocks Plate motion ~ 1 cm/yr Earthquake “Byerlee’s law” [1978] Weakening Figure from Wibberley et al., 2008 Many physical processes are proposed to explain this weakening at high slip rates, but frictional heating and temperature rise play an important role in most of them.

6. Goal: To produce a model of earthquake sequences consistent with observations and realistic rock-friction properties. Recent prior studies: 3D Sequences without high-velocity weakening (Lapusta and Liu, 2009) 2D Individual events with high-velocity weakening (Noda et al., 2009) 3D Sequences with hydrothermal effects (Noda and Lapusta, 2010) Long-term stress accumulation process and rapid dynamic ruptures

7. 2D crustal plane model Lehner et al., 1981 Solution technique: Spectral Boundary Integral Method (BIEM) [Lapusta et al., 2000; Kaneko and Lapusta, 2008]

8. Flash heating of microscopic contacts First introduced in a field of dry metal friction Bowden and Thomas, 1954; Archard, 1958/1959; Ettles, 1986; Lim and Ashby, 1987; Lim et al., 1989; Molinari et al., 1999 Very high stress (~ yield stress) and high slip rate. Extremely high temperature at the contact. (~ melting point) Weakening above about 0.1 m/s,τ(V) ~ 1/V + const. [Rice, 1999]

9. Strong rate-weakening embedded in the regularized aging law Rate- and state-dependent friction with effective stress law Steady state friction with strong rate-weakening State evolution Note: as (aging law)

10. Temperature and pore pressure change 1D diffusion of temperature and pore pressure with Gaussian shaped heat generation at each point on the fault These PDEs are integrated in time with a spectral method (Fourier basis) with logarithmic sampling in the wavenumber domain. [Noda and Lapusta, submitted]

11. Sequence of pulse-like ruptures(with Flash Heating, without Thermal Pressurization) every 2 seconds We produced a sequence of pulse-like ruptures.

12. Statically strong, but dynamically weak faults host a sequence of pulse like ruptures with a reasonable value of stress drop.

13. Without high-velocity weakening Strong fault producing a lot of frictional heating.

14. With Flash heating We have sequence of pulses. Arrested pulses make heterogeneous shear stress distribution.

15. With flash heating and thermal pressurization Almost full stress drop. Long-term frictional heating is comparable to a few MPa.

16. TP makes ruptures more crack-like. Identical frictional parameters (L = 10 mm) Without TP With TP TP makes the pulse width wider.

17. Interseismic stress is controlled by coseismic fault strength ! Coseismic friction coefficient, Fault strength at V0 = 1 mm/s, in -40 km < x < 40 km L = 10 mm, without thermal pressurization Sinusoidal inter-seismic stress distribution reflects distribution of fw.

18. Conclusions • We have simulated long term earthquake sequences accounting for the inertial effects and dynamic weakening at high slip rates (strong rate-weakening and hydro-thermal effects). • Dynamically weak faults produces low long-term frictional heating, as observed along San Andreas Fault. • We obtain a sequence of pulse-like ruptures. Thermal pressurization makes the pulses wider. • It is demonstrated that the interseismic shear stress distribution on the fault reflects the distribution of coseismic fault strength, not the frictional strength at low slip rates.