Seismic and aseismic processes in elastodynamic simulations of spontaneous fault slip Most earthquake simulations study either one large seismic event with full inertial effects or long-term slip history of a fault using simplified representation of inertial effects during seismic events. Our modeling aims to: Nadia Lapusta California Institute of Technology Studies supported by NSF, SCEC, USGS Simulate long-term slip history of the fault AND fully account for inertial effects of occasional earthquakes; Incorporate lab experiments and theories of how fault materials behave; Determine formulations and parameter choices that result in fault behavior consistent with basic observations.
Some basic laboratory and observational constraints to satisfy Large static frictional resistance of rocks found in the lab, equivalent to ~100 MPa at typical seismogenic depths Much smaller, potentially close to zero, dynamic frictional resistance based on lab experiments and theories. Static stress drops of ~1-10 MPa Pulse-like mode of rupture propagation Low-heat, low-stress fault operation The San Andreas fault generates much less frictional heat than one would predict based on static friction coefficients f of 0.6 to 0.8 (laboratory-derived) and effective normal stresses (! - p) of order 200 MPa at typical seismodenic depths (comparable to overburden minus hydrostatic pore pressure). Shear stress resolved onto the fault must be low, as the maximum compressive normal stress makes steep angles to the trace of the SAF. Low absolute shear stress levels inferred for the Denali fault, Alaska (Wesson and Boyd, Poster 15)
Backbone of the constitutive fault response in our model: Rate and state friction Laboratory-derived (Dieterich, 1979, 1981; Ruina, 1980, 1983;...) for slip velocities small ( ~ 10-9 10-3 m/s) compared to the seismic range. Unique tool for simulating all aspects of fault slip, from accelerating slip in slowly expanding nucleation zones to rapid dynamic propagation of earthquake rupture to post-seismic slip and interseismic creep to fault restrengthening between seismic events. V V ( ) ln ln o! d! V! " = # f = # & p f = # $ ' fo + a + b % ; 1 Vo L ( = & ) * dt L Base friction f o = 0.6 at V o = 1 mm/s; variations a, b ~ 0.01 L = 1-100 µm (lab values), L = 4-40 mm here for tractability a b > 0, velocity strengthening: a b < 0, velocity weakening: slow sliding (or creep) under slow loading large enough regions are locked in aseismic period, slip accumulates in earthquakes
Model of a vertical strike-slip fault z y x Fault zone, friction acts Earth s crust (24 km) 1/2 V pl http://pubs.usgs.gov/publications/text/dynamic.html Loading substrate V pl = 35 mm/ yr or ~ 10-9 m /s 1/2 V pl We use boundary integral method to simulate spontaneous slip accumulation on the interface by solving the system Shear traction on the fault = Friction strength of the fault
3D simulation with rate and state friction High shear stress to start the first rupture (work with Yi Liu, Caltech) Simulation time t, in years Variable time between movie frames, in seconds; Equal to 50 time steps 10-12 m/s 10-9 m/s 10-6 m/s 10-4 m/s 10-2 m/s 1 m/s locked (compared plate loading rate average seismic to plate rate) slip rate Movies: homogeneous fault; fault with one heterogeneity
Current and future applications of this simulation methodology Studies of dynamic weakening mechanisms and their implications for long-term fault behavior: absolute stress, nucleation, potential preferred rupture direction (collaboration with Prof. Rice, future collaboration with Prof. Shimamoto) Interaction between dynamic slip and aseismic creeping processes (example: small repeating earthquakes at SAFOD) Potential signatures of dynamic fault constitutive response in high-quality strong ground motion (future collaboration with Prof. Mori) Importance of incorporating full inertial effects of each earthquake for long-term slip history of a fault Aseismic and seismic earthquake nucleation processes Static and dynamic triggering of earthquakes Combined effects of realistic friction laws and fault heterogeneities Extension of the methodology to finite element methods to study the effects of off-fault damage, variation in bulk properties, local and large-scale fault nonplanarity, branching, and fault interaction
Theories, experimental evidence: Fault resistance at fast slip rates may be significantly lower than rate and state friction predicts Shear heating mechanisms Flash heating of contact asperities at small slips (Bowden and Thomas, 1954, Lim and Ashby, 1987, Molinary et al., 1999, Rice, 1999; Beeler and Tullis, 2003) Thermal pressurization of pore fluids in the fault zone (Sibson, 1973; Lachenbruch, 1980; Mase & Smith, 1985, 1987; Segall & Rice, 1995); Andrews, 2002; Garagash & Rudnicki, 2003a,b; Rice, 2006; and others) Partial or full melting of the shearing layer (Jeffreys, 1942; McKenzie and Brune, 1972; Tsutsumi and Shimamoto, 1997; Hirose and Shimamoto, 2005) Other possibilities Lubrication by silica gel layer (Goldsby and Tullis, 2003; Di Toro et al., 2004). Normal stress reduction from elastic mismatch (Weertman,, 1963, 1980 and others) Normal interface vibrations (Brune et al., 1993) Acoustic fluidization (Melosh, 1979, 1996) Elastohydrodynamic lubrication (Brodsky and Kanamori,, 2001)
A simplified law: Strong weakening with seismic slip velocities V friction coef-t from rate and state! ss = (" # p) 1 + V/ Vw V V! 1 + V / V " 1! rate and state friction w w V V! 1 + V / V " V / V! strong dynamic weakening w w w From theory and experiments: V w ~ 0.1 1 m/s Experiments (Tullis and Goldsby, 2003) Our law
2D depth-averaged model of a vertical strike-slip fault with a weak region z y Fault zone, friction acts Earth s crust (24 km) Loading substrate V pl = 35 mm/ yr or ~ 10-9 m /s 1/2 V pl x 1/2 V pl 2D crustal plane model: Constrained continuum, the only displacement u is in the direction of x; The equation for u is depth-averaged in z, the fault zone becomes a fault line; Variations with x and y only. Normal stress variation creates a weak patch Steady-state velocity strengthening Steady-state velocity strengthening ss velocity weakening
Stress state on the fault through many earthquake cycles (work with Jim Rice, Harvard)! av = " fault! da fault area! heat = " " time fault " " time fault! V dadt V dadt V w = 0.1 m/s Low-stress fault operation Low heat production Lower average shear stress (and more realistic stress drops) for more realistic values of L
Stress concentration at rupture front Low stress before rupture arrival Most slip occurs at very low stress (dyn. weakening) Static stress drop Shear stress evolution at a statically strong fault point during dynamic rupture Static stress drop is much smaller than what one would expect because shear stress before the earthquake is much smaller than static strength. Pulse-like rupture, slip duration is about 2.5 seconds Reasonable static stress drop A weak patch is used in this model to nucleate earthquakes under overall low shear prestress. We hypothesize that similar fault operation would result in a model that has places of sufficiently strong stress concentration, for example, at the depth of the seismogenic zone.
Scaling relationship between recurrence time T and seismic moment M 0 for small repeating earthquakes on creeping segments Observation: (such as SAFOD target earthquakes) 0.17 T! M 0 (e.g., Nadeau and Johnson 1998) Model of a circular rupture with constant stress drop and no aseismic slip: T 2/3 "# M = 1.81µ V 1/3 0 L! M 1/3 0 "! stress drop, µ shear modulus, V plate rate Proposed explanations for the discrepancy: L Stress drop scales with seismic moment, small earthquakes have very high (1GPa) stress drops (Nadeau and Johnson, 1998). Small repeating earthquakes occur at the boundary of a large locked asperity (Sammis and Rice, 2001). Significant amount of slip at places where small earthquakes occur is accommodated aseismically, due to strain hardening (Beeler et al., 2001).
Our model: Fault with rate and state friction, velocity-weakening patch surrounded by velocity-strengthening region (work with Ting Chen, Caltech) Fault zone y z x a b > 0 Vpl h Velocitystrengthening, creeping zone cell a-b<0 hnucl r x 1.5 m 40 m Simulations, theoretical analysis: To produce earthquakes, the weakening patch has to be large enough. If the patch is only slightly larger than the critical size, aseismic slip (nucleation, postseismic slip) should be a significant portion of the total slip. z a patch = 0.014, b = 0.019, patch a = 0.019, b = 0.014, L = 8 ì m Vpl fault Vpl 40 m fault = 23 mm/yr, r = 4.5! 10 m 1.5 m Velocity-weakening, potentially seismogenic patch
Moment released on the velocity-weakening patch, an example aseismic seismic td =0.002 s Max slip rate! Slip rate ~ 1 m/s For this case, most of the released moment (> 99%) is aseismic. It is difficult to precisely separate seismic and aseismic moment. The best way would be to produce synthetic seismograms and estimate seismic moment from them, just like it is done for real earthquakes. Future goal: Comparison of synthetic seismograms with SAFOD earthquakes.
Scaling of recurrence time with seismic moment in our simulations ( T! M 0 0.17 ) observed ( T! M 0 0.21 ) simulated ( T! M ) 1/3 0 theoretical 0.17 T! ( T! M 0 ) 0.21 M 0 Scaling:, similar to the observed relation Average stress drop within the typical range ~ 0.1-10 MPa The model provides a physical basis for the idea of Beeler et al (2001) that at places of small events much slip is accumulated aseismically.
Summary We can simulate seismic and aseismic slip history on a planar fault while accounting for all inertial effects of occasional earthquakes. Models that combine rate and state friction with shear-heating weakening mechanisms produce earthquake sequences that satisfy some basic observational and lab constraints, such as high static fault strength, low-heat and low-stress fault operation, and single and multiple slip pulses. Anomalous scaling of recurrence interval with seismic moment for small repeating earthquakes on creeping segments may be in large part due to interaction of a small velocity-weakening patch with the surrounding velocitystrengthening fault in a rate and state model. Directions of future and current work: More realistic representation of fault frictional behavior (with Prof. Shimamoto) Potential signatures in high-quality strong motion data (with Prof. Mori) Interaction between dynamic slip and aseismic creeping processes Static and dynamic earthquake triggering, aftershock sequences Combined effects of realistic friction laws and fault heterogeneities Off-fault damage, branching, fault non-planarity, fault interaction