S11E-01 INVITED
Heating and Weakening of Major Faults During Seismic Rupture
The absence of significant heat flow from major fault zones, and scarcity of evidence for their seismic melting, means that during earthquake slip such zones could not retain shear strength comparable to the typically high static friction strength of rocks. One line of explanation is that they are actually statically weak, which could be because materials of exceptionally low friction (smectites, talc) accumulate along fault zones, or perhaps because pore pressure within the fault core is far closer to lithostatic than hydrostatic. Without dismissing either, the focus here is on how thermal processes during the rapid slips of seismic rupture can weaken a fault which is indeed statically strong. (The discussion also leaves aside another kind of non- thermal dynamic weakening, possible when there is dissimilarity in seismic properties across the fault, and/or in poroelastic properties and permeability within fringes of damaged material immediately adjoining the slip surface. Spatially nonuniform mode II slip like near a propagating rupture front may then induce a substantial reduction in the effective normal stress \barσ.) The heating and weakening processes to be discussed divide roughly into two camps: (1) Those which are expected to be active from the start of seismic slip, and hence will be present in all earthquakes; and (2) Those that kick-in after threshold conditions of rise of temperature T or accumulation of slip are reached, and hence become a feature of larger, or at least deeper slipping, earthquakes. It has been argued that the two major players of (1) are as follows: (1.1) Flash heating and weakening of frictional contact asperities in rapid slip [Rice, 1999, 2006; Tullis and Goldsby, 2003; Goldsby and Hirth, 2006; Beeler et al., 2007; Yuan and Prakash, 2007]. That gives a strong velocity-weakening character to the friction coefficient, which is consistent with inducing self-healing rupture modes [Noda et al., 2006; Lu et al., 2007]. It is a process for which the details are still poorly understood in presence of substantial fault gouge, almost surely present in some of the large-slip experiments fitting the flash weakening theoretical model. (1.2) Thermal pressurization of pore fluid by frictional heating, a process which reduces \barσ [Sibson, 1973; Lachenbruch, 1980; Mase and Smith, 1987], and is expected to be active wherever the fault wear products, as gouge, retain porosity of a few percent or more. At some depth and temperature they may instead sinter to a coherent solid on the interseismic time scale. Those of category (2) are as follows: (2.1) Macroscopic melting of the shear zone [Tsutsumi and Shimamoto, 1997; Hirose and Shimamoto, 2005; Fialko and Khazan, 2005; Nielsen et al., 2007], a process for which conditions may not be met if (1.1) and (1.2) kill off strength rapidly enough [Rempel and Rice, 2006], or do so with the help of one of the next two items. (2.2) Thermal decomposition like in smectite or serpentine dehydration [Sulem et al., 2004, 2007; Hirose and Bystricky, 2007] or coal devolatilization [O'Hara et al., 2006], leading to a high pressure fluid phase. (2.3) Formation of a weak gel-like layer like in wet silica-rich lithologies [Goldsby and Tullis, 2002; DiToro et al., 2004]. It is argued that some large-slip experiments involving significant weakening of unsaturated specimens in lab air, and others involving dehydration, may exhibit a component of weakening from pressurization of water vapor that is desorbed from mineral surfaces or released by dehydration during frictional heating. The hydraulic diffusivity of water vapor is unexpectedly low at levels of p comparable to the low normal stresses of the experiments involved.
S11E-02 INVITED
Complex Evolution of Friction During Seismic Slip: New Experimental Results
We present initial high-speed friction experiments that indicate there are important compositionally controlled differences in the evolution of the frictional responses of faults at seismic slip velocities. Recent experimental studies show that rock friction undergoes a substantial evolution at slip rates of the order of centimeters per second and higher. A rapid decrease in the coefficient has been interpreted in terms of a number of mechanisms, including micro- and microscopic melting and formation of new amorphous phases such as silica gel. Existing experimental data covers a range of shear velocities from less than a millimeter per second up to several tens of centimeters per second. We conducted a new series of measurements of the dynamic coefficient of friction of granodiorite at slip rates ranging from 0.14 to 3 m/s (i.e., well within the seismic slip and melt generation range), and at normal stresses between 0.5 and 1.5 MPa. Experiments were carried out on a rotary shear machine. We used ring samples with outer-to-inner radii ratio of 1.5 to minimize variations in slip rate across the sample interface. Efforts were made to restrict gouge ejection from the shear zone in order to maintain the effective contact area. Our results reveal that granodiorite and diabase samples experience different evolutionary paths during frictional breakdown at high velocities. The quartz/feldspar-dominated lithology has a dynamic coefficient of friction of 0.3- 0.4 that overlaps with the high velocity end member values (between 0.14 and 0.2 m/s) recently obtain by Goldsby and Tullis (2002), Hirose and Shimamoto (2005), for quartz-dominated lithologies. However, our higher velocity data suggest the previously identified monotonic drop in frictional strength as velocities exceed ~0.1 m/s does not continue above 0.2m/s. Instead, the coefficient of friction is nearly constant in the velocity interval between ~20 cm/s and ~0.65 to 1 m/s and experiences a second weakening phase (friction drops to as low as 0.1-0.2) as velocities exceed 1m/s. However dramatic oscillations in frictional strength (coefficients jump between ~0.1 and ~0.5) also occur at the highest velocities. We attribute such jumps in strength to slip plane instability and rapid oscillations between melt and cataclastic flow dominated rheologies. In contrast, the feldspar dominated mafic lithologies experience a more monotonic weakening (coefficients drop from 0.3 to 0.2 as slip velocities exceed 0.14 m/s before they begin to melt as speeds rise above 0.65m/s. More complex frictional responses are seen during melting. The compositionally related differences in frictional evolution at high speed suggest there are complex thermo- mechanical processes occurring within the gouge layer that are impacted by variations mineralogical properties. This new experimental data suggest that the evolution of friction during seismic slip is complex, and a better theoretical understanding of the underlying physics is warranted.
S11E-03
Transition to Pulse-Like Rupture, With and Without Inclusion of Evolving Temperature and Pore Pressure, When Accounting for Extreme Weakening at High Slip Rates
We have conducted rupture propagation simulations incorporating the combined effects of thermal pressurization of pore fluid by distributed heating within a finite width shear zone, and flash heating of microscopic contacts. These are probably the primary weakening mechanisms at high coseismic slip rates. For flash heating, we use a rate- and state-dependent friction law in the slip law formulation, accounting for extreme velocity weakening above a weakening slip rate Vw ~ 0.1 m/s that depends on the background temperature, and a very short state evolution distance, L, of ~ 10 μm, which is comparable to the asperity length. We have also conducted a series of calculations with neglecting evolving change in macroscopic temperature, T, and pore pressure, p, and compared the results. Slip rate, V, at a point on a fault increases when a rupture front approaches, and decreases behind it. In the pulse-like solutions, V decreases below Vw, and the point is eventually locked. On the other hand, in the crack-like solutions, V increases again only if we allow evolving change in T and p. In the cases when we neglect changes in T and p, V continues to decrease behind the rupture front as long as we simulate. Here, a question emerges; is the solution crack-like because of the short calculation time? Zheng and Rice [1998] proposed an intuitive criterion between crack-like and pulse-like solutions as follows: If and only if the background shear stress, τb, is larger than a critical value, τpulse, there are roots of τss(V) = τb - μ V/2 cs, where τss is steady-state strength, μ is shear modulus and cs is shear speed. If TZR = - (μ/2cs)/(dτss/dV) at the largest root is near unity, the solution is pulse-like. Our calculations without T and p changes show that the pulse-like solution regime extends above τpulse, at least up to the point where TZR = 0.176, if a rupture is initiated by a perturbation in shear stress in a certain manner. The transition time to pulse-like solution increases with τb and diverges at a finite τb. If τss depends only modestly on V at high slip rate (like for flash heating), and if L is short enough, an expanding singular crack solution may be a good approximation to a hypothetical crack-like solution. At the center, slip rate is V∞ = F(Vr/cs) (Δτ/μ) Vr, where Δτ is stress drop, Vr is rupture velocity and F(Vr/cs) is near unity. Off the center, V changes from infinity at the tip to V∞. Suppose Vpulse is a slip rate at which TZR = 1. When V becomes smaller than Vpulse, the shear stress deviates from τss and V nears zero. Therefore, if V∞ is below Vpulse, we will see the transition to a pulse-like solution. Although there is an uncertainty in estimating Δτ, this criterion seems to work well. With evolving change in T and p, the crack-like solutions (V increases again) are associated with the situation that shear stress τ > τss. This indicates that increases in T and p lower τss, which passes current value of τ before V reaches Vpulse. This is possibly how the crack-like regime extends to lower τb, even below the τpulse for the initial T and p values.
S11E-04
Laboratory Experiments and Theoretical Studies of Rupture Modes and Supershear Transition
Theoretical studies have shown that the issue of rupture modes has important implications for fault constitutive laws, stress conditions on faults, energy partition and heat generation during earthquakes, scaling laws, and spatio-temporal complexity of fault slip. Early theoretical models often treated earthquakes as crack-like ruptures, but seismic inversions indicate that earthquake ruptures may propagate in a self-healing pulse-like mode. A number of explanations for the existence of slip pulses have been proposed, including strong weakening of the interface with sliding rate, interaction of rupture with local heterogeneities, and normal stress variation due to a bimaterial effect. We observe pulse-like and crack-like rupture modes in the experimental configuration of a Homalite plate with inclined interface prestressed both in compression and in shear, similarly to faults in the Earth's crust. Dynamic rupture is initiated by exploding a 0.1 mm nickel wire. Digital high-speed cameras are used to record photoelastic images. Two interferometry-based velocimeters are used to determine the history of relative sliding velocity at one location along the interface. Our results indicate that pulse-like ruptures can exist on such interfaces in the absence of a bimaterial effect or local heterogeneities. For a set of experiments with increasing ratio of shear to normal prestress, which is achieved by increasing the inclination angle of the interface, we observe a change in rupture modes from pulse-like to crack-like. This systematic variation is consistent with the theoretical study of velocity-weakening interfaces by Zheng and Rice (1998). We also establish experimentally, for the first time, that both pulse-like and crack-like rupture modes can transition to supershear speeds. After the supershear transition, both modes have speeds within the open interval \sqrt{2} Cs to Cp, where Cs and Cp are the S- and P-wave speeds of Homalite, respectively. However, the rupture speed of pulse-like ruptures is lower. These supershear speeds are consistent with the analytical predictions of the velocity-weakening model of Samudrala et al. (2002). The agreement between our experimental observations and models of velocity-weakening faults suggests that velocity-weakening friction plays an important role in dynamic behavior of ruptures and implies that expressing dynamic weakening of friction solely in terms of slip may not be a sufficiently general description. We will also present our current efforts to further analyze the experiments, including the potential effects of rupture initiation procedure. Our preliminary experimental measurements of vertical motion of points close to the interface indicate that there is no opening of the interface during sliding at locations where we determine the rupture mode, although more analysis is need to determine whether there is any significant normal stress variation. We are in the process of including normal stress variations into our existing numerical code to investigate this issue, as well as to study which friction law is most consistent with the experimental observations. We are also working on quantifying the parameters of the explosion and determining the friction properties of Homalite (collaboration with N. Beeler and B. Kilgore (USGS), C. Marone (Penn State), and G. Ravichandran (Caltech)).
S11E-05
Identification of Necessary Conditions for Super-shear Wave Rupture Speeds: The San Andreas Fault
The 2001 Kunlun, Tibet earthquake taught us that the portion of a strike-slip fault most likely to propagate at super-shear speeds are the long straight portions. This is only a necessary (but not sufficient) condition. That is, once a fault accelerates to the maximum permissible speed, it can continue at this speed provided it is straight and there are no obstacles along the way, and provided the fault friction is low. For the Tibet earthquake, the 100 km region of highest rupture speed also had the highest slip rate, the highest slip and the highest stress drop (Robinson et al., JGR, 2006). Off-fault cracks due to the passage of the Mach cone exists in only that portion of the fault identified as travelling at super-shear speed and not in other places along the fault (Bhat et al., JGR, 2007). Re-examination of earlier reports of super-shear rupture speeds on the North Anatolian fault and the Denali fault show that such speeds did occur on the straight section of these faults. Of course all straight portions of faults will not reach super-shear speeds. So what can the Tibet earthquake teach us about the San Andreas fault? Both the 1906 and the 1857 have long, straight portions, the former having been identified by Song et al. (EOS, 2005) as having reached super-shear speeds to the north of San Francisco, the region of highest slip. If the repeat of the 1857 starts in the central valley, as it is believed to have done in 1857, it has the potential to propagate at super-shear speeds through the long, straight portion of the San Andread fault in the Carrizo Plain, the region believed to have had the largest displacement in 1857 based on paleoseismic studies. The resulting shock waves would strike the highly populated regions of Santa Barbara and the Los Angeles Basin (Das, Science, 2007).
S11E-06
Energy Partition During In-plane Dynamic Rupture on a Frictional Interface
We study properties of dynamic ruptures and the partition of energy between radiation and dissipative mechanisms using two-dimensional in-plane calculations with the finite element method. The model consists of two identical isotropic elastic media separated by an interface governed by rate- and state-dependent friction. Rupture is initiated by gradually overstressing a localized nucleation zone. Our simulations with model parameters representative of Homalite-100 indicate that different values of parameters controlling the velocity dependence of friction, the strength excess parameter and the length of the nucleation zone, can lead to the following four rupture modes: supershear crack-like rupture, subshear crack-like rupture, subshear single pulse and supershear train of pulses. High initial shear stress and weak velocity dependence of friction favor crack-like ruptures, while the opposite conditions favor the pulse mode. The rupture mode can switch from a subshear single pulse to a supershear train of pulses when the width of the nucleation zone increases. The elastic strain energy released over the same propagation distance by the different rupture modes has the following order: supershear crack, subshear crack, supershear train of pulses and subshear single pulse. The same order applies also to the ratio of kinetic energy (radiation) to total change of elastic energy for the different rupture modes. Decreasing the dynamic coefficient of friction increases the fraction of stored energy that is converted to kinetic energy. In the current study we use model parameters representative of rocks instead of Homalite-100, by modeling recent results of Kilgore et al. (2007) who measured and estimated various energy components in laboratory friction experiments with granite. We are also incorporating into the code ingredients that will allow us to study rupture properties and energy partition for cases with a bimaterial interface and dynamic generation of plastic strain off the fault.
S11E-07
Self-Healing Slip Pulse Driven by Shear Heating of a Fluid-Saturated Fault Zone
Shear heating in a fluid-saturated fault zone results in an increase of pore pressure p and corresponding reduction of frictional resistance τ=f(σ-p) when dilatancy and transport of pore fluid and heat away from the shearing fault core are limited. Influence of these effects on propagation of a self-healing slip pulse are examined in two limit cases when (I) frictional heat and pressurized pore fluid are trapped inside the shearing fault core of finite thickness h (small compared to the length of the slipping patch ℓ); and (II) all frictional heat is dissipated from the shearing fault core to the surroundings, rendering irrelevant the thickness of the fault core, h=0. Solutions for a steady propagation of a self-healing slip pulse driven by uniform remote stress τ∞ are considered in the framework of antiplane elastodynamics; friction coefficient f and normal stress σ are uniform and their alterations with the slip are neglected; shear deformation and corresponding temperature and pore pressure alterations are uniform across the fault core thickness. In the case of adiabatic, undrained slip (case I) the slip pulse solution corresponds to the gradual frictional stress drop from the maximum value τo=f(σ-po) at the leading rupture edge to a value below the remote stress τ∞ at the trailing edge. Behind the trailing edge, consistent with the no-slip requirement, the recovery of shear stress takes place slower than that of the frictional resistance due to the pore pressure diffusion in the trail of the pulse. We find that distribution of the shear stress and slip with the distance from the leading edge normalized by their respective characteristic values τo, δc=(ρ c/fΛ)h, and ℓc=(μ/τo)δc, depends on a single parameter - stress ratio τ ∞/τo. (Above, ρ c and Λ=dp/dT are effective heat capacity and undrained thermal pressurization factor of the fault gouge, respectively, and μ is elastic shear modulus of the surrounding rock). Furthermore, the normalized length of the slipping patch is a function of the pulse velocity fraction β<1 of the shear wave speed and of the stress ratio: ℓ/ℓc=\sqrt{1-β2}B(τ∞/τo), where preliminary numerical results for B suggest that it is a monotone function of its argument with B(1)=2.32 and B(0)=+∞. We observe, that (i) generally, the length of the pulse is decreasing function of the propagation velocity, vanishing when the latter tends to the shear wave speed limit; (ii) at a fixed value of pulse velocity β, pulse length ℓ, slip rate, and accumulated slip increase with decreasing remote stress (consistent with increasing value of the stress drop over the duration of the pulse), diverging at zero stress. The latter zero stress limit considered at a fixed length of the pulse implies that the propagation velocity approaches the shear wave speed. Furthermore, with decreasing stress ratio, the shape of the slip-rate distribution evolves from the symmetric to highly antisymmetric with the peak approaching the leading edge. In the case of slip on a plane, h=0, (case II), when diffusion of temperature and pore pressure from the slip plane to the surroundings is dominant, we prove that no slip pulse solutions are possible in the considered idealized model. The latter suggests the thickness of the fault core may play a crucial role in the development of self-healing modes of slip.
S11E-08
Dynamic Mechanochemistry of Seismic Slip -Nano Spherules Lubrication
The Chelungpu fault, which was activated during 1999Chi-Chi Earthquake, had been drilled (Hole A, B and C) to recover the earthquake slip zone materials. We present here the results of nano-scale observations for identified slip zone materials (Ma, Tanaka et al., 2006) by using HR-TEM and TXM technique. Minimum size of grains observed under HR-TEM is 3 nm. The grain size distribution for grains larger than 100 nm in diameter follows the fractal law and grain shape is highly irregular. Grains smaller than100 nm show some specific characteristics, that is, smaller the grains, more the spherical shapes and more equi-granular. Thus, the grains smaller than 100 nm are no longer described by fractal distribution model. By SAD and EDX analysis under HR-TEM, the nano spherules are mainly composed of crystallized quartz associated with minor amounts of carbonates and amorphous materials. Results of observations lead following three conclusions, (1) nano spherules are not generated just by fracturing based on their shapes and grain size distributions. (2) nano spherules would compose viscous materials enveloping larger fractured grains from SEM observations. (3) Mica clay minerals and feldspars are disappeared in ultra-fine grained layer. This implies that chemical process of dissolution - elements dissipation - SiO2 precipitation occurred associated with mechanical fracturing. Therefore nano spherules would be generated through mechano-chemical process during co-seismic slip. Dynamic shear strength drop by rapid slip experimentsare and formation of gelled materials are recently reported. Large differences of ultra-fine products between previous reports and our observations are existence of nano spherules and their crystallinity. If the nano- spherules are generated during seismic slip, dynamic weakening would be expected because mode of friction turns into rolling friction by huge amounts of equigranular and spherical grains. This may be alternative explanations for dynamic weakening. Quantitative process of dynamic fracturing will be discussed in our presentation.