Proc. Natl. Acad. Sci. USA Vol. 93, pp. 3803-3810, April 1996 Colloquium Paper This paper was presented at a colloquium entitled "Earthquake Prediction: The Scientific Challenge," organized by Leon Knopoff (Chair), Keiiti Aki, Clarence R. Alien, James R. Rice, and Lynn R. Sykes, held February 10 and 11, 1995, at the National Academy of Sciences in Irvine, CA. Rock friction and its implications for earthquake prediction examined via models of Parkfield earthquakes (constitutive laws/numerical models) TERRY E. TULLIS Department of Geological Sciences, Brown University, Providence, RI 02912-1846 ABSTRACT The friction of rocks in the laboratory is a implications of the observed time, velocity, and displacement function of time, velocity of sliding, and displacement. Al- dependence of rock friction in the laboratory for the possible though the processes responsible for these dependencies are behavior of natural faults, recognizing that this may represent unknown, constitutive equations have been developed that do only part of the story. This approach has the advantage that it a reasonable job of describing the laboratory behavior. These is clear from work already done that the laboratory-derived constitutive laws have been used to create a model of earth- constitutive laws offer at least one likely explanation for many quakes at Parkfield, CA, by using boundary conditions ap- phenomena involved in earthquakes (1-11). propriate for the section of the fault that slips in magnitude This success, combined with the fact that accelerating slip 6 earthquakes every 20-30 years. The behavior of this model precedes unstable sliding in the laboratory, leads one to prior to the earthquakes is investigated to determine whether investigate the relevance of rock friction data for predicting or not the model earthquakes could be predicted in the real earthquakes. One, debatably encouraging, fact is that there is world by using realistic instruments and instrument locations. general agreement between observations from the earth and Premonitory slip does occur in the model, but it is relatively predictions from the modeling on the small size of any restricted in time and space and detecting it from the surface premonitory signals. The fact that at least small signals may may be difficult. The magnitude of the strain rate at the exist suggests that it might eventually be possible to detect earth's surface due to this accelerating slip seems lower than them. the detectability limit of instruments in the presence of earth noise. Although not specifically modeled, microseismicity Review of Rock Friction Behavior related to the accelerating creep and to creep events in the model should be detectable. In fact the logarithm of the Observed Behavior. Generalities. Static friction increases moment rate on the hypocentral cell of the fault due to slip with the time ofbeing static and there is an associated tendency increases linearly with minus the logarithm of the time to the for dynamic friction to decrease with increasing slip velocity. earthquake. This could conceivably be used to determine when In addition, when the velocity is changed, the transition to the the earthquake was going to occur. An unresolved question is new frictional resistance requires sliding some distance. These whether this pattern of accelerating slip could be recognized features are illustrated in Fig. 1. Two competing effects are from the microseismicity, given the discrete nature of seismic seen in the behavior shown in Fig. 1, the evolution effect and events. Nevertheless, the model results suggest that the most the direct effect. likely solution to earthquake prediction is to look for a pattern Evolution effect. The most important single aspect of rock of acceleration in microseismicity and thereby identify the friction in terms of application to earthquakes is that surfaces microearthquakes as foreshocks. in stationary contact increase in strength with time. This effect is known as the evolution effect. It is demonstrated by the Frictional sliding of rocks on laboratory scale faults or on faults slide-hold-slide test, in which sliding is stopped for some in the earth are similar. Both systems involve an interaction period of time after having attained a steady-state frictional between the frictional response of the rocks in the fault zone resistance at constant velocity. When sliding is resumed, the and the elastically distorted surroundings that can either be resistance climbs to a peak value larger than the steady-state unstable or stable. value prior to the hold, subsequently decaying to the original It is not the coefficient of friction of rocks, but the way the steady-state value. As shown in Fig. 2, there is a nearly linear coefficient of friction depends on time, sliding velocity, and relationship between the magnitude of the peak value and the displacement that is important to whether sliding will be stable logarithm of the hold time (12, 13). This phenomenon is or unstable. These relatively small effects are more subtle and responsible for the restrengthening of surfaces between slip experimentally difficult to measure, but they are of primary episodes, without which repeated unstable slip is impossible, importance in determining whether a fault will slide by creep and for a tendency for frictional resistance to be lower at or by catastrophic earthquakes. There are other factors such as higher sliding velocities. This potential for decreasing strength changes in pore fluid pressures that may also play a role in with increasing velocity is the aspect of rock friction that allows earthquake generation, but some kind of dependence on for runaway instabilities (14, 15). velocity and sliding displacement is probably needed to allow After abrupt changes in velocity the frictional resistance a sustained runaway instability. In this paper I will explore the evolves to a new steady-state resistance over a characteristic slip distance (thus the term "evolution effect"). This has been The publication costs of this article were defrayed in part by page charge interpreted (16-18) as the slip required to destroy all the payment. This article must therefore be hereby marked "advertisement" in contacts established at one velocity and to create a new set of accordance with 18 U.S.C. §1734 solely to indicate this fact. contacts having an average age appropriate to the new velocity. 3803 Downloaded by guest on October 1, 2021 3804 Colloquium Paper: Tullis Proc. Natl. Acad. Sci. USA 93 (1996) inside the pressure vessel immediately adjacent to the sample. In Fig. 3 is shown a typical sequence of stick slip events V, V2 = eV, measured with internal stress and displacement transducers in our rotary shear apparatus (26). At first glance (Fig. 3A), the events look as if they occur without warning, but successively closer examinations (Fig. 3 B-D) show that there is acceler- /1 ating slip and an associated nonlinearity in the stress-time curve that foretells each unstable event. There is no reason to I believe that this precursory accelerating slip should not occur IAL in the earth. The real question is whether it will be large enough to be usefully detected and so provide the basis for a short-term earthquake prediction. In order to answer this we need to learn how to extrapolate the laboratory results to the FIG. 1. Response of friction to an abrupt increase in sliding earth. The constitutive laws discussed in a following section velocity. The parameters a, b, and Dc are those in Eqs. la, lb, and lc. form the present basis for doing this. The behavior given by the equations for a sudden velocity change is Constitutive Laws. constitutive laws have been illustrated graphically. The magnitude of the direct effect is measured Empirical a and of the evolution effect is measured b. used by many workers to fit the frictional behavior described by by (e.g., refs. 13, 17, 26-38). Although a variety of functions have However, a complete understanding of what occurs at the been presented, two laws are most commonly used, and even contacting asperities does not yet exist. these can be cast in slightly different ways. The form used in The other effect seen in all friction experiments is an initial ref. 13 is convenient because the state variable has dimensions increase in the resistance to sliding that occurs when the of time in both laws. Both laws represent friction as a function velocity of sliding is abruptly increased (Fig. 1). This is termed of velocity and a state variable by the same equation: the direct effect because the change of resistance occurs = + a + b instantaneously and in the same sense as the change in velocity. uL pto ln(V/Vo) ln(OVo/Dc). [la] Stability ofsliding. The absolute value of frictional resistance The direct effect is contained in the term a ln(V/V*) and is unimportant for controlling the stability of sliding. However, the evolution effect in the term b ln(0Dc/V*). The nature of the time, velocity, and displacement dependence of friction the evolution is what differs in the two laws. In the law interact with the elastic stiffness of the surroundings to pro- termed the slip law, because slip is required for evolution, the duce either stable or unstable sliding. The stability has been state variable evolves according to: analyzed by using the constitutive laws described in the fol- lowing section (14, 16, 17, 19-24). d /dt = (OV/Dc)ln(OV/Dc). [lb] The stability of sliding is ultimately controlled by an inter- action between the stiffness of the loading system and the In the law termed the slowness law, because the evolution dependence of frictional resistance on displacement. In sys- depends on the slowness (inverse of velocity) or on time, the tems for which the frictional behavior is as illustrated in Figs. evolution is given by: 1 and 2, the dependence of frictional resistance on displace- ment is itself a function ofhow friction depends on velocity (15, dO/dt = 1 - OV/Dc.