Chris Marone

On the mechanics of earthquake afterslip

We propose a model for earthquake afterslip based on rate and state variable friction laws. In the model, afterslip is attributed to the interaction of a velocity-weakening region at depth (within which earthquakes nucleate) with an upper region of velocity-strengthening frictional behavior. The existence of this upper region is supported by independent seismologic observations and the results of laboratory friction experiments. In our model, afterslip is the result of relaxation of a stress perturbation within the velocity-strengthening region, which arises when an earthquake propagates into that region from below. We derive the stress perturbation and its decay from the friction constitutive law using a simple, 1 degree-of-freedom approximation for the elastic interaction between the fault and its surroundings. This approximation is based on thickness-averaged displacements and slip velocities within the velocity-strengthening region, which is assumed to slip as a rigid block. Coseismic and postseismic slip are coupled through the thickness-averaged stiffness k of the velocity-strengthening region. We assume k to be inversely proportional to the thickness of this region, which means that thicker velocity strengthening regions have a greater tendency to arrest coseismic slip. We model the afterslip-time histories of the 1966 Parkfield and 1987 Superstition Hills earthquakes and relate the model parameters to physical parameters which may govern the rheologic behavior of the faults. In accord with field observations, our model predicts (1) that afterslip on some faults scales with the thickness of the (unconsolidated) sedimentary cover and (2) that proportionally more afterslip occurs for earthquakes in which coseismic surface slip is small compared with coseismic slip at depth. Velocity-strengthening frictional behavior is to be expected for faults within poorly consolidated sediments and for those that contain significant gouge zones (about >500 m) within their shallow regions (<3–5 km). Combining our results with those of recent laboratory friction studies indicates that relatively young faults with little accumulated fault gouge should exhibit little afterslip.

Comparison of smectite- and illite-rich gouge frictional properties: application to the updip limit of the seismogenic zone along subduction megathrusts

Along plate boundary subduction thrusts, the transformation of smectite to illite within fault gouge at temperatures of ∼150°C is one of the key mineralogical changes thought to control the updip limit of seismicity. If correct, this hypothesis requires illite-rich gouges to exhibit frictionally unstable (velocity-weakening) behavior. Here, we report on laboratory experiments designed to investigate the frictional behavior of natural and synthetic clay-rich gouges. We sheared 5-mm-thick layers of commercially obtained pure Ca-smectite, a suite of smectite–quartz mixtures, and natural illite shale (grain size ranging from 2 to 500 μm) in the double-direct shear geometry to shear strains of ∼7–30 at room humidity and temperature. XRD analyses show that the illite shale contains dominantly clay minerals and quartz; within the clay-sized fraction ( 40 MPa). Our data, specifically the velocity-strengthening behavior of illite shale under a wide range of conditions, do not support the hypothesis that the smectite–illite transition is responsible for the seismic–aseismic transition in subduction zones. We suggest that other depth- and temperature-dependent processes, such as cementation, consolidation, and slip localization with increased shearing, may play an important role in changing the frictional properties of subduction zone faults, and that these processes, in addition to clay mineralogy, should be the focus of future investigation.

Fault zone fabric and fault weakness

Geological and geophysical evidence suggests that some crustal faults are weak compared to laboratory measurements of frictional strength. Explanations for fault weakness include the presence of weak minerals, high fluid pressures within the fault core and dynamic processes such as normal stress reduction, acoustic fluidization or extreme weakening at high slip velocity. Dynamic weakening mechanisms can explain some observations; however, creep and aseismic slip are thought to occur on weak faults, and quasi-static weakening mechanisms are required to initiate frictional slip on mis-oriented faults, at high angles to the tectonic stress field. Moreover, the maintenance of high fluid pressures requires specialized conditions and weak mineral phases are not present in sufficient abundance to satisfy weak fault models, so weak faults remain largely unexplained. Here we provide laboratory evidence for a brittle, frictional weakening mechanism based on common fault zone fabrics. We report on the frictional strength of intact fault rocks sheared in their in situ geometry. Samples with well-developed foliation are extremely weak compared to their powdered equivalents. Micro- and nano-structural studies show that frictional sliding occurs along very fine-grained foliations composed of phyllosilicates (talc and smectite). When the same rocks are powdered, frictional strength is high, consistent with cataclastic processes. Our data show that fault weakness can occur in cases where weak mineral phases constitute only a small percentage of the total fault rock and that low friction results from slip on a network of weak phyllosilicate-rich surfaces that define the rock fabric. The widespread documentation of foliated fault rocks along mature faults in different tectonic settings and from many different protoliths suggests that this mechanism could be a viable explanation for fault weakening in the brittle crust.

Quantitative measure of the variation in fault rheology due to fluid‐rock interactions

We analyze friction data from two published suites of laboratory tests on granite in order to explore and quantify the effects of temperature (T) and pore water pressure (Pp) on the sliding behavior of faults. Rate-stepping sliding tests were performed on laboratory faults in granite containing “gouge” (granite powder), both dry at 23° to 845°C [Lockner et al., 1986], and wet (Pp = 100 MPa) at 23° to 600°C [Blanpied et al., 1991, 1995]. Imposed slip velocities (V) ranged from 0.01 to 5.5 μm/s, and effective normal stresses were near 400 MPa. For dried granite at all temperatures, and wet granite below ∼300°C, the coefficient of friction (μ) shows low sensitivity to V, T, and Pp. For wet granite above ∼350°, μ drops rapidly with increasing T and shows a strong, positive rate dependence and protracted strength transients following steps in V, presumably reflecting the activity of a water-aided deformation process. By inverting strength data from velocity stepping tests we determined values for parameters in three formulations of a rate- and state-dependent constitutive law. One or two state variables were used to represent slip history effects. Each velocity step yielded an independent set of values for the nominal friction level, five constitutive parameters (transient parameters a, b1, and b2 and characteristic displacements Dc1 and Dc2), and the velocity dependence of steady state friction ∂μss/∂ ln V = a-b1−b2. Below 250°, data from dry and most wet tests are adequately modeled by using the “slip law” [Ruina, 1983] and one state variable (a = 0.003 to 0.018, b = 0.001 to +0.018, Dc ≈ 1 to 20 μm). Dried tests above 250° can also be fitted with one state variable. In contrast, wet tests above 350° require higher direct rate dependence (a = 0.03 to 0.12), plus a second state variable with large, negative amplitude (b2 = −0.03 to −0.14) and large characteristic displacement (Dc2 = 300 to >4000 μm). Thus the parameters a, b1, and b2 for wet granite show a pronounced change in their temperature dependence in the range 270° to 350°C, which may reflect a change in underlying deformation mechanism. We quantify the trends in parameter values from 25° to 600°C by piecewise linear regressions, which provide a straightforward means to incorporate the full constitutive response of granite into numerical models of fault slip. The modeling results suggest that the succeptibility for unstable (stick-slip) sliding is maximized between 90° and 360°C, in agreement with laboratory observations and consistent with the depth range of earthquakes on mature faults in the continental crust.

Particle-size distribution and microstructures within simulated fault gouge

This paper presents an investigation of comminution mechanisms and microstructure development within simulated fault gouge. We sheared 4.0 mm thick layers of quartz sand between rough steel surfaces using a triaxial apparatus. The layers were sheared at constant effective normal stress of 100 MPa, under saturated drained conditions, and at 45 ° to the axis of cylindrical steel samples. Porosity changes were measured throughout shear and microstructural observations were carried out on the deformed layers. Two types of load paths were investigated for shear strains (y) between 0 and 3.3; either the shear stress was repeatedly cycled from zero to failure or the sample was sheared in a single-load cycle. Multiple-cycle experiments exhibit significantly more compaction than single-cycle experiments deformed to similar strains. Gouge layers from both sets of experiments contain oblique zones of localized shear (Riedel shears bands) after 7 = 1.3-1.5. Gouge particles obey a fractal size distribution for the range 12.5--800,um; i.e. particle density vs size follows a power law, N(n)/A = bn -°, where N(n) is the number of particles in a size range, A is the area examined, n is the mean of the size range, b is a constant and D is the fractal dimension. D for particles within the bulk material increases with shear strain for y < about 1.5 after which it remains 2.6 _-. 0.15. This value of D agrees with that found for natural fault gouge and with that predicted by a comminution model in which fracture probability depends on the relative size of nearest-neighbor particles. Analyses of particles within shear bands indicate continued size reduction after ~ = 1.5. These particles do not obey a fractal size distribution for the range 6.25-100 um due to a lack of particles larger than 25-50/,tm. The rate of comminution within the bulk layer decreases at about y = 1.5, which coincides with the onset of shear localization. Our data indicate that comminution is driven by relative movement between particles and that gouge layers attain a steady state particle-size distribution at 7 = 1.5. The porosity-strain data and microstructural observations show a correlation between the onset of shear localization and the rate of dilatancy with shear strain.

The effect of loading rate on static friction and the rate of fault healing during the earthquake cycle

The seismic cycle requires that faults strengthen (heal) between earthquakes, and the rate of this healing process plays a key role in determining earthquake stress drop, rupture characteristics, and seismic scaling relations,. Frictional healing (as evidenced by increasing static friction during quasi-stationary contact between two surfaces,) is considered the mechanism most likely to be responsible for fault strengthening,,,. Previous studies, however, have shown a large discrepancy between laboratory and seismic (field) estimates of the healing rate,,,,; in the laboratory, rock friction changes by only a few per cent per order-of-magnitude change in slip rate, whereas seismic stress drop increases by a factor of 2 to 5 per order-of-magnitude increase in earthquake recurrence interval. But in such comparisons, it is assumed that healing and static friction are independent of loading rate. Here, I summarize laboratory measurements showing that static friction and healing vary with loading rate and time, as expected from friction theory. Applying these results to seismic faulting and accounting for differences in laboratory, seismic and tectonic slip rates, I demonstrate that post-seismic healing is expected to be retardedfor a period of several hundred days following an earthquake, in agreement with recent findings from repeating earthquakes,,,.

Friction of simulated fault gouge for a wide range of velocities and normal stresses

During earthquake rupture, faults slip at velocities of cm/s to m/s. Fault friction at these velocities strongly influences dynamic rupture but is at present poorly constrained. We study friction of simulated fault gouge as a function of normal stress (σn = 25 to 70 MPa) and load point velocity (V = 0.001 to 10 mm/s). Layers of granular quartz (3 mm thick) are sheared between rough surfaces in a direct shear apparatus at ambient conditions. For a constant σn, we impose regular step changes in V throughout 20 mm net slip and monitor the frictional response. A striking observation at high velocity is a dramatic reduction in the instantaneous change in frictional strength for a step change in velocity (friction direct effect) with accumulated slip. Gouge layers dilate for a step increase in velocity, and the amount of dilation decreases with slip and is systematically greater at higher velocity. The steady state friction velocity dependence (a-b) evolves from strengthening to weakening with slip but is not significantly influenced by V or σn. Measurements of dilation imply that an additional mechanism, such as grain rolling, operates at high velocity and that the active shear zone narrows with slip. Data from slow (μm/s) and fast (mm/s) tests indicate a similar displacement dependent textural evolution and comparable comminution rates. Our experiments produce a distinct shear localization fabric and velocity weakening behavior despite limited net displacements and negligible shear heating. Under these conditions we find no evidence for the strong velocity weakening or low friction values predicted by some theoretical models of dynamic rupture. Thus certain mechanisms for strong frictional weakening, such as grain rolling, can likely be ruled out for the conditions of our study.

On the relation between fault strength and frictional stability

A fundamental problem in fault mechanics is whether slip instability associated with earthquake nucleation depends on absolute fault strength. We present laboratory experimental evidence for a systematic relationship between frictional strength and friction rate dependence, one of the key parameters controlling stability, for a wide range of constituent minerals relevant to natural faults. All of the frictionally weak gouges (coefficient of sliding friction, μ < 0.5) are composed of phyllosilicate minerals and exhibit increased friction with slip velocity, known as velocity-strengthening behavior, which suppresses frictional instability. In contrast, fault gouges with higher frictional strength exhibit both velocity-weakening and velocity-strengthening frictional behavior. These materials are dominantly quartzofeldspathic in composition, but in some cases include certain phyllosilicate-rich gouges with high friction coefficients. We also find that frictional velocity dependence evolves systematically with shear strain, such that a critical shear strain is required to allow slip instability. As applied to tectonic faults, our results suggest that seismic behavior and the mode of fault slip may evolve predictably as a function of accumulated offset.

Effects of normal stress vibrations on frictional healing

We conducted laboratory experiments to study frictional healing and the effects of normal stress vibrations on healing. The experiments were carried out using a servo-controlled double-direct shear apparatus on 10 cm × 10 cm blocks separated by a 3 mm-thick gouge layer of fine-grained (grain size of 75–212 μm) quartz powder. We performed slide-hold-slide tests in which sliding surfaces were driven at a constant velocity, halted for a given interval, then restarted at the prior driving velocity. Healing varied systematically with cumulative displacement, and by conducting several sets of identical slide-hold-slides we calibrated and removed these effects. Forward modeling of the healing and relaxation curves using the rate- and state-dependent friction laws shows that a displacement-dependent increase in the parameter b can account for our observations. To study the effects of vibration, we varied the mean normal stress of 25 MPa during holds by double amplitudes ranging from 1 to 13 MPa at a frequency of 1 Hz. Vibrations increased rates and magnitudes of frictional relaxation and healing, most likely due to increased gouge compaction. These effects increased with increasing amplitude of vibration. We performed normal stress step tests and used the results to model the vibrational slide-hold-slide tests. Rate- and state-dependent constitutive laws cannot adequately describe the behavior we observed experimentally because they neglect gouge compaction. Mechanisms such as normal force oscillations may explain faster fault healing rates than would be predicted by standard laboratory measurements at constant stress.

Laboratory results indicating complex and potentially unstable frictional behavior of smectite clay

A central problem in explaining the apparent weakness of the San Andreas and other plate boundary faults has been identifying candidate fault zone materials that are both weak and capable of hosting earthquake-like unstable rupture. Our results demonstrate that smectite clay can be both weak and velocity weakening at low normal stress (<30 MPa). Our data are consistent with previous work, which has focused on higher normal stress conditions (50 MPa and greater) and found only velocity strengthening. If natural fault zones contain significant smectite, one key implication of our results is that localized zones of high pore pressure, which reduce effective normal stress, could be important in controlling potential sites of earthquake nucleation. Our experiments indicate that friction of smectite is complex, and depends upon both sliding velocity and normal stress. This complexity highlights the need for detailed experiments that reflect in-situ conditions for fault gouges.