Nick Beeler

Constitutive relationships and physical basis of fault strength due to flash heating

[1]xa0We develop a model of fault strength loss resulting from phase change at asperity contacts due to flash heating that considers a distribution of contact sizes and nonsteady state evolution of fault strength with displacement. Laboratory faulting experiments conducted at high sliding velocities, which show dramatic strength reduction below the threshold for bulk melting, are well fit by the model. The predicted slip speed for the onset of weakening is in the range of 0.05 to 2 m/s, qualitatively consistent with the limited published observations. For this model, earthquake stress drops and effective shear fracture energy should be linearly pressure-dependent, whereas the onset speed may be pressure-independent or weakly pressure-dependent. On the basis of the theory, flash weakening is expected to produce large dynamic stress drops, small effective shear fracture energy, and undershoot. Estimates of the threshold slip speed, stress drop, and fracture energy are uncertain due to poor knowledge of the average contact dimension, shear zone thickness and gouge particle size at seismogenic depths.

Pore fluid pressure, apparent friction, and Coulomb failure

Many recent studies of stress-triggered seismicity rely on a fault failure model with a single free parameter, the apparent coefficient of friction, presumed to be a material constant with possible values 0 ≤ μ′ ≤ 1. These studies may present a misleading view of fault strength and the role of pore fluid pressure in earthquake failure. The parameter μ′ is intended to incorporate the effects of both friction and pore pressure, but is a material constant only if changes in pore fluid pressure induced by changes in stress are proportional to the normal stress change across the potential failure plane. Although specific models of fault zones permit such a relation, neither is it known that fault zones within the Earth behave this way, nor is this behavior expected in all cases. In contrast, for an isotropic homogeneous poroelastic model the pore pressure changes are proportional to changes in mean stress, μ′ is not a material constant, and −∞ ≤ μ′ ≤ +∞. Analysis of the change in Coulomb failure stress for tectonically loaded reverse and strike-slip faults shows considerable differences between these two pore pressure models, suggesting that such models might be distinguished from one another using observations of triggered seismicity (e.g., aftershocks). We conclude that using the constant apparent friction model exclusively in studies of Coulomb failure stress is unwise and could lead to significant errors in estimated stress change and seismic hazard.

Why earthquakes correlate weakly with the solid Earth tides: Effects of periodic stress on the rate and probability of earthquake occurrence

[1] We provide an explanation why earthquake occurrence does not correlate well with the daily solid Earth tides. The explanation is derived from analysis of laboratory experiments in which faults are loaded to quasiperiodic failure by the combined action of a constant stressing rate, intended to simulate tectonic loading, and a small sinusoidal stress, analogous to the Earth tides. Event populations whose failure times correlate with the oscillating stress show two modes of response; the response mode depends on the stressing frequency. Correlation that is consistent with stress threshold failure models, e.g., Coulomb failure, results when the period of stress oscillation exceeds a characteristic time t n ; the degree of correlation between failure time and the phase of the driving stress depends on the amplitude and frequency of the stress oscillation and on the stressing rate. When the period of the oscillating stress is less than t n , the correlation is not consistent with threshold failure models, and much higher stress amplitudes are required to induce detectable correlation with the oscillating stress. The physical interpretation of t n is the duration of failure nucleation. Behavior at the higher frequencies is consistent with a second-order dependence of the fault strength on sliding rate which determines the duration of nucleation and damps the response to stress change at frequencies greater than 1/t n . Simple extrapolation of these results to the Earth suggests a very weak correlation of earthquakes with the daily Earth tides, one that would require >13,000 earthquakes to detect. On the basis of our experiments and analysis, the absence of definitive daily triggering of earthquakes by the Earth tides requires that for earthquakes, t n exceeds the daily tidal period. The experiments suggest that the minimum typical duration of earthquake nucleation on the San Andreas fault system is ∼1 year.

Premonitory slip and tidal triggering of earthquakes

We have conducted a series of laboratory simulations of earthquakes using granite cylinders containing precut bare fault surfaces at 50 MPa confining pressure. Axial shortening rates between 10−4and 10−6 mm/s were imposed to simulate tectonic loading. Average loading rate was then modulated by the addition of a small-amplitude sine wave to simulate periodic loading due to Earth tides or other sources. The period of the modulating signal ranged from 10 to 10,000 s. For each combination of amplitude and period of the modulating signal, multiple stick-slip events were recorded to determine the degree of correlation between the timing of simulated earthquakes and the imposed periodic loading function. Over the range of parameters studied, the degree of correlation of earthquakes was most sensitive to the amplitude of the periodic loading, with weaker dependence on the period of oscillations and the average loading rate. Accelerating premonitory slip was observed in these experiments and is a controlling factor in determining the conditions under which correlated events occur. In fact, some form of delayed failure is necessary to produce the observed correlations between simulated earthquake timing and characteristics of the periodic loading function. The transition from strongly correlated to weakly correlated model earthquake populations occurred when the amplitude of the periodic loading was approximately 0.05 to 0.1 MPa shear stress (0.03 to 0.06 MPa Coulomb failure function). Lower-amplitude oscillations produced progressively lower correlation levels. Correlations between static stress increases and earthquake aftershocks are found to degrade at similar stress levels. Typical stress variations due to Earth tides are only 0.001 to 0.004 MPa, so that the lack of correlation between Earth tides and earthquakes is also consistent with our findings. A simple extrapolation of our results suggests that approximately 1% of midcrustal earthquakes should be correlated with Earth tides. Triggered seismicity has been reported resulting from the passage of surface waves excited by the Landers earthquake. These transient waves had measured amplitudes in excess of 0.1 MPa at frequencies of 0.05 to 0.2 Hz in regions of notable seismicity increase. Similar stress oscillations in our laboratory experiments produced strongly correlated stick-slip events. We suggest that seemingly inconsistent natural observations of triggered seismicity and absence of tidal triggering indicate that failure is amplitude and frequency dependent. This is the expected result if, as in our laboratory experiments, the rheology of the Earths crust permits delayed failure.

Improved constraints on the estimated size and volatile content of the Mount St. Helens magma system from the 2004-2008 history of dome growth and deformation

[1]xa0The history of dome growth and geodetic deflation during the 2004–2008 Mount St. Helens eruption can be fit to theoretical curves with parameters such as reservoir volume, bubble content, initial overpressure, and magma rheology, here assumed to be Newtonian viscous, with or without a solid plug in the conduit center. Data from 2004–2008 are consistent with eruption from a 10–25 km3 reservoir containing 0.5–2% bubbles, an initial overpressure of 10–20 MPa, and no significant, sustained recharge. During the eruption we used curve fits to project the eruptions final duration and volume. Early projections predicted a final volume only about half of the actual value; but projections increased with each measurement, implying a temporal increase in reservoir volume or compressibility. A simple interpretation is that early effusion was driven by a 5–10 km3, integrated core of fluid magma. This core expanded with time through creep of semi-solid magma and host rock.

Earthquake stress drop and laboratory‐inferred interseismic strength recovery

We determine the scaling relationships between earthquake stress drop and recurrence interval tr that are implied by laboratory-measured fault strength. We assume that repeating earthquakes can be simulated by stick-slip sliding using a spring and slider block model. Simulations with static/kinetic strength, time-dependent strength, and rate- and state-variable-dependent strength indicate that the relationship between loading velocity and recurrence interval can be adequately described by the power law VL∝trn where n≈−1. Deviations from n=−1 arise from second order effects on strength, with n>−1 corresponding to apparent time-dependent strengthening and n<−1 corresponding to weakening. Simulations with rate and state-variable equations show that dynamic shear stress drop Δτd scales with recurrence as dΔτd/dlntr≤σe(b-a), where σe is the effective normal stress, μ=τ/σe, and (a-b)=dμss/dlnV is the steady-state slip rate dependence of strength. In addition, accounting for seismic energy radiation, we suggest that the static shear stress drop Δτs scales as dΔτs/dlntr≤σe(1 +ζ)(b-a), where ζ is the fractional overshoot. The variation of Δτs with lntr for earthquake stress drops is somewhat larger than implied by room temperature laboratory values of ζ and b-a. However, the uncertainty associated with the seismic data is large and the discrepancy between the seismic observations and the rate of strengthening predicted by room temperature experiments is less than an order of magnitude.

Stress-induced, time-dependent fracture closure at hydrothermal conditions

[1]xa0Time-dependent closure of fractures in quartz was measured in situ at 22–530°C temperature and 0.1–150 MPa water pressure. Unlike previous crack healing and rock permeability studies, in this study, fracture aperture is monitored directly and continuously using a windowed pressure vessel, a long-working-distance microscope, and reflected-light interferometry. Thus the fracture volume and geometry can be measured as a function of time, temperature, and water pressure. Relatively uniform closure occurs rapidly at temperatures and pressures where quartz becomes significantly soluble in water. During closure the aperture is reduced by as much as 80% in a few hours. We infer that this closure results from the dissolution of small particles or asperities that prop the fracture open. The driving force for closure via dissolution of the prop is the sum of three chemical potential terms: (1) the dissolution potential, proportional to the logarithm of the degree of undersaturation of the solution; (2) the coarsening potential, proportional to the radius of curvature of the prop; and (3) the pressure solution potential, proportional to the effective normal stress at the contact between propping particles and the fracture wall. Our observations suggest that closure is controlled by a pressure solution-like process. The aperture of dilatant fractures and microcracks in the Earth that are similar to those in our experiments, such as ones generated from thermal stressing or brittle failure during earthquake rupture and slip, will decrease rapidly with time, especially if the macroscopic stress is nonhydrostatic.

Scaling of stress drop with recurrence interval and loading velocity for laboratory-derived fault strength relations

[1]xa0The dynamics of a spring-slider system with a single degree of freedom was investigated, focusing on two different rate- and state-dependent friction laws. While the inertia-controlled behavior and stick-slip cycles for a system that obeys the slip law have been extensively simulated, this study presents a comparative study of a system that obeys the slowness law. A key conclusion is that for both friction laws the overall stress drops are linearly related to the logarithm of the loading velocity (and the recurrence time) through the velocity-weakening parameter b − a and normal stress. Relatively higher peak stresses, larger quasi-static stress drop, and larger effective fracture energy are associated with a system that obeys the slowness law. Consequently, the partitioning of stress drop between quasi-static and dynamic slips, as well as dynamic overshoot and strength recovery, varies according to whether the slowness or slip law has been adopted. Analytic approximations were derived that elucidate the interplay of dynamics, energetics, and frictional constitutive behavior in controlling the scaling of stress drops with loading velocity and recurrence time. Seismological implications of the scaling behavior are also discussed.

The instantaneous rate dependence in low temperature laboratory rock friction and rock deformation experiments

[1]xa0Earthquake occurrence probabilities that account for stress transfer and time-dependent failure depend on the product of the effective normal stress and a lab-derived dimensionless coefficient a. This coefficient describes the instantaneous dependence of fault strength on deformation rate, and determines the duration of precursory slip. Although an instantaneous rate dependence is observed for fracture, friction, crack growth, and low temperature plasticity in laboratory experiments, the physical origin of this effect during earthquake faulting is obscure. We examine this rate dependence in laboratory experiments on different rock types using a normalization scheme modified from one proposed by Tullis and Weeks [1987]. We compare the instantaneous rate dependence in rock friction with rate dependence measurements from higher temperature dislocation glide experiments. The same normalization scheme is used to compare rate dependence in friction to rock fracture and to low-temperature crack growth tests. For particular weak phyllosilicate minerals, the instantaneous friction rate dependence is consistent with dislocation glide. In intact rock failure tests, for each rock type considered, the instantaneous rate dependence is the same size as for friction, suggesting a common physical origin. During subcritical crack growth in strong quartzofeldspathic and carbonate rock where glide is not possible, the instantaneous rate dependence measured during failure or creep tests at high stress has long been thought to be due to crack growth; however, direct comparison between crack growth and friction tests shows poor agreement. The crack growth rate dependence appears to be higher than the rate dependence of friction and fracture by a factor of two to three for all rock types considered.

Stress drop with constant, scale independent seismic efficiency and overshoot

To model dissipated and radiated energy during earthquake stress drop, I calculate dynamic fault slip using a single degree of freedom spring-slider block and a laboratory-based static/kinetic fault strength relation with a dynamic stress drop proportional to effective normal stress. The model is scaled to earthquake size assuming a circular rupture; stiffness varies inversely with rupture radius, and rupture duration is proportional to radius. Calculated seismic efficiency, the ratio of radiated to total energy expended during stress drop, is in good agreement with laboratory and field observations. Predicted overshoot, a measure of how much the static stress drop exceeds the dynamic stress drop, is higher than previously published laboratory and seismic observations and fully elasto-dynamic calculations. Seismic efficiency and overshoot are constant, independent of normal stress and scale. Calculated variation of apparent stress with seismic moment resembles the observational constraints of McGarr [1999].