Earthquake Nucleation

 

 

Figure 1, small

Earthquakes nucleate as accelerating slip over a region of finite size.  Understanding what controls the length and time scales of this process is important for assessing earthquake early-warning systems and for interpreting data obtained by monitoring earthquake-generating faults within tens to hundreds of meters of the source (such as at the 2.5-km-deep San Andreas Fault Observatory at Depth, or SAFOD; see Figure 1). 

Theoretical models of earthquake nucleation require coupling the equations of elasticity with a constitutive law for the evolving strength of the fault surface.  For more than 2 decades the most complete constitutive laws have been various incarnations of “rate- and state dependent friction”, meaning that the frictional strength depends upon the micromechanical state of the fault surface as well as the current slip speed.  Despite this lengthy history, it is most likely that no numerical simulation has ever employed the “correct” constitutive law.  This is because no proposed law fits even all the available experimental data, let alone the conditions of temperature, pressure, and fluid chemistry that might be appropriate in situ.  To make matters worse, the strongly nonlinear nature of friction has made it very difficult to obtain an intuitive understanding of the differences between the underlying equations that people use.  This combination of poorly-constrained constitutive laws and opaque equations is a significant impediment to extrapolating from numerical simulations to fault slip in the Earth.

Over the last several years, the work I have done with post-doc Jean-Paul Ampuero (now an assistant professor at Caltech) has gone a log way toward developing this intuitive understanding.  Using standard methods of fracture mechanics, we now have analytic expressions for the length and time scales of nucleation under the most commonly-used law for the evolution of state (the “aging” law; see Figure 2).  Under this law, nucleation zones can grow to be so large that they might often be detectable from the Earth’s surface.  However, our analytical solutions also let one see immediately that the properties of the aging law that generate these large nucleation zones are directly contradicted by lab experiments. This has led to a collaboration with Chris Marone (Penn State), where we recently showed that lab data relevant to earthquake nucleation are much more consistent with the “slip” evolution law (Figure 3). 

 

Figure 2, small
Figure 2. Snapshots of slip speed, from 10-11 to 1 m/s, from a numerical simulation of nucleation under the “aging” evolution law.  Linf is our analytical prediction of the nucleation length for these parameters. The normalizing length scale Lb could be anywhere from centimeters to many meters.

 

Figure 3, small
Figure 3. Measured change in friction (black curve) as a function of slip, for step velocity increases and decreases of first 1 and then 2 orders of magnitude, on simulated quartz gouge (glass beads). Data were obtained in Chris Marone’s lab at Pen State. The symmetric response to velocity increases and decreases, and the similar decay distance for the different magnitudes of velocity step, are consistent with the slip law (red curve) but not the aging law.

 

 

Figure 5

Figure 5. Mesh plot of the logarithm of the slip speed from a numerical simulation of a 3-D “slip” law nucleation zone. The slip direction is parallel to the x coordinate axis.

Our work shows that if lab results can be safely extrapolated to the Earth (a very big if!), the “slip” law is the proper law for studies of earthquake nucleation. Nucleation under the “aging” and “slip” laws is entirely different, taking the form of an expanding crack in the first case and a unidirectional slip pulse in the second (Figure 4). The extent of this difference is surprising in that both laws have been advertised as being adequate at some level. However, this difference is understandable in terms of the much larger fracture energy at the edge of the expanding nucleation zone implied by the “aging” law. Nucleation under the “slip” law is much less likely to be observable by surface instruments.

 

Related publications:

73 Publications
Journal Article

Planar impact experiments were employed to induce dynamic tensile failure in Bedford limestone. Rock discs were impacted with aluminum and polymethyl methacralate flyer plates at velocities of 10 to 25 m/s. This resulted in tensile stresses in the range of ~11 to 160 MPa. Tensile stress durations of 0.5 and 1.3 μs induced microcrack growth…

ISBN
0148-0227
Journal Article

We compare 2-D, quasi-static earthquake nucleation on rate-and-state faults under both "aging" and "slip" versions of the state evolution law. For both versions mature nucleation zones exhibit 2 primary regimes of growth: Well above and slightly above steady state, corresponding respectively to larger and smaller fault weakening rates. Well…

ISBN
0148-0227
Journal Article

Nonvolcanic tremor is an important component of the slow slip processes which load faults from below, but accurately locating tremor has proven difficult because tremor rarely contains clear P or S wave arrivals. Here we report the observation of coherence in the shear and compressional waves of tremor at widely separated stations which allows…

ISBN
2169-9313
Journal Article
During rock friction experiments at large displacement, room temperature and humidity, and following a hold test, the fracture energy increases approximately as the square of the logarithm of hold duration. While it s been long known that failure strength increases with log hold time, here the slip weakening distance, dh, also increases. The…
Journal Article

A new state evolution law has recently been proposed by Nagata et al. (2012) that includes a dependence upon stressing rate through a laboratory derived proportionality constant c. It has been claimed that this law, while retaining the time-dependent healing of the Dieterich (or Aging) law, can also match the symmetric response of the Ruina (or…

ISBN
2169-9313
Journal Article

The popular constitutive formulations of rate-and-state friction offer two end-member views on whether friction evolves only with slip (Slip law) or with time even without slip (Aging law). While rate stepping experiments show support for the Slip law, laboratory-observed frictional behavior near zero slip rates has traditionally been inferred…

ISBN
2169-9313
Journal Article

Abstract The variations in the response of different state evolution laws to large velocity increases can dramatically alter the style of earthquake nucleation in numerical simulations. But most velocity step friction experiments do not drive the sliding surface far enough above steady state to probe this relevant portion of the parameter space…

ISBN
2169-9313
Journal Article

The duration of each subevent of 48 earthquakes with magnitude larger than 5.5 and depth greater than 100 km was determined from stacked traces of broadband records of Global Seismograph Network stations. We fitted the source time function by one or more triangles convolved with attenuation. We found that global stacks of displacement…

ISBN
0148-0227
Journal Article

Abstract We have recently suggested that the nearly constant duration of low-frequency earthquakes (LFEs) (and, equivalently, the band limitation of tectonic tremor) manifests a moment-duration scaling that is fundamentally different from regular earthquakes and is most easily explained as rupture on asperities of roughly constant dimension. In…

ISBN
2169-9313
Journal Article

Abstract We employ 130 low-frequency earthquake (LFE) templates representing tremor sources on the plate boundary below southern Vancouver Island to examine LFE magnitudes. Each template is assembled from hundreds to thousands of individual LFEs, representing over 269,000 independent detections from major episodic-tremor-and-slip (ETS) events…

ISBN
2169-9313
Journal Article

Since the discovery of slow slip events along subduction zone interfaces worldwide, dense geodetic and seismic networks have illuminated detailed characteristics of these events and associated tremor. High-resolution observations of tremor, where the spatial-temporal evolution is presumed to reflect that of the underlying slow slip events, show…

ISBN
0094-8276
Journal Article

Rate‐ and state‐dependent friction (RSF) equations are commonly used to describe the time‐dependent frictional response of fault gouge to perturbations in sliding velocity. Among the better‐known versions are the Aging and Slip laws for the evolution of state. Although the Slip law is more successful, neither can predict all the robust features…

Journal Article
The empirical constitutive modeling framework of rate- and state-dependent friction (RSF) is commonly used to describe the time-dependent frictional response of fault gouge to perturbations from steady sliding. In a previous study (Ferdowsi & Rubin, 2020), we found that a granular-physics-based model of a fault shear zone, with time-independent…
Journal Article

High confining pressure fracture tests of Indiana limestone [Abou-Sayed, 1977] and Iidate granite [Hashida et al., 1993] were simulated using boundary element techniques and a Dugdale-Barenblatt (tension-softening) model of the fracture process zone. Our results suggest a substantial (more than a factor of 2) increase in the fracture energy of…

ISBN
0148-0227
Journal Article

We investigate the dynamics of viscous pressure losses associated with lateral magma transport in volcanic rift zones by performing (1) coupled elastic-hydrodynamic simulations of downrift magma flow in dikes and (2) analog experiments mimicking lateral dike propagation in the presence of an along-rift topographic slope. It is found that near…

ISBN
0148-0227
Journal Article

We consider the thermal history and dynamics of magma emplacement in giant feeder dikes associated with continental flood basalts. For driving pressure gradients inferred for giant dike swarms, thicknesses of <10 m would enable dikes to transport magma laterally over the distances observed in the field (up to thousands of kilometers) without…

ISBN
0148-0227
Journal Article

We consider solidification of hot fluid flowing through a rigid-wall channel of infinite extent. The calculated ?thermal arrest? lengths are used to investigate the role of magma freezing in limiting the propagation distance of lateral dike intrusions. Our results demonstrate that for reasonable parameters the propagation distances of meter…

ISBN
0148-0227
Journal Article

FREQUENT shallow earthquakes within the rift zones of the Hawaiian volcano Kilauea have been interpreted as resulting from stress changes associated with a shallow magma conduit system1,2. Here, by using a precise earthquake relocation technique3, we show that what had been imaged as a diffuse cloud of seismicity in the Upper East Rift in 1991…

ISBN
1476-4687
Journal Article

We use borehole strain and seismic data to show that slow slip and tremor in central Cascadia are correlated on a range of time scales shorter than 1 day. The recorded strain rate is our proxy for the slow slip moment rate, and the seismic amplitude is our proxy for the tremor amplitude. We find that, on average, the strain rate is higher when…

ISBN
2169-9313
Journal Article

We investigate the behavior of simulated slow slip events using a rate and state friction model that is steady state velocity weakening at low slip speeds but velocity strengthening at high slip speeds. Our simulations are on a one-dimensional (line) fault, but we modify the elastic interactions to mimic the elongate geometry frequently…

ISBN
2169-9313
Journal Article

We examine tidal modulation and back-propagating fronts in simulated slow slip events using a rate and state friction law that is steady state velocity weakening at low slip rates and velocity strengthening at high slip rates. Tidal forcing causes a quasi-sinusoidal modulation of the slip rate during the events, with the maximum moment rate…

ISBN
2169-9313
Journal Article

Several studies have shown that the seismic tremor in episodic tremor and slip is tidally modulated, suggesting a sensitivity to the rather small tidal stresses. We address whether the slip rate in slow slip events is also tidally modulated by examining data from six borehole strainmeters in northwest Washington and southern Vancouver Island…

ISBN
0148-0227
Journal Article

The November 30, 1974, ML = 5.5 and November 16, 1983, ML = 6.6 earthquakes generated left-stepping, en echelon ground cracks within the Kaoiki seismic zone, on the southeast flank of Mauna Loa volcano, Hawaii. The general trend of the ruptures, N48°-55°E, parallels a nodal plane of the main shocks' focal mechanisms. The ruptures themselves…

ISBN
0148-0227
Journal Article

We use seismic waveform cross correlation to determine the relative positions of 2747 microearthquakes near Mount Lewis, California, that have waveforms recorded from 1984 to 1999. These earthquakes include the aftershock sequence of the 1986 ML5.7 Mount Lewis earthquake. Approximately 90% of these aftershocks are located beyond the tips of the…

ISBN
0148-0227
Journal Article

Eruptions on the ice moon Enceladus provide access to materials from Enceladus’ ocean. The mechanism that drives and sustains the eruptions is unclear, and it is also not known what sets the rate of volcanism. We found that a simple model in which the erupting fissures are underlain by slots that connect the surface to the ocean can explain the…

Journal Article

Abstract Whether rate- and state-dependent friction evolution is primarily slip dependent or time dependent is not well resolved. Although slide-hold-slide experiments are traditionally interpreted as supporting the aging law, implying time-dependent evolution, recent studies show that this evidence is equivocal. In contrast, the slip law…

ISBN
2169-9313
Journal Article

In the vicinity of episodic aseismic transients in several subduction zones, the presence of interstitial fluids and near-lithostatic pore pressure has been proposed to interpret seismic observations of high P to S wave speed ratio and high Poisson's ratio. Under such conditions, fault stabilization by dilatancy-induced suction during increased…

ISBN
0148-0227
Journal Article

[1] The recurrence intervals for 194 repeating clusters on the Calaveras fault follow a power‐law decay relation with elapsed time after the 1984 M6.2 Morgan Hill, California, mainshock. The decay rates of repeating aftershocks in the immediate vicinity of a high‐slip patch that failed during the mainshock systematically exceed those that…

Journal Article

Abstract In this study, we analyze high-resolution tremor catalogs from northern Cascadia, Guerrero, and northern Kii Peninsula. We find that tremor often occurs in short bursts that repeatedly occupy the same source area within a slow slip event. We hypothesize that these bursts are driven by loading from slow slip in areas surrounding the…

ISBN
0094-8276
Journal Article
We develop a cross-station method to detect and locate tremor and low-frequency earthquakes (LFEs), based on the original work of Armbruster et al. (2014) that compares waveforms from the same time window at stations separated by roughly 10 km. To improve the signal-to-noise ratio, we first rotate the horizontal components into the empirical shear…
Journal Article

Abstract Slow slip events exhibit significant complexity in slip evolution and variations in recurrence intervals. Behavior that varies systematically with recurrence interval is likely to reflect different extents of fault healing between these events. Here we use high-resolution tremor catalogs beneath Guerrero, Mexico, to investigate the…

ISBN
0094-8276
Journal Article

Abstract Episodic tremor and slip (ETS) in subduction zones is generally interpreted as the manifestation of shear slip near the base of earthquake-generating portion of the plate interface. Here we devise a new method of cross-correlating stacked Array of Arrays seismic data that provides greatly improved tremor locations, a proxy for the…

ISBN
1525-2027
Journal Article

Stress inversion methods employed by structural geologists for estimating a regional stress tensor from populations of faults containing slickenlines rely on the basic assumption that slip on each fault plane occurs in the direction of maximum resolved regional shear stress. This premise ignores directional differences in fault compliance…

ISBN
0191-8141
Journal Article

Recent relocation and focal mechanism analyses of deep earthquakes beneath Kilauea volcano, Hawaii indicate that seismicity is concentrated on a horizontal fault zone at a depth of 30 km, with seaward slip of the upper block on a low-angle plane. We discuss whether the observed localization of the earthquakes can be explained primarily by…

ISBN
0956-540X
Journal Article

We apply a new method to obtain accurate locations of tremor sources beneath southern Vancouver Island. Unlike more standard "cross-time" methods, which compare waveforms from different time windows at the same station, this "cross-station" method compares waveforms from the same time window at widely separated stations. It performs well,…

ISBN
1525-2027
Journal Article

Zhou et al. (2012) proposed that longitudinal dunes in the Qaidam Basin, China, formed like yardangs: by erosion into sediment that was not deposited by those dunes. Because erosion occurs on the upwind fl anks of most migrating dunes (Rubin and Hunter, 1982, 1985), the key to demonstrating a yardang-like origin is to show that the dunes did…

ISBN
0016-7606
Journal Article

The mechanism of magma transport at depth influences direction magma moves, the distance it travels before freezing, the degree to which it communicates chemically with the host rock, the form of surficial volcanism, and ultimately the growth of oceanic and continental crust. Commonly envisioned transport processes include porous flow in…

ISBN
0084-6597
Journal Article

Whether a dike can propagate far from a magma reservoir depends upon the competition between the rate at which propagation widens the dike and the rate at which freezing constricts the aperture available for magma flow. Various formulations are developed for a viscous fluid at temperature Tm intruding a growing crack in an elastic solid. The…

ISBN
0148-0227
Journal Article

Field observations indicate that zones of inelastic deformation produced at the tips of propagating dikes can be much larger than those produced at the tips of tensile cracks in laboratory experiments. This is in direct conflict with the concept that fracture toughness and fracture energy are rock properties, independent of crack size and…

ISBN
0148-0227
Journal Article

Dikes beginning to propagate away from a magma source are thin and grow slowly, and thus are susceptible to freezing. A self-similar solution is obtained for a dike propagating down a temperature gradient when the wallrock and magma temperatures are equal at the chamber wall. The solution applies only to the special case of a single-component…

ISBN
0094-8276
Journal Article

A striking observation from both Cascadia and Japan is that the tremor associated with slow slip often migrates along strike at speeds close to 10 km/d but updip and downdip at speeds approaching 100 km/h. In this paper I adopt the view that the friction law appropriate for these regions is unknown, and I ask what constraints the observed…

ISBN
1525-2027
Journal Article

Field observations and geodetic data indicate that dike intrusion in volcanic rift zones typically generates normal faulting and graben subsidence at the Earth's surface. Elastic models indicate that two-dimensional (infinite strike length) dikes do not lower the ground surface above the dike and that normal faults do not lower the surface…

ISBN
0148-0227
Journal Article

Planar impact experiments were employed to induce dynamic tensile failure in Bedford limestone. Rock discs were impacted with aluminum and polymethyl methacralate (PMMA) flyer plates at velocities of 10 to 25 m/s. Tensile stress magnitudes and duration were chosen so as to induce a range of microcrack growth insufficient to cause complete…

ISBN
0094-8276
Journal Article

For a wide range of conditions, earthquake nucleation zones on rate- and state-dependent faults that obey either of the popular state evolution laws expand as they accelerate. Under the "slip" evolution law, which experiments show to be the more relevant law for nucleation, this expansion takes the form of a unidirectional slip pulse. In…

ISBN
0148-0227
Journal Article

There are several ways of generating episodic slow slip events in models of rate-and-state friction. Here I explore the possibility that they arise on velocity-weakening faults whose length is "tuned" in some sense. Unlike spring-block sliders, which have a unique critical stiffness for instability, elastically deformable faults have…

ISBN
0148-0227
Journal Article

Observations of eroded volcanic rift zones indicate that dikes in Iceland are typically several times thicker than those in Hawaii. Geodetic and seismic observations of active rifts, however, suggest that dike heights in the two regions are similar. Provided the elastic properties of the rift zones are the same, this implies that dikes are…

ISBN
1432-0819
Journal Article

Geodetic data and field observations demonstrate that the emplacement of dikes in volcanic rift zones frequently generates normal faulting and graben subsidence at the Earth's surface. Elastic modeling of the vertical ground-surface displacements above dikes and faults indicates that the extent of graben subsidence can be achieved only if fault…

ISBN
0091-7613
Journal Article

Correction to “Aftershock asymmetry on a bimaterial surface”

Journal Article

We obtain quasi-static, two-dimensional solutions for earthquake nucleation on faults obeying Dieterich's ?aging? version of the rate and state friction equations. Two distinct nucleation regimes are found, separated by roughly a/b ? 0.5, where a and b are the constitutive parameters relating changes in slip rate V and state ? to frictional…

ISBN
0148-0227