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
Government Report

Seismic and geodetic data have demonstrated that dikes in the rift zones of Kilauea Volcano in Hawaii and Krafla Volcano in Iceland are typically intruded laterally from a central magma reservoir and acquire a blade-like form. A remarkable feature of many such dikes is that they propagate at shallow depths for 10s of km without erupting. Using…

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

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

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

Shock wave data to provide an equation of state of muscovite (initial density: 2.835 g/cm3) were determined up to a pressure of 141 GPa. The shock velocity (Us) versus particle velocity (Up) data are fit with a single linear relationship: Us=4.62(±0.12) +1.27(±0.04)Up (km/s). Third-order Birch-Murnaghan equation of state parameters (isentropic…

ISBN
0148-0227
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

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

Geophysical models have traditionally treated diapiric ascent as occurring in purely viscous host rock, and dike intrusion as occurring in purely elastic host rock. Such models are incapable of determining (1) what governs the transition between the two transport mechanisms, (2) the properties of diapirs that ascend via a combination of…

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

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

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
Book

G. Baer & A. Heimann (eds).

This work combines research results with review papers, discussing dykes from different scientific perspectives. Coverage includes: current dyke geometry measurements; field observation of host rock deformation; textural analyses; and geochemical and petrological studies of dyke swarms.

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

New equation of state data for a weathered granite shocked to about 125 GPa are reported and combined with the Westerly granite data of McQueen, Marsh & Fritz (1967). The shock velocity (Us)-particle velocity (Up) relations can be fitted with two linear regressions: Us = 4.40 + 0.6Up for a range of Up up to about 2 km s−1 and Us = 2.66 + 1…

ISBN
0956-540X
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

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

Earthquakes of magnitude 1 and greater seem to be ubiquitous features of dike propagation, but their origin is not well understood. We examine the elastic stress field surrounding propagating fluid‐filled cracks, with an emphasis on assessing the ambient stress required to produce earthquakes with linear dimensions of ∼100 m near dikes with…

Journal Article

In January 1983, a dike intrusion/fissure eruption generated a swarm of 375 magnitude 1 to 3 earthquakes along a 16‐km segment of Kilauea's Middle East Rift Zone. We searched the Hawaiian Volcano Observatory catalog for multiplets of similar events from this region from 1980 through 1985 and obtained precise relative locations by waveform cross…

Journal Article

Field observations indicate that dikes form and grow in magma source regions, but the mechanics of this process are poorly understood. I derive time-dependent and self-similar solutions for the growth of buoyant dikes fed by porous flow in partially molten rock. The host rock is treated as poroelastic; for basaltic (but not rhyolitic) dikes,…

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

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

Crustal faults that produce most of their slip aseismically typically generate large numbers of small earthquakes. These events have generally been interpreted as coming from localized patches of the fault that undergo unstable (stick–slip) sliding, surrounded by larger regions of stable sliding (creep). In published catalogues the…

ISBN
1476-4687
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

Using a waveform cross-correlation technique, we have obtained precise relative locations for nearly 75% of the Northern California Seismic Network catalog (4300 earthquakes) occurring between 1984 and 1997 along 50 km of the San Andreas fault. Errors in relative location are meters to tens of meters for events separated by tens to hundreds of…

ISBN
0148-0227
Journal Article

The main objective of this study is to see if a lower threshold for earthquake triggering exists. Resolving this issue is important for the understanding of earthquake mechanics and for the purpose of hazard analysis. We compute the cumulative static stress changes imposed on 63 M ≥ 4.5 earthquakes in central California between 1969 and 1998,…

ISBN
0148-0227
Journal Article

We investigate the ability of magma to propagate along preexisting fractures oblique to the least compressive stress. Relaxation of the preexisting shear stress to zero over the portion of the fracture dilated by magma (the dike) results in slip for some distance along the closed portion of the fracture ahead of the dike tip and a stress…

ISBN
0148-0227
Journal Article

Using a waveform cross-correlation technique, Rubin and Gillard [2000] obtained precise relative locations for 4300 0.5 < M < 3.5 earthquakes occurring along 50 km of the San Andreas fault. This study adds to that another 5000 earthquakes distributed along 10 km of the San Andreas fault and 20 km of the Calaveras fault. Errors in relative…

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

Waveform cross-correlation allows one to measure the relative arrival times of similar microearthquakes with errors of less than 1/10 of 1 sample. Location algorithms based on these measurements have greatly improved images of earthquake distribution. For the Northern California Seismic Network catalog, however, the relative location errors…

ISBN
0037-1106
Journal Article

We use relocated catalogs of microearthquakes to investigate earthquake interaction along sections of the Sargent, Calaveras, and San Andreas faults in California. We examine the stress dependence of seismicity rate change along the three fault segments and find that the seismicity rate following a mainshock decays approximately as 1/time, the…

ISBN
0037-1106
Journal Article

Dieterich [1994] modeled the response to a stress step of a population of faults governed by rate- and state-dependent friction. This model assumes that aftershocks nucleate over areas on the fault that at the time of the main shock are already accelerating toward failure and disregards the effect of interactions among aftershocks. The main…

ISBN
0148-0227
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
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

[1] To better understand the asymmetric distribution of microearthquake aftershocks along the central San Andreas fault, we study dynamic models of slip‐weakening ruptures on an interface separating differing elastic half‐spaces. Subshear ruptures grow as slightly asymmetric bilateral cracks, with larger propagation velocities, slip…

Journal Article

Taiwan's 1999 Mw 7.6 earthquake generated over 85 km surface rupture along the Chelungpu thrust fault. Paleoseismic studies at the Shi-Jia site near Nantou city, reveal folding as the predominant form of deformation. Stratigraphic relations across the 1999 fold scarp show the style and degree of deformation caused by the penultimate event is…

ISBN
0148-0227
Journal Article

Correction to “Aftershock asymmetry on a bimaterial surface”

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
To better understand the asymmetric distribution of microearthquake aftershocks along the central San Andreas fault, we study dynamic models of slip-weakening ruptures on an interface separating differing elastic half-spaces. Subshear ruptures grow as slightly asymmetric bilateral cracks, with larger propagation velocities, slip velocities, and…
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

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

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

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 mechanics of slow slip events (SSE) in subduction zones remain unresolved. We suggest that SSE nucleate in areas of unstable friction under drained conditions, but as slip accelerates dilatancy reduces pore pressure p quenching instability. Competition between dilatant strengthening and thermal pressurization may control whether slip is…

ISBN
0148-0227
Keywords
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

Earthquakes often occur on faults separating materials with different elastic properties. On theoretical grounds, it is expected that earthquakes on such bimaterial interfaces might have a preferred rupture propagation direction, that being the direction of motion of the more compliant material. The goal of this paper is to determine whether a…

ISBN
0956-540X
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

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