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Brian D. Kilgore

Publications and source records attributed to Brian D. Kilgore.

At least 19 recordsLinked to original sources

Earthquake stress drop, source spectra from laboratory experiments, and the apparent unsteadiness of frictional slip

Over a range of co-seismic total energy release, high sample rate slip, stress, and slip velocity measurements were made during frictional failure to determine seismic source properties. The near-field measurements were used to estimate stress drops using spectral approaches that are analogous to the standard seismological moment-corner determined Δσ and acceleration amplitude Δσ arms stress drops. Rapid frictional sliding produces slip velocity amplitude spectra that vary with frequency -1 so long as the energy dissipated by friction approaches the total energy release. Under these conditions Δσ and Δσ arms are similar in size. Since these are nearly direct measurements of fault slip velocity and because they produce flat acceleration spectra between the corner and an apparent fmax, friction in these experiments seems to produce dynamic acceleration and deceleration at all resolved frequencies. The physical origin of this unsteady motion is not known exactly but likely reflects rapid dynamic variations in fault strength or applied stress. On the other hand, when the total energy stored prior to failure is artificially made somewhat larger relative to that which can be dissipated by friction the velocity spectra vary with frequency -2 immediately below the corner. At these conditions Δσ and Δσ arms diverge. The excess stored energy is preferentially partitioned into radiated energy upon failure. Collectively the experiments imply that to produce unsteady, white noise accelerations that are observed for natural earthquakes, requires that at least 95% of the energy released does not escape the source region to be radiated to the far-field.

Bulletin of the Seismological Society of America↗

Effect of thermal and mechanical processes on hydraulic transmissivity evolution

Fracture healing is a critical component of enhanced geothermal systems, the earthquake cycle, and induced seismicity. Accordingly, there is significant interest in understanding the process of healing and its effects on fluid transport. The creation, reactivation, and sustainability of fracture networks depend on complex coupling among thermal, hydraulic, mechanical, and chemical processes. We use laboratory slide-hold-slide experiments, at temperatures from 22 to 200 ˚C, to examine effects of fracture reactivation and quasi-static loading on the evolution of fluid transport properties of simulated fractures in Westerly granite. At all temperatures, the in-plane hydraulic transmissivity consistently decays during hold periods resulting in an overall reduction in transmissivity. During the first three to fifteen hours of an experiment, transmissivity decreases rapidly due to the generation of wear products, development of a sliding surface, and compaction of the resulting gouge. Once the sliding surface has developed, the long-term transmissivity decay rate at 22 and 100 ˚C is significantly lower than the transmissivity decay rate during the initial 3 to 15 hours of the experiment. However, at 200 °C, the decay of hydraulic transmissivity remains high throughout the experiment. The long-term decay of hydraulic transmissivity can be fitted with a power law model with more rapid reduction of hydraulic transmissivity at higher temperature. Periods of sliding on the fracture surface result in transient increases in the transmissivity, due to shear dilation, as is expected for Coulomb materials. These transients are superimposed on the long-term decay. When sliding ceases and a new hold period commences, there is a rapid reduction in transmissivity and return to the long-term rate of transmissivity decay. The rate of decay of the transmissivity transients is inversely proportional to temperature, in contrast to the long-term decay and the expected behavior for processes like subcritical crack growth and indentation creep. The higher decay rates that are observed during the initial 3-15 hours of the tests and following sliding, are associated with times that the porosity of the gouge is expected to be high. The difference in decay rates suggests that when the gouge is driven far from equilibrium by active shearing, densification may be dominated by a different mechanism from long-term compaction.

Conference Paper↗

Apparent age dependence of the fault weakening distance in rock friction

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, d h , also increases. The weakening distance increase is large, hundreds of percent change over a few thousand seconds. The initial bare surface and simulated fault gouge experiments were conducted in rotary shear at 25 MPa normal stress, 21 MPa confining stress and at displacements greater than 100 mm. In contrast, initially bare surface experiments at 5 MPa normal stress, unconfined at displacements less than 10 mm show effectively no change in d h . We attribute the difference to the presence of an appreciable shear zone that develops due to wear over significant displacements, confined at elevated normal stress. Prior published studies of sheared simulated fault gouge at short displacement show both acknowledged and unacknowledged increases in d h that may relate to our observations. Since natural faults have well-developed shear zones, the observations have more direct relevance to earthquake nucleation than prior laboratory studies that use short displacement data and focus on frictional strength recovery alone. However, the physics underlying this increase in weakening distance are not known; candidates are compaction (Nakatani, 1998) and delocalization (Sleep et al., 2000). Additional caveats are that these are room temperature and humidity experiments, at a single normal stress that have not yet been reproduced in other laboratories.

Journal of Geophysical Research↗

Evolution of fluid transmissivity and strength recovery of shear fractures under hydrothermal conditions

Geothermal systems rely on the presence of long-lived and high-volume, permeable fracture systems. The creation, reactivation, and sustainability of these systems depend on complex coupling among thermal, hydraulic, mechanical, and chemical (THMC) processes occurring in geothermal reservoirs. In part due to a paucity of experimental data, the evolution of fractures at geothermal conditions in response to THMC processes is poorly understood, particularly during the process of shear. We present preliminary results of triaxial slide-hold-slide experiments, with hold periods ranging in duration from 103 s to 106 s, to constrain rates and mechanisms of healing and sealing. Experiments were conducted on simulated fault gouge composed of Westerly granite and on bare surfaces of Westerly granite. The tests were run at temperatures of 22˚ and 200˚C with confining and average pore pressures of 30 MPa and 10 MPa, respectively. We used an axial displacement rate of 0.1 μm/s during sliding periods. Deionized water was continuously flowed along the simulated fracture so we could determine in-plane transmissivity during the tests. In gouge and bare surface experiments conducted at 200˚C, we observe significant decreases in transmissivity over the course of the experiments. For the hydrothermal gouge experiment we measured an order of magnitude net reduction in transmissivity from 1.73x10-18 to 0.17x10-18 m3, over the course of 220 hours while in the room temperature gouge experiment transmissivity only decreased by 0.35x10-18 m3 over the same amount of time. In the experiments, we observe an up to 16% recovery in transmissivity during sliding periods. At room temperature the friction data showed limited fault re-strengthening with time; healing rates are on the order of 0.1 MPa/decade. A similar healing rate was observed at 200˚C in the gouge but we observe an increase in the healing rate, to 0.75 MPa/decade, for a bare surface experiment at 200˚C. The differences in the healing rate of the gouge and bare surface experiments suggest that the generation of fine particles by grinding down of asperities on the bare surface promote quartz dissolution and reprecipitation at elevated temperatures. Further work is needed to test this possibility and provide better constraints on factors influencing the evolution of fluid transport properties and strength of shear fractures at geothermal conditions.

Conference Paper↗

Strength recovery and sealing under hydrothermal conditions

While there is significant evidence for healing in natural faults, geothermal reservoirs, and lab experiments, the thermal, hydraulic, mechanical, and chemical interactions that influence healing are poorly understood. We present preliminary results of triaxial slide-hold-slide experiments to constrain rates and mechanisms of healing. Experiments were conducted on gouge composed of Westerly granite and on bare surfaces of Westerly granite and Eureka quartzite. Tests were run at 22, 100, and 200˚C. In some experiments, we also determined the in-plane fluid transmissivity. In bare surface experiments we observe that restrengthening depends on both time and temperature. At 200˚C the simulated fractures restrengthen at a rate of ∆ µ /∆log(t hold ) = 0.009/decade while at 22˚C the healing rate is ~ 0.002/decade. In the gouge experiments restrengthening appears to be independent of temperature. This may be related to the heterogenous mineral composition and thickness of the gouge layer which could allow shearing to be accommodated in unhealed zones. In the experiments, an overall reduction in fluid transmissivity is observed but sliding periods are often associated with increases in the fluid transmissivity. The transmissivity reduction tends to be greater at 200˚C relative to room temperature. Our preliminary results suggest that multiple healing mechanisms are operating under hydrothermal conditions.

Conference Paper↗

Direct evidence for fluid pressure, dilatancy, and compaction affecting slip in isolated faults

Earthquake instability occurs as a result of strength loss during sliding on a fault. It has been known for over 50 years that fault compaction or dilatancy may cause significant weakening or strengthening by dramatically changing the fluid pressure trapped in faults. Despite this fundamental importance, we have no real understanding of the exact conditions that lead to compaction or dilation during nucleation or rupture. To date, no direct measurements of pore pressure changes during slip in hydraulically isolated faults have been reported. We show direct examples of fluid pressure variations during nucleation and rupture using a miniature pressure transducer embedded in an experimental fault. We demonstrate that fluids are not only significant in controlling fault behavior, but can provide the dominant mechanism controlling fault stability. The effect of fluid pressure changes can exceed frictional variations predicted by rate- and state-dependent friction laws, exerting fundamental controls on earthquake rupture initiation.

Geophysical Research Letters↗

Near-fault velocity spectra from laboratory failures and their relation to natural ground motion

We compared near-fault velocity spectra recorded during laboratory experiments to that of natural earthquakes. We fractured crystalline rock samples at room temperature and intermediate confining pressure (50 MPa). Subsequent slip events were generated on the fracture surfaces under higher confinement (300 MPa). Velocity spectra from rock fracture resemble the inverse frequency (1/ f ) decay of natural earthquake velocity. This spectrum can be attributed to fault creation via seismic fracturing over a wide range of spatial scales. In contrast, subsequent slips on the rough fracture surfaces are depleted in high frequency energy and falloff approximately as 1/ f 2 . The 1/ f 2 spectrum is more consistent with a slider-block model obeying static-kinetic friction than a natural earthquake. The depleted high frequency content precludes the rough fault experiments from being directly analogous to natural sources. The suppression of high frequencies may have resulted from two possible factors: (1) the presence of a well-developed shear zone and coseismic damping of the fault motion by dissipation within it or, in our favored interpretation, (2) a smaller amount of energy dissipated by shearing relative to the total energy release at elevated confining pressure. In context of the latter explanation, a unifying concept that applies to these experiments, earthquakes, ground motion, and models of complex radiated motion is that high frequency radiated energy is relatively enhanced when total energy release is nearly balanced within the source region by dissipative processes. This near-critical energy release condition can be accessed at low normal stress in laboratory experiments.

Journal of Geophysical Research↗

Interaction between hydraulic fracture and a preexisting fracture under triaxial stress conditions

Enhanced reservoir connectivity generally requires maximizing the intersection between hydraulic fracture (HF) and preexisting underground natural fractures (NF), while having the hydraulic fracture cross the natural fractures (and not arrest). We have studied the interaction between a hydraulic fracture and a polished saw-cut fault. The experiments include a hydraulic fracture initiating from a pressurized axial borehole (using water) that approaches a dry fault that is inclined at an angle θ with respect to the borehole axis. The experiments are conducted on Poly(methyl) Meta Acrylate (PMMA) and Solnhofen limestone, a finely grained (<5 μm grain), low permeability (<10 nD) carbonate. The confining pressure in all experiments is 5 MPa, while the differential stress (1-80 MPa) and approach angle, θ (30, 45, 60, 90°) are experimental variables. During the hydraulic fracture, acoustic emissions (AE), slip velocity, slip magnitude, stress drop and pore pressure are recorded at a 5 MHz sampling rate. A Doppler laser vibrometer measures piston velocity outside the pressure vessel to infer fault slip duration and a strain gauge adjacent to the saw-cut provides a near-field measure of axial stress. For PMMA, the coefficient of friction was 0.30 and sliding was unstable (stick-slip). The approaching HF in PMMA created a tensile fracture detected by AE transducers ~100 μs before the significant stick-slip event (45% stress drop and slip velocity of ~60 mm/s) and was arrested by the fault at all fault orientations and differential stresses, even at 90° fault orientation and 80 MPa differential stress. For Solnhofen limestone, we observed stable sliding at a coefficient of friction of 0.12. In contrast to PMMA, the HF in Solnhofen consistently crossed to the other side of the fault. When the HF crossed the fault, it produced a small stress drop (<10%) and slip velocity of only 0.5 mm/s. Theoretical models by Blanton (1986) and Renshaw and Pollard (1995) predict that HF will be arrested for Solnhofen limestone and cross PMMA 90° fault at 80 MPa differential stress. Although the exact cause for the discrepancy between experiments and the theory is not known, one feature present in the experiments but not considered in the models, is the diffusion of fluid driven by the fault slip. Thus, the formation of a "fluid-filled patch" on the fault surface as it is intersected by the HF may substantially impact the crossing/arrest behavior. The approach angle and differential stress also influence the HF initiation azimuth and breakdown pressure. In most cases, the HF initiation azimuth was normal to the fault strike. These observations suggest that the presence of natural fractures could result in rotation of hydraulic fractures to be more normal to their strike and a subsequent change in the downhole pressure recordings. The latter could be used as a diagnostic tool for predicting this interaction.

Conference Paper↗

Role of fault gouge during Interaction between hydraulic fracture and a preexisting fracture

Enhanced reservoir connectivity generally requires maximizing the intersection between hydraulic fracture (HF) and preexisting underground natural fractures (NF), while having the hydraulic fracture continue to propagate across the natural fractures. Observations of downhole core samples suggest that these natural fractures are in fact veins filled with minerals such as calcite (Mighani et al., 2016). We study this interaction during the approach of a hydraulic fracture to a smooth saw-cut fracture under triaxial stress conditions. The specimen is Solnhofen limestone, a fine-grained (<5 µm grain), low permeability (<10 nD) carbonate. The differential stress (1-20 MPa) and inclination of the fault which determines the approach angle, θ (30, 60°) are the experimental variables. We conduct the experiments on both bare surface and gouge-filled fault surfaces. The gouge is a 1 mm thick crushed powder of Solnhofen limestone with <106 µm grain size. During the hydraulic fracture, acoustic emissions (AE), inferred slip velocity, axial stress and pore pressure are recorded at a 5 MHz sampling rate. The hydraulic fracture was able to cross the bare surface fault with small induced fault slip. The fault gouge increased the coefficient of friction significantly from 0.12 (bare, polished surface) to > 0.44 (gouged layer). However, the gouge-filled fault arrested the hydraulic fracture and generated a slip event with different characteristics: 1- The stress drop was larger while the generated AE signals had lower magnitude. 2- Slip velocity recorded by the vibrometer was of the same order of magnitude for the bare and gouge-filled faults, but the slip duration increased from 29 µsec for bare surface to ~2.5 msec (~90 times longer rise time) for the gouge-filled fault. The experiments suggest that the gouge-filled fault can accommodate much larger displacement while promoting slow slip on the fault which is harder to detect as AE signals. The observed long duration slip events are similar to the field observations of the long period and long duration (LPLD) events during the stimulation of clay-rich shale formations (Zoback et al., 2012). While the intrinsic low strength, high ductility, and unfavorably oriented natural fractures in shale formations are expected to reduce the occurrence of induced seismicity, our experiments suggest an additional mechanism for the observed LPLD events, i.e. the role of fault gouge. They also suggest that the microseismic detection techniques may under-predict the stimulated volume as the activation of natural gouge-filled fractures may proceed aseismically.

Conference Paper↗

A wideband magnetoresistive sensor for monitoring dynamic fault slip in laboratory fault friction experiments

A non-contact, wideband method of sensing dynamic fault slip in laboratory geophysical experiments employs an inexpensive magnetoresistive sensor, a small neodymium rare earth magnet, and user built application-specific wideband signal conditioning. The magnetoresistive sensor generates a voltage proportional to the changing angles of magnetic flux lines, generated by differential motion or rotation of the near-by magnet, through the sensor. The performance of an array of these sensors compares favorably to other conventional position sensing methods employed at multiple locations along a 2 m long × 0.4 m deep laboratory strike-slip fault. For these magnetoresistive sensors, the lack of resonance signals commonly encountered with cantilever-type position sensor mounting, the wide band response (DC to ≈ 100 kHz) that exceeds the capabilities of many traditional position sensors, and the small space required on the sample, make them attractive options for capturing high speed fault slip measurements in these laboratory experiments. An unanticipated observation of this study is the apparent sensitivity of this sensor to high frequency electomagnetic signals associated with fault rupture and (or) rupture propagation, which may offer new insights into the physics of earthquake faulting.

Sensors↗

Rock friction under variable normal stress

This study is to determine the detailed response of shear strength and other fault properties to changes in normal stress at room temperature using dry initially bare rock surfaces of granite at normal stresses between 5 and 7 MPa. Rapid normal stress changes result in gradual, approximately exponential changes in shear resistance with fault slip. The characteristic length of the exponential change is similar for both increases and decreases in normal stress. In contrast, changes in fault normal displacement and the amplitude of small high-frequency elastic waves transmitted across the surface follow a two stage response consisting of a large immediate and a smaller gradual response with slip. The characteristic slip distance of the small gradual response is significantly smaller than that of shear resistance. The stability of sliding in response to large step decreases in normal stress is well predicted using the shear resistance slip length observed in step increases. Analysis of the shear resistance and slip-time histories suggest nearly immediate changes in strength occur in response to rapid changes in normal stress; these are manifested as an immediate change in slip speed. These changes in slip speed can be qualitatively accounted for using a rate-independent strength model. Collectively, the observations and model show that acceleration or deceleration in response to normal stress change depends on the size of the change, the frictional characteristics of the fault surface, and the elastic properties of the loading system.

Journal of Geophysical Research B: Solid Earth↗

Earthquake source properties from instrumented laboratory stick-slip

Stick-slip experiments were performed to determine the influence of the testing apparatus on source properties, develop methods to relate stick-slip to natural earthquakes and examine the hypothesis of McGarr [2012] that the product of stiffness, k , and slip duration, Δ t , is scale-independent and the same order as for earthquakes. The experiments use the double-direct shear geometry, Sierra White granite at 2 MPa normal stress and a remote slip rate of 0.2 µm/sec. To determine apparatus effects, disc springs were added to the loading column to vary k . Duration, slip, slip rate, and stress drop decrease with increasing k , consistent with a spring-block slider model. However, neither for the data nor model is k Δ t constant; this results from varying stiffness at fixed scale. In contrast, additional analysis of laboratory stick-slip studies from a range of standard testing apparatuses is consistent with McGarr's hypothesis. k Δ t is scale-independent, similar to that of earthquakes, equivalent to the ratio of static stress drop to average slip velocity, and similar to the ratio of shear modulus to wavespeed of rock. These properties result from conducting experiments over a range of sample sizes, using rock samples with the same elastic properties as the Earth, and scale-independent design practices.

Book chapter↗

Gallery of melt textures developed in Westerly Granite during high-pressure triaxial friction experiments

Introduction Melting occurred during stick-slip faulting of granite blocks sheared at room-dry, room-temperature conditions in a triaxial apparatus at 200–400 megapascals (MPa) confining pressure. Petrographic examinations of melt textures focused largely on the 400-MPa run products. This report presents an overview of the petrographic data collected on those samples, followed by brief descriptions of annotated versions of all the images. Scanning electron microscope (SEM) images of the starting materials and the three examined 400-MPa samples are presented in this report. Secondary-electron (SE) and backscattered-electron (BSE) imaging techniques were used on different samples. The SE images look down on the sawcut surfaces, yielding topographic and three-dimensional textural information. The BSE imaging was done on samples cut to provide cross-sectional views of the glass-filled shear band (or zone) that developed along the sawcut. Brightness in the BSE images increases with increasing mean atomic number of the material. Additional chemical information about the quenched melt and adjoining minerals was obtained using the energy dispersive system of the SEM during BSE examinations. However, the very narrow shear-band thicknesses and common occurrence of very fine lamellar compositional layering limited the usefulness of this technique for estimating melt chemistry.

Open-File Report↗

Slip-pulse rupture behavior on a 2 meter granite fault

We describe observations of dynamic rupture events that spontaneously arise on meter-scale laboratory earthquake experiments. While low-frequency slip of the granite sample occurs in a relatively uniform and crack-like manner, instruments capable of detecting high frequency motions show that some parts of the fault slip abruptly (velocity >100 mm∙s-1, acceleration >20 km∙s-2) while the majority of the fault slips more slowly. Abruptly slipping regions propagate along the fault at nearly the shear wave speed. We propose that the dramatic reduction in frictional strength implied by this pulse-like rupture behavior has a common mechanism to the weakening reported in high velocity friction experiments performed on rotary machines. The slip pulses can also be identified as migrating sources of high frequency seismic waves. As observations from large earthquakes show similar propagating high frequency sources, the pulses described here may have relevance to the mechanics of larger earthquakes.

Geophysical Research Letters↗

A robust calibration technique for acoustic emission systems based on momentum transfer from a ball drop

We describe a technique to estimate the seismic moment of acoustic emissions and other extremely small seismic events. Unlike previous calibration techniques, it does not require modeling of the wave propagation, sensor response, or signal conditioning. Rather, this technique calibrates the recording system as a whole and uses a ball impact as a reference source or empirical Green’s function. To correctly apply this technique, we develop mathematical expressions that link the seismic moment $M_{0}$ of internal seismic sources (i.e., earthquakes and acoustic emissions) to the impulse, or change in momentum $\Delta p $, of externally applied seismic sources (i.e., meteor impacts or, in this case, ball impact). We find that, at low frequencies, moment and impulse are linked by a constant, which we call the force‐moment‐rate scale factor $C_{F\dot{M}} = M_{0}/\Delta p$. This constant is equal to twice the speed of sound in the material from which the seismic sources were generated. Next, we demonstrate the calibration technique on two different experimental rock mechanics facilities. The first example is a saw‐cut cylindrical granite sample that is loaded in a triaxial apparatus at 40 MPa confining pressure. The second example is a 2 m long fault cut in a granite sample and deformed in a large biaxial apparatus at lower stress levels. Using the empirical calibration technique, we are able to determine absolute source parameters including the seismic moment, corner frequency, stress drop, and radiated energy of these magnitude −2.5 to −7 seismic events.

Bulletin of the Seismological Society of America↗

Laboratory constraints on models of earthquake recurrence

In this study, rock friction ‘stick-slip’ experiments are used to develop constraints on models of earthquake recurrence. Constant-rate loading of bare rock surfaces in high quality experiments produces stick-slip recurrence that is periodic at least to second order. When the loading rate is varied, recurrence is approximately inversely proportional to loading rate. These laboratory events initiate due to a slip rate-dependent process that also determines the size of the stress drop [Dieterich, 1979; Ruina, 1983] and as a consequence, stress drop varies weakly but systematically with loading rate [e.g., Gu and Wong, 1991; Karner and Marone, 2000; McLaskey et al., 2012]. This is especially evident in experiments where the loading rate is changed by orders of magnitude, as is thought to be the loading condition of naturally occurring, small repeating earthquakes driven by afterslip, or low-frequency earthquakes loaded by episodic slip. As follows from the previous studies referred to above, experimentally observed stress drops are well described by a logarithmic dependence on recurrence interval that can be cast as a non-linear slip-predictable model. The fault’s rate dependence of strength is the key physical parameter. Additionally, even at constant loading rate the most reproducible laboratory recurrence is not exactly periodic, unlike existing friction recurrence models. We present example laboratory catalogs that document the variance and show that in large catalogs, even at constant loading rate, stress drop and recurrence co-vary systematically. The origin of this covariance is largely consistent with variability of the dependence of fault strength on slip rate. Laboratory catalogs show aspects of both slip and time predictability and successive stress drops are strongly correlated indicating a ‘memory’ of prior slip history that extends over at least one recurrence cycle.

Journal of Geophysical Research↗

High-frequency imaging of elastic contrast and contact area with implications for naturally observed changes in fault properties

During localized slip of a laboratory fault we simultaneously measure the contact area and the dynamic fault normal elastic stiffness. One objective is to determine conditions where stiffness may be used to infer changes in area of contact during sliding on nontransparent fault surfaces. Slip speeds between 0.01 and 10 µm/s and normal stresses between 1 and 2.5 MPa were imposed during velocity step, normal stress step, and slide-hold-slide tests. Stiffness and contact area have a linear interdependence during rate stepping tests and during the hold portion of slide-hold-slide tests. So long as linearity holds, measured fault stiffness can be used on nontransparent materials to infer changes in contact area. However, there are conditions where relations between contact area and stiffness are nonlinear and nonunique. A second objective is to make comparisons between the laboratory- and field-measured changes in fault properties. Time-dependent changes in fault zone normal stiffness made in stress relaxation tests imply postseismic wave speed changes on the order of 0.3% to 0.8% per year in the two or more years following an earthquake; these are smaller than postseismic increases seen within natural damage zones. Based on scaling of the experimental observations, natural postseismic fault normal contraction could be accommodated within a few decimeter wide fault core. Changes in the stiffness of laboratory shear zones exceed 10% per decade and might be detectable in the field postseismically.

Journal of Geophysical Research↗