Precursory Slip Research Articles

Observed source parameters for dynamic rupture with non-uniform initial stress and relatively high fracture energy

We have conducted dynamic rupture propagation experiments to establish the relations between in-source stress drop, fracture energy and the resulting particle velocity during slip of an unconfined 2 m long laboratory fault at normal stresses between 4 and 8 MPa. To produce high fracture energy in the source we use a rough fault that has a large slip weakening distance. An artifact of the high fracture energy is that the nucleation zone is large such that precursory slip reduces fault strength over a large fraction of the total fault length prior to dynamic rupture, making the initial stress non-uniform. Shear stress, particle velocity, fault slip and acceleration were recorded coseismically at multiple locations along strike and at small fault-normal distances. Stress drop increases weakly with normal stress. Average slip rate depends linearly on the fault strength loss and on static stress drop, both with a nonzero intercept. A minimum fracture energy of 1.8 J/m2 and a linear slip weakening distance of 33 μm are inferred from the intercept. The large slip weakening distance also affects the average slip rate which is reduced by in-source energy dissipation from on-fault fracture energy.Because of the low normal stress and small per event slip (∼86 μm), no thermal weakening such as melting or pore fluid pressurization occurs in these experiments. Despite the relatively high fracture energy, and the very low heat production, energy partitioning during these laboratory earthquakes is very similar to typical earthquake source properties. The product of fracture energy and fault area is larger than the radiated energy. Seismic efficiency is low at ∼2%. The ratio of apparent stress to static stress drop is ∼27%, consistent with measured overshoot. The fracture efficiency is ∼33%. The static and dynamic stress drops when extrapolated to crustal stresses are 2–7.3 MPa and in the range of typical earthquake stress drops. As the relatively high fracture energy reduces the slip velocities in these experiments, the extrapolated average particle velocities for crustal stresses are 0.18–0.6 m/s. That these experiments are consistent with typical earthquake source properties suggests, albeit indirectly, that thermal weakening mechanisms such as thermal pressurization and melting which lead to near complete stress drops, dominate earthquake source properties only for exceptional events unless crustal stresses are low.

Electric potential changes associated with nucleation of stick-slip of simulated gouges

Our friction experiments using simulated gouges detected premonitory changes in electric potential before stick-slip events. These precursor electric signals have been detected both in piezoelectric quartz and non-piezoelectric gabbroic gouges. The changes in the potential were locally detected by electrodes set very close to the fault surface associated with slow slip prior to stick-slip events. The magnitude of electrification is proportional to fault slip associated with gradual stress releases, indicating that the electrification is slip-dependent process. From the detailed microstructural analyses on a representative sample, Riedel (R 1) shears known to be formed during stable sliding were the most densely developed around the electrode pair which detected the precursory voltage changes. This indicates that local increases in the voltages were likely caused by frictional electrification due to slow slip on R 1 shears in nucleation phases of stick-slip events. Our experimental results imply that natural faults with thicker gouge zones would require greater precursory slips, resulting in larger electric signals in the nucleation phase of earthquakes.

Precursory seismic anomalies and transient crustal deformation prior to the 2008 Mw = 6.9 Iwate‐Miyagi Nairiku, Japan, earthquake

The epidemic‐type aftershock sequence (ETAS) model has been widely used for detecting seismicity anomalies, such as quiescence and activation during aftershock sequences of large earthquakes and background levels of seismicity. The causes of such anomalies are thought to be associated with spatiotemporal changes in stress, even tiny perturbation of local stress. Here we analyze the seismic activity during the decade prior to the 2008 Iwate‐Miyagi inland earthquake of M7.2 (Mw6.9), to fit the ETAS model to the seismicity from various regions around the source over northern Honshu, Japan. From the viewpoint of the analyses with the ETAS model, we find northern Honshu is divided into three areas of distinctive behaviors, increased seismicity, decreased seismicity, and normal seismicity relative to the ETAS prediction. As in other previously published papers, here we hypothesize that Coulomb stress changes caused by a few years of precursory slip of the Iwate‐Miyagi earthquake resulted in the seismicity changes in and around the 2008 source region. The confirmed significant seismic anomalies in respective regions are consistent with the increments of the Coulomb failure stress of the corresponding regions that are calculated by the assumed slow slip on the southern part of the faults of the main shock. The local crustal deformations observed from a dense Global Positioning System network, including a station right above the focal fault, supports that slow slip on the fault had been taking place for about 5 years prior to the occurrence of the focal earthquake and suggests that the slip terminated or migrated to down‐dip extension of the fault around 1 year before the rupture.

Anomalies of Seismic Activity and Transient Crustal Deformations Preceding the 2005 M 7.0 Earthquake West of Fukuoka

If aseismic slip occurs on a fault or its deeper extension, both seismicity and crustal deformation around the source would be affected. Anomalous phenomena of this kind are revealed from earthquake occurrence data and geodetic records during a period of 10 years leading up to the March 2005 M 7.0 earthquake west of Fukuoka that occurred off the northern coast of Kyushu, Japan. Seismicity rate anomalies (quiescence and activation) took place relative to the rates expected by the ETAS model in a number of seismic zones in and around the Kyushu District. The seismic zone of the relative quiescence and activation consistently corresponds to the zone of the negative and positive ΔCFS (Coulomb failure stress change), respectively, assuming the precursory aseismic slips on the M 7.0 source fault. In addition, we consider the time series of geodetic baseline distances between permanent GPS stations in the Kyushu District for the same period, which also supports the possible precursory slips rather than the known slow slips beneath the Bungo Straight, off the eastern coast of Kyushu.

Monitoring the Oil Field With Live-Well Microseismics

This article, written by Technology Editor Dennis Denney, contains highlights of paper OTC 19693, "Monitoring the Oil Field of the Present Using Live-Well Microseismic Technology," by Stephen A. Wilson, Gilles Le Floch, and Rob Jones, Schlumberger, prepared for the 2008 Offshore Technology Conference, Houston, 5-8 May. The paper has not been peer reviewed. Microseismics provides direct 4D information about stress changes in the reservoir that are caused by injection and production operations. These stress changes emit packets of seismic energy and information about all the small slip events triggered by oilfield operations. Until recently, microseismic monitoring required deploying seismic sensors in inactive monitor wells. It is now possible to deploy seismic monitoring in live wells. Such monitoring can take place during active injection or production and in offshore environments where monitor wells are rarely available. Introduction It is possible to detect tiny slip magnitudes corresponding to only a few microns of movement. Such movements may correspond to slip on a fracture, movement within the cement, slip on bedding, the opening of a fracture, or even precursory slip in the completion. Mapping these changes in both space and time provides unique insight into stress change in the reservoir, the overburden, and the well. Although this activity is triggered by oilfield activity, the emitted energy derives from strain energy stored within the rock mass. In the oil industry, microseismic monitoring has been limited to short-term monitoring of hydraulic-fracturing operations. Microseismic monitoring has been used to detect and, subsequently, limit integrity problems; map fault reactivation, thereby identifying drilling hazards; improve well longevity and identify compartments; map casing failure; and position wells better to improve production and injection efficiency. Successful microseismic monitoring requires the use of sensors that are acoustically well-coupled to the rock and acoustically decoupled from manmade-noise sources. Such sensors must form part of a system that is designed to record low-energy signals. Microseismic Basics Microseismic monitoring involves listening to a rock mass to detect and locate the release of seismic energy from any discrete naturally occurring seismic source (Fig. 1). In this context, "naturally occurring" could include movement of any manmade downhole structure but would exclude any manmade seismic source. In contrast, conventional reflection-seismic monitoring uses artificial seismic sources to image either subsurface layering or to infer changes in subsurface properties. Both techniques measure vibrations in the ground. However, the sources of the data are different, and each technique processes the vibration data in very different ways to derive value (Fig. 2). An individual microseismic event provides information about its source and the rock mass through which it passes in travelling from source to receiver. It is necessary to detect and accurately locate a population of microseismic events to provide useful and meaningful reservoir information. The detection rates from actively producing fields range from a single event per week to more than 100 events per day.

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

Earthquake 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.

Seismicity anomaly scenario prior to the major recurrent earthquakes off the east coast of Miyagi Prefecture, northern Japan

This paper is concerned with the intermediate-term prediction of the forthcoming M7.4–8.2 earthquake on the plate boundary, off the east coast of Miyagi Prefecture, northern Japan, which has the highest occurrence probability among the long-term forecasted events announced to the public. Seismicity and aftershocks in the regions of stress-shadow preceding each of the previous ruptures in 1936 and 1978 shows significantly lower activity than the predicted rate by the ETAS model (the relative quiescence) during some years preceding the events, whereas the seismicity is normal or even activated in the regions of neutral or increasing Coulomb failure stress (CFS), which leads to the scenario based on the likely precursory slip within or near the source. Assuming such a scenario, a number of sequences of earthquakes or aftershocks during 1979–2004 from various regions in northern Japan are selected to analyze them by fitting the ETAS model. Then the results are examined in relation to the CFS increments in the considered regions using the source models of the 1793, 1936 and 1978 interplate ruptures, and additionally the source model of recently occurred 2003 Miyagi-Ken-Oki intra-slab earthquake of M7.1. It is likely that the results of the normal activity and relative quiescence in the respective activities are due to the preslip of the intra-slab earthquake rather than the preslip of the expected rupture on the plate boundary.

Monitoring of anomaly in the aftershock sequence of the 2005 earthquake of M7.0 off coast of the western Fukuoka, Japan, by the ETAS model

Monitoring of aftershock sequences to detect lowering activity, relative to the modeled rate (the relative quiescence), becomes realistic and practical in predicting the enhancement of the likelihood of having a substantially large aftershock, or even another earthquake of similar size or larger. A significant relative quiescence in the aftershock sequence of the 2005 March earthquake of M7.0 off the western coast of Fukuoka, Japan, was reported two weeks before the largest aftershock of M5.8 that also hit the Kyushu District. The relative quiescence was discussed in relation to the stress‐shadowing as inhibiting the activity due to probable precursory slips, which are retrospectively speculated in more detail.

A laboratory experiment to monitor the contact state of a fault by transmission waves

We performed a series of laboratory experiments in which elastic waves were transmitted across a simulated fault. Two types of experiments were carried out: (1) Normal Stress Holding Test (NSHT): normal stress was kept constant for about 3 h without shear stress and transmission waves were observed. (2) Shear Stress Increasing Test (SSIT): shear stress was gradually increased until a stick-slip event occurred. Transmission waves were continuously observed throughout the process of stress accumulation. We focused on the change in transmission waves during the application of shear stress and especially during precursory slips. It was found in NSHT that the amplitude of transmission waves linearly increased with the logarithm of stationary contact time. The increase amounted to a few percent after about 3 h. Creep at asperity contacts is responsible for this phenomenon. From a theoretical consideration, it was concluded that the real contact area increased with the logarithm of stationary contact time. We observed in SSIT a significant increase in wave amplitude with shear stress application. This phenomenon cannot be attributed to the time effect observed in NSHT. Instead, it can be explained by the mechanism of “junction growth” proposed by Tabor. Junction growth yields an increase in real contact area. It is required for junction growth to occur that the material in contact is already plastic under a purely normal loading condition. A computer simulation confirmed that this requirement was satisfied in our experiments. We also found that the rate at which the amplitude increased was slightly reduced prior to a stick-slip event. The onset time of the reduction well coincides with the onset of precursory slip. The cause of the reduction is attributed to the reset of stationary contact time due to displacement. This interpretation is supported by the result of NSHT. Taking the time of stationary contact in SSIT into account, we may expect the change in wave amplitude to be, at most, only a few percent. The observed slight reduction in increasing rate is, in this sense, reasonable. The static stiffness of the fault also decreases with precursory slip. It was also found that low frequency waves are a better indicator of precursory slip than high frequency waves. This might suggest that low frequency waves with longer wavelength are a better indicator of average behavior of faults. The problem, however, merits a further investigation. The shifts in phase were also found to be a good indicator of the change in contact state of the fault. The changes in both amplitude and phase of transmission waves are unifyingly understood through the theory of transmission coefficient presented by Pyrak-Nolte et al. Rough surfaces have a tendency to give larger stick-slips than smooth surfaces. The amount of precursory slip is larger for rough surfaces than for smooth surfaces. Although it was confirmed by a computer simulation that rough surfaces have larger contact diameters than smooth surfaces, the rigorous relationship between the surface roughness (contact diameter) and the amount of precursory slips was not established.

Geodetic and seismologic evidence for slip variability along a blind normal fault in the Umbria-Marche 1997-1998 earthquakes (central Italy)

We analysed elevation changes induced by the 1997–1998 Umbria-Marche, central Apennines (Italy) earthquakes. We employed data from a first-order geodetic levelling line measured in 1951, 1992 and 1998. The line bears a record of pre-seismic and coseismic strains associated with the causative fault of the 1997 September 26, 09:40 mainshock (Mw= 6.0). A first level analysis performed under the assumption of slip homogeneity of coseismic slip shows misfits that cannot be reduced simply by altering the fault size and geometry. A more detailed analysis based on a distribution of coseismic slip obtained from broad-band seismograms provides a better fit and is in agreement with 1951–1992 elevation changes interpreted as precursory slip by previous investigators. The levelling data sets new constraints on the location, extent, dip and depth of the fault, in full agreement with seismological evidence and images from SAR interferometry. The data show no evidence for slip in the uppermost 3 km of the crust, suggesting that a major and widely recognized normal fault that exists in the area is no longer active and showing a tendency of present tectonic strains to revert the current topographic setting.

Lack of Precursory Slip to the 1999 Hector Mine, California, Earthquake as Constrained by InSAR

We looked for evidence of interseismic strain occurring between the 1992 Landers earthquake and the 1999 Hector Mine earthquake near the Lavic Lake and Bullion faults by using interferometric synthetic aperture radar (InSAR). Interferograms covering the Hector Mine epicentral region were studied for possible slip along the Bullion and Lavic Lake faults by both visual inspection and a matched filter technique intended to emphasize slip located at the nucleation point. Some indications of possible deformation associated with the 5 July 1992 M L 5.4 Pisgah event was observed, but high decorrelation prevented a conclusive determination. We have seen no evidence for precursory slip in the epicentral region up to 30 days before the Hector Mine event. We estimated that the slip equivalent to a M w 4.5 event would have been observable in the months before the Hector Mine event, and this places an upper bound on the long-term precursory slip, had it occurred. We have noted that InSAR is well suited for detecting precursory slip in general due to the high spatial resolution and the lack of ground instrumentation required but that the detection level depends on the depth and orientation of the slip. [ Back ]

Slip styles in a Spring‐Slider Model with a laboratory‐derived constitutive law for serpentinite

A spring‐slider model with a laboratory‐derived constitutive law for serpentinite generates seismic slip, aseismic slip, or a combination of both. Such behavior is observed on oceanic ridge‐transform systems and portions of the San Andreas Fault, and may be due to the presence of serpentinite. The constitutive law combines two sets of equations: a rate‐dependent flow equation which dominates at low velocities, and a rate‐ and state‐dependent set of equations which dominate at high velocities. The combined model produces transient behavior with maximum slip velocities well in excess of the loading velocity. Metastable slip prior to the onset of high‐speed slip is produced in many simulations and may be analogous to the slow precursors observed for some oceanic ridge‐transform earthquakes. This precursory slip results from the double‐valued nature of the steady‐state curve of the two‐mechanism model in which the state‐variable equations are rate weakening.

An experimental trial to detect precursory slips by transmission waves across a fault

It is known that there is a slow stage of precursory slip prior to a dynamic rupture propagation. Thus it is expected that there should be some physical contrasts between before and after the precursory slip. To detect the contrasts, we performed an observatory experiment in which P‐ and S‐waves were transmitted across a fault in a double direct shear apparatus. Two types of experiments were made: first, Normal Stress Holding Test (NSHT), in which we focused on the effect of stationary contact time on transmission waves. Second, Shear Stress Increasing Test (SSIT), in which we measured local shear stresses in addition to transmission waves. In NSHT we observed increases in amplitude of transmission waves with the logarithm of stationary contact time. The change was several percent after about 3 hours contact. In SSIT we observed a significant increase in amplitude with a shear stress application until a stick‐slip occurred. It may be explained by a strengthening of asperity interlocking. However, the detailed mechanism of this phenomenon is uncertain. Further we found a little reduction of increasing rate of amplitude which corresponds to the local precursory slips. This reduction may be attributed to the reset of stationary contact time due to local slips and replacement of asperity contacts with smaller contact sizes.

Detecting slow, long-duration slip of large earthquakes using very long-period orbital surface waves

SUMMARY In this paper, we present a simple yet effective technique for measuring the source time-delay spectrum from very long-period world-circling surface waves without relying on assumed earth models or calculation of synthetic seismograms. By using autocorrelation and self-convolution functions derived from whole seismograms of large earthquakes recorded at a seismic station it is possible to isolate the source effects and precisely (5 5 s) determine the source delay spectrum at periods as long as 600 s. Measurements at such long periods are necessary for detecting slow precursory slip and slow creep after the main ‘fast’ seismic phase of large earthquakes. We apply this technique to five recent large earthquakes: the 1989 Macquarie Ridge (M, 8.2), the 1992 Nicaragua (M, 7.6), the 1993 Mariana Islands (M, 7.8), and the 1994 deep events in Fiji (M, 7.6) and Bolivia (M, 8.3). Our results are largely in agreement with the results obtained by other investigators. The Mariana Islands, Fiji, and Bolivia earthquakes had a normal rupture duration. The Nicaragua earthquake exhibits a source time-delay spectrum with the delay increasing from 31 s at the 100 s period to 50 s at the 600 s period, indicating an unusually slow rupture process. The Macquarie Ridge earthquake is anomalous by the discrepancy between the Love-wave and Rayleighwave estimates. Love waves, in the period band of 150 to 600 s, show a normal, flat source-delay spectrum with a delay of about 28 s. The Rayleigh-wave spectrum agrees with the Love-wave spectrum for periods smaller than 200 s and greater than 400 s; however, it shows a significantly shorter source delay (about 15 s) in the 250 to 350 s period range. The unusual nature of the Macquarie Ridge earthquake’s surface wave spectrum was pointed out by Ihmli, Harabaglia & Jordan (1993) who also provided an explanation in terms of a slow, precursory moment release. This explanation is not consistent with the flat Love-wave spectrum determined here.

Testing a model of earthquake nucleation

Abstract Some laboratory models of slip find that a critical amount (or velocity) of slow slip is required over a nucleation patch before dynamic failure begins. Typically, such patch sizes, when extrapolated to earthquakes, have been thought to be very small and the precursory slip undetectable. Ohnaka (1992, 1993) has proposed a model in which foreshocks delineate a growing zone of quasi-static slip that nucleates the dynamic rupture and suggests that it could be large enough (∼10 km across) to be detectable and thus useful for short-term earthquake prediction. The 1992 Landers earthquake (M 7.3) had a distinctive foreshock sequence and initiated only 70 km from the strain meters at the Piñon Flat Observatory (PFO). We use this earthquake to investigate the validity and usefulness of Ohnaka's model. The accurate relocations of Dodge et al. (1995) show that the foreshock zone can be interpreted as expanding from an area of 800 m (along strike) by 900 m (in depth), to 2000 by 3200 m in the 6.5 hr before the mainshock. We have calculated the deformation signals expected both at PFO and 20 km from the foreshock zone, assuming either constant slip or constant stress drop on a circular patch expanding at 5 cm/sec over 6.5 hr. We find the slips or stress drops would have to have been implausibly high (meters or kilobars) to have been detectable on the strain meters at PFO. Slightly better limits are possible only 20 km from the source. Even though the distance from Landers to PFO is small compared with the average spacing of strain meters in California, we are unable to prove or disprove Ohnaka's model of earthquake nucleation. This suggests that even if the model is valid, it will not be useful for short-term prediction.

Slip patterns and earthquake populations along different classes of faults in elastic solids

Numerical simulations of slip instabilities on a vertical strike‐slip fault in an elastic half‐space are performed for various models belonging to two different categories. The first category consists of inherently discrete cellular fault models. Such are used to represent fault systems made of segments (modeled by numerical cells) that can fail independently of one another. Their quasi‐independence is assumed to provide an approximate representation of strong fault heterogeneity, due to geometric or material property disorder, that can arrest ruptures at segment boundaries. The second category consists of models having a well‐defined continuum limit. These involve a fault governed by rate‐ and state‐dependent friction and are used to evaluate what types of property heterogeneity could lead to the quasi‐independent behavior of neighboring fault segments assumed in the first category. The cases examined include models of a cellular fault subjected to various complex spatial distributions of static to kinetic strength drops, and models incorporating rate‐ and state‐dependent friction subjected to various spatial distributions of effective stress (normal stress minus pore pressure). The results indicate that gradual effective stress variations do not provide a sufficient mechanism for the generation of observed seismic response. Strong and abrupt fault heterogeneity, as envisioned in the inherently discrete category, is required for the generation of complex slip patterns and a wide spectrum of event sizes. Strong fault heterogeneity also facilitates the generation of rough rupture fronts capable of radiating high‐frequency seismic waves. The large earthquakes in both categories of models occur on a quasi‐periodic basis; the degree of periodicity increases with event size and decreases with model complexity. However, in all discrete segmented cases the models generate nonrepeating sequences of earthquakes, and the nature of the large (quasi‐periodic) events is highly variable. The results indicate that expectations for regular sequences of earthquakes and/or simple repetitive precursory slip patterns are unrealistic. The frequency‐size (FS) statistics of the small failure episodes simulated by the cellular fault models are approximately self‐similar with b ≈ 1.2 and bA ≈ 1, where b and bA are b values based on magnitude and rupture area, respectively. For failure episodes larger than a critical size, however, the simulated statistics are strongly enhanced with respect to self‐similar distributions defined by the small events. This is due to the fact that the stress concentrated at the edge of a rupture expanding in an elastic solid grows with the rupture size. When the fault properties (e.g., geometric irregularities) are characterized by a narrow range of size scales, the scaling of stress concentrations with the size of the failure zone creates a critical rupture area terminating the self‐similar earthquake statistics. In such systems, events reaching the critical size become (on the average) unstoppable, and they continue to grow to a size limited by a characteristic model dimension. When, however, the system is characterized by a broad spectrum of size scales, the above phenomena are suppressed and the range of (apparent) self‐similar FS statistics is broad and characterized by average b and bA values of about 1. The simulations indicate that power law extrapolations of low‐magnitude seismicity will often underestimate the rate of occurrence of moderate and large earthquakes. The models establish connections between features of FS statistics of earthquakes (range of self‐similar regimes, local maxima) and structural properties of faults (dominant size scales of heterogeneities, dimensions of coherent brittle zones). The results suggest that observed FS statistics can be used to obtain information on crustal thickness and fault zone structure.

Numerical simulation of three-dimensional faulting processes with heterogeneous rate- and state-dependent friction

Miyatake, T., 1992. Numerical simulation of three-dimensional faulting processes with heterogeneous rate- and state-dependent friction. In: T. Mikumo, K. Aki, M. Ohnaka, L.J. Ruff and P.K.P. Spudich (Editors), Earthquake Source Physics and Earthquake Precursors. Tectonophysics, 211: 223–232. Numerical simulations of three-dimensional faulting processes with heterogeneous rate- and state-dependent friction were carried out by using a multi-mass-spring model. The rate- and state-dependent friction law proposed by Dieterich ∗ ∗ Dieterich (1978) and later developed by Ruina ∗∗ ∗∗ Ruina (1983) has much capability to simulate a wide variety of source processes, e.g., precursory slip, post-seismic slip, co-seismic slip, creep events and earthquake cycles. Since the original equation is a stiff ordinary equation which has rapidly decaying solutions and is difficult to solve, we modified the equation so that numerical computation are made stable. This rate- and approximate state-dependent friction law is applied to a single-degree-of-freedom elastic system to compare its dynamical behaviours with those of the original friction law and found that our friction law was a good approximation of the original formula. Then we apply this modified friction law to a multi-mass-spring model to simulate a whole earthquake source process. In this paper, we studied mainly the effect of heterogeneity of frictional parameters. Three types of barriers, i.e., a strong barrier, a weak barrier and a relaxation barrier, can be simulated by certain frictional parameters. For each case, large mainshocks occurred repeatedly. In the case of a weak barrier, the barrier region slipped with some delay time during the mainshock, i.e., the occurrence of a multiple shock. In the case of a strong barrier, the barrier region was left unslipped during the mainshock. A small part of this barrier region slipped sequentially as small aftershocks, and eventually the entire barrier region slipped as the largest aftershock. A fault with a relaxation barrier was also left unslipped during the mainshock similarly to a strong barrier case, but a small part of the barrier slipped as creep events.

Slip on the Superstition Hills fault and on nearby faults associated with the 24 November 1987 Elmore Ranch and Superstition Hills earthquakes, southern California

AbstractAlignment arrays and creepmeters spanning several faults in southern California recorded slip associated with the 24 November 1987 Elmore Ranch and Superstition Hills earthquakes. No precursory slip had occurred on the Superstition Hills fault up to 27 October 1987, when the last measurement before the earthquakes was made. About 23 days before the earthquake, dextral creep events of about 13 mm and 0.5 mm may have occurred simultaneously on the Imperial and southern San Andreas faults, respectively, but the tectonic origin of the smaller event is questionable.Within 12 hr after the Superstition Hills earthquake, 20.9 cm of dextral slip occurred on the main fault trace at the Superstition Hills alignment array, and 39.8 cm of dextral slip was recorded over the entire 110-m width of the array. Despite this initial wide distribution of slip, nearly all of the postseismic slip is occurring on the main fault trace. As of 3 August 1988, the alignment array had recorded a total of 80.2 cm of dextral slip. As of 5 days after the earthquakes, 65 to 80 per cent of the total slip measured by the alignment array had occurred on discrete, mappable fractures.In addition, the two earthquakes triggered slip on the Coyote Creek fault, the southern San Andreas fault, and on the Imperial fault. Telemetered data from creepmeters on the southern San Andreas and Imperial faults indicate that triggered slip began there within 3 min or less of each of the two earthquakes. Additional triggered slip occurred on the Imperial fault beginning 3.5 hr after the second earthquake.

Comparing strain events: A case study for the Homestead Valley earthquakes

Abstract We present a procedure for comparing strain events at different sites, and apply it to observations for the Homestead Valley earthquake sequence of 15 March 1979. Coseismic strain steps occurred on two laser strainmeters at Piñon Flat Observatory (PFO) and on a creepmeter spanning the San Andreas fault at Wiebe Ranch (XWR); the creepmeter records were studied by Leary and Malin (1984). The PFO coseismic strains are consistent with a source model derived from near-field geodetic measurements, while the XWR coseismic extension is 1200 times too large and of the wrong sign. The XWR instrument showed an anomalous extension about 20 hours before the earthquake (Leary and Malin, 1984), but no such signals were detected on the PFO strainmeters at this time. To compare these preseismic observations we must make some assumption about the preseismic source, and we choose to assume that any precursory slip occurred on the fault plane that eventually ruptured. Under this assumption, the preseismic XWR and PFO records cannot be reconciled unless the preseismic dislocation is left-lateral or mostly thrust, and the fault zone at XWR magnifies strain by a factor of 2900 or more. This strain magnification implies that the fault-zone shear modulus at XWR is 107 Pa, three orders of magnitude smaller than the shear modulus of typical crustal rocks. However, earth-tide observations at XWR constrain the strain magnification at this site to be less than about 55. Thus the preseismic extension at XWR is probably not a precursor to the Homestead Valley earthquake.

Dynamics of fault creep

Observations along the surface traces of active faults in California and elsewhere indicate that tectonic displacement can occur as seismic slip or as aseismic fault creep. Fault creep occurs as secular displacement and as displacement episodes, called “creep events,” which last a few hours to days and include from a millimeter or less to a few tens of millimeters of displacement. Instrumental measurements of displacement versus time during creep events show that many events have a characteristic, simple form, including a steep beginning, followed by a gradual decay in the rate of displacement. Some creep events display small amounts of precursory slip, and many seem to be composed of several discrete “simple” events. Propagation of creep events along the San Andreas, Calaveras, and Imperial faults in California has been inferred from the nearly simultaneous observation of creep events at nearby creepmeters and from kinematic modeling of continuous measurements of strain during creep events. Fault creep can be viewed as arising from the interplay of three factors: stress applied to the fault from external sources; stress caused by the geometry and distribution of displacement on the fault, arising from the elastic response of the surrounding medium to the displacements within the anelastic fault zone itself; and the constitutive relations characterizing the resistance to slip on the fault. Analytic solutions are presented for a simple, rectangular dislocation, quasi‐static model of nonpropagating fault creep assuming viscous and quasi‐plastic (power law creep) fault zone rheology and for a multi‐element (composed of several rectangular or striplike dislocation surfaces), quasi‐static model assuming a viscous rheology. Viscous rheology implies solutions composed of exponentials that decay with time. The simple, one‐element, quasi‐plastic model is in agreement with the form of creep events observed at Melendy Ranch, California. A matrix formulation is presented to calculate dislocation stresses on a fault zone in a half‐space or plate. The formulation involves the division of the dislocation surface into strips or rectangles and the use of published solutions to calculate the stress resulting from displacement on each individual element. Results from the matrix method agree with analytic results for equilibrium displacements on “stress‐free” cracks. The matrix formulation is then used as the basis for a numerical method to simulate one‐ and two‐dimensional propagating creep assuming a quasi‐plastic rheology on the fault zone. Results from this method agree reasonably well with observations of afterslip from the 1966 Parkfield, 1975 Oroville, and 1979 Imperial Valley, California, earthquakes and of a propagating creep event observed along the southern Calaveras fault, central California, during July 1977. This method of analysis, and the assumption that creep at each point on the fault zone follows a power law rheology after the applied stress reaches a spatially varying yield stress, can explain the secular and episodic nature of fault creep; afterslip; the simple shape of some individual events and the multiple, composite shape of others; and the propagation of creep events. On the southern Calaveras fault, observations of propagating creep indicate a yield stress near zero at the surface and throughout much of the fault zone. However, they also indicate the presence of a zone at a depth of about 0.5 km, and about 5 km long, with a yield stress of about 15 bars (1.5 MPa). The methods of solution presented here should be applicable to many problems in the dynamics of faulting.