Showing papers on "Slip (materials science) published in 1996"

Quasicontinuum analysis of defects in solids

Abstract: We develop a method which permits the analysis of problems requiring the simultaneous resolution of continuum and atomistic length scales-and associated deformation processes-in a unified manner. A finite element methodology furnishes a continuum statement of the problem of interest and provides the requisite multiple-scale analysis capability by adaptively refining the mesh near lattice defects and other highly energetic regions. The method differs from conventional finite element analyses in that interatomic interactions are incorporated into the model through a crystal calculation based on the local state of deformation. This procedure endows the model with crucial properties, such as slip invariance, which enable the emergence of dislocations and other lattice defects. We assess the accuracy of the theory in the atomistic limit by way of three examples: a stacking fault on the (111) plane, and edge dislocations residing on (111) and (100) planes of an aluminium single crystal. The method correctly predicts the splitting of the (111) edge dislocation into Shockley partials. The computed separation of these partials is consistent with results obtained by direct atomistic simulations. The method predicts no splitting of the Al Lomer dislocation, in keeping with observation and the results of direct atomistic simulation. In both cases, the core structures are found to be in good agreement with direct lattice statics calculations, which attests to the accuracy of the method at the atomistic scale.

Quaternary evolution of the Corinth Rift and its implications for the Late Cenozoic evolution of the Aegean

Abstract: SUMMARY We present geological and morphological observations at different scales to constrain rates of faulting and the distribution of deformation in the seismically active Aegean region. We focus first on the 130 km long Corinth Rift, an asymmetric graben where a flight of terraces of marine origin are uplifted. We show that the edges of the terraces lie in the footwall of the normal fault bounding the Corinth Rift and correspond to sea-level highstands of laic Pleistocene age. Using a detailed analysis of aerial and SPOT imagery supported by field observations, we have mapped 10 terrace platforms and strandlines ranging in elevation from 10 to 400 m over distances of 2 to 20 km from the fault. The elevation of the terraces' inner edges was estimated at 172 sites with an error of ±5m. This data set contains a precise description of the uplift and flexure of 10 different palaeohorizontal lines with respect to the present sea level. To date the deformation, we correlate the Corinth terraces with late Pleistocene oxygen-isotope stages of high sea-level stands and with global sea-level fluctuations. Using a thick elastic plate model consistent with our current understanding of the earthquake cycle and a boundary-element technique we reproduce the geometry of the shorelines to constrain both mechanical parameters and the slip on the fault. We show that the seismogenic layer behaves over the long term as if its elastic modulus were reduced by a factor of about 1000. All the terraces are fitted for fault slip increasing in proportion to terrace age, and the component of regional uplift is found to be less than 0.3 mm yr−1. The best fits give a slip rate of 11±3 mm yr−1 on the main rift-bounding fault over the last 350 kyr. Other geological and morphologic information allows us to estimate the total age of the main fault (∼1 Ma) and to examine the mechanical evolution of the Corinth Rift. The minimum observed sediment thickness in the Gulf places an extreme check on the results of the modelling and a lower bound on slip rate of 6–7 mm yr−1 (40 per cent less than estimated with modelling). Even this slip rate is nearly 10 times higher than for comparable features in most of the Aegean and elsewhere in the world. At a larger scale, the spacing and asymmetry of the rift systems in the Aegean suggest strain localization in the upper mantle, with slow extension starting 15 Myr ago or earlier. The more recent (1 Myr), rapid phase of rifting in Corinth partly reactivated this earlier phase of extension. The younger faulting in Corinth appears to result from its present location in the inhomogeneous stress field (process zone) of the south-westward propagating tip of the southern branch of the North Anatolian Fault. We extend these relations to propose a mechanical model for the Late Cenozoic evolution of the Aegean. As the Arabia/Europe collision progressed in eastern Turkey it caused Anatolia to move to the west and the North Anatolian Fault to propagate into the Aegean, where the early slow extension started to be modified about 5 Ma ago. The process of propagation dramatically increased the activity of some but not all of the earlier rifts. The model we present is compatible with tectonic observations, as well as with the seismicity, the palaeomagnetic rotations and the displacement field now observed with GPS and SLR.

Slip-tendency analysis and fault reactivation

Abstract: Slip-tendency analysis is a new technique that permits rapid assessment of stress states and related potential fault activity. The tendency of a surface to undergo slip in a given stress field depends on its frictional characteristics (primarily controlled by rock type) and the ratio of shear to normal stress acting on the surface, here defined as slip tendency (determined by orientation of the surface within the stress field). An interactive computer tool displays the stress tensor in terms of its associated slip-tendency distribution and the relative likelihood and direction of slip on surfaces of all orientations. The technique provides easy visualization and rapid evaluation of stress in terms of its potential for causing slip on individual faults or fault populations for use in seismic-risk and fault-rupture–risk assessment, exploration for high-risk and earthquake-prone blind faults, selection of likely earthquake focal mechanism solutions, and for use in analysis of compatibility of geologic structures.

Scheduling algorithms for input-queued cell switches

Abstract: The algorithms described in this thesis are designed to schedule cells in a very high-speed, parallel, input-queued crossbar switch. We present several novel scheduling algorithms that we have devised, each aims to match the set of inputs of an input queued switch to the set of outputs more efficiently, fairly and quickly than existing techniques. In Chapter 2 we present the simplest and fastest of these algorithms: SLIP--a parallel algorithm that uses rotating priority ("round-robin") arbitration. SLIP is simple: it is readily implemented in hardware and can operate at high speed. SLIP has high performance: for uniform i.i.d. Bernoulli arrivals, SLIP is stable for any admissible load, because the arbiters tend to desynchronize. We present analytical results to model this behavior. However, SLIP is not always stable and is not always monotonic: adding more traffic can actually make the algorithm operate more efficiently. We present an approximate analytical model of this behavior. SLIP prevents starvation: all contending inputs are eventually served. We present simulation results, indicating SLIP's performance. We argue that SLIP can be readily implemented for a 32 x 32 switch on a single chip. In Chapter 3 we present i-SLIP, an iterative algorithm that improves upon SLIP by converging on a maximal size match. The performance of i-SLIP improves with up to log$\sb2N$ iterations. We show that although it has a longer running time than SLIP, an i-SLIP scheduler is little more complex to implement. In Chapter 4 we describe maximum or maximal weight matching algorithms based on the occupancy of queues, or waiting times of cells. These algorithms are stable over a wider range of traffic loads. We describe two algorithms, longest queue first (LQF) and oldest cell first (OCF) and consider their performance. We prove that LQ although too complex to implement in hardware, is stable under all admissible i.i.d. offered loads. We consider two implementable, iterative algorithms i-LQF and i-OCF which converge on a maximal weight matching. Finally, we present two interesting implementations of the Gale-Shapley algorithm, designed to solve the stable marriage problem.

The slip history of the 1994 Northridge, California, earthquake determined from strong-motion, teleseismic, GPS, and leveling data

Abstract: We present a rupture model of the Northridge earthquake, determined from the joint inversion of near-source strong ground motion recordings, P and SH teleseismic body waves, Global Positioning System (GPS) displacement vectors, and permanent uplift measured along leveling lines. The fault is defined to strike 122° and dip 40° to the south-southwest. The average rake vector is determined to be 101°, and average slip is 1.3 m; the peak slip reaches about 3 m. Our estimate of the seismic moment is 1.3 ± 0.2 × 10^(26) dyne-cm (potency of 0.4 km3). The rupture area is small relative to the overall aftershock dimensions and is approximately 15 km along strike, nearly 20 km in the dip direction, and there is no indication of slip shallower than about 5 to 6 km. The up-dip, strong-motion velocity waveforms are dominated by large S-wave pulses attributed to source directivity and are comprised of at least 2 to 3 distinct arrivals (a few seconds apart). Stations at southern azimuths indicate two main S-wave arrivals separated longer in time (about 4 to 5 sec). These observations are best modeled with a complex distribution of subevents: The initial S-wave arrival comes from an asperity that begins at the hypocenter and extends up-dip and to the north where a second, larger subevent is centered (about 12 km away). The secondary S arrivals at southern azimuths are best fit with additional energy radiation from another high slip region at a depth of 19 km, 8 km west of the hypocenter. The resolving power of the individual data sets is examined by predicting the geodetic (GPS and leveling) displacements with the dislocation model determined from the waveform data, and vice versa, and also by analyzing how well the teleseismic solution predicts the recorded strong motions. The general features of the geodetic displacements are not well predicted from the model determined independently from the strong-motion data; likewise, the slip model determined from geodetic data does not adequately reproduce the strong-motion characteristics. Whereas a particularly smooth slip pattern is sufficient to satisfy the geodetic data, the strong-motion and teleseismic data require a more heterogeneous slip distribution in order to reproduce the velocity amplitudes and frequency content. Although the teleseismic model can adequately reproduce the overall amplitude and frequency content of the strong-motion velocity recordings, it does a poor job of predicting the geodetic data. Consequently, a robust representation of the slip history and heterogeneity requires a combined analysis of these data sets.

Slip distribution along the North Anatolian fault associated with the large earthquakes of the period 1939 to 1967

Abstract: Between 1939 and 1967, six large fault ruptures formed a westward-migrating sequence of events along a 900-km-long nearly continuous portion of the North Anatolian fault. For these events—the 1939 Erzincan, 1942 Niksar-Erbaa, 1943 Tosya, 1944 Bolu-Gerede, 1957 Abant, and 1967 Mudurnu Valley earthquakes—I have compiled a record of dextral slip, which contains nearly 100 points. These data indicate that the amount of slip is irregularly distributed along the 1939 to 1967 rupture zone. The maximum slip, 7.5 m, occurred during the 1939 earthquake in the eastern 150 km of the 900-km-long rupture zone. Dextral offsets diminish very abruptly eastward but very gradually westward. The rate of westward decrease in the 1939 to 1967 offsets is only slightly greater than the rate of westward decrease of post-Miocene displacement along the North Anatolian fault. This suggests that westward decrease in slip can be expected to be a general characteristic of earthquake ruptures along the North Anatolian fault in the future. Nevertheless, within the 1939 to 1967 slip distribution, there are three regions that had less slip than the neighboring regions. These I interpret as possible sites of large future earthquakes. One of these seismic gaps has already experienced another earthquake (in 1951) and subsequent creep.

Can the Okhotsk Plate be discriminated from the North American plate

Abstract: The plate geometry in northeast Asia has been a long-standing question, with a major issue being whether the Sea of Okhotsk and northern Japanese islands are better regarded as part of the North American plate or as a separate Okhotsk plate. This question has been difficult to resolve, because earthquake slip vectors along the Kuril and Japan trenches are consistent with either Pacific-North America or Pacific-Okhotsk plate motion. To circumvent this difficulty, we also use slip vectors of earthquakes along Sakhalin Island and the eastern margin of the Japan Sea and compare them to the predicted Eurasia-Okhotsk and Eurasia-North America motions. For a model with a separate Okhotsk plate, we invert 10 Eurasia-Okhotsk and 255 Pacific-Okhotsk slip vectors with Pacific-North America and Eurasia-North America NUVEL-1 data. Alternatively, for a model without an Okhotsk plate, those Eurasia-Okhotsk and Pacific-Okhotsk data are regarded as Eurasia-North America and Pacific-North America data, respectively. The model with an Okhotsk plate fits the data better than one in which this region is treated as part of the North American plate. Because the improved fit exceeds that expected purely from the additional plate, the data indicate that the Okhotsk plate can be resolved from the North American plate. The motions on the Okhotsk plate's boundaries predicted by the best fitting Euler vectors are generally consistent with the recent tectonics. The Eurasia-Okhotsk pole is located at northernmost Sakhalin Island and predicts right-lateral strike slip motion on the NNE striking fault plane of the May 27, 1995, Neftegorsk earthquake, consistent with the centroid moment tensor focal mechanism and the surface faulting. Along the northern boundary of the Okhotsk plate, the North America-Okhotsk Euler vector predicts left-lateral strike slip, consistent with the observed focal mechanisms. On the NW boundary of the Okhotsk plate, the Eurasia-Okhotsk Euler vector predicts E-W extension, discordant with the limited focal mechanisms and geological data. This misfit may imply that another plate is necessary west of the Magadan region in southeast Siberia, but this possibility is hard to confirm without further data, such as might be obtained from space-based geodesy.

Fault trace complexity, cumulative slip, and the shape of the magnitude-frequency distribution for strike-slip faults : a global survey

Abstract: SUMMARY We examine whether the shape of the magnitude-frequency distribution for strike-slip faults is described by the Gutenburg-Richter relationship (log n = a - bM) or by the characteristic earthquake model, by analysing a data set of faults from California, Mexico, Japan, New Zealand, China and Turkey. For faults within regional seismic networks, curves of the form log n yrpl= a - bM, where n yr-' is the number of events per year equal to magnitude M, are fit to the instrumental record of seismicity, and geological data are used to estimate independently the size and recurrence rate of the largest expected earthquakes that would rupture the total length of the fault. Extrapolation of instrumentally derived curves to larger magnitudes agrees with geological estimates of the recurrence rate of the largest earthquakes for only four of the 22 faults if uncertainties in curve slope are considered, and significantly underestimates the geological recurrence rates in the remaining cases. Also, if we predict the seismicity of the faults as a function of fault length and slip rate, and the predicted seismicity is distributed in accord with the Gutenburg-Richter relationship, we find the predicted recurrence rate to be greater than the observed recurrence rates of smaller earthquakes along most faults. If individual fault zones satisfy the Gutenburg-Richter relationship over the long term, our observations imply that, during the recurrence interval of the largest expected earthquakes, the recurrence of lesser-sized events is not steady but, rather, strongly clustered in time. However, if the instrumental records provide an estimate of the long-term rate of small to moderate earthquakes along the faults, our observations imply that the faults generally exhibit a magnitude-frequency distribution consistent with the characteristic earthquake model. Also, we observe that the geometrical complexity of strike-slip faults is a decreasing function of cumulative strike-slip offset. The four faults we observe to be consistent with the GutenburgRichter relationship are among those characterized by the least amount of cumulative slip and greatest fault-trace complexity. We therefore suggest that the ratio of the recurrence rate of small to large earthquakes along a fault zone may decrease as slip accumulates and the fault becomes smoother.

Simulations of atomic-scale sliding friction

Abstract: Simulation studies of atomic-scale sliding friction have been performed for a number of tip-surface and surface-surface contacts consisting of copper atoms Both geometrically very simple tip-surface structures and more realistic interface necks formed by simulated annealing have been studied Kinetic friction is observed to be caused by atomic-scale stick and slip which occurs by nucleation and subsequent motion of dislocations preferably between close-packed {111} planes Stick and slip seems to occur in different situations For single crystalline contacts without grain boundaries at the interface the stick and slip process is clearly observed for a large number of contact areas, normal loads, and sliding velocities If the tip and substrate crystal orientations are different so that a mismatch exists in the interface, the stick and slip process is more fragile It is then caused by local pinning of atoms near the boundary of the interface and is therefore more easily observed for smaller contacts Depending on crystal orientation and load, frictional wear can also be seen in the simulations In particular, for the annealed interface necks which model contacts created by scanning tunneling microscope/atomic force microscope tip indentations the sliding process involves breaking contacts leaving tip material behind on the substrate

A new model for {1012} twin growth in hcp metals

Abstract: Computer simulation has been used to study the interaction of a perfect, basal dislocation with a {1012} twin boundary in a hcp metal for the situation where the 1/3{1120} Burgers vector is inclined at 60° to the interface. It is found that slip is not transferred from one crystal to the other with a residual dislocation left at the interface. Instead, the matrix dislocation decomposes into interfacial defects. We show that as a result of this decomposition the matrix dislocation becomes a new source of twinning dislocations that produce twin growth when the appropriate stress is applied to the crystal. The mechanism described does not require twinning dislocations to multiply by a pole process.

Slip complexity in earthquake fault models

Abstract: We summarize studies of earthquake fault models that give rise to slip complexities like those in natural earthquakes. For models of smooth faults between elastically deformable continua, it is critical that the friction laws involve a characteristic distance for slip weakening or evolution of surface state. That results in a finite nucleation size, or coherent slip patch size, h*. Models of smooth faults, using numerical cell size properly small compared to h*, show periodic response or complex and apparently chaotic histories of large events but have not been found to show small event complexity like the self-similar (power law) Gutenberg-Richter frequency-size statistics. This conclusion is supported in the present paper by fully inertial elastodynamic modeling of earthquake sequences. In contrast, some models of locally heterogeneous faults with quasi-independent fault segments, represented approximately by simulations with cell size larger than h* so that the model becomes "inherently discrete," do show small event complexity of the Gutenberg-Richter type. Models based on classical friction laws without a weakening length scale or for which the numerical procedure imposes an abrupt strength drop at the onset of slip have h* = 0 and hence always fall into the inherently discrete class. We suggest that the small-event complexity that some such models show will not survive regularization of the constitutive description, by inclusion of an appropriate length scale leading to a finite h*, and a corresponding reduction of numerical grid size.

Dynamical weakening of faults by acoustic fluidization

Abstract: When a fault slips seismically, some of the energy released may excite strong, short-wavelength vibrations near the fault core. Such vibrations can temporarily reduce the normal stress on the fault, allowing it to slip at lower shear stresses than predicted by laboratory coefficients of friction. This phenomenon of 'acoustic fluidization' provides an alternative to theories that invoke pressurized fluids as an explanation for why some faults appear to be so weak.

Stability of Newtonian and viscoelastic dynamic contact lines

Abstract: The stability of the moving contact line is examined for both Newtonian and viscoelastic fluids. Two methods for relieving the contact line singularity are chosen: matching the free surface profile to a precursor film of thickness b, and introducing slip at the solid substrate. The linear stability of the Newtonian capillary ridge with the precursor film model was first examined by Troian et al. [Europhys. Lett. 10, 25 (1989)]. Using energy analysis, we show that in this case the stability of the advancing capillary ridge is governed by rearrangement of fluid in the flow direction, whereby thicker regions develop that advance more rapidly under the influence of a body force. In addition, we solve the Newtonian linear stability problem for the slip model and obtain results very similar to those from the precursor film model. Interestingly, stability results for the two models compare quantitatively when the precursor film thickness b is numerically equal to the slip parameter α. With the slip model, it is possible to examine the effect of contact angle on the stability of the advancing front, which, for small contact angles, was found to be independent of the contact angle. The stability of an Oldroyd‐B fluid was examined via perturbation theory in Weissenberg number. It is found that elastic effects tend to stabilize the capillary ridge for the precursor film model, and this effect is more pronounced as the precursor film thickness is reduced. The perturbation result was examined in detail, indicating that viscoelastic stabilization arises primarily due to changes of momentum transfer in the flow direction, while elasticity has little effect on the response of the fluid to flow in the spanwise direction.

Efficient monte carlo technique for locating critical slip surface

Abstract: The search for the critical slip surface in slope-stability analysis is performed by means of a minimization of the safety factor. The procedures most widely used are deterministic methods of nonlinear programming, and random search methods have been neglected, since they are considered to be generally less efficient. In this paper, an efficient Monte-Carlo method for locating the critical slip surface is presented. The procedure is articulated in a sequence of stages, where each new slip surface is randomly generated by an appropriate technique. From a comparative analysis, the proposed method provides solutions of the same quality as the best nonlinear programming methods. However, the structure of the presented method is very simple, and it can be more easily programmed, integrated, and modified for particular exigencies.

Coseismic Deformation From Earthquake Faulting On A Layered Spherical Earth

Abstract: SUMMARY A method for calculating the static displacement field following earthquake faulting in a layered spherical earth is presented At shallow levels, the Earth’s layering is characterized by sharp jumps in bulk and shear moduli at the Conrad discontinuity and the Moho and is therefore important to consider when evaluating crustal deformation The solution to the equations of static equilibrium is represented as a superposition of spheroidal and toroidal components that each depend on spherical harmonic degree and the moment tensor A method that has recently been applied to the problem of wave propagation on a layered spherical earth is here applied to the static deformation field By representing the point source in terms of discontinuities in the displacement-stress vector, the Green’s function for a particular source geometry is derived directly Numerical tests are presented to verify the accuracy of the method and to illustrate the effects of sphericity and layering on the calculated deformation fields The effect of sphericity is generally less than about 2 per cent (of maximum deformation) within 100 km of an earthquake source at crustal depths Comparisons between the deformation calculated on a spherical homogeneous earth and spherical layered earth show that up to 20 per cent errors would be introduced if the Earth’s layered structure were ignored The effect of layering is strongest for sources with a strong horizontal slip component

Joint Inversion of Near- and Far-field Waveforms and Geodetic Data for the Rupture Process of the 1995 Kobe Earthquake

Abstract: The geodetic data, strong-motion waveforms, and far-field waveforms from the 1995 Kobe earthquake (MJMA 7.2) were inverted to determine the rupture process. The geodetic data, including the horizontal displacements measured at 43 stations and the vertical displacements measured at 61 stations, were provided by the Geographical Survey Institute of Japan and the Japanese University Consortium for GPS Research. We assumed two fault planes, one each Awaji Island and Kobe, with different strike directions and dip angles, and which were consistent with the active fault map and the aftershock distribution. We first inverted the geodetic data alone to determine the heterogeneous distribution of slip on the assumed faults. Second, the strong-motion records provided by the Japan Meteorological Agency, the Committee of Earthquake Observation and Research in the Kansai Area, and the Kobe City government were inverted to obtain the temporal variation of slip. Third, the displacement waveforms of far-field P- and SH-waves were analyzed. Finally, we performed a triple joint inversion to determine the source model most suitable for explaining all the data sets. The solution of the joint inversion expressed very strong ground motions, which well simulated the ones observed in Kobe at frequencies lower than 1 Hz. Concentrated slips are recovered in the shallow northeastern portion of the Nojima fault on Awaji Island and beneath the Strait of Akashi between Awaji and Kobe. Using the geodetic data, we also examined the possibility of another hidden fault beneath the extremely damaged area in Kobe, but matching of the data was not improved by the introduction of this fault.

Implications of fault constitutive properties for earthquake prediction.

Abstract: The rate- and state-dependent constitutive formulation for fault slip characterizes an exceptional variety of materials over a wide range of sliding conditions. This formulation provides a unified representation of diverse sliding phenomena including slip weakening over a characteristic sliding distance Dc, apparent fracture energy at a rupture front, time-dependent healing after rapid slip, and various other transient and slip rate effects. Laboratory observations and theoretical models both indicate that earthquake nucleation is accompanied by long intervals of accelerating slip. Strains from the nucleation process on buried faults generally could not be detected if laboratory values of Dc apply to faults in nature. However, scaling of Dc is presently an open question and the possibility exists that measurable premonitory creep may precede some earthquakes. Earthquake activity is modeled as a sequence of earthquake nucleation events. In this model, earthquake clustering arises from sensitivity of nucleation times to the stress changes induced by prior earthquakes. The model gives the characteristic Omori aftershock decay law and assigns physical interpretation to aftershock parameters. The seismicity formulation predicts large changes of earthquake probabilities result from stress changes. Two mechanisms for foreshocks are proposed that describe observed frequency of occurrence of foreshock-mainshock pairs by time and magnitude. With the first mechanism, foreshocks represent a manifestation of earthquake clustering in which the stress change at the time of the foreshock increases the probability of earthquakes at all magnitudes including the eventual mainshock. With the second model, accelerating fault slip on the mainshock nucleation zone triggers foreshocks.

On the controllability of the 2-D incompressible Navier-Stokes equations with the Navier slip boundary conditions

Abstract: For boundary or distributed controls, we get an approximate controllability result for the Navier-Stokes equations in dimension 2 in the case where the fluid is incompressible and slips on the boundary in agreement with the Navier slip boundary conditions.

The 1964 Prince William Sound earthquake: Joint inversion of tsunami and geodetic data

Abstract: The 1964 Prince William Sound (Alaska) earthquake, Mw = 9.2, ruptured a large area beneath the continental margin of Alaska from Prince William Sound to Kodiak Island. A joint inversion of tsunami waveforms and geodetic data, consisting of vertical displacements and horizontal vectors, gives a detailed slip distribution. Two areas of high slip correspond to seismologically determined areas of high moment release: the Prince William Sound asperity with average slip of 18 m and the Kodiak asperity with average slip of 10 m. The average slip on the fault is 8.6 m and the seismic moment is estimated as 6.3 × 1022 N m, or over 75% of the seismic moment determined from long-period surface waves.

Global Positioning System constraints on fault slip rates in southern California and northern Baja, Mexico

Abstract: We use Global Positioning System (GPS) estimates of horizontal site velocity to constrain slip rates on faults comprising the Pacific-North America plate boundary in southern California and northern Mexico. We enlist a simple elastic block model to parameterize the distribution and sum of deformation within and across the plate boundary. We estimate a Pacific-North America relative plate motion rate of 49 ± 3 mm/yr (one standard deviation), consistent with NUVEL-1A estimates. We are able to resolve robust slip rate estimates for the southernmost San Andreas, San Jacinto, and Elsinore faults (26 ± 2, 9 ± 2, and 6 ± 2 mm/yr, respectively) and for the Imperial and Cerro Prieto faults (35 ± 2 and 42 ± 1 mm/yr, respectively), accounting for about 86% of the total plate motion. The remaining 14% appears to be accommodated to the west of these fault systems, probably via slip along the San Clemente fault and/or the San Miguel, Vallecitos, Rose Canyon, and Newport-Inglewood fault systems. These results are highly consistent with paleoseismic estimates for slip rates implying that off-fault strain accumulation within the deforming zone of the plate boundary is largely elastic. We estimate that the seismically quiescent, southernmost San Andreas fault has incurred about 8.2 m of slip deficit over the last few hundred years, presumably to be recovered during a future large earthquake.

Frictional constraints on crustal faulting

Abstract: We consider how variations in fault frictional properties affect the phenomenology of earthquake faulting. In particular, we propose that lateral variations in fault friction produce the marked heterogeneity of slip observed in large earthquakes. We model these variations using a rate- and state-dependent friction law, where we differentiate velocity-weakening behavior into two fields: the strong seismic field is very velocity weakening and the weak seismic field is slightly velocity weakening. Similarly, we differentiate velocity-strengthening behavior into two fields: the compliant field is slightly velocity strengthening and the viscous field is very velocity strengthening. The strong seismic field comprises the seismic slip concentrations, or asperities. The two “intermediate” fields, weak seismic and compliant, have frictional velocity dependences that are close to velocity neutral: these fields modulate both the tectonic loading and the dynamic rupture process. During the interseismic period, the weak seismic and compliant regions slip aseismically, while the strong seismic regions remain locked, evolving into stress concentrations that fail only in main shocks. The weak seismic areas exhibit most of the interseismic activity and aftershocks but can also creep seismically. This “mixed” frictional behavior can be obtained from a sufficiently heterogeneous distribution of the critical slip distance. The model also provides a mechanism for rupture arrest: dynamic rupture fronts decelerate as they penetrate into unloaded complaint or weak seismic areas, producing broad areas of accelerated afterslip. Aftershocks occur on both the weak seismic and compliant areas around a fault, but most of the stress is diffused through aseismic slip. Rapid afterslip on these peripheral areas can also produce aftershocks within the main shock rupture area by reloading weak fault areas that slipped in the main shock and then healed. We test this frictional model by comparing the seismicity and the coseismic slip for the 1966 Parkfield, 1979 Coyote Lake, and 1984 Morgan Hill earthquakes. The interevent seismicity and aftershocks appear to occur on fault areas outside the regions of significant slip: these regions are interpreted as either weak seismic or compliant, depending on whether or not they manifest interevent seismicity.

Short slip duration in dynamic rupture in the presence of heterogeneous fault properties

Abstract: Recent studies of strong motion data consistently show that the risetime (duration of slip at particular locations on the fault) is significantly shorter than the overall rupture duration. The physical explanation for this observation and its implications have become central issues in earthquake source studies. Two classes of mechanisms have been proposed to explain short risetimes. One explanation is that velocity-weakening frictional behavior on the fault surface causes the fault to self-heal. This possibility is suggested by rate-dependent friction observed in laboratory experiments and by some two-dimensional dynamic numerical simulations of earthquake rupture. It has recently been demonstrated, however, that the velocity dependence of friction observed in the laboratory is too weak to cause faults to self-heal. An alternative explanation for short risetimes is that spatially heterogeneous fault strength (e.g., barriers) limit the slip duration. In this paper we investigate this second explanation for short risetimes by constructing a three-dimensional dynamic rupture model for the 1984 Morgan Hill, California earthquake (Mw = 6.2) using a kinematic model previously obtained from waveform inversion of strong motion data. We assume velocity-independent friction and a critical stress fracture criterion and derive a dynamic model specified by the spatial distribution of dynamic stress drop and strength excess that reproduces the slip and rupture time of the kinematic model. The slip velocity time functions calculated from this dynamic model are then used in a subsequent inversion to fit the strong motion data. By alternating between dynamic and kinematic modeling, we obtain a dynamic model that provides an acceptable fit to the recorded waveforms. In this dynamic model the risetime is short over most of the fault, which is attributable entirely to the short scale-length slip/stress drop heterogeneity required by the strong motion data. A self-healing mechanism, such as strongly velocity-dependent friction, is not required to explain the short risetimes observed in this earthquake.

The repetition of large-earthquake ruptures

Abstract: This survey of well-documented repeated fault rupture confirms that some faults have exhibited a "characteristic" behavior during repeated large earthquakes--that is, the magnitude, distribution, and style of slip on the fault has repeated during two or more consecutive events. In two cases faults exhibit slip functions that vary little from earthquake to earthquake. In one other well-documented case, however, fault lengths contrast markedly for two consecutive ruptures, but the amount of offset at individual sites was similar. Adjacent individual patches, 10 km or more in length, failed singly during one event and in tandem during the other. More complex cases of repetition may also represent the failure of several distinct patches. The faults of the 1992 Landers earthquake provide an instructive example of such complexity. Together, these examples suggest that large earthquakes commonly result from the failure of one or more patches, each characterized by a slip function that is roughly invariant through consecutive earthquake cycles. The persistence of these slip-patches through two or more large earthquakes indicates that some quasi-invariant physical property controls the pattern and magnitude of slip. These data seem incompatible with theoretical models that produce slip distributions that are highly variable in consecutive large events.

The role of strain gradients in the grain size effect for polycrystals

Abstract: The role of grain size on the overall behaviour of polycrystals is investigated by using a strain gradient constitutive law for each slip system for a reference single crystal. Variational principles of Hashin-Shtrikman type are formulated for the case where the strain energy density is a convex function of both strain and strain gradient. The variational principles are specialized to polycrystals with a general multi-slip strain gradient constitutive law. An extension of the Hashin-Shtrikman bounding methodology to general strain gradient composites is discussed in detail and then applied to derive bounds for arbitrary linear strain gradient composites or polycrystals. This is achieved by an extensive study of kernel operators related to the Green's function for a general “strain-gradient” linear isotropic incompressible comparison medium. As a simple illustrative example, upper and lower bounds are computed for linear face-centred cubic polycrystals: a size effect is noted whereby smaller grains are stiffer than large grains. The relation between the assumed form of the constitutive law for each slip system and the overall response is explored.

Late Cenozoic slip on the Talas-Ferghana fault, the Tien Shan, central Asia

Abstract: Although Cenozoic crustal shortening and thickening by thrust faulting have built the present Tien Shan, active right-lateral shear on the northwest-trending Talas-Ferghana fault appears to be the most rapid localized deformation in the belt. Ephemeral stream valleys have been offset right-laterally tens of metres. New and published radiocarbon dates of organic material deposited in depressions blocked by offset ridges place upper bounds on the average Holocene slip rate at 18 localities. Uncertainties allow 14 upper bounds to overlap the range of 8–16 mm/yr, and 95% confidence limits on such bounds at 11 sites are entirely within this range. We infer that the rate of ≈10 mm/yr is not simply an upper bound, but applies to the late Holocene Epoch. Although the bounds on rates permit more rapid slip in the northwest than the southeast, they do not place a useful constraint on variations in slip rate along the fault. Offsets of Paleozoic facies boundaries imply a total right-lateral shear of 180–250 km, but Early Cretaceous sedimentary rock appears to have been offset only 60 ± 10 km. Published paleomagnetic declinations of Cretaceous- Miocene rock demonstrate 20°–30° of counterclockwise rotation of the Ferghana Valley, which lies just west of the Talas-Ferghana fault, with respect to stable parts of Eurasia and 20° ± 11° with respect to the central Tien Shan east of the fault. These declinations are consistent with a maximum northwestward translation of 70–210 km of the Ferghana Valley at the Talas-Ferghana fault and, therefore, with a similar maximum horizontal shortening across the Chatkal Ranges, which lie between the Ferghana Valley and the Kazakh platform. Estimates of crustal thickness beneath the Chatkal Ranges, however, permit only 60–100 km of Cenozoic shortening. If <100 km of slip on the Talas-Ferghana fault accumulated at a constant rate of 10 mm/yr, it would imply an initiation of slip more recently than ca. 10 Ma, long after India collided with the rest of Eurasia.

Exploring molecular origins of sharkskin, partial slip, and slope change in flow curves of linear low density polyethylene

Abstract: This paper explores the molecular mechanism for sharkskin formation on extrudate of linear low density polyethylenes (LLDPE) and investigates the rheological origin of a characteristic curvature (i.e., a slope change) in the flow curve of LLDPE. Rheological measurements, performed at various temperatures from 160 to 240 °C with a controlled‐pressure capillary rheometer and a variety of dies, suggest that the slope change in the flow curve, interpreted by many as demonstrating wall slip in the die land, arises from a combination of interfacial slip and cohesive failure due to chain disentanglement, first initiated on the die wall in the exit region. Since the disentanglement state is unstable for the adsorbed chains within a certain stress range below the critical stress for the global stick–slip transition, a partial slip flow cannot sustain itself and occurs only periodically. This time‐dependent molecular entanglement–disentanglement fluctuation produces the sharkskin like extrudate in the regime where the slope change takes place. Sharkskin dynamics are found to precisely correlate with chain relaxation processes. Specifically, the characteristic time scale τ (i.e., the sharkskin periodicity) is found to be of the same magnitude and have the same WLF (Williams–Landel–Ferry) temperature dependence as that of the characteristic molecular relaxation time τ* as determined by oscillatory shear measurements in a parallel‐plate flow cell. The LLDPE resins are also observed to undergo interfacial stick–slip transitions as well as a rarely seen cohesive slip–slip transitions at various temperatures.