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International audience; Most earthquake ruptures propagate at speeds below the shear wave velocity within the crust, but in some rare cases, ruptures reach supershear speeds. The physics underlying the transition of natural subshear earthquakes to supershear ones is currently not fully understood. Most observational studies of supershear earthquakes have focused on determining which fault segments sustain fully grown supershear ruptures. Experimentally cross-validated numerical models have identified some of the key ingredients required to trigger a transition to supershear speed. However, the conditions for such a transition in nature are still unclear, including the precise location of this transition. In this work, we provide theoretical and numerical insights to identify the precise location of such a transition in nature. We use fracture mechanics arguments with multiple numerical models to identify the signature of supershear transition in coseismic off-fault damage. We then cross-validate this signature with high-resolution observations of fault zone width and early aftershock distributions. We confirm that the location of the transition from subshear to supershear speed is characterized by a decrease in the width of the coseismic off-fault damage zone. We thus help refine the precise location of such a transition for natural supershear earthquakes.

A catalog of low frequency events (LFEs) beneath Vancouver Island is analyzed in the context of a granular flow model. The catalog contains origin-times and magnitudes of 269,423 LFEs grouped within 130 families and recorded between 2003 and 2013. Each family represents a distinct location within the boundary between the subducting Juan de Fuca and overriding North American plates. The LFEs occurred during 10 episodic tremor and slip (ETS) events that recurred at ∼14-month intervals and lasted for about a week. With one exception, each family was active in all 10 ETS episodes. Our analysis suggests that LFEs do not follow Gutenberg-Richter statistics, but are normally distributed with respect to magnitude and, therefore, log-normally distributed with respect to moment. The Kostrov strain associated with the moments in a given family is used to estimate its size as L = 350 ± 15 m. These observations are explained through a model of granular flow in a channel that accommodates displacement along the plate boundary. In this model the LFE families correspond to granular jams in flow that persist over many ETS episodes. Each LFE is a slip between two grains in the jam. The log-normal distribution of LFE moments can be ascribed to a theoretically predicted log-normal distribution of grain sizes in each jam. This model explains the weak dependence of seismic duration on LFE moment because frictional slip between grains in an over-pressured environment need not scale like a growing rupture in an elastic medium.

Supershear earthquakes are rare but powerful ruptures with devastating consequences. How quickly an earthquake rupture attains this speed, or for that matter decelerates from it, strongly affects high-frequency ground motion and the spatial extent of coseismic off-fault damage. Traditionally, studies of supershear earthquakes have focused on determining which fault segments sustained fully-grown supershear ruptures. Knowing that the rupture first propagated at subshear rupture speeds, these studies usually guessed an approximate location for the transition from subshear to supershear regimes. The rarity of confirmed supershear ruptures, combined with the fact that conditions for supershear transition are still debated, complicates the investigation of supershear transition in real earthquakes. Here, we find a unique signature of the location of a supershear transition: we show that, when a rupture accelerates towards supershear speed, the stress concentration abruptly shrinks, limiting the off-fault damage and aftershock productivity. First, we use theoretical fracture mechanics to demonstrate that, before transitioning to supershear, the stress concentration around the rupture tip shrinks, confining the region where damage & aftershocks are expected. Then, employing two different dynamic rupture modeling approaches, we confirm such reduction in stress concentration, further validating the expected signature in the transition region. We contrast these numerical and theoretical results with high-resolution aftershock catalogs for three natural supershear earthquakes, where we identify a small region with lower aftershock density near the supershear transition. Finally, using satellite optical image correlation techniques, we show that, for a fourth event, the transition zone is characterized by a diminution in the width of the damage zone. Our results demonstrate that the transition from subshear to supershear rupture can be clearly identified by a localized absence of aftershocks, and a decrease in off-fault damage, due to a transient reduction of the stress intensity at the rupture tip.

The 2004 M w 6 Parkfield, California, earthquake was preceded by a 4‐year period of anomalously high seismicity adjacent to, but not on, the San Andreas fault. The rate of small events ( M w 8 km, increased from 6 events per year prior to 2000 to 20 events per year between the 2000 and the 2004 earthquake. This increase in seismicity coincided with an increase in the rate of nonvolcanic tremor, which, if tremor is indicative of creep on the fault plane, suggests that creep may have driven the enhanced seismicity. Coulomb stress‐transfer calculations predict the observed spatial pattern of the seismicity, and thus support a causal relation between creep at the base of the fault zone and off‐fault seismicity. In particular, an observed southeast‐striking lineation of enhanced seismicity is shown to be a direct consequence of a deepening boundary between the crust and mantle southeast of Parkfield, as evidenced by a deepening of the tremor and low‐frequency earthquakes. Other evidence for a causal link between deep creep and off‐fault seismicity is the observation that off‐fault seismicity before and after the 2004 earthquake occurred in the same location. This is expected if the foreshocks are driven by an episode of deep creep and the aftershocks are driven by afterslip, both occurring on the same deep extension of the fault plane.

Coseismic surface deformation in large earthquakes is typically measured using field mapping and with a range of geodetic methods (e.g., InSAR, lidar differencing, and GPS). Current methods, however, either fail to capture patterns of near-field coseismic surface deformation or lack preevent data. Consequently, the characteristics of off-fault deformation and the parameters that control it remain poorly understood. We develop a standardized method to fully measure the surface, near-field, coseismic deformation patterns at high resolution using the COSI-Corr program by correlating pairs of aerial photographs taken before and after the 1992 M_w 7.3 Landers earthquake. COSI-Corr offers the advantage of measuring displacement across the entire zone of surface deformation and over a wider aperture than that available to field geologists. For the Landers earthquake, our measured displacements are systematically larger than the field measurements, indicating the presence of off-fault deformation. We show that 46% of the total surface displacement occurred as off-fault deformation, over a mean deformation width of 154 m. The magnitude and width of off-fault deformation along the rupture is primarily controlled by the macroscopic structural complexity of the fault system, with a weak correlation with the type of near-surface materials through which the rupture propagated. Both the magnitude and width of distributed deformation are largest in stepovers, bends, and at the southern termination of the surface rupture. We find that slip along the surface rupture exhibits a consistent degree of variability at all observable length scales and that the slip distribution is self-affine fractal with dimension of 1.56.

Variations in fault structure, for example, surface roughness and deformation zone width, influence the location and dynamics of large earthquakes as well as the distribution of small seismic events. In nature, changes in fault roughness and seismicity characteristics can rarely be studied simultaneously, so that little is known about their interaction and evolution. Here, we investigate the connection between fault structure and near-fault distributions of seismic events over series of stick-slip cycles in the laboratory. We conducted a set of experiments on rough faults that developed from incipient fracture surfaces. We monitored stress and seismic activity which occurred in the form of acoustic emissions (AEs). We determined AE density distributions as a function of fault normal distance based on high-accuracy hypocentre locations during subsequent interslip periods. The characteristics of these distributions were closely connected to different structural units of the faults, that is, the fault core, off-fault and background damage zone. The core deformation zone was characterized by consistently high seismic activity, whereas the off-fault damage zone displayed a power-law decay of seismic activity with increasing distance from the fault core. The exponents of the power-law-distributed off-fault activity increased with successive stick-slip events so that later interslip periods showed a more rapid spatial decay of seismic activity from the fault. The increase in exponents was strongest during the first one to three interslip periods and reached approximately constant values thereafter. The relatively rapid spatial decay of AE events during later interslip periods is likely an expression of decreasing fault zone complexity and roughness. Our results indicate a close relationship between fault structure, stress and seismic off-fault activity. A more extensive mapping of seismic off-fault activity-decay has the potential to significantly advance the understanding of fault zone properties including variations in fault roughness and stress.

[1] The statistics of large earthquakes commonly involve large uncertainties due to the lack of long-term, robust earthquake recordings. Small-scale seismic events are abundant and can be used to examine variations in fault structure and stress. We report on the connection between stress and microseismic event statistics prior to the possibly smallest earthquakes: those generated in the laboratory. We investigate variations in seismic b value of acoustic emission events during the stress buildup and release on laboratory-created fault zones. We show that b values mirror periodic stress changes that occur during series of stick-slip events, and are correlated with stress over many seismic cycles. Moreover, the amount of b value increase associated with slip events indicates the extent of the corresponding stress drop. Consequently, b value variations can be used to approximate the stress state on a fault: a possible tool for the advancement of time-dependent seismic hazard assessment. Citation: Goebel, T. H. W., D. Schorlemmer, T. W. Becker, G. Dresen, and C. G. Sammis (2013), Acoustic emissions document stress changes over many seismic cycles in stick-slip experiments, Geophys. Res. Lett., 40, 2049–2054, doi:10.1002/grl.50507.

A system of non-linear coupled relaxation oscillators is used to show how the communication between large earthquakes on a global scale can align their seismic cycles to produce a worldwide clustering of large events. Our model builds on recent observations that the seismic waves from a large earthquake can trigger an episode of non-volcanic tremor at the base of a distant fault. We assume that tremor is indicative of creep on the ductile extension of the fault zone that loads its overlying seismogenic layer thus advancing the fault toward failure. If this advance is larger toward the end of the seismic cycle, we show that two or more interacting faults will align their cycles, even if their recurrence intervals are not identical.

We provide estimates of temperature changes produced in fault damage zones during brittle deformation associated with distributed cracking and pulverization. In contrast to localized faulting accompanied by significant frictional weakening, the relatively high friction coefficient on the multitudinous small cracks generated in the fracturing process can lead to significant shear heating. Simple calculations with parameter values constrained by laboratory experiments and simulations indicate that the temperature can increase during the generation of rock damage and pulverization by 100 °C or more. The results can help explain signatures of elevated temperature observed in geometrically complex fault zone sections with significant rock damage and regions with broad distributed deformation.

Anomalously low values of friction observed in layers of submicron particles deformed in simple shear at high slip velocities are explained as the consequence of a one nanometer thick layer of water adsorbed on the particles. The observed transition from normal friction with an apparent coefficient near μ = 0.6 at low slip speeds to a coefficient near μ = 0.3 at higher slip speeds is attributed to competition between the time required to extrude the water layer from between neighboring particles in a force chain and the average lifetime of the chain. At low slip speeds the time required for extrusion is less than the average lifetime of a chain so the particles make contact and lock. As slip speed increases, the average lifetime of a chain decreases until it is less than the extrusion time and the particles in a force chain never come into direct contact. If the adsorbed water layer enables the otherwise rough particles to rotate, the coefficient of friction will drop to μ = 0.3, appropriate for rotating spheres. At the highest slip speeds particle temperatures rise above 100°C, the water layer vaporizes, the particles contact and lock, and the coefficient of friction rises to μ = 0.6. The observed onset of weakening at slip speeds near 0.001 m/s is consistent with the measured viscosity of a 1 nm thick layer of adsorbed water, with a minimum particle radius of approximately 20 nm, and with reasonable assumptions about the distribution of force chains guided by experimental observation. The reduction of friction and the range of velocities over which it occurs decrease with increasing normal stress, as predicted by the model. Moreover, the analysis predicts that this high-speed weakening mechanism should operate only for particles with radii smaller than approximately 1 μm. For larger particles the slip speed required for weakening is so large that frictional heating will evaporate the adsorbed water and weakening will not occur.

The micromechanical damage mechanics formulated by Ashby and Sammis (Pure Appl Geophys 133(3) 489–521, 1990) has been shown to give an adequate description of the triaxial failure surface for a wide variety of rocks at low confining pressure. However, it does not produce the large negative curvature in the failure surface observed in Westerly granite at high confining pressure. We show that this discrepancy between theory and data is not caused by the two most basic simplifying assumptions in the damage model: (1) that all the initial flaws are the same size or (2) that they all have the same orientation relative to the largest compressive stress. We also show that the stress–strain curve calculated from the strain energy density significantly underestimates the nonlinear strain near failure in Westerly granite. Both the observed curvature in the failure surface and the nonlinear strain at failure observed in Westerly granite can be quantitatively fit using a simple bi-mineral model in which the feldspar grains have a lower flow stress than do the quartz grains. The conclusion is that nonlinearity in the failure surface and stress–strain curves observed in triaxial experiments on Westerly granite at low loading rates is probably due to low-temperature dislocation flow and not simplifying assumptions in the damage mechanics. The important implication is that discrepancies between experiment and theory should decrease with increased loading rates, and therefore, the micromechanical damage mechanics, as formulated, can be expected to give an adequate description of high strain-rate phenomena like earthquake rupture, underground explosions, and meteorite impact.

We investigate asymmetric rupture propagation on an interface that combines a bulk elastic mismatch with a contrast in off-fault damage. Mode II ruptures propagating on the interface between thermally shocked (damaged) Homalite and polycarbonate plates were studied using high-speed photographs of the photoelastic fringes. The anelastic asymmetry introduced by damage is defined by ‘T’ and ‘C’ directions depending on whether the tensile or compressive lobe of the rupture tip stress concentration lies on the damaged side of the fault. The elastic asymmetry is commonly defined by ‘+’ and ‘−’ directions where ‘+’ is the direction of displacement of the more compliant material. Since damaged Homalite is stiffer than polycarbonate, the propagation directions in our experiments were ‘T+’ and ‘C−’. Theoretical and numerical studies predict that a shear rupture on an elastic bimaterial interfaces propagates in the ‘+’ direction at the generalized Rayleigh wave speed or in some numerical cases at the P-wave speed of the stiffer material, P_(fast). We present the first experimental evidence for propagation at P_(fast) in the ‘+’ direction for the bimaterial system undamaged Homalite in contact with polycarbonate. In the ‘−’ direction, both theory and experiments find ruptures in elastic bimaterials propagate either at sub-shear speed or at the P-wave speed of the softer material, P_(slow), depending on the loading conditions. We observe that the off-fault damage effect dominates the elastic bimaterial effect in dynamic rupture propagation. In the ‘C−’ direction the rupture propagates at sub-shear to supershear speeds, as in undamaged bimaterial systems, reaching a maximum speed of P_(slow). In the ‘T+’ direction however the rupture propagates at sub-shear speeds or comes to a complete stop due to increased damaged activation (slip and opening along micro-cracks) which results in a reduction in stored elastic potential energy and energy dissipation. Biegel et al. (2010-this issue) found similar results for propagation on the interface between Homalite and damaged Homalite where rupture speeds were slowed or even stopped in the ‘T−’ direction but were almost unaffected in the ‘C+’ direction.

The brittle portion of the Earth’s lithosphere contains a distribution of joints, faults and cataclastic zones that exist on a wide range of scale-lengths and usually have complex geometries including bends, jogs, and intersections. The material around these complexities is subjected to large stress concentrations, which lead during continuing deformation to the generation of new fracture and granular damage with an associated evolution of the elasticity, permeability and geometry of the actively deforming regions. The evolving material and geometrical properties within and around the fault zone can lead, in turn, to evolution of various aspects of earthquake and fault mechanics.

We review the results of a recent series of papers in which the interaction between a dynamic mode II fracture on a fault plane and off-fault damage has been studied using high-speed photography. In these experiments, fracture damage was created in photoelastic Homalite plates by thermal shock in liquid nitrogen and rupture velocities were measured by imaging fringes at the tips. In this paper we review these experiments and discuss how they might be scaled from lab to field using a recent theoretical model for dynamic rupture propagation. Three experimental configurations were investigated: An interface between two damaged Homalite plates, an interface between damaged and undamaged Homalite plates, and the interface between damaged Homalite and undamaged polycarbonate plates. In each case, the velocity was compared with that on a fault between the equivalent undamaged plates at the same load. Ruptures on the interface between two damaged Homalite plates travel at sub-Rayleigh velocities indicating that sliding on off-fault fractures dissipates energy, even though no new damage is created. Propagation on the interface between damaged and undamaged Homalite is asymmetric. Ruptures propagating in the direction for which the compressional lobe of their crack-tip stress field is in the damage (which we term the ‘C’ direction) are unaffected by the damage. In the opposite ‘T’ direction, the rupture velocity is significantly slower than the velocity in undamaged plates at the same load. Specifically, transitions to supershear observed using undamaged plates are not observed in the ‘T’ direction. Propagation on the interface between damaged Homalite and undamaged polycarbonate exhibits the same asymmetry, even though the elastically “favored” ‘+’ direction coincides with the ‘T’ direction in this case. The scaling properties of the interaction between the crack-tip field and pre-existing off-fault damage (i.e., no new damage is created) are explored using an analytic model for a nonsingular slip-weakening shear slip-pulse and verified using the velocity history of a slip pulse measured in the laboratory and a direct laboratory measurement of the interaction range using damage zones of various widths adjacent to the fault.

High-pass filtering (>20 Hz) of acceleration records from the 1999 Chi-Chi, Taiwan, and 2004 Parkfield, California, earthquakes reveals a series of bursts that occur only during strong shaking. Initially interpreted as originating from asperity failure on the Chelungpu fault, bursts observed during the Chi-Chi earthquake were subsequently determined to be a local effect within about 1 km of the seismic stations. Similar bursts were observed at the U.S. Geological Survey Parkfield seismic array during the Parkfield earthquake and were constrained to originate less than 20 m from the instruments. Such small shallow events cannot result from the triggered release of stored elastic energy because rate-and-state friction rules out stick-slip instability on such small, shallow patches. Our hypothesis is that the bursts are not triggered but are driven by simultaneous shear and tensile stresses near the surface during the strong motion. At 2 Hz, SV - to P -wave mode conversion at the free surface produces tensile stresses to depths of 70 m. Where standard triggering releases stored elastic energy and adds to the incident wave field, this new driving mechanism takes energy out of the 2 Hz strong motion and reradiates it at high frequencies. It is thus an attenuation mechanism that we estimate can contribute 3% to the net attenuation in the very shallow crust.

Nuclear monitoring agencies often use seismic amplitudes to estimate the yields of underground nuclear tests. Any emplacement phenomena that can alter those amplitudes and lead to bias in estimated yields must be considered in the analysis. One condition that might cause such a bias is detonation in frozen rock. Laboratory analyses (Mellor, 1971; Miller and Florence, 1991) have shown that frozen rock has faster seismic velocity and greater compressive strength than unfrozen rock. This increased strength is hypothesized to reduce the seismically estimated yield of an explosion in frozen rock. To test this hypothesis, we conducted the Frozen Rock Experiment (FRE), a series of explosions in frozen and unfrozen rock, in central Alaska during August 2006. Over 120 seismic instruments were deployed to record six detonations—three in frozen and three in unfrozen-dry media—at a wide range of distances and azimuths. The data acquired show that the frozen test site explosions had significantly larger amplitudes for all phases ( P , S , and surface waves) above 8–10 Hz. These data confirm that the frozen rock medium was stronger and resulted in a smaller seismic source radius for the explosions, thus increasing the corner frequency when compared to the unfrozen rock explosions. Between 3 and 9 Hz, the unfrozen shots produced slightly larger S and surface waves resulting in different P / S spectral ratio plots for the frozen and unfrozen shots, possibly affecting regional phase discrimination. We show that the observed amplitude differences for these shots can be effectively modeled using the Mueller-Murphy (1971) explosion source and the in situ P - and S -wave velocities for the two test sites. Differences in the velocities at the frozen and unfrozen rock test sites are caused by minor metamorphic facies changes, saturated versus dry conditions, and the presence of ice in the pores and fractures at the frozen test site. Extrapolation of the results of this study to synthetic nuclear explosions suggests there may not be significant coupling differences between explosions in frozen and unfrozen hard rock.

High-frequency band-pass filtering of acceleration records from the 1999 Chi-Chi, Taiwan, earthquake ( M w 7.6) resolves the continuous signal into a series of relatively short-duration discrete-energy bursts. We hypothesize that these bursts originate near the individual stations as small, shallow events that have been dynamically triggered by the P and S waves generated by the Chi-Chi mainshock; however, we cannot rule out the possibility that they originate from some nonseismic source associated with the surface, such as buildings or trees. Bursts are observed only during the seismic signal and not in the pre- or postsignal noise. The bursts are not likely to be generated by the instruments because groupings of three colocated individual instruments record identical bursts. Also, we show that the bursts are not due to the band-pass filtering of instrumentally generated step functions. The hypothesis that they are local events is supported by the observation of bursts in the 40-Hz frequency band at distances up to 170 km from the epicenter. If the bursts originated on the Chi-Chi fault plane, as hypothesized by Chen et al. (2006), based on their analysis of recordings within 20 km from the Chelungpu fault, then they should not be observable at this distance, assuming any reasonable value of crustal attenuation. Assuming a local origin, we estimate an average local event magnitude of M w 0.2 and a source-receiver distance of approximately 1 km. We extended our analysis to lower stress levels by analyzing records from a smaller ( M w 5.3) event that was recorded by many of the same instruments used in the Chi-Chi analysis. For this event, bursts are observed only on the accelerograms from stations relatively close to the mainshock hypocenter. Analysis of the combined data set from both mainshocks suggests a stress threshold for triggering in the range 0.03–0.05 Mpa for S -wave triggering and 0.0013–0.0033 Mpa for P -wave triggering, consistent with prior observations of surface-wave triggering.

Spontaneous bilateral mode II shear ruptures were nucleated on faults in photoelastic Homalite plates loaded in uniaxial compression. Rupture velocities were measured and the interaction between the rupture front and short fault branches was observed using high-speed digital photography. Fault branches were formed by machining slits of varying lengths that intersected the fault plane over a range of angles. These branches were frictionless because they did not close under static loading prior to shear rupture nucleation. Three types of behavior were observed. First, the velocity of both rupture fronts was unaffected when the fault branches were oriented 45 to the main slip surface and the length of the branches were less than or equal to � 0.75 R0* (where R0* is the slip-weakening distance in the limit of low rupture speed and an infinitely long slip-pulse). Second, rupture propagation stopped at the branch on the compressive side of the rupture tip but was unaffected by the branch on the tensile side when the branches were � 1.5 R0* in length and remained oriented 45 to the principle slip surface. Third, branches on the tensile side of the rupture tip nucleated tensile ''wing tip'' extensions when the branches were oriented at 70 to the interface. Third, when the branches were oriented at 70 to the interface, branches on the tensile side of the rupture tip nucleated tensile ''wing-crack'' extensions. We explain these observations using a model in which the initial uniaxial load produces stress concentrations at the tips of the branches, which perturb the initial stress field on the rupture plane. These stress perturbations affect both the resolved shear stress driving the rupture and the fault-normal stress that controls the fault strength, and together they explain the observed changes in rupture speed.

High-frequency bandpass filtering of broadband strong-motion seismograms recorded immediately adjacent to the fault plane of the 1999 Chi-Chi, Taiwan, earthquake reveals a sequence of distinct bursts, many of which contain quasi-periodic subbursts with repeat times on the order of a few tenths of a second. The subevents that produce these bursts do not appear in conventional slip-maps, presumably because of the low-pass filtering used in the waveform inversions. The origin times, locations, and magnitudes of of about 500 of these subevents were determined. Those closest to the hypocenter appear to have been triggered by the P wave, while the earliest subevents at greater distances are consistent with a rupture front propagating at about 2.0 km/sec. Later subevents at a given distance follow Omori9s law and may be interpreted as aftershocks that begin before the Chi-Chi rupture has terminated. The frequency-magnitude distribution of these subevents has a b -value equal to 1.1. The subevents are clustered in space, with most clusters located at shallow depth along the Chelungpu surface rupture. The larger subevents tend to occur at greater depth, while the small subevents are only located at shallower depths. Cluster locations generally coincide with the large-amplitude slip-patches found by source inversions at lower frequencies. Relocation of the deeper subevents suggests a nonplaner rupture surface where dip increases with depth at the southern end.

We test the Bowman and King [Bowman, D.D., King, G.C.P., 2001a, Accelerating seismicity and stress accumulation before large earthquakes. Geophys. Res. Lett., 28 (21), 4039–4042, Bowman, D.D., King, G.C.P., 2001b. Stress transfer and seismicity changes before large earthquakes. C. R. Acad. Sci. Paris, 333, 591–599] Stress Accumulation model by examining the evolution of seismicity rates prior to the 1992 Landers, California earthquake. The Stress Accumulation (SA) model was developed to explain observations of accelerating seismicity preceding large earthquakes. The model proposes that accelerating seismicity sequences result from the tectonic loading of large fault structures through aseismic slip in the elasto-plastic lower crust. This loading progressively increases the stress on smaller faults within a critical region around the main structure, thereby causing the observed acceleration of precursory activity. A secondary prediction of the SA model is that the precursory seismicity rates should increase first at the edges of the critical region, with the rates gradually rising over time at closer distances to the main fault. We test this prediction by examining year-long seismicity rates between 1960 and 2004, as a function of distance from the Landers rupture. To quantify the significance of trends in the seismicity rates, we auto-correlate the data, using a range of spatial and temporal lags. We find weak evidence for increased seismicity rates propagating towards the Landers rupture, but cannot conclusively distinguish these results from those obtained for a random earthquake catalog. However, we find a strong indication of periodicity in the rate fluctuations, as well as high correlation between activity 130–170 km from Landers and seismicity rates within 50 km of the Landers rupture temporally offset 1.5–2 years. The implications of this spatio–temporal correlation will be addressed in future studies.

We develop a 2D slip-weakening description of a self-healing slip pulse that propagates dynamically in a steady-state configuration. The model is used to estimate patterns of off-fault secondary failure induced by the rupture, and also to infer fracture energies G for large earthquakes. This extends an analysis for a semi-infinite rupture (Poliakov et al. , 2002) to the case of a finite slipping zone length L of the pulse. The dynamic stress drop, when divided by the drop from peak to residual strength, determines the ratio of L to the slip-weakening zone length R . Predicted off-fault damage is controlled by that scaled stress drop, static and dynamic friction coefficients, rupture velocity, principal prestress orientation, and poroelastic Skempton coefficient. All damage zone lengths can be scaled by ![Graphic][1] , which is proportional G /(strength drop)2 and is the value of R in the low-rupture-velocity, low-stress-drop, limit. In contrast to the Poliakov et al. (2002) case R / L = 0, the region that supports Coulomb failure reaches a maximum size on the order of ![Graphic][2] when mode II rupture speed approaches the Rayleigh speed. Analysis of slip pulses documented by Heaton (1990) leads to estimates of G , each with a factor-of-two model uncertainty, from 0.1 to 9 MJ/m2 (including the factor), averaging 2–4 MJ/m2; G tends to increase with the amount of slip in the event. In most cases, secondary faulting should extend, at high rupture speeds, to distances from the principal fault surface on the order of 1 to 2 ![Graphic][3] ≈ 1–80 m for a 100-MPa strength drop; that distance should vary with depth, being larger near the surface. We also discuss gouge and damage processes. [1]: /embed/inline-graphic-1.gif [2]: /embed/inline-graphic-2.gif [3]: /embed/inline-graphic-3.gif

We tested the hypotheses (1) that the fractal dimension, D, of hypocenters are different in a locked and a creeping segment of the San Andreas fault and (2) that the relationship D~`2b holds approximately, where b is the slope of the frequency–magnitude relationship. The test area was the 30- to 50-km fault segment north of Parkfield for which two earthquake catalogs exist: the borehole High Resolution Seismic Network data, and the U.S. Geological Survey data, which have a minimum magnitude of completeness of Mc 0.4 and Mc 1.0–1.2, respectively. The relative location errors in the two catalogs are estimated as 0.25 km and less than 1 km, respectively. The periods of high-quality data available extend from 1987 to 1998.5 and 1981 to 2000.2, respectively, furnishing 2609 and 3775 events for analysis, in the two catalogs. In the locked part, 0.5 < b < 0.7 and 0.96 < D < 1.14, whereas in the creeping segment, 1.1 < b < 1.6 and 1.45 < D < 1.72. However, the spatial distribution of the hypocenters in the creeping segment is not well approximated by a fractal distribution. We conclude (1) that the frequency–magnitude distribution as described by b, as well as the fractal dimension (D), are different in the locked and creeping segments near Parkfield; (2) that the spatial distribution in the creeping segment is not well approximated by a fractal distribution; and (3) that the relationship D~2b holds in the locked segment, where both parameters can be measured accurately. Thus, we propose that the heterogeneity of seismogenic volumes lead to differences in D and b and that these differences, where established by high-quality data, may furnish clues concerning properties of fault zones.

Recent measurements of slip profiles on normal faults have found that they are usually triangular in shape. This has been explained to be a consequence of on-fault processes such as slip-dependent friction. However, the recent observation that cumulative slip profiles on normal faults and fault systems in Afar are both triangular and self-similar excludes this explanation and requires some form of off-fault deformation. Here, we use elastic modelling to show that large triangular zones of off-fault damage can explain the observed triangular slip profiles provided damage is anisotropic in the form of cracks sub-parallel to the fault. Our modelling suggests that these triangular damage zones result from the enlargement of the crack tip damage area as the fault (or system) lengthens. Our modelling also demonstrates that different types of ‘barriers’ can cause the slip profiles to terminate abruptly at one or both fault ends, as observed in Afar and elsewhere.

A quasi-static numerical method was used to simulate the failure of a strong stuck asperity on an otherwise creeping fault plane. The numerical model produced the same slip distribution as analytical asperity models, which, for constant loading rate, produced repeating events having a period T that scales with moment M 0 as \(T{\propto}M_{0}^{1{/}6}\) , the scaling relation observed by Nadeau and Johnson (1998) at Parkfield. When the asperity is a composite of smaller hard unit asperities, we still find \(T{\propto}M_{0}^{1{/}6}\) but the constant of proportionality depends on the density of unit asperities within the cluster. Since only clusters with a fixed asperity density follow the observed \(T{\propto}M_{0}^{1{/}6}\) scaling, this result rules out the fractal spatial distribution (Cantor dust) of unit asperities at Parkfield suggested by Sammis et al. (1999). For solid asperities, the average stress drop on the asperity is on the order of 100 MPa, but the average stress drop over the entire rupture area is significantly lower, equivalent to that estimated from spectral analysis. However, the stress drop for asperity models is not independent of seismic moment but decreases with earthquake size. The energy release rate for asperity events is estimated to be \(\mathcal{G}{\gtrsim}10^{7}\) J/m 2 , near the upper limit of estimates by Li (1987) using parameters from large events on the San Andreas Fault.

Fault zones contain structural complexity on all scales. This complexity influences fault mechanics including the dynamics of large earthquakes as well as the spatial and temporal distribution of small seismic events. Incomplete earthquake records, unknown stresses, and unresolved fault structures within the crust complicate a quantitative assessment of the parameters that control factors affecting seismicity. To better understand the relationship between fault structure and seismicity, we examined dynamic faulting under controlled conditions in the laboratory by creating saw-cut-guided natural fractures in cylindrical granite samples. The resulting rough surfaces were triaxially loaded to produce a sequence of stick–slip events. During these experiments, we monitored stress, strain, and seismic activity. After the experiments, fault structures were imaged in thin sections and using computer tomography. The laboratory fault zones showed many structural characteristics observed in upper crustal faults, including zones of localized slip embedded in a layer of fault gouge. Laboratory faults also exhibited a several millimeter wide damage zone with decreasing micro-crack density at larger distances from the fault axis. In addition to the structural similarities, we also observed many similarities between our observed distribution of acoustic emissions (AEs) and natural seismicity. The AEs followed the Gutenberg–Richter and Omori–Utsu relationships commonly used to describe natural seismicity. Moreover, we observed a connection between along-strike fault heterogeneity and variations of the Gutenberg–Richter b value. As suggested by natural seismicity studies, areas of low b value marked the nucleation points of large slip events and were located at large asperities within the fault zone that were revealed by post-experimental tomography scans. Our results emphasize the importance of stick–slip experiments for the study of fault mechanics. The direct correlation of acoustic activity with fault zone structure is a unique characteristic of our laboratory studies that has been impossible to observe in nature.

Crustal fault zones are complex regions of localized deformation with fractured, cataclastic and pulverized rocks having evolving geometries and altered rheological properties from those of the host material. At some level of fracture density (damage) the cohesive matrix of the material is destroyed and the associated volume becomes granular. The occurrence of seismic ruptures, and healing phases in the interseismic periods, continually modify the damage and granularity. This produces evolution of the elasticity, permeability and geometry of the actively deforming regions. The evolution of fault zone structures leads, in turn, to changes in the properties of dynamic earthquake ruptures, seismic radiation, inter- and post-seismic deformation, and local seismicity patterns. Many fundamental aspects of brittle deformation in crustal rocks remain unsolved. Basic examples include: What are the proper metrics to characterize brittle rock damage and the transitions between damaged rock and granular material? What are the main similarities and differences between the dynamics of damaged rocks and granular media? What are the characteristics of nonlinear stress–strain behavior of damaged rocks and how can they be modeled quantitatively? How much slip is localized on main rupture surfaces and how much is distributed in the bulk for various fault environments? The 16 papers in this volume provide recent theoretical and observational perspectives that address the above and related issues. Topics include damage rheology models, high-resolution measurements of nonlinear evolving elasticity, high-resolution experiments on frictional instabilities and dynamic ruptures, theoretical and observational results on different dynamic regimes of sheared solids and granular materials, effects of fluids and roughness on fault zone rheology, seismic radiation near fault kinks, and geological and laboratory characterizations of fault surfaces and damaged rocks.

In studying the physical processes involved in the generation of seismic waves by explosions, it is important to understand what happens in the region of high stresses immediately surrounding the explosion. This paper examines one of the processes that takes place in this region, the growth of pre-existing cracks, which is described quantitatively as an increase in rock damage. An equivalent elastic method is used to approximate the stress field surrounding the explosion and a micro-mechanical model of damage is used to calculate the increase in damage. Simulations for a 1 kt explosion reveal that the region of increased damage can be quite large, up to ten times the cavity radius. The damage is initiated on a damage front that propagates outward behind the explosive stress wave with a velocity intermediate between that of P and S waves. Calculations suggest that the amount of increased damage is controlled primarily by the initial damage and the extent of the region of increased damage is controlled primarily by the initial crack radius. The motions that occur on individual cracks when damage increases are converted to seismic moment tensors which are then used to calculate secondary elastic waves which radiate into the far field. It is found that, while the contribution from an individual crack is small, the combined effect of many cracks in a large region of increased damage can generate secondary waves that are comparable in amplitude to the primary waves generated by the explosion. Provided that there is asymmetry in the damage pattern, this process is quite effective in generating S waves, thus providing a quantitative explanation of how S waves can be generated by an explosion. Two types of asymmetry are investigated, a shear pre-stress and a preferred orientation of cracks, and it is found that both produce similar effects.

The source of repeating earthquakes on creeping faults is modeled as a weak asperity at a border between much larger locked and creeping patches on the fault plane. The x –1/2 decrease in stress concentration with distance x from the boundary is shown to lead directly to the observed scaling 〈 T 〉∞〈 M 〉1/6 between the average repeat time and average scalar moment for a repeating sequence. The stress drop in such small events at the border depends on the size of the large locked patch. For a circular patch of radius R and representative fault parameters, Δσ = 7.6( m / R )3/5 MPa, which yields stress drops between 0.08 and 0.5 MPa (0.8–5 bars) for R between 2 km and 100 m. These low stress drops are consistent with estimates of stress drop for small earthquakes based on their seismic spectra. However, they are orders of magnitude smaller than stress drops calculated under the assumption that repeating sources are isolated stuck asperities on an otherwise creeping fault plane, whose seismic slips keep pace with the surrounding creep rate. Linear streaks of microearthquakes observed on creeping fault planes are trivially explained by the present model as alignments on the boundaries between locked and creeping patches.

Earth is a dynamic planet. Solid state convection in the deep interior is coupled to the motion of about a dozen rigid plates at the surface. Earthquakes, volcanoes and mountains are located mainly at the boundaries between plates and reflect the relative motion between them. The associated deformation processes span a wide range of regimes from high temperature dislocation and diffusion accommodated creep to brittle fracture, friction, fragmentation and granular flow. There is a long history of collaboration between earth and materials scientists in modeling the relevant micromechanics and formulating appropriate constitutive relations. Materials analysis in the Earth and planetary sciences pose special challenges. Pressure and temperature conditions in the Earth's interior reach 360 GPa and 8000 K so that constitutive equations must often be extended to pressure and temperature regimes well beyond laboratory limits. Deformation occurs over a range of temporal and spatial scales difficult to simulate in the laboratory. The emergence of deformation structures spanning many spatial orders of magnitude has made Earth sciences the test bed for modern ideas of self-organization and scaling. Finally, deformation mechanisms in earth materials are extremely sensitive to environmental factors, especially water. This factor alone explains most differences between large-scale deformation structures observed on Earth and those on the other terrestrial planets. Current problems in the Earth sciences that require a better understanding of material behavior include the mechanics of the earthquake instability, the migration of magma in the crust, the source and dynamical significance of observed heterogeneity in the deep interior, and the generation of the magnetic field.

—A cellular automaton is used to study the relation between the structure of a regional fault network and the temporal and spatial patterns of regional seismicity. Automata in which the cell sizes form discrete fractal hierarchies are compared with those having a uniform cell size. Conservative models in which all the stress is transferred at each step of a cascade are compared with nonconservative ("lossy") models in which a specified fraction of the stress energy is lost from each step. Particular attention is given to the behavior of the system as it is driven toward the critical state by uniform external loading. All automata exhibit a scaling region at times close to the critical state in which the events become larger and energy release increases as a power-law of the time to the critical state. For the hierarchical fractal automata, this power-law behavior is often modulated by fluctuations that are periodic in the logarithm of the time to criticality. These fluctuations are enhanced in the nonconservative models, but are not robust. The degree to which they develop appears to depend on the particular distribution of stresses in the larger cells which varies from cycle to cycle. Once the critical state is reached, seismicity in the uniform conservative automaton remains random in time, space, and magnitude. Large events do not significantly perturb the stress distribution in the system. However, large events in the nonconservative uniform automaton and in the fractal systems produce large stress perturbations that move the system out of the critical state. The result is a seismic cycle in which a large event is followed by a shadow period of quiescence and then a new approach back toward the critical state. This seismic cycle does not depend on the fractal structure, but is a direct consequence of large-scale heterogeneity of these systems in which the size of the largest cell (or the size of the largest nonconservative event) is a significant fraction of the size of the network. In essence, seismic cycles in these models are boundary effects. The largest events tend to cluster in time and the rate of small events remains relatively constant throughout a cycle in agreement with observed seismicity.

This article reports on the state of physics governing the behavior of earthquakes and faults, based on discussions held during a workshop of the Southern California Earthquake Center (SCEC) suggested by Tom Henyey and convened by Yehuda Ben-Zion and Charles Sammis at Snowbird, Utah, June 21-23, 1998. The objective of the workshop was to assess the current state of understanding of earthquake processes including event nucleation, propagation and arrest of ruptures, spatiotemporal seismicity patterns, interactions between faults, and evolution of fault systems. A better understanding of the earthquake process should enable scientists to develop seismic hazard assessment tools based upon improved estimates of the locations and sizes of future earthquakes and the time-dependent probabilities of their occurrence. It will allow incorporation of realistic simulations of dynamic rupture and wave propagation into hazard models so that time histories of strong ground-shaking from scenario earthquakes needed in performance-based seismic design of structures...

A recent study of repeating earthquakes on the San Andreas Fault in central California by Nadeau and Johnson [1998] found that the smallest events occurred on patches having a linear dimension of the order of 0.5 m, displacements of about 2 cm, and stress drops of the order of 2000 MPa, roughly 10 times larger than rock strengths measured in the laboratory. The stress drop for larger events was observed to decrease as a power law of the seismic moment reaching the commonly observed value of 10 MPa at about magnitude 6. These large strengths are shown here to be consistent with laboratory data if the preexisting microcracks are all healed. A hierarchical fractal asperity model is presented, which is based on recent laboratory observations of contact distributions in sliding friction experiments. This “Cantor dust” model is shown to be consistent with the observed power law decrease in stress drop and increase in displacement with increasing event size. The spatial distribution of hypocenters in the Parkfield area is shown to be consistent with this simple fractal model and with a hierarchical clustering of asperities having a fractal dimension of D=1 and discrete rescaling factor of about 20.

A composite model is proposed to describe the time-dependent response of the Earth's lower crust. The motivation for such a model is twofold: First, new observations of widespread postseismic deformation indicate that the deep continental crust responds viscoelastically, having both long- and short-term decay times. Second, by any number of observationally based rationales, the lower crust is compositionally and structurally heterogeneous over many length scales. For heterogeneities that have much smaller characteristic lengths than the minimum deformation wavelength of interest, the aggregate rheology can be described by composite media theory. For wavelengths of the order of the thickness of the lower crust (≈25–40 km) and larger, composite theory may be applied to heterogeneities that are smaller than about several hundred meters, or equivalent to the vertical extent of a thick lower crustal mylonitic shear zone. The composite media theory developed here is constructed using both Eshelby-Mori-Tanaka theory for aligned generalized spheroidal inclusions and a generalized self-consistent method. The inclusions and matrix are considered to be Maxwellian viscoelastic: a rheology that is consistent with past homogeneous models of postseismic stress relaxation. The composite theory presented here introduces a transient response to a suddenly imposed stress field which does not appear in homogeneous Maxwell models. Analytic expressions for the amplitude and duration of the transient and for the effective long- and short-term viscosities of the composite are given which describe the sensitivity to inclusion concentration (Φ), to shape, and to ratio of inclusion-to-matrix viscosity (R).

We discuss in detail the concept of discrete scale invariance and show how it leads to complex critical exponents and hence to the log-periodic corrections to scaling exhibited by various measures of seismic activity close to a large earthquake singularity. Discrete scale invariance is first illustrated on a geometrical fractal, the Sierpinsky gasket, which is shown to be fully described by a complex fractal dimension whose imaginary part is a simple function (inverse of the logarithm) of the discrete scaling factor. Then, a set of simple physical systems (spins and percolation) on hierarchical lattices is analyzed to exemplify the origin of the different terms in the discrete renormalization group formalism introduced to tackle this problem. As a more specific example of rupture relevant for earthquakes, we propose a solution of the hierarchical time-dependent fiber bundle of Newman et al. [1994] which exhibits explicitly a discrete renormalization group from which log-periodic corrections follow. We end by pointing out that discrete scale invariance does not necessarily require an underlying geometrical hierarchical structure. A hierarchy may appear “spontaneously” from the physics and/or the dynamics in a Euclidean (nonhierarchical) heterogeneous system. We briefly discuss a simple dynamical model of such mechanism, in terms of a random walk (or diffusion) of the seismic energy in a random heterogeneous system.

A new experimental technique has been developed to study fault development in layers of moist granular materials (clay and fault gouge) in shear. Faults nucleated on pre-existing pores and on low-displacement protofaults in flaw-free areas. Only a small number of the protofaults developed significant displacement, forming conjugate simple fault sets. After nucleation, simple faults propagated in-plane. As these simple faults grew in length and new simple fault sets nucleated, they began to interact and coalesce. Simple faults linked up to form compound faults, and compound faults linked up to form even larger through-going strike-slip faults. The fault patterns produced in the shear experiments were integrated fault networks consisting of several sets of conjugate shears and tensile structures. Compound faults exhibited both releasing and restraining steps formed during fault coalescence. Displacement along such a compound strike-slip fault caused a mismatch of the two walls. A few points became resistant barriers while the remaining segments became pull-apart basins. Both releasing and restraining steps led to the development of pull-apart basins. Fault displacement and propagation rate were linear functions of fault length. The difference between the experiment described here and traditional Riedel experiments is that the new experiments do not have a pre-existing fault in the experimental setup. Therefore they are more suitable to study fault nucleation and evolution in a broad shear zone.

A 2-D computer automaton is developed which simulates the growth and coalescence of a network of faults, leading to the formation of a large, through-going shear zone. The simulation begins with a field of initial fault seeds which have a power-law size distribution of the form N∝L−m, were N is the number of fault seeds of length L and m a constant. Following fracture mechanics, the growth rate v of each fault is assumed to be a power law of its length L ( v∝L n 2 ) where n is a constant. Based on simple shear experiments with moist clay and gouge layers, faults are assumed to propagate obliquely to the simple shear direction (15° from the simple shear and 30° to the maximum compression σ1). The rules governing fault interaction are developed by observations of the simple shear experiments and a statistical study of strike-slip faults. The extent of the interaction zone W of a fault is assumed to be proportional to the fault length L, i.e., W = RL where R is a constant. Parameters n and R are determined by comparing the automaton simulations with regional fault patterns, which gives n to be about 2 and R to be about 0.1. The resultant fault pattern is also sensitive to the initial fault seed distribution for which the acceptable range of the power-law parameter is 1 Analysis of the results indicates that the through-going shear zone which develops is fractal with a dimension of 1.02, consistent with that found by mapping natural shear zones. The length distribution of fault segments is found to be approximately log-normal and to be consistent with the displacement scaling relation observed by Wesnousky (1989) for natural faults.

Several authors have proposed discrete renormalization group models of earthquakes, viewing them as a kind of dynamical critical phenomena. Here, we propose that the assumed discrete scale invariance stems from the irreversible and intermittent nature of rupture which ensures a breakdown of translational invariance. As a consequence, we show that the renormalization group entails complex critical exponents, describing log-periodic corrections to the leading scaling behavior. We use the mathematical form of this solution to fit the time to failure dependence of the Benioff strain on the approach of large earthquakes. This might provide a new technique for earthquake prediction for which we present preliminary tests on the 1989 Loma Prieta earthquake in northern California and on a recent build-up of seismic activity on a segment of the Aleutian-Island seismic zone. The earthquake phenomenology of precursory phenomena such as the causal sequence of quiescence and foreshocks is captured by the general structure of the mathematical solution of the renormalization group

Although many studies have shown that faults and fractures are self-similar over a large range of scales, none have tested the fault structure for self-similarity in three dimensions. In this study, earthquake hypocentral locations in central and southern California were used to illuminate three-dimensional (3-D) fault structures, for which we measured the fractal capacity dimension, D0(3-D). Hypocentral distributions from the Joshua Tree, Big Bear, and Upland aftershock sequences, as well as background seismicity at Parkfield were found to be fractal, where D0(3-D) increased with increasing event density, asymptotically approaching a stable value. The Joshua Tree data set stabilized at D0(3-D) = 1.92 ± 0.02, the Parkfield data set asymptotically approached D0(3-D) = 1.82, and the Big Bear data set approached D0(3-D) = 2.01. As a test of the effects of location errors upon the measured value of D0(3-D), the Upland aftershock data were located with both the southern California Hadley and Kanamori (1977) (H-K) velocity model, and the more accurate Hauksson and Jones (1991) (H-J) velocity model. Events located with the H-K model asymptotically approached D0(3-D) = 2.07, and events located with the H-J model approached D0(3-D) = 1.79, suggesting that improved hypocentral locations may decrease the measured fractal dimension. One interpretation of our results of D0(3-D) ≤ 2.0 for all of the hypocentral data is that earthquakes only occur on the “percolation backbone” of a fault network, i.e., the active part of the network that accommodates finite strain deformation (Sahimi et al., 1993). We show that a percolation model that allows for healing of previously broken bonds is consistent with this interpretation.

The micromechanical damage mechanics formulated by Ashby and Sammis, 1990, “The Damage Mechanics of Brittle Solids in Compression,” Pure Appl. Geophys., 133(3), pp. 489–521, and generalized by Deshpande and Evans 2008, “Inelastic Deformation and Energy Dissipation in Ceramics: A Mechanism-Based Constitutive Model,” J. Mech. Phys. Solids, 56(10), pp. 3077–3100. has been extended to allow for a more generalized stress state and to incorporate an experimentally motivated new crack growth (damage evolution) law that is valid over a wide range of loading rates. This law is sensitive to both the crack tip stress field and its time derivative. Incorporating this feature produces additional strain-rate sensitivity in the constitutive response. The model is also experimentally verified by predicting the failure strength of Dionysus-Pentelicon marble over strain rates ranging from ∼10− 6to 103s− 1. Model parameters determined from quasi-static experiments were used to predict the failure strength at higher loading rates. Agreement with experimental results was excellent.

The quasistatic micromechanical damage mechanics originally formulated by Ashby and Sammis has been made fully dynamical by the incorporation of physically motivated crack growth laws. This rate-dependent damage mechanics has been implemented in the ABAQUS dynamic finite element code and tested by simulating strength data for marble measured over a ten order of magnitude range of loading rates. The model is used here to explore the effect of burn rate (loading rate) on the spatial extent of fracture damage (and hence the elastic radius) and on the S waves generated by an underground explosion. The recent observation by that explosives with low burn rates produce more shear wave radiation than do those with high burn rates can be explained by dynamic fracture effects, and may not be due to gas wedging as originally hypothesized.

[1] Seismicity clusters within fault zones can be connected to the structure, geometric complexity and size of asperities which perturb and intensify the stress field in their periphery. To gain further insight into fault mechanical processes, we study stick-slip sequences in an analog, laboratory setting. Analysis of small scale fracture processes expressed by acoustic emissions (AEs) provide the possibility to investigate how microseismicity is linked to fault heterogeneities and the occurrence of dynamic slip events. The present work connects X-ray computer tomography (CT) scans of faulted rock samples with spatial maps of b values (slope of the frequency-magnitude distribution), seismic moments and event densities. Our current experimental setup facilitates the creation of a series of stick-slips on one fault plane thus allowing us to document how individual stick-slips can change the characteristics of AE event populations in connection to the evolution of the fault structure. We found that geometric asperities identified in CT scan images were connected to regions of low b values, increased event densities and moment release over multiple stick-slip cycles. Our experiments underline several parallels between laboratory findings and studies of crustal seismicity, for example, that asperity regions in lab and field are connected to spatial b value anomalies. These regions appear to play an important role in controlling the nucleation spots of dynamic slip events and crustal earthquakes.

The particle size distributions of fault gouge from the San Andreas, the San Gabriel, and the Lopez Canyon faults in Southern California were measured using sieving and Coulter-Counter techniques over a range of particle sizes from 2 μm to 16 mm. The distributions were found to be power law (fractal) for the smaller fragments and log-normal by mass for sizes near and above the peak size. The apparent fractal dimensionD of the smaller particles in gouge samples from the San Andreas fault, the San Gabriel fault and the Lopez Canyon gouge were 2.4–3.6, 2.6–2.9 and 2.4–3.0, respectively. The averageD for the Lopez Canyon gouge was 2.7±0.2, which is in agreement with earlier studies of this gouge using planar 2-D sections. The fractal dimension of the finer fragments from all three faults is observed to be correlated with the peak fragment size, with finer gouges tending to have a largerD. A computer automaton is used to show that this observation may be explained as resulting from a fragmentation process which has a “grinding limit” at which particle reduction stops.

Triaxial compression experiments were performed on samples of natural granular fault gouge from the Lopez Fault in Southern California. This material consists primarily of quartz and has a self-similar grain size distribution thought to result from natural cataclasis. The experiments were performed at a constant mean effective stress of 150 MPa, to expose the volumetric strains associated with shear failure. The failure strength is parameterized by the coefficient of internal friction μ, based on the Mohr-Coulomb failure criterion.

A grain bridge model is used to provide a physical interpretation of the rate- and state-dependent friction parameters for the simple shear of a granular layer. This model differs from the simpler asperity model in that it recognizes the difference between the fracture of a grain and the fracture of an adhesion between grains, and it explicitly accounts for dilation in the granular layer. The model provides an explanation for the observed differences in the friction of granular layers deformed between rough surfaces and those deformed between smooth surfaces and for the evolution of the friction parameters with displacement. The observed evolution from velocity strengthening to velocity weakening with displacement is interpreted as being due to the change in the micromechanics of strain accommodation from grain crushing to slip between adjacent grains; this change is associated with the observed evolution of a fractal grain structure.

The quasistatic damage mechanics formulated by Ashby and Sammis has been made fully dynamic by incorporating the results of recent experimental and theoretical studies of dynamic crack growth. The model has been verified by building it into the ABAQUS dynamic finite element code and using it to simulate high-speed fracture experiments. Simulation of explosions has shown that the spatial extent and pattern of the resultant fracture damage is sensitive to loading rate. High loading rates of short duration produce spherically symmetric compact damage patterns. Slower loading rates of longer duration are more effective in producing long radial fractures. Any asymmetry in the pattern of such radial fractures generates S wave radiation in the far-field, even in the absence of other factors known to generate S waves such as tectonic shear stress or anisotropy in the initial fracture distribution.

We argue that percolation provides a unified theory for the geometry of fault patterns and the spatial distribution of earthquakes. We analyze the structure of fracture patterns in heterogeneous rocks and find that, at large length scales, they are percolation fractals with a fractal dimension D\ensuremath{\simeq}1.9 and 2.5, in 2D and 3D, respectively. A model is proposed that can predict these results. Three-dimensional fractal analysis of spatial distribution of earthquake hypocenters yields a fractal dimension of about 1.8, the same as that of the backbone of 3D percolation clusters.

A radially stratified and incompressible earth model with secular variation of the second degree gravity field J-dot(2) is used here to test sensitivity of data to viscosity increases with depth and convective boundary layer structure. Prior estimates and observed nontidal J-dot(23)(-C-dot(20)) are consistent with a layered lower mantle viscosity. Details of this layering are examined by comparing predicted and observed J-dot(3), J-dot(4). Speculation that a high-velocity layer exists above D-double prime is considered. With a 650-km thick deep high-viscosity layer, the remaining lower mantle is in one of two ranges: 1.5 to 3.5 x 10 exp 20 or 3.5 to about 10 exp 22 Pa s.

Using computer simulations and analyzing experimental data, we investigate the structure of fault patterns in heterogeneous rock, and the distribution of earthquake hypocentral locations. At large length scales, the fracture networks of rock are fractal with a fractal dimension D ⋍1.9 and 2.5, in 2D and 3D, respectively. We present a computer simulation model that explains these results in terms of percolation fractals. Three-dimensional fractal analysis of regional hypocentral locations yields a fractal dimension of about 1.8. This result can be explained if earthquakes are distributed on the backbone of the fractal network of fault structure with a fractal dimension equal to that of the percolation backbone. Thus, percolation provides a unified theory for the geometry of fault patterns and the spatial distribution of earthquakes.