redistribution of dynamic stress during coseismic ruptures evidence for fault interaction and earthquake triggering we investigate the spatiotemporal evolution of dynamic stress outside a rupturing extended fault the dynamic stress variations caused by a coseismic rupture in a half space are computed by using the discrete wavenumber and reflectivity methods after a transient phase the stress time history evolves to the final static stress value we compare the static stress changes resulting from this model with those computed from a static dislocation model we have applied this method to study the interactions between the first two normal faults which ruptured during the 1980 ms 6 9 irpinia earthquake these two subevents are separated in time by nearly 20 s while the third and last subevent occurred 40 s after the rupture onset we compute the dynamic stress changes caused by the rupture of the first subevent our modeling results show that the dynamic stress peak on the second subevent fault plane is reached between 7 s and 8 s after the rupture initiation on the main fault on the average the static stress level on the second subevent 20 s fault plane is reached nearly after 14 s the dynamic rupture did not jump from a rupturing segment to the adjacent one immediately but the triggering of the 20 s subevent is delayed by roughly 10 s with respect to the instant of occurrence of the dynamic stress peak induced by the 0 s event the dynamic stress pulse propagates along the strike direction of the second subevent fault plane at an average velocity of nearly 3 4 km s the delayed triggering of the second subevent can be interpreted in terms of the frictional properties of the faults in particular rate and state dependent frictional law can explain a delayed instability after a sudden change in stress using the estimated values of the subevent triggering delay and the shear stress change we attempt to constrain the parameter a on the 20 s fault the values here inferred agree well with those resulting from previous studies

when and where the aftershock activity was depressed contrasting decay patterns of the proximate large earthquakes in southern california 1 seismic quiescence has attracted attention as a possible precursor to a large earthquake however sensitive detection of quiescence requires accurate modeling of normal aftershock activity we apply the epidemic type aftershock sequence etas model that is a natural extension of the modified omori formula for aftershock decay allowing further clusters secondary aftershocks within an aftershock sequence the hector mine aftershock activity has been normal relative to the decay predicted by the etas model during the 14 months of available data in contrast although the aftershock sequence of the 1992 landers earthquake m 7 3 including the 1992 big bear earthquake m 6 4 and its aftershocks fits very well to the etas up until about 6 months after the main shock the activity showed clear lowering relative to the modeled rate relative quiescence and lasted nearly 7 years leading up to the hector mine earthquake m 7 1 in 1999 specifically the relative quiescence occurred only in the shallow aftershock activity down to depths of 5 6 km the sequence of deeper events showed clear normal aftershock activity well fitted to the etas throughout the whole period we argue several physical explanations for these results among them we strongly suspect aseismic slips within the hector mine rupture source that could inhibit the crustal relaxation process within shadow zones of the coulomb s failure stress change furthermore the aftershock activity of the 1992 joshua tree earthquake m 6 1 sharply lowered in the same day of the main shock which can be explained by a similar scenario

a model of tectonic stress state and rate using the 1994 northridge earthquake sequence a model of the spatial and temporal distribution of seismicity both before and after the northridge california earthquake has been used to estimate the background stress state loading rate and some parameters relating to fault friction a detailed source model was used to calculate the stress change field from the northridge mainshock which was fit to the spatial distribution of seismicity agreement between the best fitting background stress state from seismicity modeling and the background stress state inferred from focal mechanisms was found to be 99 significant showing that the spatial distribution of seismicity contains information about the stress state the stress rate found for the northridge area 1 2 pa day 0 004 bar a is approximately a factor of 9 less than the stress rate expected from observed strain rates which implies that aseismic deformation is reducing seismic hazard in the los angeles basin the resulting estimate of the friction parameter a d 0 008 is similar to laboratory values if an effective normal stress much smaller than the overburden and similar to background stress magnitudes 70 mpa from the seismicity modeling is assumed to apply estimates of the magnitude of background stress gradient of stress with depth and effective coefficient of friction are quite uncertain

aftershocks of microearthquakes as probes of the mechanics of rupture 1 using a waveform cross correlation technique rubin and gillard 2000 obtained precise relative locations for 4300 0 5 m 3 5 earthquakes occurring along 50 km of the san andreas fault this study adds to that another 5000 earthquakes distributed along 10 km of the san andreas fault and 20 km of the calaveras fault errors in relative location are typically tens of meters for earthquakes separated by hundreds of meters and after correcting for time dependent station delays meters for earthquakes separated by tens of meters along both faults the minimum separation between consecutive earthquakes scales with magnitude in a manner consistent with a magnitude independent stress drop by treating each earthquake on the san andreas as if it were a main shock scaling the distances to all subsequent earthquakes by main shock size and stacking the results a composite aftershock sequence is produced that has many of the characteristics predicted by rate and state friction models projected onto the fault surface these aftershocks outline a quasi elliptical roughly 4 mpa stress drop main shock elongate in the slip parallel direction by 40 at the ends of the major axes of this ellipse over twice as many aftershocks occur to the nw than to the se an asymmetry attributed to the contrast in material properties across the fault unlike the san andreas the calaveras fault exhibits little p wave velocity contrast and no discernible aftershock asymmetry however the earliest part of the aftershock sequence on the calaveras might be truncated by the 30 s blind time of the network following a triggering event

a model for seismicity rates observed during the 1982 1984 unrest at campi flegrei caldera italy abstract we consider the space time distribution of seismicity during the 1982 1984 unrest at campi flegrei caldera italy where a correlation between seismicity and rate of ground uplift was suggested in order to investigate this effect we present a model based on stress transfer from the deformation source responsible for the unrest to potential faults we compute static stress changes caused by an inflating source in a layered half space stress changes are evaluated on optimally oriented planes for shear failure assuming a regional stress with horizontal extensional axis trending nne ssw the inflating source is modeled as inferred by previous studies from inversion of geodetic data with the same crustal model here assumed the magnitude of the regional stress is constrained by imposing an initial condition of close to failure to potential faults the resulting spatial distribution of stress changes is in agreement with observations we assume that the temporal evolution of ground displacement observed by a tide gauge at pozzuoli was due mainly to time dependent processes occurring at the inflating source we approximate this time dependence in piecewise linear way and we attribute it to each component of average stress change in the region interested by the observed seismicity then we evaluate the effect of a time dependent stressing rate on seismicity by following the approach indicated by dieterich 1994 on the basis of the rate and state dependent rheology of faults the seismicity rate history resulting from our model is in general agreement with data during the period 1982 1984 for reasonable values of unconstrained model parameters the initial value of the direct effect of friction and the reference shear stressing rate in particular this application shows that a decreasing stressing rate is effective in damping the seismicity rate

implications of diverse fault orientations imaged in relocated aftershocks of the mount lewis ml 5 7 california earthquake 1 we use seismic waveform cross correlation to determine the relative positions of 2747 microearthquakes near mount lewis california that have waveforms recorded from 1984 to 1999 these earthquakes include the aftershock sequence of the 1986 ml5 7 mount lewis earthquake approximately 90 of these aftershocks are located beyond the tips of the approximately north striking main shock defining an hourglass with the long axis aligned approximately with the main shock surprisingly our relocation demonstrates that many of these aftershocks illuminate a series of near vertical east west faults that are 0 5 1 km long and separated by as little as 200 m we propose that these structures result from the growth of a relatively young fault in which displacement across a right lateral approximately north striking fault zone is accommodated by slip on secondary left lateral approximately east striking faults we derive the main shock induced static coulomb failure function f on the dominant fault orientation in our study area using a three dimensional 3 d boundary element program to bound viable friction coefficients we measure the correlation between the rank ordering of relative amplitudes of f and seismicity rate change we find that likely friction coefficients are 0 2 0 6 and that the assumed main shock geometry introduces the largest uncertainties in the favored friction values we obtain similar results from a visual correlation of calculated f contours with the distribution of aftershocks viable rate and state constitutive parameters bound the observed relationship between magnitude of f and seismicity rate change and for our favored main shock model a maximum correlation is achieved when f is computed with friction coefficients of 0 3 0 6 these values are below those previously cited for young faults

remotely triggered seismicity in continental china following the 2008 mw 7 9 wenchuan earthquake we perform a systematic search of remotely triggered seismicity in con tinental china following the 2008 mw 7 9 wenchuan earthquake we visually identify earthquakes as impulsive seismic energy with clear p and s arrivals on 5 hz high pass filtered three component velocity seismograms 1 hr before and after the wenchuan earthquake out of the 271 stations in the updated chinese digital seismic network csn 17 stations show statistically significant seismicity increase with statistic values larger than 2 following the wenchuan earthquake these include 11 stations in the north china block which is seismically active and is in the rupture propagation direction of the wenchuan earthquake three stations along the coastal lines in the relatively stable south china block one station near the haiyuan fault zone in north west china and two stations near the tanlu fault zone and the longgang volcano in northeast china these observations suggest that dynamic triggering in intraplate regions tends to occur near active faults that have ruptured in historic times and in the rupture propagation directions of the mainshock however it is worth noting that many sites that satisfy the criteria are not triggered suggesting that these conditions would help but are not sufficient enough to guarantee remote triggering in intraplate regions the tectonic environments near the sites with clear triggered activity range from transpressional to tranextentional and most regions are not associated with active geothermal or volcanic activity indicating that dynamic triggering could occur in a wide range of tectonic environments online material tables of station information and measured parameters and two supplementary figures showing locally triggered earthquakes

preparation of accurate geological and structural maps cross sections or block diagrams from colour slides using multi model photogrammetry abstract the multi model photogrammetric method is a new technique that allows field geologists to make accurate three dimensional models of their choice using standard colour slides taken with ordinary field cameras the method greatly expands the geological potential of photogrammetry beyond conventional methods based on vertical aerial photographs or satellite data a computerized stereoscopic instrument in which the commercial software is replaced by multi model software is used for interpretation the multi model technique links a series of stereoscopic images of the same target viewed at different scales or from different angles to form one composite three dimensional model and permits instantaneous image shifts to be performed during interpretation the method can be applied to numerous geological situations where accuracy is required but where access or overview is difficult or impossible a significant proportion of geological and structural analysis can thus be moved from the field to the laboratory examples of geological and structural applications include studies of tertiary basalts in west greenland and precambrian gneisses in south india the scale of these studies varies from 1 200 000 to 1 25

viscoelastic deformation for a clustered earthquake cycle 1 the clustering of earthquakes in time on the same fault affects the rate and pattern of interseismic deformation we develop a simple analytic viscoelastic model of the surface velocity field through a clustered earthquake cycle by superposing the velocities of individual earthquake cycles of constant period but varying phase velocity profiles prior to and after an earthquake show a wider range of behavior than they do for earthquake cycles with constant repeat times these new types of behavior provide possible explanations for discrepancies between geologic estimates of long term fault slip rates and slip rate estimates from geodetic data

triggering of seismicity at short timescales following californian earthquakes 1 a method for measuring seismicity rate changes caused by the occurrence of major earthquakes in the surrounding crust is proposed it is based on a nonstationary poisson modeling of earthquake activity an estimate of the seismicity rate change and a probability measure of seismicity triggering following a large shock are derived and the removal of the influence of independent aftershock sequences of other nearby previous earthquakes is attempted without using more traditional declustering techniques the seismicity rate change estimator is corrected for its natural bias in favor of positive changes at short timescales that has so far strongly hindered measures of seismicity quiescences three californian earthquakes are examined using this method the 1989 m7 1 loma prieta the 1992 m7 3 landers and the 1994 m6 7 northridge earthquakes positive triggering is very commonly observed as expected but quiescence is however more seldomly obtained for timescales up to 100 days after the main shock this relative absence of quiescence as compared to typical predictions of coulomb modeling for example is also independently observed through direct correlation analyses of californian seismicity the possibility that the stresses caused by the main shock are spatially highly variable may explain these observations

fault interaction and stress triggering of twentieth century earthquakes in mongolia 1 a cluster of exceptionally large earthquakes in the interior of asia occurred from 1905 to 1967 the 1905 m7 9 tsetserleg and m8 4 bolnai earthquakes the 1931 m8 0 fu yun earthquake the 1957 m8 1 gobi altai earthquake and the 1967 m7 1 mogod earthquake sequence each of the larger m 8 earthquakes involved strike slip faulting averaging more than 5 m and rupture lengths of several hundred kilometers available geologic data indicate that recurrence intervals on the major source faults are several thousands of years and distances of about 400 km separate the respective rupture areas we propose that the occurrences of these and many smaller earthquakes are related and controlled to a large extent by stress changes generated by the compounded static deformation of the preceding earthquakes and subsequent viscoelastic relaxation of the lower crust and upper mantle beneath mongolia we employ a spherically layered viscoelastic model constrained by the 1994 2002 gps velocity field in western mongolia vergnolle et al 2003 using the succession of twentieth century earthquakes as sources of deformation we then analyze the time dependent change in coulomb failure stress f at remote interaction distances static f values are small however modeled postseismic stress changes typically accumulate to several tenths of a bar over time intervals of decades almost all significant twentieth century regional earthquakes m 6 with well constrained fault geometry lie in positive f lobes of magnitude about 0 5 bar our results suggest that significant stress transfer is possible among continental faults separated by hundreds of kilometers and on timescales of decades

nucleation and triggering of earthquake slip effect of periodic stresses abstract results of stability analyses for spring and slider systems with state variable constitutive properties are applied to slip on embedded fault patches unstable slip may nucleate only if the slipping patch exceeds some minimum size subsequent to the onset of instability the earthquake slip may propagate well beyond the patch it is proposed that the seismicity of a volume of the earth s crust is determined by the distribution of initial conditions on the population of fault patches that nucleate earthquake slip and the loading history acting upon the volume patches with constitutive properties inferred from laboratory experiments are characterized by an interval of self driven accelerating slip prior to instability if initial stress exceeds a minimum threshold this delayed instability of the patches provides an explanation for the occurrence of aftershocks and foreshocks including decay of earthquake rates by time 1 a population of patches subjected to loading with a periodic component results in periodic variation of the rate of occurrence of instabilities the change of the rate of seismicity for a sinusoidal load is proportional to the amplitude of the periodic stress component and inversely proportional to both the normal stress acting on the fault patches and the constitutive parameter a 1 that controls the direct velocity dependence of fault slip values of a 1 representative of laboratory experiments indicate that in a homogeneous crust correlation of earthquake rates with earth tides should not be detectable at normal stresses in excess of about 8 mpa correlation of earthquakes with tides at higher normal stresses can be explained if there exist inhomogeneities that locally amplify the magnitude of the tidal stresses such amplification might occur near magma chambers or other soft inclusions in the crust and possibly near the ends of creeping fault segments if the creep or afterslip rates vary in response to tides observations of seismicity rate variations associated with seasonal fluctuations of reservoir levels appear to be consistent with the model

a frictional population model of seismicity rate change 1 we study models of seismicity rate changes caused by the application of a static stress perturbation to a population of faults and discuss our results with respect to the model proposed by dieterich 1994 these models assume a distribution of nucleation sites e g faults obeying rate state frictional relations that fail at constant rate under tectonic loading alone and predicts a positive static stress step at time t0 will cause an immediate increased seismicity rate that decays according to omori s law we show one way in which the dieterich model may be constructed from simple general ideas illustrated using numerically computed synthetic seismicity and mathematical formulation we show that seismicity rate changes predicted by these models 1 depend on the particular relationship between the clock advanced failure and fault maturity 2 are largest for the faults closest to failure at t0 3 depend strongly on which state evolution law faults obey and 4 are insensitive to some types of population heterogeneity we also find that if individual faults fail repeatedly and populations are finite at timescales much longer than typical aftershock durations quiescence follows a seismicity rate increase regardless of the specific frictional relations for the examined models the quiescence duration is comparable to the ratio of stress change to stressing rate which occurs after a time comparable to the average recurrence interval of the individual faults in the population and repeats in the absence of any new load perturbations this simple model may partly explain observations of repeated clustering of earthquakes

delayed triggering of the 1999 hector mine earthquake by viscoelastic stress transfer stress changes in the crust due to an earthquake can hasten the failure of neighbouring faults and induce earthquake sequences in some cases1 2 3 4 5 the 1999 hector mine earthquake in southern california magnitude 7 1 occurred only 20 km from and 7 years after the 1992 landers earthquake magnitude 7 3 this suggests that the hector mine earthquake was triggered in some fashion by the earlier event but uncertainties in the slip distribution and rock friction properties associated with the landers earthquake have led to widely varying estimates of both the magnitude and sign of the resulting stress change that would be induced at the location of the hector mine hypocentre with estimates varying from 1 4 bar ref 6 to 0 5 bar ref 7 more importantly coseismic stress changes alone cannot satisfactorily explain the delay of 7 years between the two events here we present the results of a three dimensional viscoelastic model that simulates stress transfer from the ductile lower crust and upper mantle to the brittle upper crust in the 7 years following the landers earthquake using viscoelastic parameters that can reproduce the observed horizontal surface deformation following the landers earthquake our calculations suggest that lower crustal or upper mantle flow can lead to postseismic stress increases of up to 1 2 bar at the location of the hector mine hypocentre during this time period contributing to the eventual occurrence of the 1999 hector mine earthquake these results attest to the importance of considering viscoelastic processes in the assessment of seismic hazard8 9 10 11

estimating tectonic stress rate and state with landers aftershocks a new method of analyzing the location and timing of aftershocks that makes possible estimates of the rate at which faults in the area are being loaded with stress has been developed this new method is an application of a theory of aftershocks proposed by dieterich 1994 the stress step from the mainshock triggers the aftershocks which release energy stored by tectonic loading and the mainshock and the tectonic stressing rate is responsible for the background activity thus a comparison of the number of aftershocks with the rate of background activity as a function of stress step can provide an estimate of tectonic stress rate this method requires analysis of a catalog which includes background activity as well as aftershocks the method has been applied to the aftershocks of the 1992 landers california earthquake the tectonic stress rate estimated for the mojave block is 1 2 pa d which corresponds to a repeat time for large events of 14 000 years and suggests that much of the observed strain in the mojave is anelastic the southern san andreas fault system is found to have a stress fate of 100 pa d which corresponds to a repeat time of 270 years and is consistent with primarily elastic strain accommodation inversions for the best fitting background stress state are consistent with fits of focal mechanisms and support an effective friction coefficient near 0 6 fits to the aftershock decay provide estimates of the dieterich friction parameter ad ranging from 0 02 if lithostatic pore fluids are present to 0 0003 if they are not

modeling seismicity rate changes during the 1997 umbria marche sequence central italy through a rate and state dependent model 1 we model the spatial and temporal pattern of seismicity during a sequence of moderate magnitude normal faulting earthquakes which struck in 1997 the umbria marche sector of northern apennines italy by applying the dieterich 1994 rate and state dependent constitutive approach the goal is to investigate the rate of earthquake production caused by repeated coseismic stress changes computed through a 3 d elastic dislocation model in a homogeneous half space the reference seismicity rate is assumed time independent and it is estimated by smoothing the seismicity that occurred in the previous decade without declustering we propose an analytical relation for deriving the stressing rate directly from the reference seismicity rate this allows us to perform a tuning of the constitutive parameter a where a accounts for the direct effect of friction in the rate and state dependent model and is the effective normal stress into the dieterich model through a maximum likelihood method which yields for this seismic sequence a best fitting value equal to 0 04 mpa our computations show that although seven out of eight main shocks are located in areas of increased rate of earthquake production numerous aftershocks are located in seismicity shadows our simulations point out that the adopted value of a strongly affects the pattern of both seismicity shadow and areas of enhanced rate of earthquake production we conclude that solely accounting for static stress changes caused by the main shocks of this seismic sequence is not sufficient to forecast the complex spatial and temporal evolution of seismicity

the failure of earthquake failure models in this study i show that simple heuristic models and numerical calculations suggest that an entire class of commonly invoked models of earthquake failure processes cannot explain triggering of seismicity by transient or dynamic stress changes such as stress changes associated with passing seismic waves the models of this class have the common feature that the physical property characterizing failure increases at an accelerating rate when a fault is loaded stressed at a constant rate examples include models that invoke rate state friction or subcritical crack growth in which the properties characterizing failure are slip or crack length respectively failure occurs when the rate at which these grow accelerates to values exceeding some critical threshold these accelerating failure models do not predict the finite durations of dynamically triggered earthquake sequences e g at aftershock or remote distances some of the failure models belonging to this class have been used to explain static stress triggering of aftershocks this may imply that the physical processes underlying dynamic triggering differs or that currently applied models of static triggering require modification if the former is the case we might appeal to physical mechanisms relying on oscillatory deformations such as compaction of saturated fault gouge leading to pore pressure increase or cyclic fatigue however if dynamic and static triggering mechanisms differ one still needs to ask why static triggering models that neglect these dynamic mechanisms appear to explain many observations if the static and dynamic triggering mechanisms are the same perhaps assumptions about accelerating failure and or that triggering advances the failure times of a population of inevitable earthquakes are incorrect

evidence of instantaneous dynamic triggering during the seismic sequence of year 2000 in south iceland 1 we analyze the coseismic stress perturbation during the 17 june 2000 south iceland seismic sequence the main shock ms 6 6 was followed by three large events within a few tens of seconds 8 26 and 30 s located within 80 km the aim of this paper is to investigate short term fault interaction and instantaneous triggering this happens when a fault perturbed by a stress change fails before the end of the transient stress perturbation we compute the shear normal and coulomb stress changes as functions of time in a stratified elastic half space by using discrete wave number and reflectivity methods we calculate dynamic stresses caused by the main shock at the hypocenters of these three subsequent events our numerical results show that the onset of the last two events is slightly delayed with respect to the arrival time of the second positive peak of coulomb stress variation while the first event occurred after the first positive stress peak we have also analyzed the response of a spring slider system representing a fault governed by a rate and state dependent friction law perturbed by shear and normal stress variations caused by the main shock the fault response to the computed stress perturbations is always clock advanced we have found suitable constitutive parameters of the modeled fault that allow the instantaneous dynamic triggering of these three earthquakes if the initial sliding velocity is comparable with the tectonic loading velocity we obtained failure times close to the observed origin times for low values of the initial effective normal stress

toggling of seismicity by the 1997 kagoshima earthquake couplet a demonstration of time dependent stress transfer 1 two m 6 well recorded strike slip earthquakes struck just 4 km and 48 days apart in kagoshima prefecture japan in 1997 providing an opportunity to study earthquake interaction aftershocks are abundant where the coulomb stress is calculated to have been increased by the first event and they abruptly stop where the stress is dropped by the second event this ability of the main shocks to toggle seismicity on and off argues that static stress changes play a major role in exciting aftershocks whereas the dynamic coulomb stresses which should only promote seismicity appear to play a secondary role if true the net stress changes from a sequence of earthquakes might be expected to govern the subsequent seismicity distribution however adding the stress changes from the two kagoshima events does not fully capture the ensuing seismicity such as its rate change temporal decay or migration away from the ends of the ruptures we therefore implement a stress transfer model that incorporates rate state friction in which seismicity is treated as a sequence of independent nucleation events that are dependent on the fault slip slip rate and elapsed time since the last event the model reproduces the temporal response of seismicity to successive stress changes including toggling decay and aftershock migration nevertheless the match of observed to predicted seismicity is quite imperfect due perhaps to inadequate knowledge of several model parameters however to demonstrate the potential of this approach we build a probabilistic forecast of larger earthquakes on the expected rate of small aftershocks taking advantage of the large statistical sample the small shocks afford not surprisingly such probabilities are highly time and location dependent during the first decade after the main shocks the seismicity rate and the chance of successive large shocks are about an order of magnitude higher than the background rate and are concentrated exclusively in the stress triggering zones

earthquake triggering by static and dynamic stress changes 1 in this study we aim to understand the effect of static and dynamic stress changes in promoting earthquake failures on secondary faults toward this goal we solve the equation of motion of a spring slider dynamic system including inertia and using rate and state dependent constitutive laws we separately investigate the dynamic response of this fault analog system to a sudden stress change represented either as a stress step or as a stress pulse which are used to model permanent static and transient dynamic stress perturbations the induced earthquake failure does not occur immediately at the application of the coseismic stress change but it is delayed in time we define this time interval as the triggering delay for a given stress perturbation we analyze the dependence of triggering delays on different system conditions and constitutive parameters our results clearly show that the effects of static and dynamic stress changes are quite different while a static stress change is able to advance as well as to delay an induced instability depending on its sign a dynamic stress pulse is only able to promote a nearly instantaneous failure provided its amplitude is positive and large enough with respect to the direct effect of friction in other words dynamic stress changes can only cause nearly instantaneous failures without any relevant triggering delay these results should be considered in interpreting the seismicity rate changes caused by large earthquakes at least as long as seismic events are interpreted as sliding instabilities obeying rate and state dependent friction laws

stress transferred by the 1995 mw 6 9 kobe japan shock effect on aftershocks and future earthquake probabilities the kobe earthquake struck at the edge of the densely populated osaka kyoto corridor in southwest japan we investigate how the earthquake transferred stress to nearby faults altering their proximity to failure and thus changing earthquake probabilities we find that relative to the pre kobe seismicity kobe aftershocks were concentrated in regions of calculated coulomb stress increase and less common in regions of stress decrease we quantify this relationship by forming the spatial correlation between the seismicity rate change and the coulomb stress change the correlation is significant for stress changes greater than 0 2 1 0 bars 0 02 0 1 mpa and the nonlinear dependence of seismicity rate change on stress change is compatible with a state and rate dependent formulation for earthquake occurrence we extend this analysis to future mainshocks by resolving the stress changes on major faults within 100 km of kobe and calculating the change in probability caused by these stress changes transient effects of the stress changes are incorporated by the state dependent constitutive relation which amplifies the permanent stress changes during the aftershock period earthquake probability framed in this manner is highly time dependent much more so than is assumed in current practice because the probabilities depend on several poorly known parameters of the major faults we estimate uncertainties of the probabilities by monte carlo simulation this enables us to include uncertainties on the elapsed time since the last earthquake the repeat time and its variability and the period of aftershock decay we estimate that a calculated 3 bar 0 3 mpa stress increase on the eastern section of the arima takatsuki tectonic line attl near kyoto causes fivefold increase in the 30 year probability of a subsequent large earthquake near kyoto a 2 bar 0 2 mpa stress decrease on the western section of the attl results in a reduction in probability by a factor of 140 to 2000 the probability of a mw 6 9 earthquake within 50 km of osaka during 1997 2007 is estimated to have risen from 5 6 before the kobe earthquake to 7 11 afterward during 1997 2027 it is estimated to have risen from 14 16 before kobe to 16 22

elevation change of the greenland ice sheet and its measurement with satellite radar altimetry satellite radar altimetry is presently the only method that has provided the spatial coverage and density of observations needed to reduce the present uncertainty in the mass balance of the greenland ice sheet and its contribution to change in eustatic sea level the only such measurement reported however estimated that southern greenland was thickening at 23 6 cm a 1 which is larger than was thought hitherto this value is reconsidered given more recent information concerning the errors in the measurement a survey of measurements of specific mass balance of the greenland ice sheet is given together with estimates of its sensitivity to temperature change the expected behaviour is described of errors in the satellite position and errors in the range measurement to the ice sheet surface the treatment of biases and the number of independent observations of random errors is described it is found in particular that a higher degree of independence was given to the random errors than should have been the case the total error is recalculated with this accounted for and is found to remain dominated by the bias estimate and therefore largely unaffected by this change the estimate is 23 7 cm a 1 it is concluded that the observation does support a recent thickening of the southern greenland ice sheet

spatiotemporal analyses of earthquake productivity and size distribution observations and simulations we use relocated catalogs of microearthquakes to investigate earthquake interaction along sections of the sargent calaveras and san andreas faults in cali fornia we examine the stress dependence of seismicity rate change along the three fault segments and find that the seismicity rate following a mainshock decays ap proximately as 1 time the duration of the aftershock activity seems to be independent of distance from the mainshock and the seismicity rate at lag times of up to about 100 sec is nearly constant in the san andreas and the calaveras catalogs where the return of the seismicity rate to the background level is well resolved we find that the return to the background in the distance range of 1 2 rupture radii from a previous earthquake is preceded by a period during which the seismicity rate falls about 30 below the background rate we also examine the effect of a stress step on earthquake size distribution along these faults and find that the exponent of the power law dis tribution of earthquake magnitudes within 10 4 sec of a previous earthquake is sig nificantly lower than that of the long term while the 1 time decay of seismicity rate the independence of aftershock duration from distance from the mainshock and the constant seismicity rate at short lag times are predicted by dieterich s 1994 model the decrease of seismicity rate below the background level and the changes in earth quake size distribution are not for comparison with our observations we simulate earthquake activity on an in herently discrete fault model that is governed by an approximate constitutive friction law similar to the one used by dieterich 1994 we find that the observed response of earthquake productivity and size distribution to a stress step are produced by these simulations the effect of the mainshock is not only to raise the local seismicity rate but also to systematically modify the earthquake size distribution this is because fault patches that are near failure at the time of the stress step are strengthened whereas fault patches that at the same time were far from failure are weakened as a result similar to what is observed for the calaveras and the san andreas segments late during the aftershock sequence the seismicity rate may decrease below the back ground rate we suggest that the time dependent modification of the earthquake size distribution by a stress step can explain observations of lower b values immediately following a stress step

effects of a revised rate and state dependent friction law on aftershock triggering model abstract seismicity may be considered as a sequence of earthquake nucleation events controlled by regional loading history on the basis of this concept dieterich 1994 modeled aftershock seismicity following an imposed stress step by using a laboratory derived rate and state dependent friction law rsf although this model predicts the canonical 1 t decay of aftershock rate two huge gaps from observations are known the model with frictional parameters assumed to be laboratory observed values predicts too low aftershock productivity and also too long a delay before the decay onset these gaps are by orders of magnitude we suspected that the problem might be the incorrectness of traditional rsfs none of which was free from contradictions with laboratory data hence we modeled aftershock triggering with a revised rsf nagata et al 2012 which seems to have resolved the previously known flaws in reproducing laboratory data the original analytic approach of dieterich 1994 was found invalid for the revised rsf so we did an equivalent analysis by numerically tracking individual nucleation sources the revised rsf produced generally similar aftershock seismicity with the gaps mentioned above narrowed by a factor though these are far too small improvements of the huge gaps that is the revised rsf did not fully resolve the problem on the other hand our simulations found a counterintuitive response of a fault obeying the revised rsf if imposed during a certain stage in the seismic cycle a positive stress step can cause oscillatory slow slip events before eventual seismic instability instead of a usual response of further monotonic acceleration to seismic instability this delays the timing of the next earthquake due to this behavior the exponent of the aftershock decay can be greater than unity also the decay can once overshoot below the background seismicity before eventually returning to the background level

remote triggering of tremor along the san andreas fault in central california received 30 august 2008 accepted 16 april 2009 published 18 july 2009 1 we perform a systematic survey of triggered tremor along the san andreas fault in central california for the 31 teleseismic earthquakes with mw 7 5 since 2001 we identify 10 teleseismic events associated with clear triggered tremor about 52 of the tremor is concentrated south of parkfield near cholame where ambient tremor has been identified previously and the rest is widely distributed in the creeping section of the san andreas fault north of parkfield tremor is generally initiated and is in phase with the love wave particle velocity however the pattern becomes complicated with the arrival of the rayleigh waves and sometimes tremor continues after the passage of the surface waves we identify two cases in which tremor is triggered during the teleseismic pkp phase these results suggest that while shear stress from the passage of the love waves plays the most important role in triggering tremor in central california other factors such as dilatational stresses from the rayleigh and p waves also contribute we also examine the ambient tremor occurrence rate before and after the teleseismic events and find a transient increase of stacked tremor rate during the passage of the teleseismic surface waves this observation implies that the occurrence time of tremor is temporally advanced by the dynamic stresses of the teleseismic waves the amplitude of the teleseismic waves correlates with the occurrence of triggered tremor and the inferred tremor triggering threshold is 2 3 kpa the relatively low triggering threshold indicates that the effective stress at the tremor source region is very low most likely due to near lithostatic fluid pressure

suppression of large earthquakes by stress shadows a comparison of coulomb and rate and state failure stress shadows generated by california s two most recent great earthquakes 1857 fort tejon and 1906 san francisco substantially modified 19th and 20th century earthquake history in the los angeles basin and in the san francisco bay area simple coulomb failure calculations which assume that earthquakes can be modeled as static dislocations in an elastic half space have done quite well at approximating how long the stress shadows or relaxing effects should last and at predicting where subsequent large earthquakes will not occur there has however been at least one apparent exception to the predictions of such simple models the 1911 m 6 0 earthquake near morgan hill california occurred at a relaxed site on the calaveras fault we examine how the more complex rate and state friction formalism based on laboratory experiments might have allowed the 1911 earthquake rate and state time to failure calculations are consistent with the occurrence of the 1911 event just 5 years after 1906 if the calaveras fault was already close to failure before the effects of 1906 we also examine the likelihood that the entire 78 years of relative quiet only four m 6 earthquakes in the bay area after 1906 is consistent with rate and state assumptions given that the previous 7 decades produced 18 m 6 earthquakes combinations of rate and state variables can be found that are consistent with this pattern of large bay area earthquakes assuming that the rate of earthquakes in the 7 decades before 1906 would have continued had 1906 not occurred these results demonstrate that rate and state offers a consistent explanation for the 78 year quiescence and the 1911 anomaly although they do not rule out several alternate explanations

transient triggering of near and distant earthquakes we demonstrate qualitatively that frictional instability theory provides a context for understanding how earthquakes may be triggered by transient loads associated with seismic waves from near and distance earthquakes we assume that earthquake triggering is a stick slip process and test two hypotheses about the effect of transients on the timing of instabilities using a simple spring slider model and a rate and state dependent friction constitutive law a critical triggering threshold is implicit in such a model formulation our first hypothesis is that transient loads lead to clock advances i e transients hasten the time of earthquakes that would have happened eventually due to constant background loading alone modeling results demonstrate that transient loads do lead to clock advances and that the triggered instabilities may occur after the transient has ceased i e triggering may be delayed these simple clock advance models predict complex relationships between the triggering delay the clock advance and the transient characteristics the triggering delay and the degree of clock advance both depend nonlinearly on when in the earthquake cycle the transient load is applied this implies that the stress required to bring about failure does not depend linearly on loading time even when the fault is loaded at a constant rate the timing of instability also depends nonlinearly on the transient loading rate faster rates more rapidly hastening instability this implies that higher frequency and or longer duration seismic waves should increase the amount of clock advance these modeling results and simple calculations suggest that near tens of kilometers small moderate earthquakes and remote thousands of kilometers earthquakes with magnitudes 2 to 3 units larger may be equally effective at triggering seismicity our second hypothesis is that some triggered seismicity represents earthquakes that would not have happened without the transient load i e accumulated strain energy would have been relieved via other mechanisms we test this using two new seismicity models that 1 are inherently unstable but slide at steady state conditions under the background load and 2 are conditionally stable such that instability occurs only for sufficiently large perturbations for the new seismicity models very small amplitude transients trigger instability relative to the clock advance models the unstable steady state models predict that the triggering delay depends inversely and nonlinearly on the transient amplitude as in the clock advance models we were unable to generate delayed triggering with conditionally stable models for both new seismicity models the potential for triggering is independent of when the transient load is applied or equivalently of the prestress unlike in the clock advance models in these models a critical triggering threshold appears to be inversely proportional to frequency further advancement of our understanding will require more sophisticated quantitative models and observations that distinguish between our qualitative yet distinctly different model predictions

can coseismic stress variability suppress seismicity shadows insights from a rate and state friction model 1 the paucity of detectable seismicity shadows in the days months following a main shock has raised the question as to whether dynamic rather than static triggering could be the main mechanism driving the seismicity at these timescales the lack of correlation between the stress unloading of the main fault and the typically vigourous aftershock production taking place on it however suggests that the spatial heterogeneity of the coseismic stress change could also be a factor in the apparent suppression of seismicity shadows at least on the main fault here we study whether this stress variability can indeed be an important aspect in the stress modeling of earthquake sequences a rate and state friction model of seismicity is used in conjunction with realistic levels of stress heterogeneity at the earthquake nucleation scale 1 10 m as predicted from these friction laws based on scale invariant models of coseismic slip distribution in this model a relatively weak on fault quiescence is delayed by months to years because of the high stress heterogeneity delayed quiescences due to slip heterogeneity are similarly predicted at distances of up to about half the rupture length away from the fault we also postulate that off fault seismicity can be significantly controlled by stress variability that originates from small scale crustal heterogeneity and the complexity in fault geometries rather than mapping stress changes by providing a single stress value at every grid point these results suggest that an estimate of the likely stress variability acting at the nucleation scale is also needed especially when trying to account for the seismicity occurring at relatively short timescales

testing the stress shadow hypothesis 1 a fundamental question in earthquake physics is whether aftershocks are predominantly triggered by static stress changes permanent stress changes associated with fault displacement or dynamic stresses temporary stress changes associated with earthquake shaking both classes of models provide plausible explanations for earthquake triggering of aftershocks but only the static stress model predicts stress shadows or regions in which activity is decreased by a nearby earthquake to test for whether a main shock has produced a stress shadow we calculate time ratios defined as the ratio of the time between the main shock and the first earthquake to follow it and the time between the last earthquake to precede the main shock and the first earthquake to follow it a single value of the time ratio is calculated for each 10 10 km bin within 1 5 fault lengths of the main shock epicenter large values of the time ratio indicate a long wait for the first earthquake to follow the main shock and thus a potential stress shadow whereas small values indicate the presence of aftershocks simulations indicate that the time ratio test should have sufficient sensitivity to detect stress shadows if they are produced in accordance with the rate and state friction model we evaluate the 1989 mw 7 0 loma prieta 1992 mw 7 3 landers 1994 mw 6 7 northridge and 1999 mw 7 1 hector mine main shocks for each main shock there is a pronounced concentration of small time ratios indicating the presence of aftershocks but the number of large time ratios is less than at other times in the catalog this suggests that stress shadows are not present by comparing our results to simulations we estimate that we can be at least 98 confident that the loma prieta and landers main shocks did not produce stress shadows and 91 and 84 confident that stress shadows were not generated by the hector mine and northridge main shocks respectively we also investigate the long hypothesized existence of a stress shadow following the 1906 san francisco bay area earthquake we find that while bay area catalog seismicity rates are lower in the first half of the twentieth century than in the last half of the nineteenth this seismicity contrast is also true outside of the bay area in regions not expected to contain a stress shadow this suggests that the rate change is due to a more system wide effect such as errors in the historical catalog or the decay of aftershocks of the larger 1857 fort tejon earthquake

rate and state of background stress estimated from the aftershocks of the 1989 loma prieta california earthquake estimates of the tectonic stress state including loading rate and magnitude of background stress are derived from the spatial and temporal distribution of loma prieta aftershocks this technique was previously applied to the landers aftershock sequence gross and kisslinger 1997 and is based upon the seismicity model of dieterich 1994 dieterich s theory suggests that background seismicity should be proportional to stress rate and the number of aftershocks in an area should be proportional to the stress step experienced in that area we used two independently derived source models to compute the stress step from the mainshock and to determine how effective that stress step was in triggering aftershocks a background stress state is then chosen which makes the stress steps at the aftershock locations most distinct from the stress steps at hypocenters of background seismicity the best fitting background stress state has its greatest compressive stress plunging 17 to n13 e and an intermediate stress very close in magnitude to the least principal stress the small shear stresses at depth and low coefficient of friction suggest that high pressure pore fluids may be present inside active faults the estimated stress rate of 70 pa d 0 25 bar yr is comparable to the stress rate found for the southern san andreas fault system we found a best fitting effective coefficient of friction 0 2 for the loma prieta area significantly less than 0 6 estimated for landers in previous work variations in aftershock decay rate within the loma prieta aftershock zone are correlated with static stresses caused by postseismic slip as modeled by burgmann et al 1997 some of the postseismic slip occurred on structures that did not slip during the mainshock so the postseismic and coseismic stress step fields have different spatial distributions the effectiveness of slowly accumulated postseismic static stresses in triggering aftershocks is especially interesting because dynamic stresses are insignificant in this case

variability of earthquake nucleation in continuum models of rate and state faults and implications for aftershock rates using two continuum models of rate and state faults one with a weaker patch and the other with rheological transition from steady state velocity weakening to velocity strengthening friction we simulate several scenarios of spontaneous earthquake nucleation plausible for natural faults investigate their response to static shear stress steps and infer the corresponding aftershock rates overall nucleation processes at weaker patches behave similarly to theories based on spring slider models with some notable deviations in particular nucleation and aftershock rates are affected by normal stress heterogeneity in the nucleation zone nucleation processes at rheological transitions behave differently producing complex slip velocity histories nonmonotonic responses to static stress changes and aftershock rates with pronounced peaks and seismic quiescence for such processes positive stress steps sometimes delay nucleation of seismic events by inducing aseismic transients that relieve stress and postpone seismic slip superposition of the complex aftershock response for spatially variable stress changes results in omori s law for a period of time followed by seismic quiescence such behavior was observed at the base of the seismogenic zone near the 1984 morgan hill earthquake we show that the computed aftershock rates are linked to unperturbed slip velocity evolution in the nucleation zone and construct simplified analytical scenarios that explain some features of the response the qualitative differences that we find between the two nucleation models indicate that aftershock response of rate and state faults to static stress changes would depend on the conditions under which nucleation occurs on natural faults and may be different from predictions based on spring slider models

on the increase of background seismicity rate during the 1997 1998 umbria marche central italy sequence apparent variation or fluid driven triggering abstract we investigate the temporal evolution of background seismicity rate in the umbria marche sector of the northern apennines that was struck by the 1997 1998 colfiorito seismic sequence specifically we apply the epidemic type aftershock sequences etas model to separate the background seismicity rate from the coseismic triggered rate of earthquake production analyzed data are extracted from the catalogo della sismicita italiana csi1 1 catalog of italian seismicity 1981 2002 which contains for the study area 12 163 events with m l 1 5 the capability of the etas model to match the observed seismicity rate is tested by analyzing the model residuals and by applying two nonparametric statistical tests the runs and the kolmogorov smirnov tests to verify the fit of residuals to poisson hypothesis we first apply the etas model to the seismicity that occurred in the study area during the whole period covered by the csi1 1 catalog our results show that the etas model does not explain the temporal evolution of seismicity in a time interval defined by change points identified from time evolution of residuals and encompassing the colfiorito seismic sequence we therefore restrict our analysis to this period and analyze only those events belonging to the 1997 1998 seismic sequence we again obtain the inadequacy of a stationary etas model with constant background rate to reproduce the temporal pattern of observed seismicity we verify that the failure of the etas model to fit the observed data is caused by the increase of the background seismicity rate associated with the repeated colfiorito mainshocks we interpret the inferred increase of background rate as a consequence of the perturbation to the coseismic stress field caused by fluid flow and or pore pressure relaxation in particular we show that the transient perturbation caused by poroelastic relaxation can explain the temporal increase of background rate that therefore represents a fluid signal in the seismicity pattern

estimating rate and state friction parameters using a two node stochastic model for aftershocks abstract the well known omori and modified omori omori utsu empirical formulae describe the decay in the rate of occurrence of aftershocks dieterich s rate and state dependent constitutive law for aftershock production produces a similar temporal formula with physically interpretable parameters such as the shear stressing rates the normal stress and a fault constitutive parameter this naturally leads to an interest in estimating these parameters from earthquake catalogs which requires a simpler stochastic model an alternative to the epidemic type aftershock sequence etas model is the two node seismic transfer and release model where one node represents the mainshock process and a secondary node represents the aftershock zone the aftershock decay rate in the two node model equals that derived from dieterich s rate and state dependent constitutive law and the inclusion of aseismic slip in the aftershock zone allows for values of p 1 in the best matching modified omori law the two node model can be easily fitted to aftershock data and has an application to aftershock stacking for estimating p values the equivalence between the rate and state and two node aftershock rates forms a bridge between a formula derived from physical considerations and a phenomenological stochastic model we show how this can be exploited by identifying physical units for the parameters in the latter to estimate the fault constitutive parameters and the stressing rates in dieterich s formula through a best fit inversion on real aftershock sequences the procedure is illustrated using data from four japanese earthquakes

stress triggering and earthquake probability estimates 1 stress triggering and fault interaction concepts are beginning to be incorporated into quantitative earthquake probability estimates however the current methods are limited in their range of compatible earthquake nucleation models i introduce a new general method for translating stress changes into earthquake probability changes which can potentially be used with any physical fault model given the large uncertainties in earthquake probability calculations it is unclear whether the small probability changes resulting from stress transfer are significant and meaningful for the purposes of seismic hazard assessment i present a case study of the effect of the 1992 m7 3 landers california earthquake on the probability of a major earthquake on the san andreas fault in southern california this is a large event in a well studied region which should maximize the probability change signal and minimize the uncertainty even for this scenario the earthquake probability change for a 30 year period is not significant with respect to the initial uncertainty in the earthquake probability this example comparisons with other studies and exploration of parameter space imply that the probability changes due to stress triggering are significant only for time intervals which are short compared to the repeat time of the target fault therefore stress change calculations will be useful in long term seismic hazard assessment only for low slip rate faults otherwise stress triggering calculations are best utilized in the short term immediately following a major earthquake

a constitutive law for rate of earthquake production and its application to earthquake clustering seismicity is modeled as a sequence of earthquake nucleation events in which the distribution of initial conditions over the population of nucleation sources and stress ing history control the timing of earthquakes the model is implemented using solutions for nucleation of unstable fault slip on faults with experimentally derived rate and state dependent fault properties this yields a general state variable constitutive formulation for rate of earthquake production resulting from an applied stressing history to illustrate and test the model some characteristics of seismicity following a stress step have been explored it is proposed that various features of earthquake clustering arise from sensi tivity of nucleation times to the stress changes induced by prior earthquakes the model gives the characteristic omori aftershock decay law and interprets aftershock parameters in terms of stress change and stressing rate earthquake data appear to support a model prediction that aftershock duration defined as the time for rates to return to the back ground seismicity rate is proportional to mainshock recurrence time observed spatial and temporal clustering of earthquake pairs arises as a consequence of the spatial depen dence of stress changes of the first event of the pair and stress sensitive time dependent nucleation applications of the constitutive formulation are not restricted to the simple stress step models investigated here it may be applied to stressing histories of arbitrary complexity the apparent success at modeling clustering phenomena suggests the possibil ity of using the formulation to estimate short to intermediate term earthquake probabil ities following occurrence of other earthquakes and for inversion of temporal variations of earthquake rates for changes in driving stress

creep modulation of omori law generated by a coulomb stress perturbation in a 3 d rate and state asperity model we present numerical simulations conducted with a quasi dynamic 3 d rate and state asperity model and an analytical approach in order to study the behavior of a seismic asperity surrounded by aseismic creep in response to external coulomb stress perturbations this work is inspired by the observation of omori decay characterizing the recurrence time of isolated repeating earthquakes such as at the parkfield segment of the san andreas fault during the postseismic phase of the 2004 mw 6 event based on the numerical results and on an analysis of phase diagrams we identify two possible regimes that characterize the response of an asperity surrounded by aseismic creep to a stress step depending on an effective steady state friction parameter a for the specific perturbation used in this study we observe that when a is positive the relaxation of the system is governed by the response of the creeping segments of the fault and the asperity ruptures in an omori sequence in this regime we demonstrate that the duration of the relaxation process depends on a furthermore we show that this effective strengthening behavior is equivalent to a subcritical density of asperities meaning that the shape of the omori decay is controlled by the relative proportion of seismic and aseismic material within the fault on the other hand a fault characterized by effective steady state weakening a 0 behaves like a spring and slider system that loses the memory of the stress perturbation once the first aftershock occurred at least in the simulations presented here