interpretation of significant ground response and structure strong motions recorded during the 1994 northridge earthquake abstract some of the largest accelerations and velocities ever recorded at ground response and structural sites occurred during the northridge earthquake these motions are greater than most existing attenuation models would have predicted although the motions are large the correspondence between measured acceleration and damage requires further study since some sites with high acceleration experienced only moderate damage also some peak vertical accelerations were larger than the horizontal but in general they are smaller and fit the pattern observed in previous earthquakes strong motion records processed to date show significant differences in acceleration and velocity waveforms and amplitudes across the san fernando valley analysis of processed data from several buildings in the san fernando valley indicates that short period buildings such as shear wall buildings experienced large forces and relatively low inter story drift during the northridge earthquake however long period 1 to 5 sec steel or concrete moment frame buildings experienced large inter story drift for this earthquake accelerations did not always amplify from base to roof for flexible structures like the moment frame buildings but the displacements were always larger at the roof the drifts at many of the moment frame buildings were larger than the drift limit for working stress design in the building code the records from a base isolated building indicate that high frequency motion was reduced significantly by the isolators the isolators deformed about 3 5 cm which is much less than the design displacement the records from a parking structure show important features of the seismic response of this class of structure

a novel direction finding algorithm for directional borehole radar a directional borehole radar system has been developed for the purpose of 3 d imaging of subsurface targets in a single hole measurement the radar system is equipped with a uniform circular array consisting of four dipole antennas as a receiver in order to realize azimuth bearing sensitivity we propose a new direction finding df algorithm that is suitable for directional borehole radar measurement and we apply this algorithm to actual field measurement data this algorithm is based on the adcock df antenna principle where the complex time series analytic signal expression the optimization and the filtering procedure are incorporated to provide more accurate estimation the algorithm was first verified in a transmission measurement in boreholes with a cross hole configuration 15 m apart from each other by estimating a direction of the incident wave from a transmitter to the receiver finally the algorithm was applied to single hole measurement data to demonstrate the ability to detect the 3 d location of a subsurface tunnel which was located 5 5 m from the borehole the result showed fairly good agreement with the actual location of the tunnel i e to an azimuth estimation error of within 10deg

southern san andreas fault seismicity is consistent with the gutenberg richter magnitude frequency distribution the magnitudes of any collection of earthquakes nucleating in a region are generally observed to follow the gutenberg richter gr distribution on some major faults however paleoseismic rates are higher than a gr extrapolation from the modern rate of small earthquakes would predict this along with other observations led to the formulation of the characteristic earthquake hypothesis which holds that the rate of small to moderate earthquakes is permanently low on large faults relative to the large earthquake rate wesnousky et al 1983 schwartz and coppersmith 1984 we examine the rate difference between recent small to moderate earthquakes on the southern san andreas fault ssaf and the paleoseismic record hypothesizing that the discrepancy can be explained as a rate change in time rather than a deviation from gr statistics we find that with reasonable assumptions the rate changes necessary to bring the small and large earthquake rates into alignment agree with the size of rate changes seen in epidemic type aftershock sequence modeling where aftershock triggering of large earthquakes drives strong fluctuations in the seismicity rates for earthquakes of all magnitudes the necessary rate changes are also comparable to rate changes observed for other faults worldwide these results are consistent with paleoseismic observations of temporally clustered bursts of large earthquakes on the ssaf and the absence of m 7 earthquakes on the ssaf since 1857

seismic moment distribution revisited i statistical results summary an accumulation of seismic moment data gathered over the previous decade justifies a new attempt at a comprehensive statistical analysis of these data herein more rigourous statistical techniques are introduced their properties investigated and these methods are employed for analysis of large modern data sets several theoretical distributions of earthquake size seismic moment frequency relations are described and compared we discuss the requirements for such distributions and introduce an upper bound or a corner moment for a distribution to have a finite energy or moment flux we derive expressions for probability density functions and statistical moments of the distributions we also describe parameter evaluation in particular how to estimate the seismic moment distribution for the largest earthquakes simulating earthquake size distributions allows for a more rigourous evaluation of distribution parameters and points to the limitations of the classical statistical analysis of earthquake data simulations suggest that several earthquakes approaching or exceeding the corner magnitude mc limit need to be registered to evaluate mc with reasonable accuracy using the harvard catalogue data we compare moment distribution parameters for various temporal spans of the catalogue for different tectonic provinces and depth ranges and for earthquakes with various focal mechanisms the statistical analysis suggests that the exponent b is universal b 0 60 0 65 for all moderate earthquakes the corner moment mc value determined by the maximum likelihood method both in subduction zones and globally is about 10 21 n m corresponding to the corner moment magnitude mc 8 0 for midoceanic earthquakes mc is apparently smaller for spreading ridges it is about 5 8 and for strike slip earthquakes on transform faults it decreases from 7 2 to 6 5 as the relative slip velocity of faults increases we investigate the seismic moment errors both random and systematic and their dependence on earthquake size the relative errors seem to decrease for larger events the influence of moment uncertainties on the parameter estimates is studied whereas the b values do not appear to be significantly influenced by the errors for the corner moment large errors can lead to substantially biased estimates we compare the harvard catalogue results with the earthquake data from instrumental catalogues in the first three quarters of the 20th century several very large earthquakes mi9 occurred around the middle of the century their magnitude values cannot be fitted by a modified gutenberg richter law with mc 8 0 8 5 among other factors this discrepancy can be explained by either substantially higher errors in the earlier magnitude values or by mc being higher for some subduction zones it is unlikely that data available presently or soon will be sufficient to determine the corner magnitude of 9 and above with reasonable precision using purely statistical methods

the gutenberg richter or characteristic earthquake distribution which is it abstract paleoearthquake and fault slip rate data are combined with the cit usgs catalog for the period 1944 to 1992 to examine the shape of the magnitude frequency distribution along the major strike slip faults of southern california the resulting distributions for the newport inglewood elsinore garlock and san andreas faults are in accord with the characteristic earthquake model of fault behavior the distribution observed along the san jacinto fault satisfies the gutenberg richter relationship if attention is limited to segments of the san jacinto that are marked by the rupture zones of large historical earthquakes or distinct steps in fault trace the observed distribution along each segment is consistent with the characteristic earthquake model the gutenberg richter distribution observed for the entirety of the san jacinto may reflect the sum of seismicity along a number of distinct fault segments each of which displays a characteristic earthquake distribution the limited period of instrumental recording is insufficient to disprove the hypothesis that all faults will display a gutenberg richter distribution when averaged over the course of a complete earthquake cycle but given that 1 the last 5 decades of seismicity are the best indicators of the expected level of small to moderate size earthquakes in the next 50 years and 2 it is generally about this period of time that is of interest in seismic hazard and engineering analysis the answer to the question posed in the title of the article at least when concerned with practical implementation of seismic hazard analysis at sites along these major faults appears to be the characteristic earthquake distribution

statistical physics seismogenesis and seismic hazard the scaling properties of earthquake populations show remarkable similarities to those observed at or near the critical point of other composite systems in statistical physics this has led to the development of a variety of different physical models of seismogenesis as a critical phenomenon involving locally nonlinear dynamics with simplified rheologies exhibiting instability or avalanche type behavior in a material composed of a large number of discrete elements in particular it has been suggested that earthquakes are an example of a self organized critical phenomenon analogous to a sandpile that spontaneously evolves to a critical angle of repose in response to the steady supply of new grains at the summit in this stationary state of marginal stability the distribution of avalanche energies is a power law equivalent to the gutenberg richter frequency magnitude law and the behavior is relatively insensitive to the details of the dynamics here we review the results of some of the composite physical models that have been developed to simulate seismogenesis on different scales during 1 dynamic slip on a preexisting fault 2 fault growth and 3 fault nucleation the individual physical models share some generic features such as a dynamic energy flux applied by tectonic loading at a constant strain rate strong local interactions and fluctuations generated either dynamically or by fixed material heterogeneity but they differ significantly in the details of the assumed dynamics and in the methods of numerical solution however all exhibit critical or near critical behavior with behavior quantitatively consistent with many of the observed fractal or multifractal scaling laws of brittle faulting and earthquakes including the gutenberg richter law some of the results are sensitive to the details of the dynamics and hence are not strict examples of self organized criticality nevertheless the results of these different physical models share some generic statistical properties similar to the universal behavior seen in a wide variety of critical phenomena with significant implications for practical problems in probabilistic seismic hazard evaluation in particular the notion of self organized criticality or near criticality gives a scientific rationale for the a priori assumption of stationarity used as a first step in the prediction of the future level of hazard the gutenberg richter law a power law in energy or seismic moment is found to apply only within a finite scale range both in model and natural seismicity accordingly the frequency magnitude distribution can be generalized to a gamma distribution in energy or seismic moment a power law with an exponential tail this allows extrapolations of the frequency magnitude distribution and the maximum credible magnitude to be constrained by observed seismic or tectonic moment release rates the answers to other questions raised are less clear for example the effect of the a priori assumption of a poisson process in a system with strong local interactions and the impact of zoning a potentially multifractal distribution of epicentres with smooth polygons the results of some models show premonitory patterns of seismicity which could in principle be used as mainshock precursors however there remains no consensus on both theoretical and practical grounds on the possibility or otherwise of reliable intermediate term earthquake prediction

seismic moment distribution summary we review possible errors in determining the size of earthquakes we propose that the size distribution can be effectively defined only for earthquake sequences not for individual earthquakes as a result of the error analysis we question the validity of many reported correlations between the 6 value and spatio temporal characteristics of tectonics and seismicity the study of the distribution of earthquake seismic moment largely avoids the influence of these errors and biases and is therefore superior to the standard analysis of the magnitude frequency law the gamma distribution is applied to describe the distribution of seismic moments of earthquake sequences this distribution which generalizes the well known gutenberg richter g r relation is characterized by two parameters we use the maximum likelihood method to determine the parameters of the gamma distribution for worldwide earthquakes in different depth ranges the empirical distribution is derived from the moment tensor catalogue compiled by the harvard group the p value for scalar seismic moment of earthquake sequences an analogue of the 6 value in the g r magnitude frequency law is close to 1 2 for all earthquakes the value predicted by a critical branching model of seismicity this result which will be improved as more seismic moment data become available provides input for modelling of seismicity based on percolation or on self organized criticality models if 3 equals 1 2 then using the critical branching model we find that most small earthquakes in available catalogues are dependent shocks i e aftershocks even among earthquakes of intermediate magnitudes the number of dependent events may exceed that of independent events

self organized fractal seismicity and b value of aftershocks of the 2001 bhuj earthquake in kutch india the devastating intraplate earthquake of m w 7 7 of 26 january 2001 took place along the south dipping reverse fault in the lower crust 23 km of kutch gujarat india obliterating some 14 000 people the aftershock activity has ensued for three years we analyzed 997 aftershocks of m 3 0 to study the b value and fractal correlation dimensions in time and space the b value is found to be 0 8 0 03 from the gutenberg richter relation and 0 76 0 02 from the maximum likelihood suggesting a typical value for the intraplate region the spatial correlation is 1 71 0 02 indicating that events are approaching a two dimensional region further the temporal correlation dimension is estimated to be 0 78 0 02 confirming the structure is mono fractal in time domain the depth section of b value shows a peak at 15 35 km depth range coinciding with the maximum occurrence of aftershocks 47 which is inferred as a fluid filled highly fractured rock matrix with fractures of high density it will be important to note that tomographic results also suggest a low vp low vs and a large poisson s ratio for the same depth range further confirming this inference additionally we have studied the variation of d2 s and b value with time during the first two months of aftershock activity the results show a marked negative correlation between spatial correlation dimension d2 large and b value low indicating the predominance of large events associated with weak clustering the negative correlation means the stress release along faults of a larger surface area after two months the fractal dimension d2 s and b value suggests a positive correlation implying more numerous smaller shocks with stress release along faults of a smaller surface area this would indicate a reduced probability of large magnitude earthquakes due to fragmentation of the fault zone

identifying an asperity through 3 d mapping of the frequency magnitude distribution following the idea introduced by wiemer and wyss 1997 here is an attempt to map the seismic hazard in terms of the b value in the frequency magnitude distribution in a region with moderate seismic activity bearn region french pyrenees in this area the complexity of the geology makes it necessary to perform a 3 d mapping b values are computed within 5 km radius spherical volumes that contain an average of 140 events strong lateral variations between 0 45 and 1 8 are observed at short scales in the whole investigated volume the minimum of the b value is clearly correlated with a historically active zone which last ruptured in 1980 mb 5 1 interpretating low b values in terms of high stresses may lead us to consider this minimum b patch as a 5 km radius asperity this study allows to define its location and dimensions

trench curvature and deformation of the subducting lithosphere summary the subduction of oceanic lithosphere is generally accompanied by downdip and lateral deformation the downdip component of strain is associated with external forces that are applied to the slab during its sinking namely the gravitational force and the mantle resistance to penetration here we present theoretical arguments showing that a tectonic plate is also subject to a predictable amount of lateral deformation as a consequence of its bending along an arcuate trench zone independently from the long term physical processes that have determined the actual curvature of the subduction zone in particular we show that the state of lateral strain and the lateral strain rate of a subducting slab depend from geometric and kinematic parameters such as trench curvature dip function and subduction velocity we also demonstrate that the relationship between the state of lateral strain in a subducting slab and the geometry of bending at the corresponding active margin implies a small component of lateral shortening at shallow depths and may include large extensional lateral deformation at intermediate depths whereas a state of lateral mechanical equilibrium can only represent a localized exception our formulation overcomes the flaws of the classic ping pong ball model for the bending of the lithosphere at subduction zones which lead to severe discrepancies with the observed geometry and style of deformation of the modern subducting slabs a study of the geometry and seismicity of eight modern subduction zones is performed to assess the validity of the theoretical relationship between trench curvature slab dip function and lateral strain rate the strain pattern within the eight present day slabs which is reconstructed through an analysis of harvard cmt solutions shows that tectonic plates cannot be considered as flexible inextensible spherical caps whereas the lateral intraslab deformation which is accommodated through seismic slip can be explained in terms of deviations from the mechanical equilibrium

a synthetic seismicity model for southern california cycles probabilities and hazard the absence of a long historical catalog of observed seismicity with which to constrain earthquake recurrence behaviors is a fundamental stumbling block to earthquake prediction in california conceding that this limitation is not likely to relax in the foreseeable future alternative approaches must be sought to extend the catalog artificially in this article i evaluate the long term behaviors of earthquakes on a map like set of southern california faults through computer simulations that incorporate the physics of earthquake stress transfer and are constrained by excellent but restricted bodies of geological and seismological data i find that model seismicity fluctuates on both short decades and long centuries timescales but that it possesses a well defined mean and standard deviation seismicity fluctuations correlate across different magnitudes and the long term cycles of smaller events seem to lead cycles of larger events short period seismicity fluctuations do not exhibit this tendency and short term changes in low magnitude m5 seismicity are not likely to be an effective predictor of future large events at least for the region as a whole as do real faults the model faults produce characteristic and power law quakes in variable ratios with diverse periodic and nonperiodic behaviors generally larger events tend to occur quasi periodically and smaller ones tend to cluster however only for a few earthquake classes and certain locations is recurrence notably non poissonian an important use of synthetic seismicity is in the construction of earthquake hazard maps because it firmly grounds previously ad hoc assumptions regarding frequency magnitude distributions multiple segment failure statistics and rupture extents while satisfying a spectrum of geological constraints such as fault slip rate segment recurrence interval and slip per event with its depth of temporal and spatial coverage synthetic seismicity also provides a means to investigate the time dependence of seismic hazard because hazard likelihood is a concatenation of the recurrence statistics from many seismic sources in only about 40 50 of the regions near the major faults do sequences of 0 1 g or 0 2 g exceedances differ from poissonian

fundamental questions of earthquake statistics source behavior and the estimation of earthquake probabilities from possible foreshocks abstract estimates of the probability that an m l 4 8 earthquake which occurred near the southern end of the san andreas fault on 24 march 2009 would be followed by an m 7 mainshock over the following three days vary from 0 0009 using a gutenberg richter model of aftershock statistics reasenberg and jones 1989 to 0 04 using a statistical model of foreshock behavior and long term estimates of large earthquake probabilities including characteristic earthquakes agnew and jones 1991 i demonstrate that the disparity between the existing approaches depends on whether or not they conform to gutenberg richter behavior while gutenberg richter behavior is well established over large regions it could be violated on individual faults if they have characteristic earthquakes or over small areas if the spatial distribution of large event nucleations is disproportional to the rate of smaller events i develop a new form of the aftershock model that includes characteristic behavior and combines the features of both models this new model and the older foreshock model yield the same results when given the same inputs but the new model has the advantage of producing probabilities for events of all magnitudes rather than just for events larger than the initial one compared with the aftershock model the new model has the advantage of taking into account long term earthquake probability models using consistent parameters the probability of an m 7 mainshock on the southernmost san andreas fault is 0 0001 for three days from long term models and the clustering probabilities following the m l 4 8 event are 0 00035 for a gutenberg richter distribution and 0 013 for a characteristic earthquake magnitude frequency distribution our decisions about the existence of characteristic earthquakes and how large earthquakes nucleate have a first order effect on the probabilities obtained from short term clustering models for these large events

earthquake frequency distribution and the mechanics of faulting the level of intraplate seismicity in japan generally shows a positive correlation with the density of quaternary faulting in southwest japan where intraplate seismicity is concentrated on land rates of seismic moment release m 0 are similar when calculated from either the 400 year historical record of seismicity or geologically determined slip rates of quaternary faults a data set of 18 earthquakes with seismic moments m0 ranging from 0 01 to 3 1027 dyn cm shows a relationship between rupture lengthl and m0 log m0 23 5 1 94 log l when seismic moment on each quaternary fault is assumed to occur in discrete events every t m0 m 0g years where m0 is estimated for a rupture extended over the entire fault length and m 0g is proportional to the slip rate of each quaternary fault the moment frequency distribution of earthquakes log n a b log m0 predicted from the geologic record is virtually identical to that seen with the 400 year record of seismicity in contrast if it is assumed that earthquakes on each fault occur according to the gutenberg richter relation we obtain poor agreement with the observed seismicity thus while regional seismicity satisfies the relation log n a b log m0 or equivalently log n a b log m where m is magnitude it appears that seismicity on individual faults does not this further implies that the primary factor that leads to the magnitude frequency distribution in regional seismicity studies is the relative distribution of the slip rates and lengths of preexisting faults

statistics of small earthquakes and frequency of occurrence of large earthquakes along the mexican subduction zone abstract the validity of the gutenberg richter g r frequency magnitude relation over a wide range of magnitudes is usually accepted and the statistics of small earthquakes is often extrapolated to predict the frequency of occurrence of large earthquakes we take noaa and pde data from 1963 to 1981 related to the mexican subduction zone h 65 km and convert m b to m s in the range of 3 3 m b 5 7 for this conversion we use regression of m s on m b for mexican and central american events as well as an m s m b regression based on worldwide data wyss and habermann 1982 we also take into account the standard error in m s this may be important since the number of events decreases as m b increases the m s data of 18 5 yr is normalized to 75 5 yr and is compared to the statistics of observed large earthquakes m s 6 4 for the period 1906 to 1981 it is found that the g r relation in the range 4 5 m s 6 0 when extrapolated grossly underestimates the observed frequency of large earthquakes m s 6 5 for the oaxaca and jalisco regions there is strong evidence that the plate interface in the oaxaca region consists of a few 3 or 4 large fault zones each of which cyclically ruptures over its entire dimension without giving rise to smaller events in the manner implied by the g r relation the result is of profound importance in seismic risk analysis and in the understanding of fault mechanics this phenomenon has been reported for only a few regions e g turkey bath 1981 japan wesnousky et al 1983 it may have escaped detection in other regions due to a variety of causes the most important being the long recurrence periods of large earthquakes

a model of characteristic earthquakes and its implications for regional seismicity regional seismicity i e that averaged over large enough areas over long enough periods of time has a size frequency relationship the gutenberg richter law which differs from that found for some seismic faults the characteristic earthquake relationship but all seismicity comes in the end from active faults so the question arises of how one seismicity pattern could emerge from the other the recently introduced minimalist model of vazquez prada et al of characteristic earthquakes provides a simple representation of the seismicity originating from a single fault here we show that a characteristic earthquake relationship together with a fractal distribution of fault lengths can accurately describe the total seismicity produced in a region the resulting earthquake catalogue accounts for the addition of both all the characteristic and all the non characteristic events triggered in the faults the global accumulated size frequency relationship strongly depends on the fault length fractal exponent and for fractal exponents close to 2 correctly describes a gutenberg richter distribution with a b exponent compatible with real seismicity

mid continental earthquakes spatiotemporal occurrences causes and hazards abstract large earthquakes in north china australia northwestern europe central and eastern united states and other mid continents show complex spatiotemporal patterns that do not fit existing earthquake models individual faults or fault zones tend to fall into long term thousands of years or longer dormancy after a cluster of ruptures whereas large earthquakes seem to roam between widespread faults these behaviors are characteristic of complex dynamic systems of interacting faults in such systems widespread faults collectively accommodate slow tectonic loading and a major fault rupture both transfers stress to the neighboring faults and perturbs loading conditions on distant faults because of the slow tectonic loading local stress variations from fault interaction or nontectonic processes or changes of fault strength could trigger mid continental earthquakes the precise spatiotemporal occurrence of large mid continental earthquakes may be unknowable an intrinsic limitation of complex dynamic systems but their qualitative system behavior may be understood by a system approach this approach would render some commonly used concepts such as seismic cycles recurrence intervals characteristic earthquakes and seismic gaps inadequate or irrelevant in mid continents and calls for rethinking of the probability estimates based on these concepts it requires a better understanding of fault interactions on multiple spatial and temporal scales rather than focusing solely on the balance of tectonic loading and yield strength of individual faults or fault segments it also indicates the need for paleoseismic and geodetic studies extending beyond areas where recent large earthquakes occurred and for hazard assessments to reduce the biasing influence of the most recent large earthquakes that tend to dominate the short and incomplete earthquake records

earthquake statistics at parkfield 2 probabilistic forecasting and testing construct two probabilistic forecasts h 1 with a spatially varying b value and h 2 with a uniform b value and test these hypotheses against each other both hypotheses use a spatially varying seismicity level a value determined from past seismicity we used a range of sampling parameters magnitude threshold cell size etc to assure robust results we found that in most of the tests hypothesis h 1 showed a higher likelihood than h 2 although both are a poor approximation to the seismicity data the most positive results for h 1 are obtained for testing magnitude ranges down to m 1 5 and with sampling radii as defined in paper 1 as appropriate for parkfield the superior performance of h 1 suggests that spatially varying b values should be considered in earthquake forecasts index terms 7215 seismology earthquake parameters 7223 seismology seismic hazard assessment and prediction 7230 seismology seismicity and seismotectonics keywords earthquake statistics probabilistic forecasting parkfield

statistical self similarity of hotspot seamount volumes modeled as self similar criticality the processes responsible for hotspot seamount formation are complex yet the cumulative frequency volume distribution of hotspot seamounts in the easter island salas y gomez chain esc is found to be well described by an upper truncated power law we develop a model for hotspot seamount formation where uniform energy input produces events initiated on a self similar distribution of critical cells we call this model self similar criticality ssc by allowing the spatial distribution of magma migration to be self similar the ssc model recreates the observed esc seamount volume distribution the ssc model may have broad applicability to other natural systems

constraints on the frequency magnitude relation and maximum magnitudes in the uk from observed seismicity and glacio isostatic recovery rates summary earthquake populations have recently been shown to have many similarities with critical point phenomena with fractal scaling of source sizes energy or seismic moment corresponding to the observed gutenberg richter g r frequency magnitude law holding at low magnitudes at high magnitudes the form of the distribution depends on the seismic moment release rate mand the maximum magnitude m max the g r law requires a sharp truncation at an absolute maximum magnitude for finite m i n contrast the gamma distribution has an exponential tail which allows a soft or credible maximum to be determined by negligible contribution to the total seismic moment release here we apply both distributions to seismic hazard in the mainland uk and its immediate continental shelf constrained by a mixture of instrumental historical and neotectonic data tectonic moment release rates for the seismogenic part of the lithosphere are calculated from a flexural plate model for glacio isostatic recovery constrained by vertical deformation rates from tide gauge and geomorphological data earthquake focal mechanisms in the uk show near vertical strike slip faulting with implied directions of maximum compressive stress approximately in the nnw sse direction consistent with the tectonic model maximum magnitudes are found to be in the range 6 3 7 5 for the g r law or 7 0 8 2 m l for the gamma distribution which compare with a maximum observed in the time period of interest of 6 1 m l the upper bounds are conservative estimates based on 100 per cent seismic release of the observed vertical neotectonic deformation glacio isostatic recovery is predominantly an elastic rather than a seismic process so the true value of m max is likely to be nearer the lower end of the quoted range

heterogeneity and the earthquake magnitude frequency distribution regional earthquake populations are widely observed to have power law magnitude frequency statistics whether earthquake distributions on individual faults are similarly power law is presently the subject of considerable research effort recent careful observations suggest that event statistics on rough faults are power law whereas earthquake distributions on smooth faults are better described by a characteristic model in which there are more large earthquakes than would be expected by extrapolation from the distribution of small events here the relation between heterogeneity and the magnitude frequency distribution is investigated in a cellular automaton that includes new nearest neighbor stress transfer rules which produce realistic stress concentrations the results agree with the suggestion that smooth faults have more characteristic earthquake distributions and support the view that an earthquake s size is controlled by rupture arrest

clustering and periodic recurrence of microearthquakes on the san andreas fault at parkfield california the san andreas fault at parkfield california apparently late in an interval between repeating magnitude 6 earthquakes is yielding to tectonic loading partly by seismic slip concentrated in a relatively sparse distribution of small clusters 20 meter radius of microearthquakes within these clusters which account for 63 of the earthquakes in a 1987 92 study interval virtually identical small earthquakes occurred with a regularity that can be described by the statistical model used previously in forecasting large characteristic earthquakes sympathetic occurrence of microearthquakes in nearby clusters was observed within a range of about 200 meters at communication speeds of 10 to 100 centimeters per second the rate of earthquake occurrence particularly at depth increased significantly during the study period but the fraction of earthquakes that were cluster members decreased

seismicity in a model governed by competing frictional weakening and healing mechanisms summary observations from laboratory field and numerical work spanning a wide range of space and time scales suggest a strain dependent progressive evolution of material properties that control the stability of earthquake faults the associated weakening mechanisms are counterbalanced by a variety of restrengthening mechanisms the efficiency of the healing processes depends on local material properties and on rheologic temperature and hydraulic conditions we investigate the relative effects of these competing non linear feedbacks on seismogenesis in the context of evolving frictional properties using a mechanical earthquake model that is governed by slip weakening friction weakening and strengthening mechanisms are parametrized by the evolution of the frictional control variable the slip weakening rate r using empirical relationships obtained from laboratory experiments in our model weakening depends on the slip of an earthquake and tends to increase r following the behaviour of real and simulated frictional interfaces healing causes r to decrease and depends on the time passed since the last slip results from models with these competing feedbacks are compared with simulations using non evolving friction compared to fixed r conditions evolving properties result in a significantly increased variability in the system dynamics we find that for a given set of weakening parameters the resulting seismicity patterns are sensitive to details of the restrengthening process such as the healing rate b and a lower cutoff time t c up to which no significant change in the friction parameter is observed for relatively large and small cutoff times the statistics are typical of fixed large and small r values respectively however a wide range of intermediate values leads to significant fluctuations in the internal energy levels the frequency size statistics of earthquake occurrence show corresponding non stationary characteristics on time scales over which negligible fluctuations are observed in the fixed r case the progressive evolution implies that except for extreme weakening and healing rates faults and fault networks possibly are not well characterized by steady states on typical catalogue time scales thus highlighting the essential role of memory and history dependence in seismogenesis the results suggest that an extrapolation to future seismicity occurrence based on temporally limited data may be misleading due to variability in seismicity patterns associated with competing mechanisms that affect fault stability

seismic gap hypothesis ten years after the seismic gap hypothesis states that earthquake hazard increases with time since the last large earthquake on certain faults or plate boundaries one of the earliest and clearest applications of the seismic gap theory to earthquake forecasting was by mccann et al 1979 who postulated zones of high medium and low seismic potential around the pacific rim in the 10 years since there have been over 40 large m 7 0 earthquakes enough to test statistically the earlier forecast we also analyze another forecast of long term earthquake risk that by kelleher et al 1973 the hypothesis of increased earthquake potential after a long quiet period can be rejected with a large confidence the data suggest that contrary to these forecasts places of recent earthquake activity have larger than usual seismic hazard whereas the segments of the circum pacific belt with no large earthquakes in recent decades have remained relatively quiet the clustering of earthquake times does not contradict the plate tectonic model which constrains only the long term average slip rate not the regularity of earthquakes

earthquakes quaternary faults and seismic hazard in california data describing the locations slip rates and lengths of quaternary faults are the primary basis in this work for constructing maps that characterize seismic hazard in california the expected seismic moment m0e and the strength of ground shaking resulting from the entire rupture of each mapped fault or fault segment are estimated using empirical relations between seismic moment m0 rupture length source to site distance and strong ground motions assuming a fault model whereby the repeat time t of earthquakes on each fault equals m0e m0g where the moment rate m0g is proportional to fault slip rate it is observed that the moment frequency distribution of earthquakes predicted from the geologic data agrees well with the distribution determined from a 150 year historical record the agreement is consistent with the argument that the geologic record of quaternary fault offsets contains information sufficient to predict the average spatial and size distribution of earthquakes through time in california the estimates of t for each fault are the foundation for constructing maps that depict the average return period of 0 1g peak horizontal ground accelerations and the horizontal components of peak acceleration peak velocity and the pseudovelocity response at 1 period and 5 damping expected to occur at the level of 0 1 probability during a 50 year period of time a map is also formulated to show the probability that 0 1g horizontal ground accelerations will occur during the next 50 years the maps serve to illustrate the potential value of quaternary fault studies for assessing seismic hazard interpretation of available slip rates indicates that the largest and most frequent occurrence of potentially destructive strong ground motions are associated principally with the san andreas san jacinto calaveras hayward and ventura basin fault zones other regions of similarly high hazard may yet remain unrecognized this inadequacy results primarily from an incomplete data set numerous faults for example are mapped along the coastal region of northern california and within the modoc plateau but relatively few studies relating to fault slip rate are reported a similar problem exists for other stretches of coastal california where marine reflection studies provide evidence of active faulting offshore yet yield little or no information of fault slip rate geological and geophysical field studies can work to remove these deficiencies a concerted effort to locate and define rates of activity on all faults in california is the most promising means to further quantify present levels of seismic hazard in california

variability of displacement at a point implications for earthquake size distribution and rupture hazard on faults abstract to investigate the nature of earthquake magnitude distributions on faults we compare the interevent variability of surface displacement at a point on a fault from a composite global data set of paleoseismic observations with the variability expected from two prevailing magnitude frequency distributions the truncated exponential model and the characteristic earthquake model we use forward modeling to predict the coefficient of variation cv for the alternative earthquake distributions incorporating factors that would effect observations of displacement at a site the characteristic earthquake model with a characteristic magnitude range of 0 25 produces cv values consistent with the data cv 0 5 only if the variability for a given earthquake magnitude is small this condition implies that rupture patterns on a fault are stable in keeping with the concept behind the model this constraint also bears upon fault rupture hazard analysis which for lack of point specific information has used global scaling relations to infer variability in average displacement for a given size earthquake exponential distributions of earthquakes from m 5 to the maximum magnitude give rise to cv values that are significantly larger than the empirical constraint a version of the model truncated at m 7 however yields values consistent with a larger cv 0 6 determined for small displacement sites although this result allows for a difference in the magnitude distribution of smaller surface rupturing earthquakes it may reflect in part less stability in the displacement profile of smaller ruptures and or the tails of larger ruptures online material global surface displacement data and identified sources of uncertainty

order and diversity in the modes of circum pacific earthquake recurrence recurrence characteristics of great circum pacific earthquakes and determinations of spatial distribution of seismic moment release are surveyed in order to delineate their general features and relate earthquake slip distribution to models of recurrent rupture as noted by others the pattern of moment release is typically very irregular with strong concentrations in a few isolated regions of a much larger aftershock zone despite this complexity rupture nucleation is notably systematic with mainshock epicenter showing a strong tendency to locate in or immediately adjacent to identified regions of high moment release this generalization suggests that earthquake recurrence is more likely to be controlled by maximum rather than average fault slip well documented case histories from twelve plate boundary regions demonstrate that seismic strain release tends to be temporally well ordered while source dimensions slip and cumulative moment release vary considerably from cycle to cycle on none of the segments studied do earthquakes consistently recur in nearly identical events instead individual great earthquakes differ significantly from cycle to cycle or rerupture takes place in a sequence of two or more smaller events despite these differences the duration of the seismic cycle is approximately uniform furthermore when strain release occurs in a sequence of large earthquakes these events take place towards the end of the cycle and occur with increasing rupture length and magnitude these ordered and irregular features of earthquake recurrence argue for the existence of corresponding elements on plate boundary faults the ordered characteristics are identified with zones of concentrated moment release that slip comparable amounts in each cycle and have high shear strength the irregular features are associated with intervening weaker regions that move in response to the stress concentration of dynamic rupture and slip by differing amounts in each event although these mechanistic associations are indirect and tentative the features of recurrent behavior documented here have implications for long term earthquake hazard assessment that are not dependent on the models proposed to explain them chief among these are the cycle to cycle differences among gap filling events and the absence of shocks that fill major slip deficient regions early in the seismic cycle

probabilistic models for earthquakes with large return periods in himalaya region determination of the frequency of large earthquakes is of paramount importance for seismic risk assessment as large events contribute to significant fraction of the total deformation and these long return period events with low probability of occurrence are not easily captured by classical distributions generally with a small catalogue these larger events follow different distribution function from the smaller and intermediate events it is thus of special importance to use statistical methods that analyse as closely as possible the range of its extreme values or the tail of the distributions in addition to the main distributions the generalised pareto distribution family is widely used for modelling the events which are crossing a specified threshold value the pareto truncated pareto and tapered pareto are the special cases of the generalised pareto family in this work the probability of earthquake occurrence has been estimated using the pareto truncated pareto and tapered pareto distributions as a case study the himalayas whose orogeny lies in generation of large earthquakes and which is one of the most active zones of the world has been considered the whole himalayan region has been divided into five seismic source zones according to seismotectonic and clustering of events estimated probabilities of occurrence of earthquakes have also been compared with the modified gutenberg richter distribution and the characteristics recurrence distribution the statistical analysis reveals that the tapered pareto distribution better describes seismicity for the seismic source zones in comparison to other distributions considered in the present study

implications of fault slip rates and earthquake recurrence models to probabilistic seismic hazard estimates abstract increasingly fault slip rates are being used to constrain earthquake recurrence relationships for site specific probabilistic seismic hazard ground motion assessments this paper shows the sensitivity of seismic hazard assessments to variations in recurrence models and parameters that incorporate fault slip rates two models are considered to describe the partitioning of the slip rate or seismic moment rate into various magnitude earthquakes an exponential magnitude distribution and a characteristic earthquake distribution assuming an exponential distribution the activity rate n m 0 is constrained by the upper bound magnitude m u the b value for the region and the fault slip rate s for a given s variations in m u and b value have significant effects on recurrence and computed hazard depending on whether the assumption is made that the seismicity rate is constant or the moment rate is constant there is increasing evidence that the characteristic earthquake model is more appropriate for individual faults than the exponential magnitude distribution based on seismicity data from areas having repeated large earthquakes a generalized recurrence density function is developed and the resulting recurrence relationship requires only m u b value and s a comparison of the recurrence relationships from this model with the historical seismicity and paleoseismicity data on the wasatch and san andreas faults shows a good match the computed hazard based on the characteristic earthquake model differs from that obtained for the exponential model as a function of the fault to site distance and the acceleration level one check on the recurrence models using slip rate is to compare over large regions activity rates based on seismicity data and slip rate data such a comparison in the western transverse ranges shows a reasonable match for both the exponential and characteristic earthquake models in the moderate to large magnitude range

does maximum earthquake size depend on focal depth abstract while the gutenberg richter law gr with b value of 1 0 is an inexact description of the earthquake frequency magnitude distribution it does provide a convenient statistical basis for identifying when the largest earthquakes in a catalog are either anomalously large or anomalously small when the largest earthquakes are as predicted by the gr distribution it is inappropriate to infer that the largest historically known earthquake is the largest possible only when the largest observed earthquakes are significantly smaller than predicted can we infer that the largest possible earthquakes have occurred analysis of the global historical catalog demonstrates that at nearly all depths the largest deep and intermediate earthquakes have sizes close to those predicted by a gr distribution with b of 1 0 only between about 300 to 450 km and beneath 600 km are the largest known earthquakes somewhat larger than predicted however when geographically isolatable subgroups within catalogs are considered separately largest earthquakes that are either anomalously large or small are quite common often this is because individual regions have b values much different than 1 0 alternatively sometimes there appear to be physical constraints limiting the size of the largest possible earthquake as examples illustrating these assertions this article evaluates two subgroups deep focus earthquakes occurring beneath spain and intermediate depth earthquakes in the bucaramanga colombia nest

seismotectonics and seismic hazard modelling for southern bulgaria the seismotectonics of southern bulgaria and its surroundings have been reviewed and analysed and a catalogue has been compiled for the region we show that for southern bulgaria the seismicity characteristics focal mechanisms and stress inversions a confirm the hypothesis that the neotectonics of this region are similar to that of northern greece and the northern aegean sea with presently n s extension b indicate that the seismic energy release is mostly related to normal faulting with possibly some small strike slip component in the struma fault zone c result for this region in a frequency magnitude relation that suggest characteristic magnitudes around ms 7 0 and d indicate that seismic activity occurs in crustal fault zones rather than crisp fault planes a probabilistic seismic hazard analysis psha for southern bulgaria represents a typical case of seismic hazard for a tectonically complex region with large uncertainties in model parameters we show using a monte carlo approach that large uncertainties in seismic characteristics have relatively little effect on the psha output especially when compared with uncertainties associated with the attenuation function uncertainties in the seismotectonic model emerge strongest for the regions around pazardjik and jambol the western and eastern tails of the maritsa fault zone for six important economic centers in southern bulgaria we present the seismic hazard and their uncertainties with respect to attenuation and seismicity modelling our psha maps show for example regions with significant seismic hazard that exceed with 50 confidence a 1 annual probability of the peak ground acceleration exceeding 0 3 g future psha improvements for the region can be obtained by in order of decreasing significance a carefully mapped site responses or more accurate regional attenuation models b additional constraints on the seismic zones and c better constrained magnitude frequency distributions for example with independent regional strain rate information

a simplified spring block model of earthquakes the time interval between earthquakes is much larger than the actual time involved during slip in an individual event the authors have used this fact to construct a cellular automaton model of earthquakes this model describes the time evolution of a 2 d system of coupled masses and springs sliding on a frictional surface the model exhibits power law frequency size relations and can exhibit large earthquakes with the same scatter in the recurrence time observed for actual earthquakes

long term earthquake clustering summary we analyse statistically the long term properties of several instrumental earthquake catalogues complete catalogues exhibit both short and long term clustering for earthquakes of all depth ranges after accounting for the effect of short term clustering we find that in residual declustered catalogues long term clustering not periodicity characterizes the occurrence of all earthquakes shallow intermediate and deep the degree of clustering in residual catalogues is the same for earthquakes in different depth ranges circumstantial evidence indicates that the long term v ariation of seismicity is governed by a power law temporal distribution as in short term clustering it is scale invariant the fractal dimension of an earthquake set on the time axis is of the order of 0 8 0 9 therefore mainshock occurrence is closer to a stationary poisson process than standard aftershock sequences of shallow earthquakes

long term probabilistic forecasting of earthquakes we estimate long term worldwide earthquake probabilities by extrapolating catalogs of seismic moment solutions we base the forecast on correlations of seismic moment tensor solutions the forecast is expressed as a map showing predicted rate densities for earthquake occurrence and for focal mechanism orientation focal mechanisms are used first to smooth seismicity maps to obtain expected hazard maps and then to forecast mechanisms for future earthquakes several types of smoothing kernels are used in space domain we use the 1 distance kernel for the distribution of seismicity around any epicenter the kernel is parameterized using two adjustable parameters maximum distance and directivity distribution of seismicity around an epicenter with regard to the focal mechanism of an earthquake for temporal prediction we use the poisson hypothesis of earthquake temporal behavior we test these forecasts we use the first half of a catalog to smooth seismicity level and the second half of the catalog is used to validate and optimize the prediction to illustrate the technique we use available data in the harvard catalog of seismic moment solutions to evaluate seismicity maps for several seismic regions the method can be used with similar catalogs the technique is completely formal and does not require human operator intervention hence the prediction results can be objectively tested moreover the maps can be used as the poisson null hypothesis for testing by the likelihood method against any other prediction model which shares the same sample space the same zones time window and acceptance criteria

time intervals between characteristic earthquakes and correlations with smaller events an analysis based on a mechanical model of a fault certain correlations between characteristic events and smaller events are studied in the context of a spatially homogeneous mechanical model for a fault the model satisfies a one dimensional quasi linear wave equation in which the key nonlinearity is associated with the slipstick friction force at the interface between tectonic plates we find that the model gives rise to slipping events of all sizes the smaller events are consistent with the gutenberg richter statistical law whereas the characteristic events have a separate statistical distribution the crossover from smaller events to characteristic events coincides with a correlation length which sets the scale for clustering of smaller events before the characteristic rupture numerical results and scaling arguments relate the features of the distribution of characteristic events to the corresponding features of the distribution of smaller events as well as the length of the fault the distribution of time intervals between characteristic events has the distinguishing features of asymmetry and a finite upper cutoff the mean t and standard deviation of the time interval distribution are found to be related to features of the magnitude versus frequency distribution of smaller events and the coefficient of variation t is independent of the driving rate because this analysis relates properties of characteristic earthquakes to statistical features of smaller more numerous events as well as geometric features of the fault it may ultimately be useful for long term earthquake prediction

circum pacific seismic potential 1989 1999 the seismic potential for 96 segments of simple plate boundaries around the circum pacific region is presented in terms of the conditional probability for the occurrence of either large or great interplate earthquakes during the next 5 10 and 20 years i e 1989 1994 1989 1999 and 1989 2009 this study represents the first probabilistic summary of seismic potential on this scale and involves the comparison of plate boundary segments that exhibit varying recurrence times magnitudes and tectonic regimes presenting these data in a probabilistic framework provides a basis for the uniform comparison of seismic hazard between these differing fault segments as well as accounting for individual variations in recurrence time along a specific fault segment and uncertainties in the determination of the average recurrence time

the magnitude distribution of declustered earthquakes in southern california abstract the binned distribution densities of magnitudes in both the complete and the declustered catalogs of earthquakes in the southern california region have two significantly different branches with crossover magnitude near m 4 8 in the case of declustered earthquakes the b values on the two branches differ significantly from each other by a factor of about two the absence of self similarity across a broad range of magnitudes in the distribution of declustered earthquakes is an argument against the application of an assumption of scale independence to models of main shock earthquake occurrence and in turn to the use of such models to justify the assertion that earthquakes are unpredictable the presumption of scale independence for complete local earthquake catalogs is attributable not to a universal process of self organization leading to future large earthquakes but to the universality of the process that produces aftershocks which dominate complete catalogs

characteristic earthquake model and seismicity around late quaternary active faults in japan a total of 172 late quaternary active fault zones in japan are examined to determine whether the gutenberg richter relationship or the characteristic earthquake model more adequately describes the magnitude frequency distribution during one seismic cycle by combining seismicity data for more than 100 active fault zones at various stages in their seismic cycles we reduced the short instrumental observation period compared to the average recurrence interval in only 5 of the active fault zones were the number of observed events equal to or larger than the number of events expected by the gutenberg richter relationship the average and median frequency ratios of the number of observed events to the number of expected events from the gutenberg richter relationship are only 0 33 and 0 06 respectively suggesting that the characteristic earthquake model more appropriately describes the magnitude frequency distribution along the late quaternary active faults during one seismic cycle moreover the larger an average slip rate is or the shorter an average recurrence interval the larger the gap in magnitude tends to be between the characteristic earthquake and the largest among other events a fault zone with a shorter average recurrence interval and or a larger average slip rate has generally produced more earthquakes in the past or is likely to be at a more mature or developed stage thus these tendencies may reflect a change in the magnitude frequency distribution related to the maturity or development of fault zones

fault behavior and characteristic earthquakes examples from the wasatch and san andreas fault zones paleoseismological data for the wasatch and san andreas fault zones have led to the formulation of the characteristic earthquake model which postulates that individual faults and fault segments tend to generate essentially same size or characteristic earthquakes having a relatively narrow range of magnitudes near the maximum analysis of scarp derived colluvium in trench exposures across the wasatch fault provides estimates of the timing and displacement associated with individual surface faulting earthquakes at all of the sites studied the displacement per event has been consistently large measured values range from 1 6 to 2 6 m and the average is about 2 m on the basis of variability in the timing of individual events as well as changes in scarp morphology and fault geometry six major segments are recognized along the wasatch fault on the basis of the most likely number of surface faulting events 18 that have occurred on segments of the wasatch fault zone during the past 8000 years an average recurrence interval of 400 666 years with a preferred average of 444 years is calculated for the entire zone geologic data on the distribution of slip associated with prehistoric earthquakes and slip rates along the south central segment of the san andreas fault suggest that the m 8 1857 earthquake is a characteristic earthquake for this segment comparisons of earthquake recurrence relationships on both the wasatch and san andreas faults based on historical seismicity data and geologic data show that a linear constant b value extrapolation of the cumulative recurrence curve from the smaller magnitudes leads to gross underestimates of the frequency of occurrence of the large or characteristic earthquakes only by assuming a low b value in the moderate magnitude range can the seismicity data on small earthquakes be reconciled with geologic data on large earthquakes the characteristic earthquake appears to be a fundamental aspect of the behavior of the wasatch and san andreas faults and may apply to many other faults as well

frequency moment distribution of earthquakes in the aleutian arc a test of the characteristic earthquake model the frequency moment distribution of earthquakes is derived for discrete regions of the entire aleutian arc both for segments which have ruptured in historic times and those regions which have been identified as seismic gaps this distribution is then compared to the moment of the largest event in the respective region or for gaps the largest event which is likely to occur based on a plate kinematic model of accumulated moment data for this study are based upon three data sources instrumental data are utilized for the 18 yr subsequent to the establishment of the world wide standardized seismograph network wwssn data for events of magnitude 7 and greater have been carefully collected and are presumed to be complete for the time period 1899 to present the last data set is comprised of the largest event in each region either an actual earthquake or the moment estimate based on current plate slip rates data were normalized to the recurrence time of the largest event in the respective zone in all cases the data seriously underestimate the largest moment event indicating that a characteristic earthquake model is appropriate for individual fault zones however if the data are combined for the entire arc the largest event is closely predicted this indicates that a b value model may be utilized only for regions in which there is a distribution in the size of earthquake producing faults

statistics of characteristic earthquakes statistical methods are used to test the characteristic earthquake hypothesis several distributions of earthquake size seismic moment frequency relations are described based on the results of other researchers as well as my own tests evidence of the characteristic earthquake hypothesis can be explained either by statistical bias or statistical artifact since other distributions of earthquake size provide a simpler explanation for available information the hypothesis cannot be regarded as proven

slip patterns and earthquake populations along different classes of faults in elastic solids numerical simulations of slip instabilities on a vertical strike slip fault in an elastic half space are performed for various models belonging to two different categories the first category consists of inherently discrete cellular fault models such are used to represent fault systems made of segments modeled by numerical cells that can fail independently of one another their quasi independence is assumed to provide an approximate representation of strong fault heterogeneity due to geometric or material property disorder that can arrest ruptures at segment boundaries the second category consists of models having a well defined continuum limit these involve a fault governed by rate and state dependent friction and are used to evaluate what types of property heterogeneity could lead to the quasi independent behavior of neighboring fault segments assumed in the first category the cases examined include models of a cellular fault subjected to various complex spatial distributions of static to kinetic strength drops and models incorporating rate and state dependent friction subjected to various spatial distributions of effective stress normal stress minus pore pressure the results indicate that gradual effective stress variations do not provide a sufficient mechanism for the generation of observed seismic response strong and abrupt fault heterogeneity as envisioned in the inherently discrete category is required for the generation of complex slip patterns and a wide spectrum of event sizes strong fault heterogeneity also facilitates the generation of rough rupture fronts capable of radiating high frequency seismic waves the large earthquakes in both categories of models occur on a quasi periodic basis the degree of periodicity increases with event size and decreases with model complexity however in all discrete segmented cases the models generate nonrepeating sequences of earthquakes and the nature of the large quasi periodic events is highly variable the results indicate that expectations for regular sequences of earthquakes and or simple repetitive precursory slip patterns are unrealistic the frequency size fs statistics of the small failure episodes simulated by the cellular fault models are approximately self similar with b 1 2 and ba 1 where b and ba are b values based on magnitude and rupture area respectively for failure episodes larger than a critical size however the simulated statistics are strongly enhanced with respect to self similar distributions defined by the small events this is due to the fact that the stress concentrated at the edge of a rupture expanding in an elastic solid grows with the rupture size when the fault properties e g geometric irregularities are characterized by a narrow range of size scales the scaling of stress concentrations with the size of the failure zone creates a critical rupture area terminating the self similar earthquake statistics in such systems events reaching the critical size become on the average unstoppable and they continue to grow to a size limited by a characteristic model dimension when however the system is characterized by a broad spectrum of size scales the above phenomena are suppressed and the range of apparent self similar fs statistics is broad and characterized by average b and ba values of about 1 the simulations indicate that power law extrapolations of low magnitude seismicity will often underestimate the rate of occurrence of moderate and large earthquakes the models establish connections between features of fs statistics of earthquakes range of self similar regimes local maxima and structural properties of faults dominant size scales of heterogeneities dimensions of coherent brittle zones the results suggest that observed fs statistics can be used to obtain information on crustal thickness and fault zone structure

earthquake failure sequences along a cellular fault zone in a three dimensional elastic solid containing asperity and nonasperity regions numerical simulations of earthquake failure sequences along a discrete cellular fault zone are performed for a three dimensional 3 d model representing approximately the central san andreas fault the model consists of an upper crust overlying a lower crust and mantle region together defining an elastic half space with a vertical half plane fault the fault contains a region where slip is calculated on a uniform grid of cells governed by a static kinetic friction law and regions where slip is prescribed so as to represent tectonic loading aseismic fault creep and adjacent great earthquakes the computational region models a 70 km long and 17 5 km deep section of the san andreas fault to the nw of the great 1857 rupture zone different distributions of stress drops on failing computational cells are used to model asperity parkfield asperity and nonasperity fault regions the model is inherently discrete and corresponds to a situation in which a characteristic size of geometric disorder within the fault i e cell size here a few hundreds of meters is much larger than the nucleation size of the order of tens of centimeters to tens of meters based on slip weakening or state evolution slip distances the computational grid is loaded by a constant plate motion imposed at the lower crust upper mantle and creeping fault regions and by a staircase slip history imposed at the 1857 and 1906 rupture zones stress transfer along and outside the fault due to the imposed loadings and failure episodes along the computational grid is calculated using 3 d elastic dislocation theory the resulting displacement field in the computational region is compatible with geodetic and seismological observations only when the asperity and nonasperity regions are characterized by significantly different average stress drops the frequency magnitude statistics of the simulated failure episodes are approximately self similar for small events with b 1 2 the b value of statistics based on rupture area ba is about 1 but are strongly enhanced with respect to self similarity for events larger than a critical size this is interpreted as a direct manifestation of our 3 d elastic stress transfer calculations beyond certain rupture area and potency seismic moment divided by rigidity release values the event is usually unstoppable and it continues to grow to a size limited by a characteristic model dimension this effect is not accounted for by cellular automata and block spring models in which the adopted simplified stress transfer laws fail to scale properly with increasing rupture size the simulations suggest that local maxima in observed frequency magnitude statistics correspond to dimensions of coherent brittle zones such as the width of the seismogenic layer or the length of a fault segment bounded by barriers the analysis indicates that a single cell size representing approximately a single scale of geometric disorder cannot induce self similarity in a 3 d elastic model over a broad range of magnitudes a representation of geometric disorder covering a range of scales may thus be required to generate a wide domain of self similar gutenberg richter statistics our simulations show a great diversity in the mode of failure of the parkfield asperity the earthquakes themselves define an irregular sequence of events the modeling like many other discrete fault models suggests that expectations for periodic parkfield earthquakes and or simple precursory patterns repeating from one event to the other are unrealistic

an indication of time dependent seismic behavior an assessment of paleoseismic evidence from the arava fault israel abstract we discuss the implications of 56 kyr of paleoseismic data from a fault on the southern segment of the arava fault system in israel at least nine events are evident beginning 37 ka we study in detail the frequency magnitude relation for the fault and develop a bayesian analysis to compare the characteristic earthquake ce model and the gutenberg richter gr model our analysis leads to the conclusion that there was a change in seismic behavior at about 14 ka from 37 ka to 14 ka the seismic activity is best described by the ce model from 14 ka to the present there is no strong indication favoring one model over the other the earthquake record is somewhat more consistent with the classical gr equation than with the ce model if one does assume that the ce model is appropriate for the younger episode then there is evidence of a change in the characteristic magnitude thus there is evidence of a change in earthquake behavior on the fault segment 14 ka

general theory of the modified gutenberg richter law for large seismic moments abstract it is well known that the gutenberg richter power law distribution has to be modified for large seismic moments because of energy conservation and geometrical reasons several models have been proposed either in terms of a second power law with a larger b value beyond a crossover magnitude or based on a hard magnitude cut off or a soft magnitude cut off using an exponential taper since large scale tectonic deformation is dominated by the very largest earthquakes and since their impact on loss of life and properties is huge it is of great importance to constrain as much as possible the shape of their distribution we present a simple and powerful probabilistic theoretical approach that shows that the gamma distribution is the best model given the two hypotheses that the gutenberg richter power law distribution holds in absence of any condition and that one or several constraints are imposed either based on conservation laws or on the nature of the observations themselves the selection of the gamma distribution does not depend on the specific nature of the constraint we illustrate the approach with two constraints the existence of a finite moment release rate and the observation of the size of a maximum earthquake in a finite catalog our predicted soft maximum magnitudes compare favorably with those obtained by kagan for the flinn engdahl regionalization of subduction zones collision zones and midocean ridges

earthquake prediction a political problem earthquake prediction is an area of research of great scientific and public fascination the reason for this is not only that earthquakes can cause extremely large numbers of fatalities in a short time but also because earthquakes can have a large social and economic impact on society earthquake prediction in the sense of making deterministic predictions about the place time and magnitude of earthquakes may very well be fundamentally impossible however based on a variety of data earth scientists can make statements about the probability that earthquakes with a certain size will occur in a certain region over a specified time period in this context one speaks of earthquake forecasting a number of methods to achieve this are presented however it is not obvious how society should respond to these forecasts it is shown that there is a fundamental dilemma for decision makers that statements of scientists concerning earthquake occurrence either contain very specific information but are very uncertain or contain very general information but are very certain earthquake hazard can to a large extent be reduced by formulating and enforcing appropriate building codes however given the fact that the majority of the population that is threatened by earthquakes is living in the third world it is clear that this cannot easily be realized for these reasons earthquake prediction is not only a scientific problem it also has a complex political dimension

maximum earthquake magnitudes in the aegean area constrained by tectonic moment release rates summary seismic moment release is usually dominated by the largest but rarest events making the estimation of seismic hazard inherently uncertain this uncertainty can be reduced by combining long term tectonic deformation rates with short term recurrence rates here we adopt this strategy to estimate recurrence rates and maximum magnitudes for tectonic zones in the aegean area we first form a merged catalogue for historical and instrumentally recorded earthquakes in the aegean based on a recently published catalogue for greece and surrounding areas covering the time period 550 bc 2000 ad at varying degrees of completeness the historical data are recalibrated to allow for changes in damping in seismic instruments around 1911 we divide the area up into zones that correspond to recent determinations of deformation rate from satellite data in all zones we find that the gutenberg richter gr law holds at low magnitudes we use akaike s information criterion to determine the best fitting distribution at high magnitudes and classify the resulting frequency magnitude distributions of the zones as critical gr law subcritical gamma density distribution or supercritical characteristic earthquake model where appropriate we determine the ratio of seismic to tectonic moment release rate low values of 1 0 the seismic and tectonic moment release rates are then combined to constrain recurrence rates and maximum credible magnitudes in the range 6 7 7 6 m w where the results are well constrained based on extrapolating the short term seismic data with current earthquake data many of the tectonic zones show a characteristic distribution that leads to an elevated probability of magnitudes around 7 but a reduced probability of larger magnitudes above this value when compared with the gr trend a modification of the generalized gamma distribution is suggested to account for this based on a finite statistical second moment for the seismic moment distribution