volatile fluxes integrated over four decades at grimsvotn volcano iceland samples of the subglacial lake in the crater of the tholeiitic basaltic caldera grimsvotn in iceland were obtained by using a hot water drill to sink two boreholes through the 250 m thick ice shelf covering the lake the lake generally shows an increase in solutes with increased depth as solutes are added from the lake s bottom and dilute glacial meltwater is added continuously from above the crater lake temperature ranges from 0 c in the upper part to temperatures of 1 c to 4 c near the bottom of the lake the lake water ph ranges between 7 0 and 5 7 the crater lake is assumed to be closed with respect to volatile components released from subsurface magma except for periodic draining by jokulhlaups from the periodicity and water chemistry of the jokulhlaups we have estimated the volcano s average release rates of carbon sulfur chlorine and fluorine between 1954 and 1991 and corrected these rates for dissolution of bedrock into the lake water and seepage of solutes to groundwater the corrected mean release rates are 5 3 107 kg c yr 1 5 3 106 kg s yr 1 6 6 105 kg cl yr 1 and 1 5 105 kg f yr 1 the emission rate estimates for grimsvotn one of the most active volcanoes in iceland are the longest integrated estimates obtained for an active volcano and are equal to or lower than those of other major active volcanoes worldwide this difference may imply that published release rates for other volcanoes are overestimated because they are usually not integrated over time the values of the s cl and f cl ratios for noneruptive periods are 0 53 0 20 and 0 013 0 003 and for the two eruptive events are 0 69 and 2 14 and 0 034 and 0 041 respectively the response of the elemental ratios to eruptive events followed by the return to lower ratios supports the assumption of steady state because no long term accumulation of volatiles occurs the energy output from the volcano estimated from the amount of ice melted by hydrothermal heat is 4250 mw over the last four decades using the energy output to calculate magma solidification rates and maximum possible volatile release rates we observe that emissions of f and s are strongly suppressed at grimsvotn while a significant portion of available cl and c are released these calculations also reveal that coverage of a volcano by a glacier and subsequent raising of the water table may cause significant scrubbing of magmatic gases so that these gases do not reach the atmosphere

importance of small earthquakes for stress transfers and earthquake triggering 1 we estimate the relative importance of small and large earthquakes for static stress changes and for earthquake triggering assuming that earthquakes are triggered by static stress changes and that earthquakes are located on a fractal network of dimension d this model predicts that both the number of events triggered by an earthquake of magnitude m and the stress change induced by this earthquake at the location of other earthquakes increase with m as similar to 10 dm 2 the stronger the spatial clustering the larger the influence of small earthquakes on stress changes at the location of a future event as well as earthquake triggering if earthquake magnitudes follow the gutenberg richter law with b d 2 small earthquakes collectively dominate stress transfer and earthquake triggering because their greater frequency overcomes their smaller individual triggering potential using a southern california catalog we observe that the rate of seismicity triggered by an earthquake of magnitude m increases with m as 10 alpha m where alpha 1 05 0 05 we also find that the magnitude distribution of triggered earthquakes is independent of the triggering earthquake s magnitude m when alpha approximate to b small earthquakes are roughly as important to earthquake triggering as larger ones we evaluate the fractal correlation dimension d of hypocenters using two relocated catalogs for southern california the value of d measured for distances 0 1 r 5 km is d 1 54 for the shearer et al catalog and d 1 73 for the hauksson et al catalog the value of d reflects both the structure of the fault network and the nature of earthquake interactions by considering only those earthquake pairs with interevent times larger than 1000 days we can largely remove the effects of short term clustering then d approximate to 2 close to the value d 2 alpha 2 1 predicted by assuming that earthquake triggering is due to static stress the value d approximate to 2b implies that small earthquakes are as important as larger ones for stress transfers between earthquakes and that considering stress changes induced by small earthquakes should improve models of earthquake interactions

stress sensitivity of fault seismicity a comparison between limited offset oblique and major strike slip faults we present a new three dimensional inventory of the southern san francisco bay area faults and use it to calculate stress applied principally by the 1989 m 7 1 loma prieta earthquake and to compare fault seismicity rates before and after 1989 the major high angle right lateral faults exhibit a different response to the stress change than do minor oblique right lateral thrust faults seismicity on oblique slip faults in the southern santa clara valley thrust belt increased where the faults were unclamped the strong dependence of seismicity change on normal stress change implies a high coefficient of static friction in contrast we observe that faults with significant offset 50 100 km behave differently microseismicity on the hayward fault diminished where right lateral shear stress was reduced and where it was unclamped by the loma prieta earthquake we observe a similar response on the san andreas fault zone in southern california after the landers earthquake sequence additionally the offshore san gregorio fault shows a seismicity rate increase where right lateral oblique shear stress was increased by the loma prieta earthquake despite also being clamped by it these responses are consistent with either a low coefficient of static friction or high pore fluid pressures within the fault zones we can explain the different behavior of the two styles of faults if those with large cumulative offset become impermeable through gouge buildup coseismically pressurized pore fluids could be trapped and negate imposed normal stress changes whereas in more limited offset faults fluids could rapidly escape the difference in behavior between minor and major faults may explain why frictional failure criteria that apply intermediate coefficients of static friction can be effective in describing the broad distributions of aftershocks that follow large earthquakes since many of these events occur both inside and outside major fault zones

stochastic synthesis of earthquake catalogs a model of earthquake occurrence is proposed that is based on results of statistical studies of earthquake catalogs we assume that each earthquake generates additional a probability that depends on time as t 1 this assumption together with one regarding the independence of branching events on adjacent branches of the event tree is sufficient to permit the generation of complete catalogs of earthquakes that have the same time magnitude statistical properties as real earthquake catalogs if is about 0 5 the process generates sequences that have statistical properties similar to those for shallow earthquakes many well known relations are reproduced including the magnitude frequency law omori s law of the rate of aftershock and foreshock occurrence the duration of a recorded seismic event versus its magnitude the self similarity or lack of scale of rate of earthquake occurrence in different magnitude ranges etc a value of closer to 0 8 or 0 9 seems to simulate the statistical properties of intermediate and deep shocks a formula for seismic risk prediction is proposed and the implications of the model for risk evaluation are outlined the possibilities of the determination of long term risk from real or synthetic catalogs that have the property of self similarity are dim

faulting style controls for the space time aftershock patterns abstract to understand the complexity and thus to predict earthquake occurrence in size time and space seismicity patterns are characterized by two robust empirical laws the exponential distribution of magnitude and the power law decrease of aftershock rate over time these laws are known as the gutenberg richter law and the omori law respectively using global earthquake catalogs we resolve that on average the k aftershock productivity and the p value exponent of the power law decrease of aftershock rate over time are dependent on the mainshock faulting style strike slip events have a lower aftershock rate n and k values and a larger p value than thrust and normal events respectively within the epidemic type aftershock sequence model strong k n values are driven by a high branching ratio value n within the same framework a relatively higher n value for the thrust events also predicts the lower p value we observe for thrust events as compared to strike slip and normal faulting events respectively furthermore we observed that earthquake interactions through time and space are a function of the faulting style when measured by t the exponent of the power law decrease of earthquake density over space the t values of thrust events for different time windows always remain smaller than those of the strike slip events when changes in faulting styles are driven by stress pattern the anderson faulting theory predicts thrust faulting that requires somewhat larger stresses in absolute magnitude than do normal and strike slip faulting within the framework of rate and state friction law changes in the stress heterogeneity patterns reproduce the p value changes we observe our results suggest that only stress perturbations associated with mainshock rupture affect the productivity and decay rate over time of aftershocks

new empirical relationships among magnitude rupture length rupture width rupture area and surface displacement source parameters for historical earthquakes worldwide are compiled to develop a series of empirical relationships among moment magnitude m surface rupture length subsurface rupture length downdip rupture width rupture area and maximum and average displacement per event the resulting data base is a significant update of previous compilations and includes the additional source parameters of seismic moment moment magnitude subsurface rupture length downdip rupture width and average surface displacement each source parameter is classified as reliable or unreliable based on our evaluation of the accuracy of individual values only the reliable source parameters are used in the final analyses in comparing source parameters we note the following trends 1 generally the length of rupture at the surface is equal to 75 of the subsurface rupture length however the ratio of surface rupture length to subsurface rupture length increases with magnitude 2 the average surface displacement per event is about one half the maximum surface displacement per event and 3 the average subsurface displacement on the fault plane is less than the maximum surface displacement but more than the average surface displacement thus for most earthquakes in this data base slip on the fault plane at seismogenic depths is manifested by similar displacements at the surface log linear regressions between earthquake magnitude and surface rupture length subsurface rupture length and rupture area are especially well correlated showing standard deviations of 0 25 to 0 35 magnitude units most relationships are not statistically different at a 95 significance level as a function of the style of faulting thus we consider the regressions for all slip types to be appropriate for most applications regressions between magnitude and displacement magnitude and rupture width and between displacement and rupture length are less well correlated and have larger standard deviation than regressions between magnitude and length or area the large number of data points in most of these regressions and their statistical stability suggest that they are unlikely to change significantly in response to additional data separating the data according to extensional and compressional tectonic environments neither provides statistically different results nor improves the statistical significance of the regressions regressions for cases in which earthquake magnitude is either the independent or the dependent parameter can be used to estimate maximum earthquake magnitudes both for surface faults and for subsurface seismic sources such as blind faults and to estimate the expected surface displacement along a fault for a given size earthquake

seismic waveform attributes before and after the loma prieta earthquake scattering change near the earthquake and temporal recovery during 1987 1995 several clusters of nearly identical seismic events multiplets occurred near the loma prieta source region these multiplets allow us to investigate and demonstrate spatial and temporal changes in seismic wave character associated with the 1989 loma prieta main shock for seismogram pairs we use a moving window technique to compute coherencies depending on lapse time and frequency post loma prieta events have reduced coherencies with pre loma prieta events in a spatially limited region close to the loma prieta hypocenter while other paths remain nearly unaffected these changes gradually recover within a time interval of 5 years after the loma prieta earthquake a possible explanation for the time dependence is coseismically opened cracks which cause scattering increase for wavefields after the loma prieta event postseismic relaxation processes such as crack healing fluid diffusion or after deformations lead to progressive closure of these cracks with time after the main shock thus the scattering properties of the local crust approach the pre main shock state

response of the san andreas fault to the 1983 coalinga nunez earthquakes an application of interaction based probabilities for parkfield 1 the parkfield cholame section of the san andreas fault site of an unfulfilled earthquake forecast in 1985 is the best monitored section of the world s most closely watched fault in 1983 the m 6 5 coalinga and m 6 0 nunez events struck 25 km northeast of parkfield seismicity rates climbed for 18 months along the creeping section of the san andreas north of parkfield and dropped for 6 years along the locked section to the south right lateral creep also slowed or reversed from parkfield south here we calculate that the coalinga sequence increased the shear and coulomb stress on the creeping section causing the rate of small shocks to rise until the added stress was shed by additional slip however the 1983 events decreased the shear and coulomb stress on the parkfield segment causing surface creep and seismicity rates to drop we use these observations to cast the likelihood of a parkfield earthquake into an interaction based probability which includes both the renewal of stress following the 1966 parkfield earthquake and the stress transfer from the 1983 coalinga events we calculate that the 1983 shocks dropped the 10 year probability of a m 6 parkfield earthquake by 22 from 54 22 to 42 23 and that the probability did not recover until about 1991 when seismicity and creep resumed our analysis may thus explain why the parkfield earthquake did not strike in the 1980s but not why it was absent in the 1990s we calculate a 58 17 probability of a m 6 parkfield earthquake during 2001 2011 index terms 7223 seismology seismic hazard assessment and prediction 7230 seismology seismicity and seismotectonics 7260 seismology theory and modeling keywords coalinga earthquake parkfield stress change earthquake probability seismicity rate

properties of aftershock sequences in southern california the temporal behavior of 39 aftershock sequences in southern california 1933 1988 was modeled by the modified omori relation minimum magnitudes for completeness of each sequence catalog were determined and the maximum likelihood estimates of the parameters k p and c with the standard errors on each were determined by the ogata algorithm the b value of each sequence was also calculated many of the active faults in the region both strike slip and thrust were sampled the p values were graded in terms of the size of the standard error relative to the p value itself most of the sequences were modeled well by the omori relation many of the sequences had p values close to the mean of the whole data set 1 11 0 25 but values significantly different from the mean as low as 0 7 and as high as 1 8 exist no correlation of p with either the b value of the sequence or the mainshock magnitude was found the results suggest a direct correlation of p values is with surface heat flow with high values in the salton trough high heat flow and one low value in the san bernardino mountains and on the edge of the ventura basin both low heat flow the large fraction of the sequences with p values near the mean are at locations where the heat flow is near the regional mean 74 mw m2 if the hypothesis that aftershock decay rate is controlled by temperature at depth is valid the effects of other factors such as heterogeneity of the fault zone properties are superimposed on the background rate determined by temperature surface heat flow is taken as an indicator of crustal temperature at hypocentral depths but the effects on heat flow of convective heat transport and variations in near surface thermal conductivity invalidate any simple association of local variations in heat flow with details of the subsurface temperature distribution the interpretation is that higher temperatures in the aftershock source volume caused shortened stress relaxation times in the fault zone materials leading to a faster decay rate higher p value in 1967 mogi proposed such a relation on the basis of japanese data seismic velocity distributions published for southern california generally support the hypothesis with low velocities higher temperatures corresponding to high p values and vice versa

foreshocks aftershocks and remote triggering in quasi static fault models 1 we present the results of time space analysis of synthetic catalogs generated using a quasi static discrete fault model that is governed by rate and state dependent friction these analyses reveal that increase in the postmain shock earthquake production rate occurs over an area surrounding the main shock rupture with dimensions that are several times larger than the main shock dimensions we show that the increase in seismicity rate far from the main shock where the static stress changes imposed by the main shock were small is a consequence of multiple stress transfers and that the very distant aftershocks are not directly triggered by the main shock but that instead they are aftershocks of previous aftershocks snapshots of the fault state at progressive times prior to each main shock show that the regions which accelerated toward failure covered areas that were much larger than the final size of the main shock ruptures as a result as time approached the main shock time the seismicity rate in these regions increased while the b value of the earthquake size distribution decreased it has been previously suggested that remote seismicity rate increase could be triggered by the passage of seismic waves remote triggering in a quasi static model indicates that it is not necessary to invoke such a dynamic effect in order to explain distant aftershocks

statistical analysis of the spatial distribution of earthquakes variation of the spatial distribution of earthquakes before and after large earthquakes abstract we have investigated the spatial distribution of earthquakes using the polya eggenberger model and the morishita index which is used for the analysis of the spatial dispersion of bio species first we found that the spatial distribution of earthquakes is characterised by clustering when we divide the certain area into equal area meshes the frequency distribution of meshes with same number of events fits well to the polya eggenberger model on the basis of this result we examined the degree of spatial clustering of earthquakes by using the morishita index defined by i q i 1 q n i n i 1 n n 1 where q n and ni are the numbers of meshes total events and events of the i th mesh respectively the index i corresponds to the contagious coefficient plus 1 in the polya eggenberger statistics the dependence of i on the mesh size provides information about clustering we analysed the actual distribution patterns of earthquakes before and after the miyagi oki 1978 m 7 4 the tokachi oki 1968 m 7 9 and the nihonkai chubu 1983 m 7 7 earthquakes large scale clusters of about 50 100 km are dominant in the aftershock sequences after the aftershock activity earthquakes tend to distribute randomly prior to large earthquakes small patches of 10 20 km are created this statistical feature of the earthquake distribution seems to be related to the phenomena of the precursory clusterings of earthquakes doughnut patterns preseismic quiescence and foreshocks prior to large earthquakes

spatial variability of seismicity parameters in aftershock zones the spatial variability of the b value of the frequency magnitude relationship and the decay rate of aftershocks as described by the p value of the modified omori law is investigated by using dense spatial grids we map out the distribution of b and p values within the landers northridge morgan hill and kobe aftershock sequences considerable spatial variability is found with b values of independent subvolumes ranging from 0 6 to 1 4 and p values ranging from 0 6 to 1 8 these systematic and statistically highly significant differences argue that it is an oversimplification to assign one single p and b value to an aftershock sequence that extends up to 100 km the spatial distribution of these two parameters is compared with the slip distribution during the mainshock suggesting that the areas of largest slip release correlate with high b value regions we hypothesize that the frictional heat created during the event may influence the p value distribution within an aftershock zone while applied shear stress crack density and pore pressure govern the frequency magnitude distribution by investigating the frequency magnitude distribution separately for preseismic and postseismic periods for the morgan hill mainshock we find that only the volume in the vicinity of the highest slip release shows a significant increase in the b value which decays to premainshock values within a year surrounding areas of the aftershock zone show an approximately constant b value with time because the aftershock hazard after a mainshock depends strongly on both the b and p value we propose that aftershock hazard assessment can be improved by taking into account the spatial distribution of the parameters

stress triggering in thrust and subduction earthquakes and stress interaction between the southern san andreas and nearby thrust and strike slip faults 1 we argue that key features of thrust earthquake triggering inhibition and clustering can be explained by coulomb stress changes which we illustrate by a suite of representative models and by detailed examples whereas slip on surface cutting thrust faults drops the stress in most of the adjacent crust slip on blind thrust faults increases the stress on some nearby zones particularly above the source fault blind thrusts can thus trigger slip on secondary faults at shallow depth and typically produce broadly distributed aftershocks short thrust ruptures are particularly efficient at triggering earthquakes of similar size on adjacent thrust faults we calculate that during a progressive thrust sequence in central california the 1983 mw 6 7 coalinga earthquake brought the subsequent 1983 mw 6 0 nunez and 1985 mw 6 0 kettleman hills ruptures 10 bars and 1 bar closer to coulomb failure the idealized stress change calculations also reconcile the distribution of seismicity accompanying large subduction events in agreement with findings of prior investigations subduction zone ruptures are calculated to promote normal faulting events in the outer rise and to promote thrust faulting events on the periphery of the seismic rupture and its downdip extension these features are evident in aftershocks of the 1957 mw 9 1 aleutian and other large subduction earthquakes we further examine stress changes on the rupture surface imparted by the 1960 mw 9 5 and 1995 mw 8 1 chile earthquakes for which detailed slip models are available calculated coulomb stress increases of 2 20 bars correspond closely to sites of aftershocks and postseismic slip whereas aftershocks are absent where the stress drops by more than 10 bars we also argue that slip on major strike slip systems modulates the stress acting on nearby thrust and strike slip faults we calculate that the 1857 mw 7 9 fort tejon earthquake on the san andreas fault and subsequent interseismic slip brought the coalinga fault 1 bar closer to failure but inhibited failure elsewhere on the coast ranges thrust faults the 1857 earthquake also promoted failure on the white wolf reverse fault by 8 bars which ruptured in the 1952 mw 7 3 kern county shock but inhibited slip on the left lateral garlock fault which has not ruptured since 1857 we thus contend that stress transfer exerts a control on the seismicity of thrust faults across a broad spectrum of spatial and temporal scales

earthquake forecasting in diverse tectonic zones of the globe we present a simple method for long and short term earthquake forecasting estimating earthquake rate per unit area time and magnitude for illustration we apply the method to the pacific plate boundary region and the mediterranean area surrounding italy and greece our ultimate goal is to develop forecasting and testing methods to validate or falsify common assumptions regarding earthquake potential our immediate purpose is to extend the forecasts we made starting in 1999 for the northwest and southwest pacific to include somewhat smaller earthquakes and then adapt the methods to apply in other areas the previous forecasts used the cmt earthquake catalog to forecast magnitude 5 8 and larger earthquakes like our previous forecasts the new ones here are based on smoothed maps of past seismicity and assume spatial clustering our short term forecasts also assume temporal clustering an important adaptation in the new forecasts is to abandon the use of tensor focal mechanisms this permits use of earthquake catalogs that reliably report many smaller quakes with no such mechanism estimates the result is that we can forecast earthquakes at higher spatial resolution and down to a magnitude threshold of 4 7 the new forecasts can be tested far more quickly because smaller events are considerably more frequent also our previous method used the focal mechanisms of past earthquakes to estimate the preferred directions of earthquake clustering however the method made assumptions that generally hold in subduction zones only the new approach escapes those assumptions in the northwest pacific the new method gives estimated earthquake rate density very similar to that of the previous forecast

statistical physics approach to understanding the multiscale dynamics of earthquake fault systems 1 earthquakes and the faults upon which they occur interact over a wide range of spatial and temporal scales in addition many aspects of regional seismicity appear to be stochastic both in space and time however within this complexity there is considerable self organization we argue that the occurrence of earthquakes is a problem that can be attacked using the fundamentals of statistical physics concepts of statistical physics associated with phase changes and critical points have been successfully applied to a variety of cellular automata models examples include sandpile models forest fire models and particularly slider block models these models exhibit avalanche behavior very similar to observed seismicity a fundamental question is whether variations in seismicity can be used to successfully forecast the occurrence of earthquakes several attempts have been made to utilize precursory seismic activation and quiescence to make earthquake forecasts some of which show promise

systematic variations in recurrence interval and moment of repeating aftershocks 1 the recurrence intervals for 194 repeating clusters on the calaveras fault follow a power law decay relation with elapsed time after the 1984 m6 2 morgan hill california mainshock the decay rates of repeating aftershocks in the immediate vicinity of a high slip patch that failed during the mainshock systematically exceed those that are farther away the trend between relative moment and recurrence interval which is a measure of the fault healing rate varies systematically with depth and changes from negative to positive value as the distance between the repeating aftershock and the mainshock slip patch increases we speculate that high strain rate in the early postseismic period may cause transient embrittlement and strengthening of the deep repeating clusters in the areas adjacent to the mainshock slip patch resulting in large moments that decrease with time as the strain rate diminishes our observations suggest that systematic behavior of repeating aftershocks reflect variations in the fault zone rheology

the largest aftershock how strong how far away how delayed 1 proposed in the 1950 s bath s law states that the largest aftershock has a magnitude that is typically 1 2 less than that of the mainshock thirty years of the global earthquake catalog allow us to extend bath s law in time space and focal mechanism on average reverse faults have a smaller magnitude and distance from the mainshock to largest aftershock than strike slip faults the distribution of the time intervals between mainshocks and their largest aftershocks obeys power law but with a somewhat faster rate of decay than for aftershocks in general this implies that the largest aftershocks are more likely to occur earlier rather than later in a given sequence of aftershocks

observation of diffusion processes in earthquake populations and implications for the predictability of seismicity systems scale invariance either in space or in time has been shown in many papers to characterize earthquake distributions unfortunately little work has been dedicated to looking at the general space time scaling invariance of seismicity systems even though a better understanding of how the two domains spatial and temporal link together could help the development of the stochastic dynamical modeling of earthquake populations in this paper we report the observation of diffusion processes of temporally correlated seismic activity for three different data sets a mine creighton mine canada the long valley caldera in eastern california and a 7 year period of recorded seismic activity in southern california the observed subdiffusion processes are indicative of the general space time scaling of the system taking the form of a slow power law growth r t similar to t h of the mean distance r t between the main event arid the temporally correlated afterevents occuring after a delay t h is found on average to be small 0 1 for creighton mine 0 22 for the long valley caldera and 0 22 for the southern california main events with magnitude greater than or equal to 1 5 but fluctuates significantly from one main event to the other the diffusion is found to be intermittent non gaussian and multiscaling and except for the long valley caldera a systematic correlation between the sizes of the main event and subsequent afterevents and the growth exponent h is observed while classical viscous relaxation models e g elastic listhosphere plastic asthenosphere coupling or fluid flow triggered by sudden changes in pore pressure have been proposed to characterize this relaxation by homogeneous i e nonintermittent normal h 0 5 diffusion processes the direct implication of the reported results is that seismicity systems at spatial scales from meters to hundreds of kilometers and small microearthquakes in a mine to intermediate magnitudes relax spatiotemporally in a nonelastic way revealing the stochastic space time scale invariant nature of such systems since these diffusion processes correspond to a loss of information with time on the location of the main event they can be used to investigate the limits of predictability at all spatial scales of seismicity systems in terms of the spatiotemporal clustering of temporally correlated earthquakes

forecasting the evolution of seismicity in southern california animations built on earthquake stress transfer 1 we develop a forecast model to reproduce the distribution of main shocks aftershocks and surrounding seismicity observed during 1986 2003 in a 300 310 km area centered on the 1992 m 7 3 landers earthquake to parse the catalog into frames with equal numbers of aftershocks we animate seismicity in log time increments that lengthen after each main shock this reveals aftershock zone migration expansion and densification we implement a rate state algorithm that incorporates the static stress transferred by each m 6 shock and then evolves coulomb stress changes amplify the background seismicity so small stress changes produce large changes in seismicity rate in areas of high background seismicity similarly seismicity rate declines in the stress shadows are evident only in areas with previously high seismicity rates thus a key constituent of the model is the background seismicity rate which we smooth from 1981 to 1986 seismicity the mean correlation coefficient between observed and predicted m 1 4 shocks the minimum magnitude of completeness is 0 52 for 1986 2003 and 0 63 for 1992 2003 a control standard aftershock model yields 0 54 and 0 52 for the same periods four m 6 0 shocks struck during the test period three are located at sites where the expected seismicity rate falls above the 92 percentile and one is located above the 75 percentile the model thus reproduces much but certainly not all of the observed spatial and temporal seismicity from which we infer that the decaying effect of stress transferred by successive main shocks influences seismicity for decades finally we offer a m 5 earthquake forecast for 2005 2015 assigning probabilities to 324 10 10 km cells

omori law for eruption foreshocks and aftershocks 1 using the 1973 2009 worldwide catalogs for m 4 8 seismicity and vei 0 volcano eruptions we compare the properties of seismic damage patterns contemporary with eruption with the properties of foreshocks and aftershocks of classic tectonic earthquakes using superposed epoch analysis we demonstrated that the seismicity rate after eruption decreases as a power law similar to the omori law of earthquake aftershocks we further show that a complete mapping of omori law of earthquake aftershocks onto eruption aftershocks does exist as rerup t k0 10 vei t c p volcanic explosivity index vei being an empirical measure that exponentially scales with eruption size close to 0 4 is the value reported for m 5 6 5 earthquakes from the same catalog the p values are in the 0 7 range i e robustly smaller than the 0 9 1 0 range for earthquake aftershocks we estimated in the volcanic area k value for eruptions is 2 10 times smaller than for earthquakes and it scales with vei values all those parameters characterize a slower damage relaxation after eruptions than after earthquakes when earthquakes foreshock rates are proposed to be independent of the main shock magnitude we resolved a strong increase in foreshock rates including an increase of the p value of the inverse omori law prior eruptions with eruption size these patterns all emerging from mean field analysis are evidence of the volcanic eruptions being contemporary with a stochastic brittle damage in the earth crust these results suggest a generic damage relaxation within the earth crust as power law distributed after or before events the loading and relaxation exponents and the damage rate emerge as being controlled by the loading rate as reported during lab scale experiments the more impulsive the loading i e km s for the slip velocity during earthquakes against km h for dyke propagation the faster the relaxation 0 9 1 0 p values for earthquakes aftershocks against 0 7 for eruptions aftershocks before eruptions the larger the impending events the higher the p values all the observations converge toward the amplitude and frequency of the stress step to drive the omori law parameters as qualitatively reproduced by the rate and state friction law response of brittle crust faults to loading

decay of aftershock density with distance does not indicate triggering by dynamic stress the most predictable earthquakes are aftershocks which invariably follow mainshocks so what triggers aftershocks it was recently argued controversially that the decay of aftershocks with distance from the main earthquake could only be explained by dynamic triggering keith richards dinger and colleagues have tested this hypothesis and conclude that the observed decay can be better explained by static triggering resolving whether static or dynamic stress triggers most aftershocks and subsequent mainshocks is essential to understand earthquake interaction and to forecast seismic hazard it has recently been argued that the decay of aftershocks with distance from the main earthquake could be explained only by dynamic triggering this hypothesis has now been tested the conclusion being that the observed decay can be better explained by static triggering resolving whether static1 2 3 or dynamic4 5 6 7 8 stress triggers most aftershocks and subsequent mainshocks is essential to understand earthquake interaction and to forecast seismic hazard9 felzer and brodsky10 examined the distance distribution of earthquakes occurring in the first five minutes after 2 m 3 and 3 m 4 mainshocks and found that their magnitude m 2 aftershocks showed a uniform power law decay with slope 1 35 out to 50 km from the mainshocks from this they argued that the distance decay could be explained only by dynamic triggering here we propose an alternative explanation for the decay and subject their hypothesis to a series of tests none of which it passes at distances more than 300 m from the 2 m 3 mainshocks the seismicity decay 5 min before the mainshocks is indistinguishable from the decay five minutes afterwards indicating that the mainshocks have no effect at distances outside their static triggering range omori temporal decay the fundamental signature of aftershocks is absent at distances exceeding 10 km from the mainshocks finally the distance decay is found among aftershocks that occur before the arrival of the seismic wave front from the mainshock which violates causality we argue that felzer and brodsky10 implicitly assume that the first of two independent aftershocks along a fault rupture triggers the second and that the first of two shocks in a creep or intrusion driven swarm triggers the second when this need not be the case

global omori law decay of triggered earthquakes large aftershocks outside the classical aftershock zone 1 triggered earthquakes can be large damaging and lethal as evidenced by the1999 shocks in turkey and the 2001 earthquakes in el salvador in this study earthquakes with ms 7 0 from the harvard centroid moment tensor cmt catalog are modeled as dislocations to calculate shear stress changes on subsequent earthquake rupture planes near enough to be affected about 61 of earthquakes that occurred near defined as having shear stress change 0 01 mpa the ms 7 0 shocks are associated with calculated shear stress increases while 39 are associated with shear stress decreases if earthquakes associated with calculated shear stress increases are interpreted as triggered then such events make up at least 8 of the cmt catalog globally these triggered earthquakes obey an omori law rate decay that lasts between 7 11 years after the main shock earthquakes associated with calculated shear stress increases occur at higher rates than background up to 240 km away from the main shock centroid omori s law is one of the few time predictable patterns evident in the global occurrence of earthquakes if large triggered earthquakes habitually obey omori s law then their hazard can be more readily assessed the characteristic rate change with time and spatial distribution can be used to rapidly assess the likelihood of triggered earthquakes following events of ms 7 0 i show an example application to the m 7 7 13 january 2001 el salvador earthquake where use of global statistics appears to provide a better rapid hazard estimate than coulomb stress change calculations

the influence of tectonic regimes on the earthquake size distribution a case study for italy an edited version of this paper was published by agu copyright 2010 american geophysical union

foreshocks explained by cascades of triggered seismicity 1 the observation of foreshocks preceding large earthquakes and the suggestion that foreshocks have specific properties that may be used to distinguish them from other earthquakes have raised the hope that large earthquakes may be predictable among proposed anomalous properties are the larger proportion than normal of large versus small foreshocks the power law acceleration of seismicity rate as a function of time to the mainshock and the spatial migration of foreshocks toward the mainshock when averaging over many sequences using southern california seismicity we show that these properties and others arise naturally from the simple model that any earthquake may trigger other earthquakes without arbitrary distinction between foreshocks aftershocks and mainshocks we find that foreshock precursory properties are independent of the mainshock size this implies that earthquakes large or small are predictable to the same degree as seismicity rate is predictable from past seismicity by taking into account cascades of triggering the cascades of triggering give rise naturally to long range and long time interactions which can explain the observations of correlations in seismicity over surprisingly large length scales

theory of time dependent rupture in the earth at a velocity x which is a well defined function of k this propagation is stable and quasi static and is referred to as subcritical crack growth we shall use the terms stable quasistatic and subcritical to mean propagation at velocities much less than the sonic velocities of the medium this behavior results from stress induced corrosion at the crack tip the principal corrodent for the present application being h20 this behavior has been firmly established in the laboratory for mode i tensile cracks in a wide variety of materials ineluding silicates and silicate glasses see cholz 1968a 1972a martin 1972 wiederhorn and bolz 1970 atkinson 1979 lawn and wilshaw 1975 knott 1973 the form of the relationship between k and x does not vary significantly with the material only the parameters in the law vary as an example we show in figure 1 data on subcritical crack growth in quartz after atkinson 1979 the empirical relationship is found to take the form