long range earthquake forecasting with every earthquake a precursor according to scale scaling relations previously derived from examples of the precursory scale increase before major earthquakes show that the precursor is a long term predictor of the time magnitude and location of the major earthquake these relations are here taken as the basis of a stochastic forecasting model in which every earthquake is regarded as a precursor the problem of identifying those earthquakes that are actually precursory is thus set aside at the cost of limiting the strength of the resulting forecast the contribution of an individual earthquake to the future distribution of hazard in time magnitude and location is on a scale determined through the scaling relations by its magnitude provision is made for a contribution to be affected by other earthquakes close in time and location e g an aftershock may be given low weight using the new zealand catalogue the model has been fitted to the forecasting of shallow earthquakes exceeding magnitude 5 75 over the period 1965 2000 it fits the data much better than a baseline poisson model with a location distribution based on proximity to the epicenters of past earthquakes further the model has been applied with unchanged parameters to the california region over the period 1975 2001 there also it performs much better than the baseline model fitted to the same region over the period 1951 1974 the likelihood ratio is 1015 in favor of the present model these results lend credence to the precursory scale increase phenomenon and show that the scaling relations are pervasive in earthquake catalogues the forecasting model provides a new baseline model against which future refinements and other proposed models can be tested it may also prove to be useful in practice its applicability to other regions has still to be established

the critical slip distance for seismic faulting experimentally based friction laws1 2 have been found to predict virtually the entire range of observed behaviour of natural faults3 4 these laws contain a critical slip distance l which plays a key role in determining the degree of fault instability the size of the zone of earthquake nucleation the frictional breakdown width and the proportion of pre and post seismic slip to co seismic slip in laboratory measurements l is found to be about 10 5m but modelling results show that it must be about 10 2m if natural earthquake behaviour is to be simulated the discovery that fault surfaces are fractal over the scale range 10 5 105 refs 5 6 even for faults with large net slip has confused the problem of scaling this parameter from laboratory experiments to natural faults because fractal surfaces have no characteristic length here i show that geometrically unmated fractal surfaces when in contact under a normal load develop a characteristic length in their contact because long wavelength apertures close under load whereas short wavelength apertures may remain open this critical distance may be identified with l and calculations based on fault topography data show that at seismogenic depths it will be in the range anticipated from the earthquake modelling studies

scaling of the critical slip distance for seismic faulting with shear strain in fault zones theoretical and experimentally based laws for seismic faulting contain a critical slip distance1 5 dc which is the slip over which strength breaks down during earthquake nucleation on an earthquake generating fault this distance plays a key role in determining the rupture nucleation dimension6 the amount of premonitory and post seismic slip7 10 and the maximum seismic ground acceleration1 11 in laboratory friction experiments d c has been related to the size of surface contact junctions2 5 12 thus the discrepancy between laboratory measurements of dc 10 5m and values obtained from modelling earthquakes 10 2m has been attributed to differences in roughness between laboratory surfaces and natural faults5 this interpretation predicts a dependence of dc on the particle size of fault gouge2 breccia and wear material but not on shear strain here we present experimental results showing that dc scales with shear strain in simulated fault gouge our data suggest a new physical interpretation for the critical slip distance in which dc is controlled by the thickness of the zone of localized shear strain as gouge zones of mature faults are commonly 102 103 m thick12 17 whereas laboratory gouge layers are 1 10 mm thick our data offer an alternative interpretation of the discrepancy between laboratory and field based estimates of dc

an integrated approach to define new plays in mature oil basins the example from the middle magdalena valley basin colombia an integrated approach to detect new areas of potential interest associated with stratigraphic traps in mature basins is presented the study was carried out in the middle magdalena valley basin colombia the workflow integrates outcrop and subsurface interpretations of facies activity of faults and distribution of depocenters and paleocurrents and makes use of them to construct a three dimensional exploration scale geocellular facies model of the basin the outcrop and well log sedimentological analysis distinguished facies associations of alluvial fan overbank floodplain and channel fill the last one constituting the reservoir rock the seismic analysis showed that tectonic activity was coeval with the deposition of the productive units in the basin and that the activity ended earlier before the middle miocene along the western margin than along the eastern margin paleogeographic reconstructions depict transverse and longitudinal fluvial systems alluvial fans adjacent to the active basin margins and floodplain facies dominating the structural highs and the southwestern depositional limit these reconstructions provided statistical data lateral variograms to construct the model the exploration scale facies model depicts the complete structure of the basin in three dimensions and the gross distribution of the reservoir and seal rocks the predictive capability of the model was evaluated positively and the model was employed to detect zones of high channel fill facies probability that form bodies that are isolated or that terminate upward in pinchouts or are truncated by a fault our approach can prove helpful in improving general exploration workflows in similar settings

spatial modelling and uncertainty assessment of pyroclastic cover thickness in the sorrento peninsula assessing spatial variability of soil thickness is a critical issue for understanding and predicting slope processes the present work was aimed at estimating the spatial scales at which the variation of pyroclastic cover thickness occurs in a sample area in the sorrento peninsula italy stochastic simulation was used to understand the spatial variability of pyroclastic cover thickness on mount pendolo and to assess its spatial uncertainty in the study area covering about 0 7 km2 thickness measurements were collected using electrical resistivity tomography profiles continuous core drillings and steel rod penetrometric tests variographic analysis revealed the occurrence of an anisotropic behaviour along the n50 and n140 directions in the latter anisotropic direction a nested variogram was fitted including 1 a long range component which could be related to large scale factors like the curvature of the slope and contributing area and 2 a shorter scale variation which is probably associated with the occurrence of denudation processes or to the articulate cover bedrock interface to assess the spatial variability and uncertainty of pyroclastic cover thickness a stochastic simulation algorithm was used and 500 equally probable images of cover thickness were yielded the results showed that a better thickness distribution map can be drawn by simulating the data collected on the slope and at the footslope separately the approach also allowed delineating the areas characterized by greater uncertainty suggesting supplementary measurements to further improve the cover thickness distribution model thus reducing the uncertainty

revised estimates for the probabilities of earthquakes following observation of unreliable precursors abstract this paper treats in a statistical manner the class of geophysical observations that sometimes are precursors to a large earthquake but at other times occur apparently unrelated to any earthquakes in time or space each such observation is handled by associating it with the largest ensuing earthquake in a definite time and spatial window then the probability that the observation is useful is estimated from the difference between this extreme value distribution and the long term average extreme value distribution for the same region this probability that the precursor is useful can then be incorporated into calculations of the revised probability of an earthquake following observation of one a trivial case or several unreliable precursors to derive the revised probability of a significant earthquake the model takes full account of the magnitude distribution of earthquakes and of discrete levels of precursor observations the united states earthquake prediction program is still many years from being able to obtain the full benefits of the model however the model suggests useful statistics which the program should gather on unreliable precursors

generalized omori law for aftershocks and foreshocks from a simple dynamics a theory of the time dependence of earthquake foreshocks and aftershocks is presented the theory involves the response to sudden forcing of a dynamics of self driven acceleration to failure the empirically observed omori law which says that the rate of aftershocks as a function of time falls as a power law in time is derived theoretically the exponent of the falloff in time is shown to generically give a value close to one for rapidly accelerating dynamics to see if the theory is consistent with other features of real data foreshocks and aftershocks of small magnitude mainshocks are analyzed in a catalogue of real earthquakes results show that the spatial and temporal distribution of aftershocks is separable into a dependence on space and a dependence on time that the spatial distribution of aftershocks is consistent with the hypothesis that stress changes from the mainshock cause aftershocks and that the number of foreshocks approaches the number of aftershocks as the magnitude of the mainshock becomes smaller

periodic energy release in the new madrid seismic zone the annual release of strain energy by earthquakes in the new madrid seismic zone as represented by the strain factor is calculated and cumulated when the main annual energy release in the form of a linear regression is subtracted from the data the residual curve suggests that the energy release rate is cyclical with a period of 30 to 35 yr for earthquakes of magnitude 5 5 or less furthermore the current rate is well below normal and may be expected to significantly increase in the near future although the increase may be in the form of several small earthquakes the historical pattern suggests that at least one earthquake of body wave magnitude 5 0 to 5 2 may be anticipated

non gaussian data expansion in the earth sciences a formalism is proposed to generate alternative equiprobable images of an underlying population spatial distribution the resulting images honour data values at their locations and reflect important characteristics of the data such as patterns of spatial connectivity of extreme values the formalism capitalizes on a coding of all information available into bits 0 l which are then processed all together accounting for their patterns of correlation in space such common coding allows accounting for qualitative information possibly of an interpretative nature to complement the usually sparse hard data available in earth sciences applications the approach proposed although of a probabilistic nature does not call for any gaussian type modelling or hypothesis

geostatistical earth modeling of cyclic depositional facies and diagenesis in siliciclastic and carbonate reservoirs depositional facies are often described as being organized in cyclic successions that are overprinted by diagenesis most reservoir modelling workflows are not able to reproduce stochastically such patterns herein a novel geostatistical method is developed to model depositional facies architectures that are rhythmic and cyclic together with superimposed diagenetic facies the method uses truncated pluri gaussian random functions constrained by transiograms cyclicity is defined as an asymmetric ordering between facies and its direction is given by a three dimensional vector called shift this method is illustrated on two case studies outcrop data of the triassic latemar carbonate platform northern italy are used to model shallowing upward facies cycles in the vertical direction a satellite image of the modern bermuda platform interior is used to model facies cycles in the windward to leeward lateral direction as depositional facies architectures are modelled using two gaussian random functions a third gaussian random function is added to model diagenesis thereby depositional and diagenetic facies can exhibit spatial asymmetric relations the method is applied in two regions of the latemar carbonate platform that experience two different types of diagenetic transformation syn depositional dolomite formation and post depositional fracture related diagenesis the method can also incorporate proportion curves to model non stationary facies proportions this is illustrated in cretaceous shallow marine sandstones and mudstones book cliffs utah for which cyclic facies and diagenetic patterns are constrained by embedded transition probabilities

stochastic simulation methods for characterization of lithoclasses in carbonate reservoirs abstract the construction of a reservoir model begins with the geology specifically a geological conceptual model sub division into layers top and bottom limits surfaces and characterization of rock types or facies within the layers to model the geology in heterogeneous case studies of which carbonate reservoirs are a good example conceptual and deterministic models are unable to adequately represent the internal geometry and for this reason stochastic models are most particularly used mainly for the spatial characterization of rock types this paper presents a comparison of bi point geostatistical simulation methods for characterization of lithoclasses making use of a carbonated reservoir as a case study to cope with the geological complexity and to assist in understanding the internal distribution of properties the lithoclasses were derived from cores based on their lithology petrophysical properties and capillary pressure and subsequently extended to log data five simulation methodologies able to deal with categorical variables are compared in a multi phase framework 1 truncated gaussian simulation posterior conditioning and classification of simulated probabilities based on local and global proportions tgspc 2 truncated gaussian simulation posterior conditioning and classification using simulated annealing tgspc sa 3 sequential indicator simulation with correction for local probabilities sis 4 simulated annealing post processing of sequential indicator simulation images sis sa and 5 probability field simulation pfs matched to experimental data theoretical multi phase variogram models and proportions are observed as well as the presence of artefacts to evaluate the range of uncertainty of the simulated images 30 realizations are generated and entropy and average geobody volumes connected blocks belonging to the same lithoclass are computed and compared

seismic activity in north aegean region as middle term precursor of calabrian earthquakes abstract a comparative analysis of seismicity patterns in the italian and balkan regions both related to the dynamics of the adriatic plate has revealed a noticeable correlation between the time patterns of seismic energy release in the calabrian arc southern italy and in the northernmost aegean region the systematic occurrence of damaging earthquakes in the calabrian arc within a few years after the most intense seismic periods in the north aegean zone may be useful for middle term earthquake prediction

time variable factors in earthquake hazard abstract the development of a model for time variable hazard estimation involves both subjective and objective elements in eight identifiable stages the final stage adoption of the model for practical use is reached only after the conclusion of a successful performance test at the present state of knowledge such a test consists in measuring the performance of the time variable model against that of the present static model i e seismic zoning precursory phenomena provide a basis for the quantification of the time variable hazard provided the data are sufficient to allow certain intermediate quantities the probability distributions for location magnitude and time of occurrence the valid alarm rate and the failure rate to be evaluated similar quantification should also be attainable on the basis of various types of regularity which have been suggested in the occurrence of large earthquakes but the details of these models have yet to be fully ascertained

fault heterogeneity and the connection between aftershocks and afterslip whether aftershocks originate directly from the mainshock and surrounding stress environment or from afterslip dynamics is crucial to the understanding of the nature of aftershocks we build on a classical description of the fault and creeping regions as two blocks connected elastically subject to different friction laws we show analytically that upon introduction of variability in the fault plane s static friction threshold a non trivial stick slip dynamics ensues in particular we support the hypothesis that the aftershock occurrence rate is proportional to the afterslip rate up to a corrective factor that is also computed thus the omori law originates from the afterslip s logarithmic evolution in the velocity strengthening region we confirm these analytical results with numerical simulations generating synthetic catalogs with statistical features in good agreement with instrumental catalogs in particular we recover the gutenberg richter law with a realistic b value b 1 when coulomb stress thresholds obey a power law distribution

demarcation and scaling of long term seismogenesis a space time envelope of minor seismicity related to major shallow earthquakes is identified from observations of the long term precursory scale increase phenomenon which quantifies the three stage faulting model of seismogenesis the envelope which includes the source area of the major earthquake is here demarcated for 47 earthquakes from four regions with tectonic regimes ranging from subduction to continental collision and continental transform the earthquakes range in magnitude from 5 8 to 8 2 and include the 24 most recent mainshocks of magnitude 6 4 and larger in the san andreas system of california the hellenic arc region of greece and the new zealand region together with the six most recent mainshocks of magnitude 7 4 and larger in the pacific arc region of japan also included are the destructive earthquakes that occurred at kobe japan 1995 magnitude 7 2 izmit turkey 1999 magnitude 7 4 and w tottori japan 2000 magnitude 7 3 the space a p in the space time envelope is optimised with respect to the scale increase while the time t p is the interval between the onset of the scale increase and the occurrence of the earthquake a strong correlation is found between the envelope a p t p and the magnitude of the earthquake hence the conclusion that the set of precursory earthquakes contained in the envelope is intrinsic to the seismogenic process yet a p and t p are correlated only weakly with each other suggesting that a p is affected by differences in statical conditions such as geological structure and lithology and t p by differences in dynamical conditions such as plate velocity among other scaling relations predictive regressions are found between on the one hand the magnitude level of the precursory seismicity and on the other hand both t p and the major earthquake magnitude hence the method as here applied to retrospective analysis is potentially adaptable to long range forecasting of the place time and magnitude of major earthquakes

spatial connectivity in a highly heterogeneous aquifer from cores to preferential flow paths 1 this study investigates connectivity in a small portion of the extremely heterogeneous aquifer at the macrodispersion experiment made site in columbus mississippi a total of 19 fully penetrating soil cores were collected from a rectangular grid of 4 m by 4 m detailed grain size analysis was performed on 5 cm segments of each core yielding 1740 hydraulic conductivity k estimates three different geostatistical simulation methods were used to generate 3 d conditional realizations of the k field for the sampled block particle tracking calculations showed that the fastest particles as represented by the first 5 to arrive converge along preferential flow paths and exit the model domain within preferred areas these 5 fastest flow paths accounted for about 40 of the flow the distribution of preferential flow paths and particle exit locations is clearly influenced by the occurrence of clusters formed by interconnected cells with k equal to or greater than the 0 9 decile of the data distribution 10 of the volume the fraction of particle paths within the high k clusters ranges from 43 to 69 in variogram based k fields some of the fastest paths are through media with lower k values suggesting that transport connectivity may not require fully connected zones of relatively homogenous k the high degree of flow and transport connectivity was confirmed by the values of two groups of connectivity indicators in particular the ratio between effective and geometric mean k on average about 2 and the ratio between the average arrival time and the arrival time of the fastest particles on average about 9 are consistent with flow and advective transport behavior characterized by channeling along preferential flow paths

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

postseismic relaxation driven by brittle creep a possible mechanism to reconcile geodetic measurements and the decay rate of aftershocks application to the chi chi earthquake taiwan we evaluate the effect of coseismic stress changes on the fault slip at midcrustal depth assuming a velocity strengthening brittle creep rheology we show that this model can help reconcile the time evolution of afterslip as measured from geodesy with aftershocks decay we propose an analytical expression for slip of the brittle creeping fault zone bcfz that applies to any dynamic or static stress perturbation including shear stress and normal stress changes the model predicts an initial logarithmic increase of slip with time postseismic slip rate decays over a characteristic time t r a that does not depend on the amplitude of the stress perturbation and it asymptotically joins the long term creep imposed by interseismic stress buildup given that the seismicity rate might be considered proportional to the sliding velocity of the bcfz the model predicts a decay rate of aftershocks that follows omori s law with a mathematical formalism identical to that of dieterich 1994 although based on a different mechanical rationale our model also differs from dieterich s model in that it requires that aftershock sequences and deep afterslip as constrained from geodetic measurements should follow the same temporal evolution we test this for the 1999 chi chi earthquake m w 7 6 and find that both sets of data are consistent with a model of afterslip due to the response of the bcfz the inferred relaxation time t r 8 5 years requires a value for a log v being the coefficient of friction in the range between 1 3 10 3 and 10 2

foreshock statistics and their possible relationship to earthquake prediction in the italian region this study focuses on the foreshocks of earthquake sequences recorded by the italian national seismological network between 1975 and 1991 we consider as foreshocks events exceeding a given threshold magnitude that follow a period of quiescence and come before a mainshock occurring within a given time distance range the total number of potential foreshocks identified by the algorithm depends on the size and the duration of the predefined quiescence area whereas the number of mainshocks preceded by foreshocks depends also on the size of the area in which the event is expected and the duration of the alarm period our aim was to optimize the choice of the parameters defining potential foreshocks as precursors of stronger earthquakes in order to improve their validity and reliability a preliminary investigation carried over the whole italian territory allowed the definition of zones where foreshocks mainshocks series are likely to occur one of these zones is an area of about 32 000 km2 in central italy including a total of 2671 events of m 2 5 where there is a significant tendency of moderate shocks to be followed at short distance and in short time by larger shocks our method would lead to issuing 63 alarms with the optimal definition of foreshocks as events of magnitude exceeding 3 0 after at least 80 days of quiescence in an area of 140 km radius the rate of occurrence for mainshocks of magnitude exceeding 4 0 during the following 48 hours in the specified area of 30 km radius is 6 of 23 events the corresponding probability gain is about 150 for comparison another larger zone po valley with 453 events of m 2 5 exhibits only a rate of 1 of 82 precursors in this area most events are single shocks our analysis shows that the foreshock activity can be regarded as a significant earthquake precursor so suggesting that real time observation of seismicity can be used to improve the quality of an earthquake prediction system

earthquakes as self organized critical phenomena a cellular automation model with threshold elements previously proposed by bak et al 1988 which generates 1 f noise and self organizes into a critical state is studied as a model for earthquake occurrence the model explains some of fractal features of earthquakes such as the power law distribution of the size of the earthquake the model is modified so that every earthquake may trigger aftershocks the modified trigger model explains other fractal features of earthquakes such as the power law decay of aftershock frequency and the power law decay of aftershock frequency and the power law correlation of the hypocenter distribution

physical model of aftershock temporal behaviour abstract the aim of the model is to describe the temporal behaviour of cumulative seismic moment released in aftershock sequences it therefore constitutes an alternative approach with respect to the omori and utsu laws which model the number of events against time static fatigue is assumed to be the principal explanation of the aftershock temporal behaviour as a result aftershocks can originate at a stress intensity factor lower than the fracture toughness under the condition that the mainshock causes a redistribution of stress the initial stress condition of the aftershock sequence at mainshock origin time t0 can be considered as the superposition of the stress before the mainshock and of the stress step d caused by the dynamic rupture of the mainshock the model can be written in the form s t d rt ln t where s t is the cumulative stress drop at time t after the mainshock t the temperature r the universal gas constant and a constant dependent on material type the model is derived from the empirical static fatigue law t s exp u rt widely applied in fracture mechanics is the stress s a constant and the other parameters as above the fit of the model to five aftershock sequences obtained by linear regression analysis is quite good with the r2 greater than 0 85 for all the sequences but the imperial valley sequence where r2 0 7 the results seem to favour the hypothesis that the decay of the rate of seismic moment release depends on temperature in agreement with other evidences based on the evaluation of the decay rate of omori law but in contrast to some static fatigue results obtained in laboratory tests on granite rocks the scarcity of field data on underground temperature does not allow any definitive conclusion about this subject

a mechanism for spatial and temporal earthquake clustering 1 the gutenberg richter law states that the size frequency distribution of earthquakes follows a power law this trend is usually justified using spring block models where slips with the appropriate statistics of sizes have been numerically observed however prominent spatial and temporal clustering features of earthquakes as those implied by the omori law of aftershocks are not accounted for by this kind of model unless they are complemented with ad hoc assumptions such as stress recovery laws after slip events or the phenomenological rate and state equations to describe friction we show that when a mechanism of structural relaxation is incorporated into a spring block model realistic earthquake patterns following the gutenberg richter and omori laws are obtained moreover features well known from laboratory friction experiments such as velocity weakening and increase of static friction with contact time appear as a consequence of the relaxational mechanism as well without making any a priori assumptions on the velocity dependence of the friction force in the model in this way our model shows that a single physical mechanism may be a unifying concept behind the gutenberg richter and omori laws and the rate and state equations of rock friction

impact of geologic heterogeneity on recharge estimation using environmental tracers numerical modeling investigation this paper presents a numerical modeling approach for assessing the impacts of geologic heterogeneity on groundwater recharge estimates derived from environmental tracers common to many of the environmental tracer methods used to infer recharge in arid environments is an assumption of one dimensional vertical downward flow of water and solutes however in recent years there has been a growing recognition that fluid flux rates through geologic materials can be spatially variable owing to heterogeneities in porous media properties previous studies have suggested that local flow directions are dependent upon the stratigraphic and sedimentologic characteristics of the medium and may not be vertical even when application of water at the surface is spatially uniform and hydraulic gradients are vertical consequently environmental tracer movement will also be spatially variable and the one dimensional assumption invoked to interpret unsaturated environmental tracer concentration profiles may be unrealistic two different numerical simulation experiments were performed to investigate the problems with using environmental tracers to infer recharge the first involves simulation of flow and tracer transport through heterogeneous flat lying media and the second considers dipping layered anisotropic media the results of these simulations show that recharge inferred using environmental tracer methods is also highly spatially variable and that recharge estimates obtained by tracer profiles tend to overestimate recharge and should be considered accurate only to within an order of magnitude particularly in situations with significant media heterogeneity consequently recharge estimates obtained from tracer profiles should be critically evaluated with regard to impacts of spatially variable flow

comparative performance of time invariant long range and short range forecasting models on the earthquake catalogue of greece 1 time invariant long range and short range forecasting models were fitted to the earthquake catalogue of greece for magnitudes 4 0 and greater to optimize their ability to forecast events of magnitude 6 0 and greater in the period 1966 1980 the models considered were stationary spatially uniform and spatially varying poisson models a long range forecasting model based on the precursory scale increase phenomenon with every earthquake regarded as a precursor according to scale and epidemic type short range forecasting models with spatially uniform and spatially varying spontaneous seismicity each of the models was then applied to the catalogue for 1981 2002 and their forecasting performance was compared using the log likelihood statistic the long range forecasting model performed substantially better than the time invariant models and the short range forecasting models performed substantially better again the results show that the information value to be gained from modeling temporal and spatial variation of earthquake occurrence rate at both long and short range is much greater than can be gained from modeling spatial variation alone

waves of destruction in the east indies the wichmann catalogue of earthquakes and tsunami in the indonesian region from 1538 to 1877

stochastic slip predictable model for earthquake occurrences recent geophysical studies have indicated that an earthquake recurrence interval and the size of the preceding event are positively correlated this observation is the basis for the deterministic time predictable recurrence model of shimazaki and nakata using the basic assumptions of the time predictable recurrence model we develop a stochastic model of earthquake occurrence that incorporates temporal dependence this paper discusses the formulation of the model and the effect of including temporal dependence hazard estimates for a section of the san andreas fault near parkfield where data has suggested time predictable behavior are obtained for illustrative purposes comparisons are made with the poisson model results indicate that currently used poisson models may give lower estimates of the seismic hazard when there has been a seismic gap of the various sensitivity analyses performed it is observed that slip rate has the largest effect on exceedence probabilites computed from the stochastic time predictable model therefore accurate determinations of slip rates both seismic and aseismic can substantially reduce the uncertainty in seismic hazard estimates

estimates of long term probabilities for future great earthquakes in the aleutians we compute probabilities for future great earthquakes in the aleutian arc probability distributions are fitted to recurrence periods of great aleutian evens m sub w or 7 8 since 1788 given a probability distribution and data of the last grat earthquake in each arc segment time dependent conditional probabilities are determined for future periods of interest we obtain for the next two decades high probabilities 99 to 30 for great earthquakes in the shumagin yakataga unalaska and kommandorski seismic gaps these probabilities are higher than for any other assessed region of the u s believed to be capable of great earthquakes low probabilities 17 to 9 are found for segments that ruptured most recently in 1965 1964 and 1957 recurrence periods for great earthquakes measure on average about 80 years but vary substantially whether recurrence periods for great aleutian earthquakes follow a normal log normal or any other probability distribution is not resolved because in most arc segments the known seismic record embraces at best one or two recurrences the resulting uncertainty affects the magnitude of estimated probabilities especially in seismic gaps that have not ruptured for a long time in some instances a normal distribution yields a three times higher probability than the correspondingmore log normal distribution less

increased mean depth of earthquakes at parkfield the mean focal depth of earthquakes in the northern and southern parts of the parkfield segment of the san andreas fault was greater than long term average by 1km during the last 4 years approximately it is proposed that this is a precursor to the next characteristic parkfield earthquake because the same phenomenon occurred before at least three other mainshocks along the san andreas fault in the northern segment the increase in mean depth is mostly due to reduction of shallow activity in the southern segment deeper than usual activity seems to have increased within about 8 km from the 1966 epicenter no significant increase of mean depth is observed but seismic quiescence wyss et al 1990a and a decrease in deformation rate wyss et al 1990b was documented these observations are interpreted to suggest that the precursory process at parkfield varies along strike and that the next rupture may extend further north than the last one

conditional probabilities for the recurrence of large and great interplate earthquakes along the mexican subduction zone abstract time dependent conditional probabilities for the recurrence of large and great interplate earthquakes along the mexican subduction zone are presented for time intervals of 5 10 and 20 yr duration i e 1986 1991 1986 1996 and 1986 2006 at present the central oaxaca 97 3 to 97 7 w ometepec san marcos 98 2 to 99 5 w and central guerrero 100 to 101 w segments stand out as having the highest probability for the recurrence of large and great earthquakes in the near future segmentation of the margin is delineated by the rupture zones of the most recent earthquakes occurring in each area for segments of the mexican margin with one or more known recurrence intervals probability estimates are based on the observed average recurrence time for each segment and the lognormal probability distribution function use of a generic distribution function nishenko and buland 1987 allows a more stable estimate of average recurrence times than are available from a few observations a long term prediction time window is also defined based on the 90 per cent confidence interval for our estimates of the recurrence time use of a predetermined confidence interval conveys valuable additional information as to the precision and information content of the forecast for those segments of the margin with only one prior event and hence no historically observed recurrence times repeat times are estimated by extrapolating the observed recurrence time behavior in oaxaca subject to the assumptions that recurrence time scales only as a function of the ratio of seismic displacement and convergence rate and that all events are characterized as simple sources i e involve the rupture of a single asperity

probabilities of occurrence of large plate rupturing earthquakes for the san andreas san jacinto and imperial faults california 1983 2003 the san andreas san jacinto and imperial faults in california are divided into 19 segments conditional probabilities are calculated that a particular segment will be the site of a large plate rupturing earthquake i e an event that breaks the entire down dip extent of the seismogenic zone during the next 20 years the sizes of such events which account for most of the slip that occurs seismically appear to vary greatly for different segments of these faults repeat time of large shocks coseismic displacement moment release rupture length and seismic magnitude appear to correlate with one another and to be a function of the tectonic style of different parts of those fault zones tectonic inhomogeneities on a scale of about 1 to 100 km are much larger than displacement in any single seismic event and may be regarded as being invariant in their effects upon earthquake generation over many cycles of large shocks it is this invariance that appears to lead to a given segment of a fault rupturing repeatedly in events of nearly the same size since repeat time varies however for a given segment of a fault a simple probabilistic approach is used to forecast the likelihood of large future earthquakes for each segment using as input the time of the last large shock the average recurrence time and the standard deviation of time intervals between events dates of the last large shocks are available for most of the segments investigated repeat times are estimated from times of historic and prehistoric events tectonic similarity and times calculated from coseismic displacement in the last large shock divided by a rate of fault motion or strain buildup the standard deviation of time intervals divided by the average repeat time is close to 1 3 for three fault segments in california for which data are available on historic and prehistoric earthquakes that normalized value is adopted for all calculations of conditional probability magnitudes and seismic moments of future plate rupturing events are estimated for each fault segment several of the segments have well constrained probabilities for rupture during the next 20 years whereas others have large uncertainties eight of the segments constituting about 40 of the total lengths of the three faults have moderate to high probability and thus should be instrumented and studied extensively so as to provide shorter time warnings in some cases two adjacent segments may be nearly in phase in their loading history and may break in a single event the segment of the san andreas fault from opposite san jose to san juan bautista which ruptured less than 1 5 m in 1906 and which probably also broke in 1838 is calculated to have a moderate to high probability of an earthquake of magnitude 6 to during the next 20 years a 325 km section of the southern san andreas between tejon pass and the salton sea has about a 25 chance of rupturing in a shock of magnitude near 8 during the next 20 years all the other segments have only a small chance i e less than 5 to 10 of rupturing in an event of magnitude near 8 during that interval

aftershocks resulting from creeping sections in a heterogeneous fault 1 we show that realistic aftershock sequences with space time characteristics compatible with observations are generated by a model consisting of brittle fault segments separated by creeping zones the dynamics of the brittle regions is governed by static kinetic friction 3d elastic stress transfer and small creep deformation the creeping parts are characterized by high ongoing creep velocities these regions store stress during earthquake failures and then release it in the interseismic periods the resulting postseismic deformation leads to aftershock sequences following the modified omori law the ratio of creep coefficients in the brittle and creeping sections determines the duration of the postseismic transients and the exponent p of the modified omori law

foreshocks and time dependent earthquake hazard assessment in southern california the probability that an earthquake in southern california m 3 0 will be followed by an earthquake of larger magnitude within 5 days and 10 km i e will be a foreshock is 6 0 5 per cent 1 s d and is not significantly dependent on the magnitude of the possible foreshock between m 3 and m 5 the probability that an earthquake will be followed by an m 5 0 main shock however increases with magnitude of the foreshock from less than 1 per cent at m 3 to 6 5 2 5 per cent 1 s d at m 5 the main shock will most likely occur in the first hour after the foreshock and the probability that a main shock will occur decreases with elapsed time from the occurrence of the possible foreshock by approximately the inverse of time thus the occurrence of an earthquake of m 3 0 in southern california increases the earthquake hazard within a small space time window several orders of magnitude above the normal background level

model of earthquake energy periodicity in the alpide himalayan seismotectonic belt abstract the statistical model based on the autocorrelation function reveals only the stationarity of the time series but no periodic effect in the occurrence of the shallow shocks in any of the seismotectonic zones of the alpide himalayan belt on the other hand the autocorrelation function of the time series of the total seismic energy released annually by shallow earthquakes indicates periodicities ranging from 3 to 12 years which are significant at 5 level in most of the risk zones of the alpide belt whereas with the exception of the pamirs hindukush and tibet regions the periodicities indicated in the himalayan region are not tenable even at 10 significance level

long term seismogenic process for major earthquakes in subduction zones abstract a qualitative physical process for the long term seismogenesis of major earthquakes in subduction zones is proposed on the basis of quantitative empirical evidence that swarms mainshocks and aftershocks are closely related phenomena the relations which have been identified in the comprehensive long term catalogues of new zealand and japan represent swarms as predictors of mainshocks with respect to location time and magnitude clustering of swarms and of mainshock aftershock events is allowed for with a database of 15 sequences of swarms mainshocks and aftershocks tests are being conducted with the object of refining the relations and evaluating them as a possible means of practical synoptic forecasting three sequences have culminated in major earthquakes since the tests began and the systematic study now relates a total of 36 swarms with 29 mainshock aftershock events these empirical results strengthen and quantify the connection between swarms and major earthquakes which several authors have demonstrated by means of numerical physical modelling the proposed seismogenic process includes swarms mainshocks and aftershocks as separate event stages which are related by predictability interevent conditions are specified according to the mogi criteria for the medium cracks at which fractures subsequently occur constitute nonuniformity in the mogi sense and post earthquake healing restores uniformity where the gutenberg richter relation occurs it is accepted as possible evidence of deterministic chaos and unpredictability as a corollary the process is noncyclical the principle of scaling is held to apply except when modified by large scale boundaries in the medium subduction zones and some other localities where water is abundant are indicated by the main empirical studies as favourable to the occurrence of swarms fluid overpressuring is therefore proposed as a mechanism for the self triggering of swarms and this is supported by additional examples of the predictive relations occurring in conditions of high fluid pressure including the vicinity of large man made reservoirs the process can be tested by systematic studies in other subduction regions given adequate catalogues for quantifying the algorithm it also has implications for other tectonic environments with swarms replaced by cognate more protracted seismicity precursors

afterslip and aftershocks in the rate and state friction law istituto nazionale di geofisica e vulcanologia italy ingv centre national de la recherche scientifique cnrs exxonmobil upstream research company

similar power laws for foreshock and aftershock sequences in a spring block model for earthquakes we introduce a crust relaxation process in a continuous cellular automaton version of the burridge and knopoff 1967 model the most important model parameters are the level of conservation and the ratio of the crust relaxation time to the tectonic reloading time in correspondence with the original spring block model the modified model displays a robust power law distribution of event sizes the principal new result obtained with our model is the spatiotemporal clustering of events exhibiting several characteristics of earthquakes in nature large events are followed by aftershock sequences obeying the omori 1894 law and preceded by localized foreshocks which are initiated after a time period of seismic quiescence while we observe a considerable variability of precursory seismicity we find that the rate of foreshocks increases on average according to a power law with an exponent q which is in good agreement with the exponent p of the omori law in contrast to other events the distribution of foreshock sizes is characterized by a significantly smaller richter b value our model reproduces simultaneously the empirically observed values of the power law exponents the richter b p and q and their variability

integrated facies modeling in unconventional reservoirs using a frequentist approach example from a south texas field abstractmodeling of rock types or facies in unconventional reservoirs presents numerous challenges that are not encountered in conventional reservoirs because the exploitation of unconventional reservoirs frequently relies on the use of large numbers of long data poor horizontal wells routine tasks in conventional reservoirs such as petrophysical analyses and rock physics diagnostics become problematic in unconventional reservoirs due to insufficient data similarly the inability to generate synthetic seismograms in the horizontal section of the wells makes seismic well ties and time depth conversions more difficult our approach for facies modeling in unconventional reservoirs attempts to overcome these challenges by using the abundant log information available along the vertical pilot well to extract discrete facies indicators facies flags from logging while drilling information along the horizontals after performing a time depth conversion constrained by geosteering information we estimate fa

the effect of loading rate on static friction and the rate of fault healing during the earthquake cycle the seismic cycle requires that faults strengthen heal between earthquakes and the rate of this healing process plays a key role in determining earthquake stress drop1 2 3 4 rupture characteristics5 6 and seismic scaling relations2 3 4 7 frictional healing as evidenced by increasing static friction during quasi stationary contact between two surfaces1 8 9 10 11 12 is considered the mechanism most likely to be responsible for fault strengthening2 3 13 14 previous studies however have shown a large discrepancy between laboratory and seismic field estimates of the healing rate2 3 4 14 15 in the laboratory rock friction changes by only a few per cent per order of magnitude change in slip rate whereas seismic stress drop increases by a factor of 2 to 5 per order of magnitude increase in earthquake recurrence interval but in such comparisons it is assumed that healing and static friction are independent of loading rate here i summarize laboratory measurements showing that static friction and healing vary with loading rate and time as expected from friction theory16 17 18 applying these results to seismic faulting and accounting for differences in laboratory seismic and tectonic slip rates i demonstrate that post seismic healing is expected to be retardedfor a period of several hundred days following an earthquake in agreement with recent findings from repeating earthquakes13 14 19 20

implications of rate and state friction for properties of aftershock sequence quasi static inherently discrete simulations 1 dieterich 1994 modeled the response to a stress step of a population of faults governed by rate and state dependent friction this model assumes that aftershocks nucleate over areas on the fault that at the time of the main shock are already accelerating toward failure and disregards the effect of interactions among aftershocks the main objective of this study is to examine consequences of relaxing these underlying assumptions aftershock activity is simulated using an inherently discrete earthquake fault model with a fault surface governed by an approximate constitutive friction law similar to the one used by dieterich we find that the governing equations in nondimensional form are a function of three main parameters and explore the effect of these parameters on the simulated catalogs we derive a simple expression for the time dependent seismicity response to a stress step that approximates the effect of multiple interactions among aftershocks as a time dependent stressing rate close match is found between the simulated seismicity response to a stress step and that predicted analytically however the numerical simulations show that the effect of the main shock is not only to raise the local seismicity rate but also to systematically modify the earthquake size distribution as a result the actual seismicity rate change early during the aftershock sequence may be higher than that predicted whereas seismicity rate late in the sequence may be lower than that predicted such a modification of the earthquake size distribution can explain observations of lower b values immediately following a stress step

spatial and temporal forecasting of large earthquakes in a spring block model of a fault summary we study a recently proposed statistical physics model of earthquake dynamics that includes stress relaxation in the plates as a fundamental ingredient the model is known to reproduce manyrealisticfeaturesofseismicphenomena suchas thegutenberg richterlawfortheevent size distribution the omori law for aftershocks and an overall velocity weakening dependence of the average friction force here we analyse the dynamics of the model in detail in order to investigate to what extent the occurrence of large events in the model can be anticipated we systematically find that large events occur in fault patches where strain accumulation has exceeded some threshold value the spatial extent of these patches which correlate with the magnitude offorthcoming events canbe calculated ifthe strainstateofthe systemissupposed tobe known inaddition wefind that some large events are preceded by well defined precursor activity thisallows inafractionofcases tocomplementtheforecastofmagnitudeandspatial location with a sensible prediction of time of occurrence although our work is exclusively limited to the numerical model analysed we argue that it gives new breath to earthquake forecast techniques that combine the historical analysis of seismic activity with a search of appropriate precursor activity

simulation of non gaussian space random functions for modeling transport in groundwater the recent developments and successful applications of covariance related stochastic methods to groundwater fields experiments suggest that further efforts in developing spatial characterization methods are warranted one area that deserves further attention is that of characterizing multimodal distributions such as fractured rock masses dolomite rocks with dissolution channels and sand shale formations traditionally used covariance functions may not be enough to fully characterize spatial continuity applications where the pattern of spatial continuity depends on the specific magnitude level of the attribute for example hydraulic conductivity alternative models based on multiple indicator covariances or mixture of populations offer greater flexibility applying such models to the case of perfect stratification a stochastic simulations is proposed which allows generating different realizations all sharing the same vertical conductivity covariance yet differing by other spatial statistics and leading to widely different transport characteristics a mere covariance based approach would have failed to distinguish between these alternatives investigation of tracer transport in bimodal stratified formations suggests a dependence of the mean advection velocity on the dispersion coefficients as a result of a mechanism that enhance longitudinal dispersion directly proportional to lateral pore scale dispersion and entails a diversion of a substantial portion of the plume into the low conductivity layers more this mechanism may not be evident when the class specific spatial structures of the conductivities are ignored less

test of the eepas forecasting model on the japan earthquake catalogue the eepas every earthquake a precursor according to scale model is a method of forecasting earthquakes based on the notion that the precursory scale increase phenomenon occurs at all scales in the seismogenic process the rate density of future earthquake occurrence is computed directly from past earthquakes in the catalogue the eepas model has previously been fitted to the new zealand earthquake catalogue and successfully tested on the california catalogue

space time clustering of seismic events and hazard assessment in the zabrze bielszowice coal mine poland the results of the statistical analysis of seismic activity recorded in the zabrze bielszowice coal mine in poland are presented in this article the monitoring was conducted by a small network consisting of four triaxial geophones deployed in vertical holes in the roof for over 1000 seismic events recorded during the two month s experiment the location of sources was realized the seismic sources were mostly located ahead of the active face of the longwall since the first day of the monitoring cluster analysis was sequentially performed for increasing number of sources at the end of the experiment 31 clusters were identified they consisted of different numbers of events and were separated in space about 40 of the events were not included in the clusters for each large cluster hazard analysis was separately performed the hazard function evaluated for the largest cluster was compared with hypocenters of high energy tremors e 1000 j recorded by the geophones in that area for some cases recorded tremors occurred after an abrupt decrease of hazard function but only one of them was located in the vicinity of the appropriate cluster we concluded that for the analyzed cluster a correlation between evaluated hazard function and time occurrences of the high energy tremors existed except for one case there is no space correlation between analyzed clusters and high energy tremors

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

seismic potential for large and great interplate earthquakes along the chilean and southern peruvian margins of south america a quantitative reappraisal the seismic potential of the chilean and southern peruvian margins of south america is reevaluated to delineate those areas or segments of the margin that may be expected to experience large or great interplate earthquakes within the next 20 years 1984 2004 long term estimates of seismic potential or the conditional probability of recurrence within a specified period of time are based on 1 statistical analysis of historic repeat time data using weibull distributions and 2 deterministic estimates of recurrence times based on the time predictable model of earthquake recurrence both methods emphasize the periodic nature of large and great earthquake recurrence and are compared with estimates of probability based on the assumption of poisson type behavior the estimates of seismic potential presented in this study are long term forecasts only as the temporal resolution or standard deviation of both methods is taken to range from 15 to 25 of the average or estimated repeat time at present the valparaiso region of central chile 32 35 s has a high potential or probability of recurrence in the next 20 years coseismic uplift data associated with previous shocks in 1822 and 1906 suggest that this area may have already started to rerupture in 1971 1973 average repeat times also suggest this area is due for a great shock within the next 20 years flanking segments of the chilean margin coquimbo illapel 30 32 s and talca concepcion 35 38 s presently have poorly constrained but possibly quite high potentials for a series of large or great shocks within the next 20 years in contrast the rupture zone of the great 1960 earthquake 37 46 s has the lowest potential along the margin and is not expected to rerupture in a great earthquake within the next 100 years in the north the seismic potentials of the mollendo arica 17 18 s and arica antofagasta 18 24 s segments which last ruptured during great earthquakes in 1868 and 1877 are also high but poorly constrained

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

independence precursors and earthquake hazard abstract the problem of combining the hazard from precursors of several different types has been found to be tractable only when assumptions of independence between precursors of different types are made it is shown that the usual conditional independence assumptions are not realistic for continuous time hazard estimation an alternative approach is presented in which the main assumptions are that the proportion of earthquakes unrelated to precursors of a particular type is independent of information on precursors of other types and that false alarms of a particular type occur at a constant rate independently of earthquakes and other alarms the method applies to hazard estimation within a domain defined by limits however wide of location and magnitude and to a general probability distribution for the time of occurrence of an earthquake following a given alarm of a particular type the problem is simplified when the precursors concerned have widely differing time 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