analyzing earthquake clustering features by using stochastic reconstruction 1 on the basis of the epidemic type aftershock sequence etas model and the thinning procedure this paper gives the method about how to classify the earthquakes in a given catalogue into different clusters stochastically the key points of this method are the probabilities of one event being triggered by another previous event and being a background event making use of these probabilities we can reconstruct the functions associated with the characteristics of earthquake clusters to test a number of important hypotheses about the earthquake clustering phenomena we applied this reconstruction method to the shallow seismic data in japan and also to a simulated catalogue the results show the following assertions 1 the functions for each component in the formulation of the space time etas model are good enough as a first order approximation for describing earthquake clusters 2 a background event triggers less offspring in expectation than a triggered event of the same magnitude 3 the magnitude distribution of the triggered event depends on the magnitude of its direct ancestor 4 the diffusion of the aftershock sequence is mainly caused by cascades of individual triggering processes while no evidence shows that each individual triggering process is diffusive and 5 the scale of the triggering region is still an exponential law as formulated in the model but not the same one for the expected number of offspring

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

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

probabilistic forecasting of earthquakes we present long term and short term forecasts for magnitude 5 8 and larger earthquakes we discuss a method for optimizing both procedures and testing their forecasting effectiveness using the likelihood function our forecasts are expressed as the rate density that is the probability per unit area and time anywhere on the earth our forecasts are for scientific testing only they are not to be construed as earthquake predictions or warnings and they carry no official endorsement for our long term forecast we assume that the rate density is proportional to a smoothed version of past seismicity using the harvard cmt catalogue this is in some ways antithetical to the seismic gap model which assumes that recent earthquakes deter future ones the estimated rate density depends linearly on the magnitude of past earthquakes and approximately on a negative power of the epicentral distance out to a few hundred kilometres we assume no explicit time dependence although the estimated rate density will vary slightly from day to day as earthquakes enter the catalogue the forecast applies to the ensemble of earthquakes during the test period it is not meant to predict any single earthquake and no single earthquake or lack of one is adequate to evaluate such a hypothesis we assume that 1 per cent of all earthquakes are surprises assumed uniformly likely to occur in those areas with no earthquakes since 1977 we have made specific forecasts for the calendar year 1999 for the northwest pacific and southwest pacific regions and we plan to expand the forecast to the whole earth we test the forecast against the earthquake catalogue using a likelihood test and present the results our short term forecast updated daily makes explicit use of statistical models describing earthquake clustering like the long term forecast the short term version is expressed as a rate density in location magnitude and time however the short term forecasts will change significantly from day to day in response to recent earthquakes the forecast applies to main shocks aftershocks aftershocks of aftershocks and main shocks preceded by foreshocks however there is no need to label each event and the method is completely automatic according to the model nearly 10 per cent of moderately sized earthquakes will be followed by larger ones within a few weeks

foreshock occurrence before large earthquakes rates of foreshock occurrence involving shallow m 6 and m 7 mainshocks and m 5 foreshocks were measured in two worldwide catalogs over 20 year intervals the overall rates observed are similar to ones measured in previous worldwide and regional studies when they are normalized for the ranges of magnitude difference they each span the observed worldwide rates were compared to a generic model of earthquake clustering based on patterns of small and moderate aftershocks in california the aftershock model was extended to the case of moderate foreshocks preceding large mainshocks overall the observed worldwide foreshock rates exceed the extended california generic model by a factor of 2 significant differences in foreshock rate were found among subsets of earthquakes defined by their focal mechanism and tectonic region with the rate before thrust events higher and the rate before strike slip events lower than the worldwide average among the thrust events a large majority composed of events located in shallow subduction zones had a high foreshock rate while a minority located in continental thrust belts had a low rate these differences may explain why previous surveys have found low foreshock rates among thrust events in california especially southern california while the worldwide observations suggests the opposite california lacking an active subduction zone in most of its territory and including a region of mountain building thrusts in the south reflects the low rate apparently typical for continental thrusts while the worldwide observations dominated by shallow subduction zone events are foreshock rich if this is so then the california generic model may significantly underestimate the conditional probability for a very large m 8 earthquake following a potential m 7 foreshock in cascadia the magnitude differences among the identified foreshock mainshock pairs in the harvard catalog are consistent with a uniform distribution over the range of observation

dependence of earthquake recurrence times and independence of magnitudes on seismicity history the fulfillment of a scaling law for earthquake recurrence time distributions is a clear indication of the importance of correlations in the structure of seismicity in order to characterize these correlations we measure conditional recurrence time and magnitude distributions for worldwide seismicity as well as for southern california during stationary periods disregarding the spatial structure we conclude that the relevant correlations in seismicity are those of the recurrence time with previous recurrence times and magnitudes in the latter case the conditional distribution verifies a scaling relation depending on the difference between the magnitudes of the two events defining the recurrence time in contrast with our present resolution magnitude seems to be independent on the history contained in the seismic catalogs except perhaps for southern california for very short time scales less than about 30 min for the magnitude ranges analyzed

spatial aftershock distribution effect of normal stress we study the spatial clustering of shallow aftershock hypocenters with respect to focal mechanisms of mainshocks we use the harvard centroid moment tensor cmt global catalog the preliminary determination of epicenters pde earthquake list the california institute of technology u s geological survey catalog of earthquakes in southern california and a catalog of focal mechanisms for all earthquakes since 1850 in southern california with magnitude larger than 6 we need to account for possible systematic bias in hypocenter distribution due to the geometry of seismogenic zones especially that of subduction zones we also select only strike slip earthquakes from the catalogs to investigate aftershock clustering in circumstances more favorable for direct observation we compare the spatial distribution of hypocenters before each strong earthquake with the distribution during the first 250 days after the earthquake and for the time interval extending beyond 250 days if the friction coefficient in the coulomb criterion is positive one expects that after a strong earthquake aftershocks and other earthquakes would concentrate in the direction of the p axis dilatational quadrant rather than in the direction of the t axis compression quadrant such correlations have been pointed out previously for selected earthquakes sequences but is such correlation a general feature of earthquake occurrence we study spatial earthquake distributions before and after each event for several choices of focal sphere partition cutoff magnitude focal mechanisms of large events time periods distance from a mainshock etc although some earthquake distributions agree with a nonzero friction coefficient others produce the opposite pattern suggesting that the concentration of events along the p and t axes is due to random effects this result implies that the friction coefficient in the coulomb law is close to zero

a common origin for aftershocks foreshocks and multiplets we demonstrate that the statistics of earthquake data in the global cen troid moment tensor cmt and national earthquake information center neic catalogs and local california council of the national seismic system cnss catalog are consistent with the idea that a single physical triggering mechanism is responsible for the occurrence of aftershocks foreshocks and multiplets specifically we test the hypothesis that tectonic earthquakes usually show clustering only as a result of an initial earthquake triggering subsequent ones and that the magnitude of each trig gered earthquake is entirely independent of the magnitude of the triggering earth quake therefore a certain percentage of the time as determined by the gutenberg richter magnitude frequency relationship an earthquake should by chance be larger than or comparable in size to the earthquake that triggered it this hypothesis predicts that the number of times foreshocks or multiplets are observed should be a fixed fraction of the number of aftershock observations we find that this is indeed the case in the global cmt and neic catalogs the average ratios between foreshock aftershock and multiplet rates are consistent with what would be predicted by the gutenberg richter relationship with b 1 we give special attention to the solomon islands where it has been claimed that unique fault structures lead to unusually high numbers of multiplets we use monte carlo trials to demonstrate that the solomon islands multiplets may be explained simply by a high regional aftershock rate and earthquake density we also verify our foreshock results from the more complete recordings of small earthquakes available in the california catalog and find that foreshock rates for a wide range of foreshock and mainshock magnitudes can be projected from aftershock rates using the gutenberg richter relationship with b 1 and the relationship that the number of earthquakes triggered varies with triggering earthquake magnitude m as c10m where c is a productivity constant and is equal to 1 finally we test an alternative model that proposes that foreshocks do not trigger their mainshocks but are instead triggered by the mainshock nucleation phase in this model the nucleation phase varies with mainshock magnitude so we would expect mainshock magnitude to be correlated with the magnitude number or spatial extent of the foreshocks we find no evidence for any of these correlations

antarctic paleolake sediments and the search for extinct life on mars evidence of lakes in mars history is substantial the proposed similarities between the ancient martian environment and certain modern environments on earth have led exobiologists to study antarctic lakes as analogs to those purported to have existed on mars we have investigated modern sedimentation processes especially with respect to 13c of carbonate and organic matter in lakes in the mcmurdo dry valleys region of east antarctica and assessed various paleolake deposits with respect to their utility as martian analogs and targets for future mars exobiology missions three main types of paleolake deposit were identified and assessed strand lines perched deltas and lacustrine sand mounds deltas are usually identified as good targets but our research shows that authigenic carbonates are not readily identifiable in the sediments large deltas although most likely to attract attention through remote sensing generally are difficult sites for discovery of paleobiological matter and 13c signals follow no coherent pattern lacustrine sand mounds on the other hand contain abundant authigenic carbonate and freeze dried organic matter and appear to be excellent records of paleolimnological conditions the advantage of studying lake bottom deposits versus lake edge deposits is retrieval of a stable lake wide signal deltas are therefore most useful in that they are generally large scale features capable of drawing attention to a region of potential for the discovery of smaller lacustrine sand mounds

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

reservoir lithology classification based on seismic inversion results by hidden markov models applying prior geological information abstract hidden markov models hmms have been applied to predict reservoir lithologies using seismic inversion results as inputs this approach takes into account the conditional probabilities between different lithologies i e the vertical transitions in sedimentary sequences these properties are used as prior geological information in order to relate the seismic inversion results to the true well log data hmms need to be trained based on the expectation maximization theory application of the resulting model on a synthetic example from the book cliffs utah usa showed that most lithologies are classified correctly even for some thin layers a comparison with point wise methods in which data samples are treated independently from each other such as k means and fuzzy logic classifiers leads to the conclusion that the spatial correlation in hmms allows better lithological predictions because the prior information accounts for the geological depositional processes a real case study with data from the vienna basin austria is performed in which lithologies in a 3d cube are obtained based on properties from seismic inversions via trained hmms while the vertical sequences are shown to be reasonably well predicted the horizontal continuities are not this indicates that the future research should focus on the lateral geological relationships

a rock physics strategy for quantifying uncertainty in common hydrocarbon indicators we present a strategy for quantifying uncertainties in rock physics interpretations by combining statistical techniques with deterministic rock physics relations derived from the laboratory and theory a simple example combines gassmann s deterministic equation for fluid substitution with statistics inferred from log core and seismic data to detect hydrocarbons from observed seismic velocities the formulation identifies the most likely pore fluid modulus corresponding to each observed seismic attribute and the uncertainty that arises because of natural variability in formation properties in addition to the measurement uncertainties we quantify the measure of information in terms of entropy and show the impact of additional data about s wave velocity on the uncertainty of the hydrocarbon indicator in some cases noisy s data along with noisy p data can convey more information than perfect p data alone while in other cases s data do not reduce the uncertainty we apply the formulation to a well log example for detecting the most likely pore fluid and quantifying the associated uncertainty from observed sonic and density logs the formulation offers a convenient way to implement deterministic fluid substitution equations in the realistic case when natural geologic variations cause the reference porosity and velocity to span a range of values

secondary aftershocks and their importance for aftershock forecasting the potential locations of aftershocks which can be large and damaging are often forecast by calculating where the mainshock increased stress we find however that the mainshock induced stress field is often rapidly altered by aftershock induced stresses we find that the percentage of aftershocks that are secondary aftershocks or aftershocks triggered by previous aftershocks increases with time after the mainshock if we only consider aftershock sequences in which all aftershocks are smaller than the mainshock the percentage of aftershocks that are secondary also increases with mainshock magnitude using the california earthquake catalog and monte carlo trials we estimate that on average more than 50 of aftershocks produced 8 or more days after m 5 mainshocks and more than 50 of all aftershocks produced by m 7 mainshocks that have aftershock sequences lasting at least 15 days are triggered by previous aftershocks these results suggest that previous aftershock times and locations may be important predictors for new aftershocks we find that for four large aftershock sequences in california an updated forecast method using previous aftershock data and neglecting mainshock induced stress changes can outperform forecasts made by calculating the static coulomb stress change induced solely by the mainshock manuscript received 20 november 2002

identification and spatiotemporal organization of aftershocks 1 we propose a fast method able to discriminate between poissonian independent earthquakes and aftershocks the method is based on the evaluation of the variability coefficient defined as the ratio between the standard deviation and the average value of the interoccurrence time between two successive earthquakes we apply this technique to the california and a properly constructed synthetic catalogue in order to estimate the level of background seismicity and identify seismic sequences we then investigate the spatiotemporal organization of aftershocks focusing on the distributions of interevent times and interevent distances between two successive events we find evidence for the existence of a characteristic spatial length scale related to the size of the aftershock zone whereas no typical timescale is detected

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

lithology and fluid prediction from prestack seismic data using a bayesian model with markov process prior lithology and fluid prediction from prestack seismic data using a bayesian model with markov process prior

trace based and geostatistical inversion of 3 d seismic data for thin sand delineation an application in san jorge basin argentina argentina s san jorge basin which straddles the southern provinces of chubut and santa cruz in the heart of patagonia has been producing hydrocarbons since 1907 the region currently accounts for 32 of the country s production the existence and early geologic evolution of the basin is due to the same rift process responsible for the opening of the atlantic ocean in early jurassic times extensive direct faulting and local erosion accompanied the rift evolution thereby facilitating the accumulation of chiefly nonmarine terrigenous sediments well into the early cretaceous at this point andean tectonism became a major source of pyroclastic concentration in the sedimentary column it was also responsible for pervasive batholitic intrusions clastic deposition in the hydrocarbon producing zone is characterized by thick shale laminations of lacustrine and floodplain origin interspersed with much thinner and laterally sparse sand bodies the hydrocarbon reservoirs

earthquake hazard after a mainshock in california after a strong earthquake the possibility of the occurrence of either significant aftershocks or an even stronger mainshock is a continuing hazard that threatens the resumption of critical services and reoccupation of essential but partially damaged structures a stochastic parametric model allows determination of probabilities for aftershocks and larger mainshocks during intervals following the mainshock the probabilities depend strongly on the model parameters which are estimated with bayesian statistics from both the ongoing aftershock sequence and from a suite of historic california aftershock sequences probabilities for damaging aftershocks and greater mainshocks are typically well constrained after the first day of the sequence with accuracy increasing with time

bayesian estimation in seismic inversion part i principles1 this paper gives a review of bayesian parameter estimation the bayesian approach is fundamental and applicable to all kinds of inverse problems its basic formulation is probabilistic information from data is combined with a priori information on model parameters the result is called the a posteriori probability density function and it is the solution to the inverse problem in practice an estimate of the parameters is obtained by taking its maximum well known estimation procedures like least squares inversion or l 1 norm inversion result depending on the type of noise and a priori information given due to the a priori information the maximum will be unique and the estimation procedures will be stable except in theory for the most pathological problems which are very unlikely to occur in practice the approach of tarantola and valette can be derived within classical probability theory the bayesian approach allows a full resolution and uncertainty analysis which is discussed in part ii of the paper

predictability in the epidemic type aftershock sequence model of interacting triggered seismicity 1 as part of an effort to develop a systematic methodology for earthquake forecasting we use a simple model of seismicity on the basis of interacting events which may trigger a cascade of earthquakes known as the epidemic type aftershock sequence model etas the etas model is constructed on a bare unrenormalized omori law the gutenberg richter law and the idea that large events trigger more numerous aftershocks for simplicity we do not use the information on the spatial location of earthquakes and work only in the time domain we demonstrate the essential role played by the cascade of triggered seismicity in controlling the rate of aftershock decay as well as the overall level of seismicity in the presence of a constant external seismicity source we offer an analytical approach to account for the yet unobserved triggered seismicity adapted to the problem of forecasting future seismic rates at varying horizons from the present tests presented on synthetic catalogs validate strongly the importance of taking into account all the cascades of still unobserved triggered events in order to predict correctly the future level of seismicity beyond a few minutes we find a strong predictability if one accepts to predict only a small fraction of the large magnitude targets specifically we find a prediction gain defined as the ratio of the fraction of predicted events over the fraction of time in alarms equal to 21 for a fraction of alarm of 1 a target magnitude m 6 an update time of 0 5 days between two predictions and for realistic parameters of the etas model however the probability gains degrade fast when one attempts to predict a larger fraction of the targets this is because a significant fraction of events remain uncorrelated from past seismicity this delineates the fundamental limits underlying forecasting skills stemming from an intrinsic stochastic component in these interacting triggered seismicity models quantitatively the fundamental limits of predictability found here are only lower bounds of the true values corresponding to the full information on the spatial location of earthquakes

petrophysical seismic inversion conditioned to well log data methods and application to a gas reservoir hydrocarbon reservoirs are characterized by seismic welllog and petrophysical information which is dissimilar in spatial distribution scale and relationship to reservoir properties we combine this diverse information in a unified inverse problem formulation using a multiproperty multiscale model linking properties statistically by petrophysical relationships and conditioningthemtowell logdata twoapproacheshelpus 1markov chainmontecarlosampling whichgeneratesmanyreservoir realizationsforestimatingmediumpropertiesandposteriormarginalprobabilities and2optimizationwithaleast squaresiterativetechniquetoobtainthemostprobablemodelconfiguration our petrophysical model applied to near vertical anglestacked seismicdataandwell logdatafromagasreservoir includesadeterministic component based on a combination of wyllie and wood relationships calibrated with the well log data and a random component based on the statistical characterization of the deviations of well log data from the petrophysical transform at the petrophysical level the effects of porosity and saturation on acoustic impedance are coupled conditioning the inversion to well log data helps resolve this ambiguity the combination of well logs petrophysics and seismic inversion builds on the correspondingstrengthsofeachtypeofinformation jointlyimproving 1 cross resolution of reservoir properties 2 vertical resolution of property fields 3 compliance to the smooth trend of property fields and 4 agreement with well log data at well positions

space time model for regional seismicity and detection of crustal stress changes 1 the regional occurrence rate of earthquakes is modeled as a function of previous activity the specific form of which is based on empirical laws in time and space such as the modified omori formula and the utsu seki scaling law of aftershock area against magnitude respectively its parameters including the p value of the aftershock decay rate vary from place to place in such a way that for example the regional p value at the locations around the main shock is similar to the one estimated from the corresponding individual aftershock sequence the estimated space time model is used to visualize features of the regional seismic activity the utility is demonstrated by applying the model to the events of m 5 in and around japan for the period 1926 1995 among the parameters of the model this paper is particularly concerned with the normalized k value of the modified omori function indicating the aftershock productivity this takes high values around the boundaries of asperities that are estimated in the wide area off the east coast of tohoku district japan by the inversion of historical strong motion seismograms furthermore this space time model enables us to identify the anomalous period and regions where the actual occurrence rates deviate systematically from the modeled one such an anomaly activation and quiescence relative to the model could sensitively reveal the change of stresses in the regions we attempt to relate this relative activation and lowering of the seismicity to the pattern of coulomb stress changes due to a rupture or silent slip elsewhere for example such anomalies seen in the seismic activity in the central japan m 2 5 during 1995 1999 and during 2001 are respectively likely the consequence of the coulomb stress changes due to the 1995 kobe rupture and the interplate aseismic slip during 2001 beneath the western tokai region

sensitivity of static stress calculations to the earthquake slip distribution 1 the apparent strong correlation between coulomb stress changes and the spatial distribution of aftershocks suggests the possibility of making near real time estimations of areas at risk of experiencing off fault aftershocks in order to do this in practice a number of issues must first be addressed including the extent to which the main shock slip must be known in detail before a meaningful stress map can be constructed here we investigate this issue by constructing a time ordered sequence of slip solutions for the landers earthquake computing coulomb stress changes for each solution and quantitatively comparing the stress field with the observed aftershocks by 1 resolving the coulomb stress change onto the aftershock nodal planes and calculating the percentage of events consistent with triggering and 2 constructing a two dimensional map of coulomb stress and computing the correlation coefficient between the positive and negative areas and the locations of the aftershocks we find that slip solutions based on empirical relations and either focal mechanism or moment tensor data produce stress fields inconsistent with the observed spatial distribution of aftershocks whereas slip solutions incorporating the correct rupture geometry but greatly simplified slip produce stress fields consistent with the aftershock distribution when very near fault events are excluded we further find that resolving stress perturbations onto earthquake nodal planes and computing the percentage of events experiencing positive coulomb stress provides a poor measure of success because of the limited range of structures on which events occur and the compatibility of the main shock stress field with these structures our results support the hypothesis that coulomb stress changes affect the spatial distribution of aftershocks and suggest that meaningful calculations of coulomb stress can be made as soon as an earthquake s rupture geometry is well constrained

extreme threshold failures within a heterogeneous elastic thin sheet and the spatial temporal development of induced seismicity within the groningen gas field measurements of the strains and earthquakes induced by fluid extraction from a subsurface reservoir reveal a transient exponential like increase in seismicity relative to the volume of fluids extracted if the frictional strength of these re activating faults is heterogeneously and randomly distributed then progressive failures of the weakest fault patches account in a general manner for this initial exponential like trend allowing for the observable elastic and geometric heterogeneity of the reservoir the spatio temporal evolution of induced seismicity over 5 years is predictable without significant bias using a statistical physics model of poro elastic reservoir deformations inducing extreme threshold frictional failures of previously inactive faults this model is used to forecast the temporal and spatial probability density of earthquakes within the groningen natural gas reservoir conditional on future gas production plans probabilistic seismic hazard and risk assessments based on these forecasts inform the current gas production policy and building strengthening plans

introducing probabilistic aftershock hazard mapping aftershocks to large earthquakes pose a significant hazard a fact that was highlighted by damaging aftershocks to the 1999 turkey and taiwan mainshocks a new approach is introduced to quantify this hazard in terms of physical parameter maps that forecast the probabilistic aftershock hazard based on the observed spatially varying aftershock activity for two case studies the landers and northridge mainshocks probabilistic aftershock hazard maps are shown to improve conventional aftershock hazard assessment

bayesian lithology fluid prediction and simulation on the basis of a markov chain prior model a technique for lithology fluid lf prediction and simulation from prestack seismic data is developed in a bayesian framework the objective is to determine the lf classes along 1d profiles through a reservoir target zone a stationary markov chain prior model is used to model vertical continuity of lf classes along the profile the likelihood relates the lf classes to the elastic properties and to the seismic data and it introduces vertical correlation because the seismic data are band limited an approximation of the likelihood model provides an approximate posterior model that is a markov chain the approximate posterior can be assessed by an exact and efficient recursive algorithm the lf inversion approach is evaluated on a synthetic 1d profile that is inspired by a north sea sandstone reservoir with a realistic wavelet colored noise model and a s n ratio of three in the seismic data the results are reliable the lf classes and the interfaces between zones are largely correct the prediction unce

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

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

does the spatial distribution of smaller earthquakes delineate areas where larger earthquakes are likely to occur in the development of the latest generation of national seismic hazard maps one of the component models used the spatial distribution of smaller earthquakes in the eastern united states to forecast the locations of larger earthquakes frankel 1995 variations of this hypothesis that smaller earthquakes indicate where larger earthquakes are likely to occur are found throughout earthquake studies in a previous study kafka and walcott 1998 we tested this hypothesis for earthquakes in the northeastern united states neus to see how well the spatial distribution of smaller earthquakes recorded by seismic networks in the neus forecasts the locations of larger earthquakes that have already occurred the essence of our procedure is to systematically analyze how often previously occurring smaller earthquakes occurred in the vicinity of larger earthquakes the purpose of this study is to extend that investigation to other areas of the world to obtain a more global perspective on this issue here we report on an extension of that investigation to the southeastern united states the new madrid seismic zone southern california northern california israel turkey and the entire eastern united states our results to date do in fact suggest that in a variety of tectonic environments the spatial distribution of smaller earthquakes delineates areas in which larger earthquakes are likely to occur in a number of cases where locations of larger earthquakes were not forecast based on this approach we suspect that the misses are at least in part due to incompleteness and quirks in the earthquake catalogs

bayesian lithology and fluid prediction from seismic prestack data a fast bayesian inversion method for 3d lithology and fluid prediction from prestack seismic data and a corresponding feasibility analysis were developed and tested on a real data set the objective of the inversion is to find the probabilities for different lithology fluid classes from seismic data and geologic knowledge the method combines stochastic rock physics relations between the elastic parameters and the different lithology fluid classes with the results from a fast bayesian seismic simultaneous inversion from seismic data to elastic parameters a method for feasibility analysis predicts the expected modification of the prior probabilities to posterior probabilities for the different lithology fluid classes the feasibility analysis can be carried out before the seismic data are analyzed both the feasibility method and the seismic lithology fluid probability inversion were applied to a prospect offshore norway the analysis improves the probability for gas sand from 0 1 to about 0 2 0 4 with s

impact of earthquake rupture extensions on parameter estimations of point process models abstract stochastic point processes are widely applied to model spatiotemporal earthquake occurrence in particular the epidemic type aftershock sequence etas model has been shown to successfully reproduce the short term clustering of earthquakes an important parameter of the model is the value describing the scaling of the aftershock productivity with magnitude of the triggering earthquake according to 10 m fitting of the space dependent etas model to empirical data yields values that are typically much smaller than the scaling inverted from more simple stacking of aftershock sequences we show by means of synthetic simulations that this is likely to result from assuming spatial isotropy of aftershock occurrence that in fact aligns along the mainshock rupture we fit the space dependent and space independent etas models to simulations where each earthquake is a line source with an empirical magnitude length relation although the space time model describes past activity quite well it overestimates the forecasted earthquake rate on the other hand the application of the space independent etas model predicts future seismicity well and can therefore be applied for forecasting purposes our test for the observed aftershock sequence following the 1992 m 7 3 landers earthquake supports these results

a monte carlo approach to the joint estimation of reservoir and elastic parameters from seismic amplitudes inversion of seismic data and quantification of reservoir properties such as porosity lithology or fluid saturation are commonly executed in two consecutive steps a geophysical inversion to estimate the elastic parameters and a petrophysical inversion to estimate the reservoir properties we combine within an integrated formulation the geophysical and petrophysical components of the problem to estimate the elastic and reservoir properties jointly we solve the inverse problem following a monte carlo sampling approach which allows us to quantify the uncertainties of the reservoir estimates accounting for the combination of geophysical data uncertainties the deviations of the elastic properties from the calibrated petrophysical transform and the nonlinearity of the geophysical and petrophysical relations we implement this method for the inference of the total porosity and the acoustic impedance in a reservoir area combining petrophysical and seismic information in our formulation the porosity and impedance are related with a statistical model based on the wyllie transform calibrated to well log data we simulate the seismic data using a convolutional model and evaluate the geophysical likelihood of the joint porosity impedance models applying the monte carlo sampling method we generate a large number of realizations that jointly explain the seismic observations and honor the petrophysical information this approach allows the calculation of marginal probabilities of the model parameters including medium porosity impedance and seismic source wavelet we show a synthetic validation of the technique and apply the method to data from an eastern venezuelan hydrocarbon reservoir satisfactorily predicting the medium stratification and adequate correlation between the seismic inversion and well log estimates for total porosity and acoustic impedance

short term properties of earthquake catalogs and models of earthquake source i review the short term properties of earthquake catalogs in particular the time and size distributions and the completeness of the early part of aftershock sequences for strong shallow earthquakes i determine the parameters of the omori and gutenberg richter laws for aftershocks close in time to a mainshock aftershock sequences of large earthquakes in southern california 1952 kern county 1992 joshua tree landers big bear sequence 1994 northridge and 1999 hector mine recorded in the caltech catalog are analyzed to demonstrate that at the beginning of these series many small earthquakes are absent from the catalog the number of missing earthquakes increases with the magnitude range of a catalog and for some data sets exceeds the number of aftershocks close to a mainshock listed in a catalog comparing global earthquake catalogs harvard centroid moment tensor and preliminary determination of epicenter with local data sets indicates that the catalogs based on longer period waves miss many early aftershocks even when their magnitudes are well above the stated magnitude threshold such short term incompleteness may introduce significant biases to the statistical analysis of the seismicity pattern in particular for branching models of earthquake occurrence incorporating the omori law for such models the likelihood function strongly depends on close aftershocks i review the techniques to alleviate this problem analyzing the source rupture process of several recent large earthquakes suggests that rupture propagation is highly inhomogeneous in space time and focal mechanism these random variations in the rupture process can be viewed as an extension of the aftershock stochastic generating mechanism toward the origin time of a mainshock i review various models of the earthquake rupture process and suggest that fractal distributions of microevents in time space and focal mechanism constitute the development of an earthquake the final identification of an individual earthquake depends on both objective and subjective factors manuscript received 21 may 2003

second order moment of central california seismicity 1969 1982 the second order moment cross correlation function of earthquakes in the u s geological survey central california catalog between 1969 and 1982 was calculated with respect to a magnitude threshold m 4 0 over interevent distances up to 80 km and interevent times up to 320 days the statistical procedure results in a representation of the spatial temporal structure of the catalog associated with m 4 0 earthquakes and is capable of revealing patterns too weak to be detected in the space time distribution of seismicity for individual earthquake sequences a method is introduced for identifying aftershocks based on a physical two parameter model of the earthquake interaction process the results show that the aftershock process dominates the second order moment and may even obscure the statistical expression of a precursory process a concentration of foreshocks within 15 km and 3 days of m 4 0 main shocks exhibits an apparent migration toward the main shock loci with velocity 2 6 5 3 km d this concentration may be related to an observed tendency for m 4 0 events to cluster auto correlate over this interevent range with the identified aftershocks removed the residual catalog is poissonion in space and time when two m 4 0 earthquakes occur within 80 km and 40 days of each other aftershock productivity appears to be relatively enhanced in the earlier sequence this suggests that aftershock populations are not solely dependent on their main shocks and that unusually productive aftershock sequences may be predictors of future moderate earthquakes

plate tectonic analysis of shallow seismicity apparent boundary width beta corner magnitude coupled lithosphere thickness and coupling in seven tectonic settings a new plate model is used to analyze the mean seismicities of seven types of plate boundary crb continental rift boundary ctf continental transform fault ccb continental convergent boundary osr oceanic spreading ridge otf oceanic transform fault ocb oceanic convergent boundary sub subduction zone we compare the platelike nonorogen regions of model pb2002 bird 2003 with the centroid moment tensor cmt catalog to select apparent boundary half widths and then assign 95 of shallow earthquakes to one of these settings a tapered gutenberg richter model of the frequency moment relation is fit to the subcatalog for each setting by maximum likelihood best fitting values range from 0 53 to 0 92 but all 95 confidence ranges are consistent with a common value of 0 61 0 66 to better determine some corner magnitudes we expand the subcatalogs by 1 inclusion of orogens and 2 inclusion of years 1900 1975 from the catalog of pacheco and sykes 1992 combining both earthquake statistics and the plate tectonic constraint on moment rate corner magnitudes include the following crb graphic 1 ctf graphic 2 ccb graphic 3 ocb graphic 4 and sub graphic 5 coupled lithosphere thicknesses are found to be the following crb graphic 6 ctf graphic 7 ccb graphic 8 osr graphic 9 for normal faulting and graphic 10 for strike slip otf graphic 11 and graphic 12 at low medium and high velocities ocb graphic 13 and sub graphic 14 in general high coupling of subduction and continental plate boundaries suggests that here all seismic gaps are dangerous unless proven to be creeping in general low coupling within oceanic lithosphere suggests a different model of isolated seismic fault patches surrounded by large seismic gaps that may be permanent online material global seismic subcatalogs of shallow earthquakes 1 embed inline graphic 1 gif 2 embed inline graphic 2 gif 3 embed inline graphic 3 gif 4 embed inline graphic 4 gif 5 embed inline graphic 5 gif 6 embed inline graphic 6 gif 7 embed inline graphic 7 gif 8 embed inline graphic 8 gif 9 embed inline graphic 9 gif 10 embed inline graphic 10 gif 11 embed inline graphic 11 gif 12 embed inline graphic 12 gif 13 embed inline graphic 13 gif 14 embed inline graphic 14 gif

universality of the seismic moment frequency relation we analyze the seismic moment frequency relation in various depth ranges and for different seismic regions using flinn engdahl s regionalization of global seismicity three earthquake lists of centroid moment tensor data have been used the harvard catalog the usgs catalog and the huang et al 1997 catalog of deep earthquakes the results confirm the universality of the values and the maximum moment for shallow earthquakes in continental regions as well as at and near continental boundaries moreover we show that although fluctuations in earthquake size distribution increase with depth the values for earthquakes in the depth range of 0 500 km exhibit no statistically significant regional variations the regional variations are significant only for deep events near the 660 km boundary for declustered shallow earthquake catalogs and deeper events we show that the worldwide values have the same value of 0 60 0 02 this finding suggests that the value is a universal constant we investigate the statistical correlations between the numbers of seismic events in different depth ranges and the correlation of the tectonic deformation rate and seismic activity the number of earthquakes above a certain threshold level per year the high level of these correlations suggests that seismic activity indicates tectonic deformation rate in subduction zones combined with the universality of the value this finding implies little if any variation in maximum earthquake seismic moment among various subduction zones if we assume that earthquakes of maximum size are similar in different depth ranges and the seismic efficiency coefficient is close to 100 for shallow seismicity then we can estimate for deeper earthquakes for intermediate earthquakes 5 and 1 for deep events these results may lead to new theoretical understanding of the earthquake process and better estimates of seismic hazard

predictive modeling of the seismic cycle of the greater san francisco bay region the seismic cycle for the san francisco bay region is synthesized by a model combining the pre and post 1906 seismic histories the long term acceleration of seismic release seismic moment benioff strain release or event count in the seismic cycle and the shorter term accelerations preceding the larger earthquakes within that cycle are modeled using an empirical predictive technique called time to failure analysis in which rate of seismic release is proportional to an inverse power of the remaining time to failure the exponent of time to failure in the accelerating sequences appears to be scale invariant and the length of the full cycle is estimated at 269 50 years the 1989 loma prieta earthquake which is the culmination of the first subcycle in the present long term seismic cycle should have been predictable with an uncertainty of 2 years in time and 0 5 in magnitude although the specific location at loma prieta was not predictable by this technique if our model is correct and if the loma prieta earthquake is the culmination of a subcycle the san francisco bay region should be entering a relatively long 20 50 years period of seismic quiescence above magnitude 6 a great earthquake such as the 1906 san francisco event would appear to be more than a century in the future

comparison of short term and time independent earthquake forecast models for southern california we have initially developed a time independent forecast for southern california by smoothing the locations of magnitude 2 and larger earthquakes we show that using small m 2 earthquakes gives a reasonably good prediction of m 5 earthquakes our forecast outperforms other time independent models kagan and jackson 1994 frankel et al 1997 mostly because it has higher spatial resolution we have then developed a method to estimate daily earthquake probabilities in south ern california by using the epidemic type earthquake sequence model kagan and knopoff 1987 ogata 1988 kagan and jackson 2000 the forecasted seismicity rate is the sum of a constant background seismicity proportional to our time independent model and of the aftershocks of all past earthquakes each earthquake triggers aftershocks with a rate that increases exponentially with its magnitude and decreases with time following omori s law we use an isotropic kernel to model the spatial distribution of aftershocks for small m 5 5 mainshocks for larger events we smooth the density of early aftershocks to model the density of future aftershocks the model also assumes that all earthquake magnitudes follow the gutenberg richter law with a uniform b value we use a maximum likelihood method to estimate the model parameters and test the short term and time independent forecasts a retro spective test using a daily update of the forecasts between 1 january 1985 and 10 march 2004 shows that the short term model increases the average probability of an earthquake occurrence by a factor 11 5 compared with the time independent forecast

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

importance of direct and indirect triggered seismicity in the etas model of seismicity 1 using the simple etas branching model of seismicity which assumes that each earthquake can trigger other earthquakes we quantify the role played by the cascade of triggered seismicity in controlling the rate of aftershock decay as well as the overall level of seismicity in the presence of a constant external seismicity source we show that in this model the fraction of earthquakes in the population that are aftershocks is equal to the fraction of aftershocks that are indirectly triggered and is given by the average number of triggered events per earthquake previous observations that a significant fraction of earthquakes are triggered earthquakes therefore imply that most aftershocks are indirectly triggered by the mainshock

likelihood analysis of earthquake catalogues summary we apply several classes of stochastic multidimensional models to statistical analysis of earthquake catalogues using likelihood methods we investigate the importance of including different earthquake parameters in the model epicentral coordinates hypocentral depth time limits for interearthquake interaction and especially spatial distribution of earthquakes as well as spatial aftershock patterns results of this study combined with other investigations suggest that most distributions controlling earthquake interaction have a fractal or scale invariant form developed models are used for statistical analysis of several earthquake catalogues to evaluate parameters of earthquake occurrence these parameters are shown to be similar for shallow earthquakes of different magnitude ranges and seismogenic regions confirming self similarity of the earthquake process whereas intermediate earthquakes seem to emulate the pattern of shallow earthquake occurrence albeit at a much smaller aftershock rate deep earthquakes differ significantly in their properties predictability of standard shallow earthquake catalogues has been analysed we present evidence that for the best availabfe catalogues the predictability is close to 10 bits per earthquake several synthetic earthquake catalogues have been created and processed through the likelihood inversion scheme the results from likelihood analysis of these catalogues confirm our approach

spatial temporal evolutions of early aftershocks following the 2013 mw 6 6 lushan earthquake in sichuan china we perform a comprehensive detection of early aftershocks following the 2013 mw 6 6 lushan earthquake which occurred in the southern longmenshan fault zone in sichuan province china about 5 years after the 2008 mw 7 9 wenchuan earthquake we use events in both standard and relocated catalogs as templates to scan through continuous waveforms 2 days before and 3 days after the main shock we successfully reduce the magnitude of completeness mc by more than 1 order and obtain up to 6 times more events than listed in both catalogs aftershocks in the first hour mostly occur around the main shock slip region and aftershocks at later times show systematic expansions in the along strike perpendicular strike and updip directions although postseismic deformation following the lushan main shock has not been clearly identified we suggest that early aftershock expansions are likely driven by afterslip of the lushan main shock this is consistent with the observations that most aftershocks were in the stress shadow of the lushan main shock and that there was significant slip deficit in the top 10 km of the crust we also find that seismicity on the back thrust fault was activated as soon as 20 min after the main shock earlier than previously reported we are unable to detect any clear foreshocks in the last 2 days before the lushan main shock