3 d inhomogeneities in the upper mantle abstract the method developed by aki christofferson and husebye for determining a 3 d seismic image of the earth s interior from the travel time data obtained at a 2 d array has been applied to seventeen arrays around the world by various authors the most outstanding results from these works are that small scale lateral velocity anomalies exist in the lower crust and upper mantle everywhere studied the reality of these deep seated anomalies is supported by 1 1 significant reduction of residual variance 2 2 resolution analysis for decoupling from shallower anomalies and 3 3 error analysis for the significance of anomalies in this paper we try to strengthen the credibility of these deep seated anomalies by drawing attention to those found where they were expected namely low velocity bodies under several geothermal areas and high velocity anomalies associated with the subducting plate

ages of late holocene earthquakes on the central garlock fault near el paso peaks california a trench across the central garlock fault within a small playa adjacent to el paso mountains revealed buried fissures and fault scarps that provide strong evidence for five surface rupturing earthquakes within the past 5 kyr weaker evidence suggested the possibility of three additional events within this same time period these observations indicate an average recurrence interval of 700 to 1200 years nearly all 28 radiocarbon dates on samples of detrital charcoal wood and shell are in correct stratigraphic order these dates constrain the ages of the individual faulting events and indicate that the recurrence interval is not periodic but is quite irregular individual recurrence intervals range from 190 to 1545 years if all eight events are actual earthquakes or from 190 to 3405 years if only the five well documented events represent earthquakes the two most recent earthquakes occurred within the past 550 years with preferred ages of about a d 1790 and a d 1600 the a d 1790 event ruptured a narrower width of the fault zone and may have been a smaller earthquake than the others the radiocarbon dates from the trench also indicate that the sedimentation rate on the playa has fluctuated within the past 5 kyr low sedimentation rates 0 1 to 0 35 mm yr and infrequent floods 1 per century prevailed from about 2000 b c to a d 100 and from a d 500 to 1300 during the remaining intervals within the past 5 kyr the sedimentation rate averaged 1 0 to 1 7 mm yr and major floods occurred two to four times per century the changes in sedimentation rate and flood frequency may reflect climatic changes or they may simply reflect changes in drainage patterns

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

earthquakes a hand on the aftershock trigger received wisdom relates that static stress change associated with an earthquake mainshock is the prime mover of its aftershocks but a fresh look at the data points the finger at wave surfing dynamic stress

nontrivial decay of aftershock density with distance in southern california the decay of the aftershock density with distance plays an important role in the discussion of the dominant underlying cause of earthquake triggering here we provide evidence that its form is more complicated than typically assumed and that in particular a transition in the power law decay occurs at length scales comparable to the thickness of the crust this is supported by an analysis of a very recent high resolution catalog for southern california sc and surrogate catalogs generated by the epidemic type aftershock sequence etas model which take into account inhomogeneous background activity short term aftershock incompleteness anisotropic triggering and variations in the observational magnitude threshold our findings indicate specifically that the asymptotic decay in the aftershock density with distance is characterized by an exponent larger than 2 which is much bigger than the observed exponent of approximately 1 35 observed for shorter distances ranging from the main shock rupture length up to a length scale comparable to the thickness of the crust this has also important consequences for time dependent seismic hazard assessment based on the etas model

basement unconformity control on alteration st francois mountains se missouri the basement lamotte formation unconformity in southeastern missouri shows evidence of several distinctive alteration events some of which may be related to migration of ore forming fluids or k rich basinal brines the alterations are spatially related to the unconformity suggesting that the unconformity was a preferred pathway for fluid migration unconformity related rocks in five cores penetrating both the lamotte formation and the basement have been characterized by bulk chemistry mineralogy textures and paleotopographic position the alteration history along the unconformity includes 1 pre lamotte hydrothermal alteration affecting basement 2 pre lamotte weathering and 3 post lamotte hydrothermal and diagenetic events the third group is particularly complex including early diagenetic hematite and calcite cementation later quartz cementation secondary biotite growth k metasomatism that generated adulaira and k leaching that left a narrow dickite rich zone along the unconformity sev

space time etas models and an improved extension for sensitive detection of anomalous seismicity such as quiescence and activation in a given region we need a suitable statistical reference model that represents a normal seismic activity in the region the regional occurrence rate of the 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 this manuscript summarizes the development of the epidemic type aftershock sequence etas model and proposes an extended version of the best fitted space time model that was suggested in ogata ogata y 1998 space time point process models for earthquake occurrences ann inst statist math 50 379 402 this model indicates significantly better fit to seismicity in various regions in and around japan d 2005 elsevier b v all rights reserved

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

viscoelastic coupling model of the san andreas fault along the big bend southern california the big bend segment of the san andreas fault is the 300 km long segment in southern california that strikes about n65 w roughly 25 counterclockwise from the local tangent to the small circle about the pacific north america pole of rotation the broad distribution of deformation of trilateration networks along this segment implies a locking depth of at least 25 km as interpreted by the conventional model of strain accumulation continuous slip on the fault below the locking depth at the rate of relative plate motion whereas the observed seismicity and laboratory data on fault strength suggest that the locking depth should be no greater than 10 to 15 km the discrepancy is explained by the viscoelastic coupling model which accounts for the viscoelastic response of the lower crust thus the broad distribution of deformation observed across the big bend segment can be largely associated with the san andreas fault itself not subsidiary faults distributed throughout the region the working group on california earthquake probabilities 1995 in using geodetic data to estimate the seismic risk in southern california has assumed that strain accumulated off the san andreas fault is released by earthquakes located off the san andreas fault thus they count the san andreas contribution to total seismic moment accumulation more than once leading to an overestimate of the seismicity for magnitude 6 and greater earthquakes in their type c zones

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

kinematics of the southern walker lane belt and motion of the sierra nevada block california deformation in the southern walker lane belt region of the southwestern great basin accommodates significant portions of both pacific north america transform motion and basin and range extension apparent kinematic inconsistencies between geodetic and fault slip data in this region have made it difficult to understand the nature of the interaction between these deformation processes and to infer the regional kinematics we model the kinematics of this region in a manner that enforces kinematic consistency and includes fault geometry and slip rate data global positioning system gps survey data and very long baseline interferometry very long baseline array vlbi vlba site velocity data a model is found that is consistent with the set of available data and this model differs significantly from prior models for the region our model has the sierra nevada block which bounds the western margin of the great basin moving n50 w 5 at 12 7 1 5 mm yr with only minor amounts of counterclockwise rotation left lateral slip on the western garlock fault is a consequence of the relatively great westerly component of sierra nevada velocity we also find that the basin and range extension east of our study area occurs at a rate of about 2 5 mm yr which is slower than the rate in the central great basin

relation between mainshock rupture process and omori s law for aftershock moment release rate summary we compare the source time functions i e moment release rates of three large california mainshocks with the seismic moment release rates during their aftershock sequences aftershock moment release rates computed by summing aftershock moments in time intervals follow a power law time dependence similar to omori s law from minutes to months after the mainshock furthermore in contrast to the previously observed saturation in numbers of aftershocks shortly after the mainshock rupture no such saturation is seen in the aftershock moment release rates which are dominated by the largest aftershocks we argue that the observed saturation in aftershock numbers described by the time offset parameter c in omori s law is likely an artefact due to the underreporting of small aftershocks which is related to the difficulty of detecting large numbers of small aftershocks in the mainshock coda we further propose that it is more natural for c to be negative i e singularity follows the onset of mainshock rupture than positive singularity precedes onset of rupture to make a more general comparison of mainshock rupture process and aftershock moment rates we then scale mainshock time functions to equalize the effects of the varied seismic moments for the three california mainshocks we compare the scaled time functions with similarly scaled aftershock moment rates finally we compare global averages of scaled time functions of many shallow events to the average scaled aftershock moment release rate for six california mainshocks in each of these comparisons the extrapolation using omori s law of the aftershock moment rates back in time to the onset of the mainshock rupture indicates that the temporal intensity of the aftershock moment release is about 1 5 orders of magnitude less than the maximum reached by the mainshock rupture this may be due to the differing amplitudes and relative importance of static and dynamic stresses in aftershock initiation compared to mainshock rupture propagation

present day kinematics of the eastern california shear zone from a geodetically constrained block model we use global positioning system gps data from 1993 2000 to determine horizontal velocities of 65 stations in eastern california and western nevada between 35 and 37 n we relate the geodetic velocities to fault slip rates using a block model that enforces path integral constraints over geologic and geodetic time scales and that includes the effects of elastic strain accumulation on faults locked to a depth of 15 km the velocity of the sierra nevada block with respect to nevada is 11 1 0 3 mm yr with slip partitioned across the death valley 2 8 0 5 mm yr panamint valley 2 5 0 8 mm yr and airport lake owens valley 5 3 0 7 4 6 0 5 mm yr faults the western mojave block rotates at 2 1 0 8 my clockwise with 3 7 0 7 mm yr of left lateral motion across the western garlock fault we infer 11 2 mm yr of right lateral motion across the mojave region of the eastern california shear zone

triggering cascades and statistical properties of aftershocks 1 applying a simple general procedure for identifying aftershocks we investigate their statistical properties for a high resolution earthquake catalog covering southern california we compare our results with those obtained by using other methods in order to show which features truly characterize aftershock sequences and which depend on the definition of aftershocks features robust across methods include the p value in the omori utsu law for large main shocks bath s law and the productivity law with an exponent smaller than the b value in the gutenberg richter law the identification of a typical aftershock distance with the rupture length is a feature we confirm as well as a power law decay in the spatial distribution of aftershocks with an exponent less than 2 other results we obtain but not common to all other works including marsan and lengline 2008 hainzl and marsan 2008 and zhuang et al 2008 are a p values that do not increase with the main shock magnitude b the duration of bare aftershock sequences that scales with the main shock magnitude c an additional power law in the temporal variation at intermediate times in the rate of aftershocks for main shocks of small and intermediate magnitude and d a b value for the gutenberg richter law of background events that is sensibly larger than that of aftershocks tests on synthetic catalogs generated by the epidemic type aftershock sequence model corroborate the validity of our approach

aftershock zone scaling we investigate the distribution of aftershock zones for large earthquakes scalar seismic moment m 10 19 5 n m moment magnitude m 7 mainshocks are selected from the harvard centroid moment tensor catalog and aftershocks are selected from the preliminary determination of epicenters neic catalog the aftershock epicenter maps are approximated by a two dimensional gaussian distribution the major ellipse axis is taken as a quantitative measure of the mainshock focal zone size the dependence of zone length l on earthquake size is studied for three representative focal mechanisms thrust normal and strike slip although the numbers of mainshocks available for analysis are limited maximum a few tens of events in each case all earthquakes show the same scaling m l 3 no observable scaling break or saturation occurs for the largest earthquakes m 10 21 n m m 8 therefore it seems that earthquake geometrical focal zone parameters are self similar

constraints on the size of the smallest triggering earthquake from the epidemic type aftershock sequence model bath s law and observed aftershock sequences 1 the physics of earthquake triggering together with simple assumptions of self similarity imply the existence of a minimum magnitude m0 below which earthquakes do not trigger other earthquakes noting that the magnitude md of completeness of a seismic catalog is not in general the same as the magnitude m0 of the smallest triggering earthquake we compare observed aftershock sequence parameters with the predictions made by the epidemic type aftershock sequence model to constrain the value of m0 in particular we use quantitative fits to observed aftershock sequences from three previous studies as well as bath s law to obtain four estimates of m0 we show that the branching ratio n average number of triggered earthquakes per earthquake also equal to the fraction of aftershocks in a seismic catalog is the key parameter controlling the estimate of the minimum triggering magnitude m0 conversely physical upper bounds for m0 estimated from rate and state friction indicate that at the very least 55 of all earthquakes are aftershocks

earthquake recurrence as a record breaking process 1 extending the central concept of recurrence times for a point process to recurrent events in space time allows us to characterize seismicity as a record breaking process using only spatiotemporal relations among events linking record breaking events with edges between nodes in a graph generates a complex dynamical network isolated from any length time or magnitude scales set by the observer for southern california the network of recurrences reveals new statistical features of seismicity with robust scaling laws the rupture length and its scaling with magnitude emerges as a generic measure for distance between recurrent events further the relative separations for subsequent records in space or time form a hierarchy with unexpected scaling properties

surficial offsets on the central and eastern garlock fault associated with prehistoric earthquakes geomorphic features offset along the central and eastern garlock fault record the amount of surface slip associated with prehistoric earthquakes along the easternmost 90 km of the fault the smallest offsets cluster around 2 3 m of left lateral slip apparently associated with the most recent earthquake on this portion of the fault larger offsets along this part of the fault especially in pilot knob valley cluster around values consistent with 2 4 m of slip in each of the past several events farther west south of el paso mountains offset geomorphic features suggest that each of the past two earthquakes on this stretch of the garlock fault was produced by about 7 m of slip whereas the third event back was produced by about 4 m of slip vertical displacements of geomorphic features range from 0 to 30 of the left lateral offsets within pilot knob valley along the southern side of the slate range vertical displacements are consistently up on the northern side whereas within the avawatz mountains both north and south side up vertical displacements are present on the basis of the geomorphic offsets the geometry of the garlock fault and the precedents set by historical strike slip earthquakes elsewhere a number of different rupture patterns are plausible these range from rupture of the entire garlock fault in a single event with a maximum magnitude of about mw 7 8 to separate rupture of the western segment and of the central and eastern segments combined with approximate magnitudes mw 1 1 and mw 7 5 respectively to separate rupture of even shorter segments producing earthquakes of magnitudes mw 6 6 to mw 7 5 in conjunction with available slip rates for the garlock fault the geomorphic offsets suggest that average recurrence intervals are probably within the range of 600 1200 years south of el paso mountains about 200 750 years in searles valley about 200 1300 years in pilot knob valley and about 200 3000 years near leach lake and in the avawatz mountains

slip generated patterns of swarm microearthquakes from west bohemia vogtland central europe evidence of their triggering mechanism 1 we investigated space time relations between consecutive events of west bohemian 2000 swarm and their association with the coulomb stress changes induced on a fault plane by prior swarm events a few thousand m 3 3 strike slip swarm earthquakes clustered along a fault plane at depths 6 5 10 5 km and showed common rake angle of 30 in order to disclose earthquake interaction we investigated the space time relations between consecutive earthquakes we determined relative position vectors for each consecutive event pair the prior event and the immediate aftershock ia and we measured time lags between them the resulting cluster of relative position vectors shows a high density of aftershocks near the origin which decays with distance it points out a triggering effect of the prior event upon subsequent aftershocks the spatial distribution of the relative positions disclosed dominance of aftershocks in the slip parallel directions which is manifested by pronounced elongation of the cluster of the relative positions and of the angular dependence of the rate of ias the temporal distribution of the relative positions indicates that some aftershocks prove high interevent velocities and occur systematically at greater distances suggesting the existence of two distinct triggering mechanisms acting at large and small timescales we evaluated the complete coulomb stress change upon the fault plane due to the prior event and showed that the observed space time distribution of the relative positions can be explained by a common effect of both static and dynamic stress changes which act on different distance and timescale

spatiotemporal correlations of aftershock sequences 1 aftershock sequences are of particular interest in seismic research because they may condition seismic activity in a given region over long time spans although they are typically identified with periods of enhanced seismic activity after a large earthquake as characterized by the omori law our knowledge of the spatiotemporal correlations between events in an aftershock sequence is limited here we study the spatiotemporal correlations of two aftershock sequences form california parkfield and hector mine using the recently introduced concept of recurrent events we find that both sequences have very similar properties and that most of them are captured by the space time epidemic type aftershock sequence etas model if one takes into account catalog incompleteness however the stochastic etas model does not capture those spatiotemporal correlations that give rise to the observed distribution of recurrent events on small spatial scales we also find that there is no clear evidence for stress shadows that have been observed for smaller earthquakes

a generalized omori s law for earthquake aftershock decay 1 earthquake aftershock sequences have been found to approximately satisfy three empirical scaling relations i the gutenberg richter frequency magnitude scaling ii bath s law for the difference in the magnitude of a mainshock and its largest aftershock and iii the modified omori s law for the temporal decay of aftershock rates the three laws are incorporated to give a generalized omori s law for aftershock decay rates that depend on several parameters specific for each given seismogenic region it is shown that the characteristic time c first introduced in the modified omori s law is no longer a constant but scales with a lower magnitude cutoff and a mainshock magnitude the generalized omori s law is tested against earthquake catalogs for the aftershock sequences of the landers northridge hector mine and san simeon earthquakes

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

anomalous early aftershock decay rate of the 2004 mw6 0 parkfield california earthquake 1 we analyze the seismicity rate immediately after the 2004 mw6 0 parkfield california earthquake from near source seismograms by scrutinizing high frequency signals we can distinguish mainshock coda from early aftershocks occurring as soon as 30 s after the mainshock we find as expected that a significant fraction of aftershocks in the first few hours after the main shock are missing in the northern california seismic network catalog we observe a steady rate of aftershocks in the first 130 s followed by a power law decay of aftershock activity thus there appears to be a distinct early stage of aftershock activity that does not fit the omori s law with a constant p value a phenomenon that we refer to as early aftershock deficiency ead our observation suggests that mainshock rupture and aftershocks are distinct processes not described by a single omori s law several physical models of aftershocks can explain the ead

strain accumulation across the eastern california shear zone at latitude 36 30 n the motion of a linear array of monuments extending across the eastern california shear zone ecsz has been measured from 1994 to 1999 with the global positioning system the linear array is oriented n54 e perpendicular to the tangent to the local small circle drawn about the pacific north america pole of rotation and the observed motion across the ecsz is approximated by differential rotation about that pole the observations suggest uniform deformation within the ecsz strike n23 w 26 nstrain yr 1 extension normal to the zone and 39 nstrain yr 1 simple right lateral shear across it with no significant deformation in the two blocks the sierra nevada mountains and southern nevada on either side the deformation may be imposed by right lateral slip at depth on the individual major fault systems within the zone if the slip rates are death valley furnace creek fault 3 2 0 9 mm yr 1 hunter mountain panamint valley fault 3 3 1 6 mm yr 1 and owens valley fault 6 9 1 6 mm yr 1 however this estimate of the slip rate on the owens valley fault is 3 times greater than the geologic estimate

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

common dependence on stress for the two fundamental laws of statistical seismology the gutenberg richter relation and the omori utsu law both power laws are two of the long standing relationships of statistical seismology here aftershock sequences are described according to the faulting style of their main shocks showing that the time delay before the onset of the power law aftershock decay rate is on average shorter for thrust main shocks than for normal fault earthquakes these similar dependences on the faulting style indicate that both the fundamental power laws are governed by the state of stress

extending earthquakes reach through cascading earthquakes whatever their size can trigger other earthquakes mainshocks cause aftershocks to occur which in turn activate their own local aftershock sequences resulting in a cascade of triggering that extends the reach of the initial mainshock a long lasting difficulty is to determine which earthquakes are connected either directly or indirectly here we show that this causal structure can be found probabilistically with no a priori model nor parameterization large regional earthquakes are found to have a short direct influence in comparison to the overall aftershock sequence duration relative to these large mainshocks small earthquakes collectively have a greater effect on triggering hence cascade triggering is a key component in earthquake interactions

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

late cenozoic history and slip rates of the fish lake valley emigrant peak and deep springs fault zones nevada and california several well dated stratigraphic markers permit detailed assessment of the temporal and spatial variation in slip rates along the interconnected faults of the fish lake valley emigrant peak and deep springs fault zones in west central nevada and east central california right lateral motion on the fish lake valley fault zone apparently began ca 10 ma 11 9 8 2 ma associated extensional faulting probably began ca 5 ma 6 9 4 ma and resulted in the opening of fish lake valley and deep springs valley the long term lateral slip rate for the fish lake valley fault zone since about 10 ma is 5 mm yr 3 12 mm yr our preferred lateral slip rate for the central most active part of the fish lake valley fault zone decreased from about 6 to 3 mm yr from the late miocene to the early pleistocene increased to about 11 mm yr during the middle pleistocene and decreased to about 4 mm yr during the late pleistocene extension may account for some of the change in lateral slip rate during the pliocene the large increase in lateral slip rate during the middle pleistocene is circumstantially linked to an increase in vertical slip rates on the fish lake valley and deep springs fault zones at about the time of the eruption of the bishop ash 0 76 ma vertical slip rates along the three fault zones are also related to fault strike vertical rates are highest on north striking faults and approach zero on northwest striking faults the long lived slip history of the fish lake valley fault zone fits a tectonic model in which the death valley furnace creek fish lake valley fault system is integrated with right lateral shear on faults of the central walker lane and the eastern california shear zone to accommodate part of the pacific north american relative plate motion our research demonstrates that the fish lake valley fault zone accounts for about half the rate of 10 12 mm yr of pacific north american plate boundary shear accommodated within the basin and range province between about lat 37 and 38 n

scaling properties of the parkfield aftershock sequence aftershock sequences present a unique opportunity to study the physics of earthquakes important questions concern the fundamental origin of three widely applicable scaling laws 1 gutenberg richter frequency magnitude scaling 2 omori s law for aftershock decay rates and 3 bath s law for the difference between the magnitude of the largest aftershock and a mainshock the high resolution parkfield seismic network provided the opportunity for detailed studies of the aftershock sequence following the 28 september 2004 m 6 0 parkfield earthquake in this article it is shown that aftershocks satisfy the gutenberg richter scaling relation only for relatively large times after the mainshock there is a systematic time delay for the establishment of this scaling law the temporal evolution of the rates of occurrence of aftershocks is quantified using the generalized omori s law this scaling law contains two characteristic times c and the analysis suggests that the parameter c plays the role of a characteristic time for the establishment of gutenberg richter scaling this time increases systematically with a decreasing lower magnitude cutoff the systematic time delay is attributed to a cascade of energy from long wavelengths to short wavelengths the parameter is a measure of the average time until the first aftershock occurs we find that slightly varies with the lower magnitude cutoff of the sequence we also note that the largest aftershock inferred from an extrapolation of gutenberg richter scaling m 5 0 is equal to the largest observed aftershock this scaling associated with the universal applicability of bath s law is attributed to a constant partitioning of energy between a mainshock and its associated aftershock sequence we also give in this article the distribution of interoccurrence times between successive aftershocks we show that this distribution is well approximated by a nonhomogeneous poissons process driven by the modified omori s law the self consistency between interoccurrence statistics and decay rates is taken as further evidence for the applicability of our studies

reconciling rapid strain accumulation with deep seismogenic fault planes in the ventura basin california global positioning system measurements across the east central ventura basin transverse ranges southern california before the nearby 1994 northridge earthquake show high strain rates interpreting this rapid strain accumulation using the usual model of deep slip on a dislocation in a uniform elastic half space requires slip to extend to within 5 km of the surface such shallow slip is difficult to reconcile with the substantial coseismic displacement at depths from 7 to 19 km during the northridge earthquake here we model the displacement and velocity fields throughout the earthquake cycle using a two dimensional finite element model with a viscoelastic rheology displacements are driven by far field and basal velocity boundary conditions and by imposed periodic earthquakes on the thrust faults bounding the basin the thrust faults rupture through an elastic upper crust to a depth of 15 km after a transient stage during which stresses and strains build up to quasi equilibrium values the behavior of the model becomes periodic the sum of the coseismic displacement divided by the repeat interval plus the average interseismic velocity is equal to the geologic velocity the temporal variation in surface velocity depends mainly on the elsasser relaxation time proportional to the product of the maxwell time of the lower crust and the ratio of the thicknesses of the entire crust and viscoelastic lower crust we are able to match the observed high strain rate only if we include the observed variations in elastic modulus associated with the deep basin sediments the model reconciles geologic geodetic and seismological observations of deformation there are trade offs among the far field convergence rate the elsasser time the earthquake repeat time and the time into the earthquake cycle acceptable convergence rates range from 8 mm yr for a relaxation time of the lower crust of 300 years to 12 mm yr for a 30 year relaxation time