impurities in pluronic triblock copolymers can induce the formation of calcite mesocrystals abstract an interesting recent report by zhou et al chemical geology 2010 279 63 74 describes the formation of calcite mesocrystals with very well defined prismatic morphologies in the presence of f 68 a pluronic triblock copolymer that this can be achieved with a polymer which is a linear nonionic polyoxyethylene polyoxypropylene runs counter to the current understanding that face selective adsorption of a polymer on the precursor mineral building blocks is required for mesocrystal formation in this paper we contrast the effect of analytical grade f 68 and the same polymer after purification by dialysis and show that a strong morphological effect on calcite precipitation is only achieved with the analytical grade polymer we therefore suggest that low molecular weight impurities present within analytical grade f 68 may have been responsible for the formation of caco3 mesocrystals rather than the f 68 macromolecules themselves

self healing slip pulses in dynamic rupture models due to velocity dependent strength abstract seismological observations of short slip duration on faults short rise time on seismograms during earthquakes are not consistent with conventional crack models of dynamic rupture and fault slip in these models the leading edge of rupture stops only when a strong region is encountered and slip at an interior point ceases only when waves from the stopped edge of slip propagate back to that point in contrast some seismological evidence suggests that the duration of slip is too short for waves to propagate from the nearest edge of the ruptured surface perhaps even if the distance used is an asperity size instead of the entire rupture dimension what controls slip duration if not dimensions of the fault or of asperities in this study dynamic earthquake rupture and slip are represented by a propagating shear crack for all propagating shear cracks slip velocity is highest near the rupture front and at a small distance behind the rupture front the slip velocity decreases as pointed out by heaton 1990 if the crack obeys a negative slip rate dependent strength relation the lower slip velocity behind the rupture front will lead to strengthening that further reduces the velocity and under certain circumstances healing of slip can occur the boundary element method of hamano 1974 is used in a program adapted from andrews 1985 for numerical simulations of mode ii rupture with two different velocity dependent strength functions for the first function after a slip weakening displacement the crack follows an exponential velocity weakening relation the characteristic velocity v 0 of the exponential determines the magnitude of the velocity dependence at dynamic velocities the velocity dependence at high velocity is essentially zero when v 0 is small and the resulting slip velocity distribution is similar to slip weakening if v 0 is larger rupture propagation initially resembles slip weakening but spontaneous healing occurs behind the rupture front the rise time and rupture propagation velocity depend on the choice of constitutive parameters the second strength function is a natural log velocity dependent form similar to constitutive laws that fit experimental rock friction data at lower velocities slip pulses also arise with this function for a reasonable choice of constitutive parameters slip pulses with this function do not propagate at speeds greater than the raleighwave velocity the calculated slip pulses are similar in many aspects to seismic observations of short rise time in all cases of self healing slip pulses the residual stress increases with distance behind the trailing edge of the pulse so that the final stress drop is much less than the dynamic stress drop in agreement with the model of brune 1976 and some recent seismological observations of rupture

distance and azimuthal dependence of ground motion variability for unilateral strike slip ruptures abstract we investigate near field ground motion variability by computing the seismic wavefield for five kinematic unilateral rupture models of the 1992 m w 7 3 landers earthquake eight simplified unilateral rupture models based on the landers event and a large m w 7 8 shakeout scenario we include the geometrical fault complexity and consider different 1d velocity density profiles for the landers simulations and a 3d heterogeneous earth structure for the shakeout scenario for the landers earthquake the computed waveforms are validated using strong motion recordings we analyze the simulated ground motion data set in terms of distance and azimuth dependence of peak ground velocity pgv our simulations reveal that intraevent ground motion variability is higher in close distances to the fault ln pgv is well described by a cauchy lorentz function that provides a novel empirical quantification to model the spatial dependency of ground motion online material figures of slip distributions residuals to ground motion prediction equations gmpes distance and azimuthal dependence and directivity predictor of ground motion variability for different source models

biomimetic mineralization of prismatic calcite mesocrystals relevance to biomineralization article i nfo morphological control during mineral crystallization is one of the prominent hallmarks of biomineralization organisms can employ some of functional macromolecules to produce crystals with special morphologies at particular tissue sites in this article a pluronic triblock copolymer f68 or f127 was used as a model organic additive for the purpose of influencing the crystallization and growth of calcium carbonate in a biomimetic mineralization process structure and morphology of the products were investigated using a range of techniques including xrd ftir fesem tem and saed the fesem and tem results demonstrate that additive f68 not only preferentially interacts with selected faces of calcite crystals to form elongated microcrystals it also induces the oriented aggregation of microcrystals along the crystallographic c direction into calcite prisms i e mesocrystal architectures in addition a series of time resolved experiments show that the initial precipitate in the presence of higher concentration f68 was an unstable amorphous calcium carbonate acc and this transient precursor phase eventually transformed into prismatic mesocrystals of calcite displaying all of features of caco3 biomineralization because f68 only contains ether oxygen and terminal hydroxyl functional groups its role in the crystallization of caco3 is considered as an analogue to an array of biomineralization associated biomacromolecules such as some glycosylated proteins hence our results suggest that the c o c groups ether or glycosidic group in biomineralization associated biomacromolecules not only influence the mineralization process but also contribute to the special morphogenesis of caco3 as such this provides a new insight into the biomineralization mechanism 2010 elsevier b v all rights reserved

aerobically incubated bacterial biomass promoted formation of disordered dolomite and implication for dolomite formation abstract with the realization that the formation of low temperature dolomite could involve the microbial activity a new pathway to understand the origin and mechanism of dolomite is emerging although microbially mediated ca mg carbonates and dolomite occur in some aerobic and high salinity conditions little information about the exact role of aerobic microbes is available herein a strain of moderately halophilic bacteria shewanella piezotolerans wp3 was selected to study the involvement of aerobically incubated bacterial biomass in the ca mg carbonate mineralization different biomass components were isolated from the bacterial cultures by a set of separation techniques and used to mediate ca mg carbonate mineralization under a carbon dioxide diffused system the experimental results showed that bacterial cells play a dominant role in the formation of disordered dolomite and the mineralization of the disordered dolomite can be attributed to the bare cells and bound extracellular polymeric substances bound eps isolated from the bacterial cells most likely due to the promotion of high concentration and density of carboxyl and phosphoryl groups on the bacterial biomass i e bare cells and bound eps hence it does imply that bacterial biomass even without the active microbial activities can also play an important role in the formation of dolomite current results can not only extend the insight into the biologically influenced mineralization of ca mg carbonates but also shed light on the precipitation of disordered dolomite dolomite in modern settings and geological records

earthquake ruptures with strongly rate weakening friction and off fault plasticity part 1 planar faults abstract observations demonstrate that faults are fractal surfaces with deviations from planarity at all scales we study dynamic rupture propagation on self similar faults having root mean square rms height fluctuations of order 10 3 to 10 2 times the profile length our 2d plane strain models feature strongly rate weakening fault friction and off fault drucker prager viscoplasticity the latter bounds otherwise unreasonably large stress concentrations in the vicinity of bends our choice of a cohesionless yield function prevents tensile stress states and thus fault opening a consequence of strongly rate weakening friction is the existence of a critical background stress level above which self sustaining rupture propagation in the form of self healing slip pulses first becomes possible around this level at which natural faults are expected to operate ruptures become extremely sensitive to fault roughness and exhibit substantial fluctuations in rupture velocity except for shallow inclinations of the maximum compressive stress to the fault less than about 20 the fluctuations are anticorrelated with the local fault slope these accelerations and decelerations of the rupture together with naturally emerging slip heterogeneity excite waves of all wavelengths and result in ground acceleration spectra that are flat at high frequency consistent with observed strong motion records

evaluating the compatibility of dynamic rupture based synthetic ground motion with empirical ground motion prediction equation we performed an assessment of a database of synthetic ground motion generated by a suite of dynamic rupture simulations to verify compatibility of the peak ground amplitudes with respect to empirical ground motion prediction equations gmpes the dynamic rupture model database developed by dalguer and mai 2011 is composed of 360 earthquake scenarios with moment magnitudes in the range of 5 5 7 for three mechanisms of faulting reverse normal and strike slip and for both buried faults and surface rupturing faults having depth and non depth dependent normal stresses initial shear stress distribution follows a von karman stochastic distribution overall we show quantitatively that the upper frequency limit of the suite of simulations is 1 0 hz up to this frequency the synthetic data are compatible with the empirical model which means that the residuals defined as the differences between observed and predicted ground motions fall in the range of of the empirical gmpe characteristics of the mean values along distance 10 45 km and period t 1 0 s including standard deviation of the synthetic response spectra and peak ground velocity are comparable to their counterpart empirical gmpe at very near source 1 2 km synthetics show supersaturation of the mean peak values which is different from the saturation features predicted by the gmpes the effect of source parameters such as stress drop peak slip velocity and rupture speed and of surface and buried rupture as well as hanging wall and footwall are highly sensitive to ground motion suggesting that these effects contribute to the variability of ground motion near the source and that inclusion of them in the source terms may contribute to reducing uncertainties in gmpes

biogeochemistry of nautiloids and paleoenvironmental aspects of buckhorn seawater pennsylvanian southern oklahoma abstract sediments in the buckhorn quarry and adjacent outcrops southern oklahoma are shallow water carbonates which are intercalated with coals and minor conglomerates they belong to the boggy formation of the deese group and are desmoinesian pennsylvanian in age strontium concentrations of shell septa and cameral deposits of pennsylvanian cephalopods are variable and fall either in the low range with 0 17 0 22 or the high range with 0 39 0 60 sr ca atomic ratios these values suggest that extrapallial and or cameral fluids responsible for the formation of all three cephalopod macrostructures were in chemical disequilibrium with ambient seawater thus the biological discrimination for sr was well establihed by pennsylvanian time for nautiloids the mg concentrations appear to be controlled at the species genus levels in contrast the na mn and fe contents of nautiloids are influenced and controlled by the physicochemical conditions of the surrounding seawater information obtained from brachiopod and from the least altered cephalopod samples suggest that buckhorn seawater was physiochemically similar to that of modern ocean water and the postulated temperature and salinity values represent the most reasonable intepretations considering paleontological sedimentological and biogeochemical data salinity of the buckhorn sea which was within 5 s of the pennsylvanian equator ranged from 29 to 34 ppt with a mean of 32 ppt this near normal salinity was complemented by an average water temperature of 36 c 34 38 c for the shallower and of 21 c 14 30 c for the deeper parts of the buckhorn sea of southern oklahoma overall water temperatures fluctuated between 14 and 38 c

complexity of seismicity due to highly rate dependent friction we study a simple antiplane fault of finite length embedded in a homogeneous isotropic elastic solid in order to understand the origin of seismic source heterogeneity in the presence of nonlinear rate dependent friction all the mechanical properties of the medium and friction are assumed to be homogeneous starting from a heterogeneous initial stress distribution we apply a slowly increasing uniform stress load far from the fault and we simulate the seismicity for more than 20 000 events in some cases the style of seismicity produced by this model is determined by a control parameter which measures the degree of rate dependence of friction for classical friction models with rate independent friction no complexity appears and seismicity is perfectly periodic for weakly rate dependent friction seismicity becomes slightly nonperiodic but most events are still characteristic earthquakes when friction is highly rate dependent seismicity is completely irregular and ruptures of all sizes occur inside the fault highly rate dependent friction destabilizes the healing process producing premature healing of slip and partial stress drop premature healing causes rupture to take the form of narrow propagating slip episodes the so called heaton s 1990 pulses partial stress drop produces large variations in the state of stress which in turn produce earthquakes of different sizes we make the conjecture that all models in which static stress drop is only a fraction of the dynamic stress drop produce stress heterogeneity

earthquake source scaling relationships from 1 to 5 ml using seismograms recorded at 2 5 km depth the scaling relationships of earthquake sources less than about magnitude 3 have been the subject of considerable controversy over the last two decades studies of such events have shown a tendency for the constant stress drop self similarity of larger earthquakes to breakdown at small magnitudes and an apparent minimum source dimension of about 100 m has been observed other studies showed that this apparent breakdown in scaling could be an artifact of severe near surface attenuation limiting the spatial resolution of surface data in this study source parameters are determined for over 100 nearby tectonic earthquakes from recordings at a depth of 2 5 km in granite in the cajon pass scientific drill hole southern california comparison of the seismograms recorded at this depth with those at the wellhead clearly demonstrates the effect of the severe attenuation in the upper kilometers of the earth s crust source parameters are calculated by spectral modeling of three component p and s waves assuming four source models based on the brune 2 n 2 model in model l n 2 is fixed and q of p and s waves is determined to be 912 581 1433 and 1078 879 1323 respectively the numbers in parentheses are 1 standard deviation in model 2 qp qs 1000 is assumed and n is allowed to vary the 2 model is a good average for the data set but there is some real scatter supported by the data in model 3 qp qs 1000 is also assumed and 2 is constrained and in model 4 attenuation is ignored and n is allowed to vary source dimensions of less than 10m are observed for all four models 10 times smaller than the proposed minimum no breakdown in constant stress drop scaling is seen in the downhole data approximately ml 1 to 5 5 m0 109 1016 nm the ratio between radiated seismic energy estimated by integrating the velocity squared spectra with adequate signal bandwidth and seismic moment appears to decrease gradually with decreasing moment in the magnitude range 1 to 7 this is not incompatible with a constant stress drop but could result from errors in calculating energy the ratio of the s wave energy to that radiated by the p waves is about 14 after correction for attenuation this low value is consistent with the corner frequency shift of about 1 3 this corner frequency shift is observed for all four source models and therefore is interpreted as being source controlled

calcite precipitation induced by bacillus cereus mrr2 cultured at different ca2 concentrations further insights into biotic and abiotic calcite abstract a key problem of how to distinguish between biotic and abiotic carbonate minerals in nature and or in the laboratory has confused researchers for some time although numerous studies have been performed to explore the formation mechanism and the unique characteristics of biotic minerals the issue needs to be studied further here biotic calcite precipitation was induced by the microorganism bacillus cereus mrr2 genbank ky810857 while organogenic and inorganogenic calcite was investigated in parallel the results indicate that carbonic anhydrase ca a common enzyme of bacteria promoted carbon dioxide hydration to release hco3 and co32 in the process of calcite precipitation the ph increased from 7 2 to 8 9 as a result of the combination effect of the released ammonia by b cereus mrr2 and the hco3 and co32 ions originating from the ca reaction glutamic acid is the most abundant amino acid in the extracellular polymeric substances of the bacteria and its free carboxyl ions with a large number of negative charges in the alkaline environment facilitated the adsorption of calcium ions the biotic calcite has a series of unique characteristics different from the organogenic and inorganogenic calcites such as particular morphologies p element composition and a variety of organic functional groups intracellular amorphous nanospheres without any crystal structure are also recorded stable carbon isotope analyses show that the biotic calcite 20 9 has more negative 13c values than the organogenic calcite 15 6 and inorganogenic calcite 11 7 indicating that microbial activity strongly affected the carbon isotope composition of biotic calcite more importantly the crystallinity and activation energy of the biotic calcite are clearly higher than those of organogenic calcite suggesting that the thermal stability of biotic calcite is much higher thus this study provides important insights into understanding the mechanisms of microbial biomineralization and the processes of biotic calcite formation especially the roles microbes played in mineral nucleation and growth as well as the unique characteristics of the resulting minerals this study may provide useful evidence for further recognizing biotic and abiotic calcite in the geological record

variability of seismic source spectra estimated stress drop and radiated energy derived from cohesive zone models of symmetrical and asymmetrical circular and elliptical ruptures large variability of earthquake stress drops and scaled energy has been commonly reported in the literature but it is difficult to assess how much of this variability is caused by underlying physical source processes rather than simply observational uncertainties here we examine a variety of dynamically realistic rupture scenarios for circular and elliptical faults and investigate to what extent the variability in seismically estimated stress drops and scaled energy comes from differences in source geometry rupture directivity and rupture speeds we numerically simulate earthquake source scenarios using a cohesive zone model with the small scale yielding limit where the solution approaches a singular crack model with spontaneous healing of slip compared to symmetrical circular source models asymmetrical models result in larger variability of estimated corner frequencies and scaled energy over the focal sphere the general behavior of the spherical averages of corner frequencies and scaled energy in the subshear regime extends to the supershear regime although shear mach waves generated by the propagation of supershear rupture lead to much higher corner frequency and scaled energy estimates locally our results suggest that at least a factor of 2 difference in the spherical average of corner frequencies is expected in observational studies simply from variability in source characteristics almost independent of the actual stress drops translating into a factor of 8 difference in estimated stress drops furthermore radiation efficiency estimates derived from observed seismic spectra should not be directly interpreted as describing rupture properties unless there are independent constraints on rupture speed and geometry

dynamics of the 2015 m7 8 nepal earthquake the 2015 m7 8 nepal earthquake ruptured part of the main himalayan thrust beneath kathmandu to study the dynamics of this event we compute p wave spectra of the main shock and of two large aftershocks to estimate stress drop and radiated energy we find that surface reflections depth phases of these shallow earthquakes produce interference that severely biases spectral measurements unless corrections are applied measures of earthquake dynamics for the main shock are within the range of estimates from global and regional earthquakes we explore the azimuthal and temporal variations of radiated energy and highlight unique aspects of the m7 8 rupture the beginning of the earthquake likely experienced a dynamic weakening mechanism immediately followed by an abrupt change in fault geometry correlation of backprojection results with frequency dependent variations in the radiated energy rate and with the suggested geometry of the main himalayan thrust yields new constraints on dynamic ruptures through geometrical barriers

small earthquakes deviate from the omega square model as revealed by multiple spectral ratio analysis we examine the omega square model by estimating the source spectra of 196 m w 3 2 4 0 shallow earthquakes in the northern ibaraki prefecture and the fukushima prefecture hamadori area of japan using multiple spectral ratio analysis spectral ratios of the seismograms of target events to those of multiple nearby small events empirical green s function egf events allow for negation of path and site effects and are fitted by the omega square model the residual spectra for different egf events exhibit similar curves indicating how the source spectra of the target events deviate from the omega square model many earthquakes deviate remarkably whereas other events fit well the possible implications of these findings are incoherencies in the rupture process the double corner frequency model and a high frequency falloff exponent value slightly higher than 2 although this is still an open question this study will help to improve the source spectrum model enhancing not only source studies but strong motion assessments and other seismological studies online material figures showing results of spectral analysis of the events with the largest and smallest peak to peak amplitudes

structure and morphology of magnetite anaerobically produced by a marine magnetotactic bacterium and a dissimilatory iron reducing bacterium intracellular crystals of magnetite synthesized by cells of the magnetotactic vibroid organism mv 1 and extracellular crystals of magnetite produced by the non magnetotactic dissimilatory iron reducing bacterium strain gs 15 were examined using high resolution transmission electron microscopy electron diffraction and57fe mo ssbauer spectroscopy the magnetotactic bacterium contained a single chain of approximately 10 crystals aligned along the long axis of the cell the crystals were essentially pure stoichiometric magnetite when viewed along the crystal long axis the particles had a hexagonal cross section whereas side on they appeared as rectangules or truncated rectangles of average dimension 53 35 nm these findings are explained in terms of a three dimensional morphology comprising a hexagonal prism of 110 faces which are capped and truncated by 111 end faces electron diffraction and lattice imaging studies indicated that the particles were structurally well defined single crystals in contrast magnetite particles produced by the strain gs 15 were irregular in shape and had smaller mean dimensions 14 nm single crystals were imaged but these were not of high structural perfection these results highlight the influence of intracellular control on the crystallochemical specificity of bacterial magnetites the characterization of these crystals is important in aiding the identification of biogenic magnetic materials in paleomagnetism and in studies of sediment magnetization

variability in earthquake stress drop and apparent stress 1 we apply empirical green s function coda based analysis to four earthquake sequences in japan that span a magnitude range of 1 8 to 6 9 to measure radiated energy corner frequency and stress drop we find no systematic dependence of apparent stress or stress drop on seismic moment for these sequences and find they both are log normally distributed however we identify several anomalous events both energetic and enervated that show sharply different spectral signatures from the rest of the population these events indicate that much of the variation in apparent stress and stress drop is statistically significant which may have important implications for seismic hazard analysis

rupture process and energy budget of the 29 july 2008 mw 5 4 chino hills california earthquake the source model of the 2008 m w 5 4 chino hills california earthquake is constrained using near field seismic body waves recorded by the california integrated seismic network cisn finite fault inversions are preformed for the two fault models based on the nodal planes derived from the cisn moment tensor solution the northeast dipping plane strike 289 dip 62 which has a similar strike as the nearby whittier fault is chosen as the causative fault because it fits the data significantly better our inversion result indicates that the majority of the chino hills earthquake rupture occurred in a compact area in particular 48 of the total seismic moment 1 6 10 17 nm was released by the failure of a 1 8 km 2 asperity located east of the hypocenter in a short time window from 0 4 to 0 8 s after the rupture initiation the average slip is approximately 0 5 m but the maximum slip is 1 8 m the average rupture velocity is 1 9 km s the static stress drop calculated using the slip model is up to 80 mpa and the average stress drop changes from 19 to 38 mpa depending on the average schemes the weighted average slip velocity is 6 5 m s for entire rupture and is 11 m s for the east asperity the inferred available energy and radiated energy are 8 10 13 j and 2 5 10 13 j respectively radiation efficiency is then 0 31 which is moderately low compared with previous earthquakes but consistent with the inferred high average fracture energy density ranging from 6 5 to 14 8 mj m 2

source parameters of the 1980 mammoth lakes california earthquake sequence from the more than 1500 mammoth lakes earthquakes recorded on three component digital seismographs spudich et al 1981 150 were used in an analysis of the locations mechanism and source parameters a composite fault plane solution of nine earthquakes 3 9 m 5 1 defines a right lateral strike slip mechanism on a steeply dipping nearly east west plane striking s75 e or left lateral strike slip on a nearly north south plane striking n10 e vertical cross sections of well located aftershocks indicate possibly three east west planes that coincide with the locations of the four largest earthquakes with ml 6 0 using the spectral analysis of s waves brune 1970 source parameters for 67 earthquakes were determined forty eight had magnitudes greater than or equal to 3 0 seismic moments ranged from 9 20 1018 dyn cm to 2 33 1024 dyn cm earthquakes with seismic moment greater than about 1 0 1021 dyn cm had nearly constant stress drops 50 bars earthquakes with seismic moment less than about 1 0 1021 dyn cm had stress drops that apparently decrease as seismic moment decreases

evidence for and implications of self healing pulses of slip in earthquake rupture dislocation time histories of models derived from waveforms of seven earthquakes are discussed in each model dislocation rise times the duration of slip for a given point on the fault are found to be short compared to the overall duration of the earthquake 10 however in many crack like numerical models of dynamic rupture the slip duration at a given point is comparable to the overall duration of the rupture i e slip at a given point continues until information is received that the rupture has stopped propagating alternative explanations for the discrepancy between the short slip durations used to model waveforms and the long slip durations inferred from dynamic crack models are 1 the dislocation models are unable to resolve the relatively slow parts of earthquake slip and have seriously underestimated the dislocations for these earthquakes 2 earthquakes are composed of a sequence of small dimension short duration events that are separated by locked regions barriers 3 rupture occurs in a narrow self healing pulse of slip that travels along the fault surface evidence is discussed that suggests that slip durations are indeed short and that the self healing slip pulse model is the most appropriate explanation a qualitative model is presented that produces self healing slip pulses the key feature of the model is the assumption that friction on the fault surface is inversely related to the local slip velocity the model has the following features high static strength of materials kilobar range low static stress drops in the range of tens of bars and relatively low frictional stress during slip less than several hundreds of bars it is suggested that the reason that the average dislocation scales with fault length is because large amplitude slip pulses are difficult to stop and hence tend to propagate large distances this model may explain why seismicity and ambient stress are low along fault segments that have experienced large earthquakes it also qualitatively explains why the recurrence time for large earthquakes may be irregular

new perspectives on self similarity for shallow thrust earthquakes scaling of dynamic rupture processes from small to large earthquakes is critical to seismic hazard assessment large subduction earthquakes are typically remote and we mostly rely on teleseismic body waves to extract information on their slip rate functions we estimate the p wave source spectra of 942 thrust earthquakes of magnitude mw 5 5 and above by carefully removing wave propagation effects geometrical spreading attenuation and free surface effects the conventional spectral model of a single corner frequency and high frequency falloff rate does not explain our data and we instead introduce a double corner frequency model modified from the haskell propagating source model with an intermediate falloff of f 1 the first corner frequency f1 relates closely to the source duration t1 its scaling follows m0 t13 for mw 7 5 and changes to m0 t12 for larger earthquakes an elliptical rupture geometry better explains the observed scaling than circular crack models the second time scale t2 varies more weakly with moment m0 t25 varies weakly with depth and can be interpreted either as expressions of starting and stopping phases as a pulse like rupture or a dynamic weakening process estimated stress drops and scaled energy ratio of radiated energy over seismic moment are both invariant with seismic moment however the observed earthquakes are not self similar because their source geometry and spectral shapes vary with earthquake size we find and map global variations of these source parameters

dynamic rupture models for the southern san andreas fault abstract dynamic rupture and resultant ground motions up to 0 25 hz are simulated for an m w 7 6 earthquake on the southern san andreas fault spontaneous rupture is modeled with slip weakening friction and 3d viscoelastic wave solutions are computed with a support operator numerical method the initial traction model is derived from inversions of the m w 7 3 1992 landers strong ground motion records and borrows heavily from that used for the terashake2 simulations by olsen et al 2008 heterogeneity in the traction model leads to focusing of the rupture front and the focusing produces cases of supershear rupture velocity in asperities areas of high initial traction as well as cases of high peak slip rate and cohesive zone contraction in antiasperities separate solutions are computed for version 3 0 and 4 0 respectively of the southern california earthquake center community velocity model scec cvm we also compare the case of a flat ground surface a common simplification made for finite difference simulations to the case of the ground surface conformed to regional topography the overall distribution of simulated ground motion intensity is consistent with that derived from the empirical model of campbell and bozorgnia 2008 in the sense that the bulk of simulated pseudospectral velocity psv values are within the 68 confidence intervals of the empirical model simulated psvs corresponding to low probability in the empirical model are principally associated with basin wave guide and directivity effects an important example first identified by the terashake1 simulations olsen et al 2006 is the stronger than expected ground motions at the site of montebello due to a basin wave guide effect we find that this effect is lessened for version 4 0 of the scec cvm relative to version 3 0 due to a shallower model for the chino basin

short slip duration in dynamic rupture in the presence of heterogeneous fault properties recent studies of strong motion data consistently show that the risetime duration of slip at particular locations on the fault is significantly shorter than the overall rupture duration the physical explanation for this observation and its implications have become central issues in earthquake source studies two classes of mechanisms have been proposed to explain short risetimes one explanation is that velocity weakening frictional behavior on the fault surface causes the fault to self heal this possibility is suggested by rate dependent friction observed in laboratory experiments and by some two dimensional dynamic numerical simulations of earthquake rupture it has recently been demonstrated however that the velocity dependence of friction observed in the laboratory is too weak to cause faults to self heal an alternative explanation for short risetimes is that spatially heterogeneous fault strength e g barriers limit the slip duration in this paper we investigate this second explanation for short risetimes by constructing a three dimensional dynamic rupture model for the 1984 morgan hill california earthquake mw 6 2 using a kinematic model previously obtained from waveform inversion of strong motion data we assume velocity independent friction and a critical stress fracture criterion and derive a dynamic model specified by the spatial distribution of dynamic stress drop and strength excess that reproduces the slip and rupture time of the kinematic model the slip velocity time functions calculated from this dynamic model are then used in a subsequent inversion to fit the strong motion data by alternating between dynamic and kinematic modeling we obtain a dynamic model that provides an acceptable fit to the recorded waveforms in this dynamic model the risetime is short over most of the fault which is attributable entirely to the short scale length slip stress drop heterogeneity required by the strong motion data a self healing mechanism such as strongly velocity dependent friction is not required to explain the short risetimes observed in this earthquake

seismic source spectral properties of crack like and pulse like modes of dynamic rupture earthquake source properties such as seismic moment and stress drop are routinely estimated from far field body wave amplitude spectra some quantitative but model dependent relations have been established between seismic spectra and source parameters however large variability is seen in the parameter estimates and it is uncertain how the variability is partitioned among real variability in the source parameters observational error and modeling error due to complexity of earthquake behaviors earthquake models with dynamic weakening have been found to exhibit two different modes of rupture expanding crack and self healing pulse modes four representative models are generated to model the transition from crack like to pulse like pulse like rupture leads to development of a second corner frequency and the intermediate spectral slope is approximately 2 in most cases the focal sphere averaged lower p and s wave corner frequencies are systematically higher for pulse like models than crack models of comparable rupture velocity the slip weighted stress drop e exceeds the moment based stress drop m for pulse like ruptures with the ratio ranging from about 1 3 to 1 65 while they are equal for the crack like case the variations in rupture mode introduce variability of the order of a factor of two in standard i e crack model based spectral estimates of stress drop the transition from arresting to growing pulse rupture is accompanied by a large factor of 1 6 increase in the radiation ratio thus variations in rupture mode may account for the portion of the scatter in observational spectral estimates of source parameters

dynamic stress changes during earthquake rupture we assess two competing dynamic interpretations that have been pro posed for the short slip durations characteristic of kinematic earthquake models de rived by inversion of earthquake waveform and geodetic data the first interpretation would require a fault constitutive relationship in which rapid dynamic restrengthen ing of the fault surface occurs after passage of the rupture front a hypothesized mechanical behavior that has been referred to as self healing the second inter pretation would require sufficient spatial heterogeneity of stress drop to permit rapid equilibration of elastic stresses with the residual dynamic friction level a condition we refer to as geometrical constraint these interpretations imply contrasting pre dictions for the time dependence of the fault plane shear stresses we compare these predictions with dynamic shear stress changes for the 1992 landers m 7 3 1994 northridge m 6 7 and 1995 kobe m 6 9 earthquakes stress changes are com puted from kinematic slip models of these earthquakes using a finite difference method for each event static stress drop is highly variable spatially with high stress drop patches embedded in a background of low and largely negative stress drop the time histories of stress change show predominantly monotonic stress change after passage of the rupture front settling to a residual level without significant evidence for dynamic restrengthening the stress change at the rupture front is usu ally gradual rather than abrupt probably reflecting the limited resolution inherent in the underlying kinematic inversions on the basis of this analysis as well as recent similar results obtained independently for the kobe and morgan hill earthquakes we conclude that at the present time the self healing hypothesis is unnecessary to explain earthquake kinematics

a support operator method for 3 d rupture dynamics summary we present a numerical method to simulate spontaneous shear crack propagation within a heterogeneous 3 d viscoelastic medium wave motions are computed on a logically rectangular hexahedral mesh using the generalized finite difference method of support operators som this approach enables modelling of non planar surfaces and non planar fault ruptures our implementation the support operator rupture dynamics sord code is highly scalable enabling large scale multiprocessors calculations the fault surface is modelled by coupled double nodes where rupture occurs as dictated by the local stress conditions and a frictional failure law the method successfully performs test problems developed for the southern california earthquake center scec u s geological survey usgs dynamic earthquake rupture code validation exercise showing good agreement with semi analytical boundary integral method results we undertake further dynamic rupture tests to quantify numerical errors introduced by shear deformations to the hexahedral mesh we generate a family of meshes distorted by simple shearing in the along strike direction up to a maximum of 73 for scec usgs validation problem number 3 grid induced errors increase with mesh shear angle with the logarithm of error approximately proportional to angle over the range tested at 73 rms misfits are about 10 per cent for peak slip rate and 0 5 per cent for both rupture time and total slip indicating that the method which up to now we have applied mainly to near vertical strike slip faulting is also capable of handling geometries appropriate to low angle surface rupturing thrust earthquakes additionally we demonstrate non planar rupture effects by modifying the test geometry to include respectively cylindrical curvature and sharp kinks

stochastic fault stress implications for fault dynamics and ground motion up to the present time ground motion calculations for future earthquakes have almost exclusively been made from kinematic models however dynamic faulting models offer many benefits over kinematic models including the assurance the faulting models obey at least the general rules of elastodynamics and friction and contain a natural relationship between stress drop slip rise time and rupture velocity dynamic models also offer insight into the physics of the rupture and slip processes and can show how these processes lead to patterns of ground motion in the current work we use the 3d finite difference method and a suite of stochastic stress patterns with variable assumptions on strength and stress inhomogeneity to investigate two issues 1 the effect of assumptions about stress pattern on the evolution of rupture and slip on the fault and 2 the effect of these assumptions on the resultant ground motion we find that stress drop has a complicated relationship with slip rise time and rupture velocity especially in faults with strongly heterogeneous strength we also find that these inhomogeneous strength faults can produce highly inhomogeneous slip even without any form of frictional restrengthening at healing time finally we find that smoother strength models produce a better fit than the coarse models to the directivity pulse often observed on the surface the results help to shed light on the transition of the faulting system between locally controlled and more globally controlled rupture and also show how dynamic models may be used to generate ground motion estimates for seismic hazard calculations

an empirical study of earthquake source spectra for california earthquakes we generalize source path and site effects for california earthquakes as functions of magnitude and distance based on regression analysis of 1000 fourier acceleration spectra from 43 california earthquakes in the moment magnitude range from 4 4 to 7 4 recorded at rupture distances from 1 to 200 km empirically derived source spectra for california earthquakes are generally inconsistent with the spectral shape implied by a brune omega squared point source model this is manifested by magnitude and frequency dependence of the brune model parameters for ex ample the brune stress parameter that best matches the data at high frequencies decreases from a value of about 120 bars at m5 5 to a value near 50 bars at m7 5 at frequencies below 1 hz though source spectra have much lower spectral ampli tudes than predicted by the brune point source model for these values of stress this discrepancy grows with increasing magnitude finite fault simulations indicate that this is a consequence of the breakdown of the validity of the point source approxi mation for large ruptures a stochastic finite fault model in which the fault is dis cretized as a number of subfaults each of which is represented by a brune omega squared point source correctly matches the observed spectral shapes and amplitudes the spectral decay parameter kappa representing average near surface attenuation of high frequency motion at rock sites increases with increasing magnitude from values near 0 035 sec at m5 5 to 0 050 sec at m7 5 magnitude dependence of kappa may be interpreted as evidence of nonlinearity for typical california sites subjected to strong ground motion comparisons of our empirical source spectra for california to corresponding spec tra for eastern north america suggest that the spectral amplitudes are similar in the two regions for low frequency motions f 2 hz for m5 5 f 0 5 hz for m7 5 for equivalent crustal conditions the eastern events appear to have enhanced high frequency near source amplitudes relative to the california events this is particularly pronounced for large magnitude earthquakes

comprehensive analysis of earthquake source spectra in southern california we compute and analyze p wave spectra from earthquakes in southern california between 1989 and 2001 using a method that isolates source receiver and path dependent terms we correct observed source spectra for attenuation using both fixed and spatially varying empirical green s function methods estimated brune type stress drops for over 60 000 m l 1 5 to 3 1 earthquakes range from 0 2 to 20 mpa with no dependence on moment or local b value median computed stress drop increases with depth in the upper crust from about 0 6 mpa at the surface to about 2 2 mpa at 8 km where it levels off and remains nearly constant in the midcrust down to about 20 km however the results at shallow depths could also be explained as reduced rupture velocities near the surface rather than a change in stress drop spatially coherent variations in median stress drop are observed with generally low values for the imperial valley and northridge aftershocks and higher values for the eastern transverse ranges and the north end of the san jacinto fault we find no correlation between observed stress drop and distance from the san andreas and other major faults significant along strike variations in stress drop exist for aftershocks of the 1992 landers earthquake which may correlate with differences in main shock slip

the influence of the lithospheric thickness on bilateral slip summary a 2 d model of slip formation and dynamic propagation in an elastic lithospheric plate coupled to the asthenosphere and having a fault plane is investigated using a finite element method slip is nucleated at a weak portion of the fault plane and propagates bilaterally at the edges slip is assumed to develop according to a critical shear stress criterion combined with a slip weakening law except for the weak portion the slip resistance is constant along the fault plane the influence of resistive stresses from the asthenosphere at the bottom of the plate is taken into account the results indicate that bilateral slip lengths are limited to about the lithospheric plate thickness or somewhat larger such lengths will only be reached for sufficiently high tectonic loading after maximum slip length has been reached the slipping region is split into two regions of unidirectional slip moving in opposite directions the results thus illustrate one mechanism which limits the maximum amount of slip during an earthquake even in the absence of strong barriers

global variations of stress drop for moderate to large earthquakes 1 we investigate the global variation of earthquake stress drops using spectra of about 2000 events of mb 5 5 between 1990 and 2007 we use an iterative least squares method to isolate source displacement spectra from travel path and receiver contributions based on a convolutional model the observed p wave source spectra are corrected with a globally averaged empirical correction spectrum and estimates of near source attenuation assuming a brune type source model we estimate corner frequencies and compute stress drops stress drop estimates for individual earthquakes range from about 0 3 to 50 mpa but the median stress drop of about 4 mpa does not vary with moment implying earthquake self similarity over the mw 5 2 to 8 3 range of our data a comparison of our results with previous studies confirms this observation over most of the instrumentally observable magnitude range while the absolute values of our estimated stress drops depend upon the assumed source model we identify relative regional variations of stress drop that are robust with respect to the processing parameters and modeling assumptions which includes an inherent assumption of constant rupture velocity we find a dependence of median stress drop on focal mechanism with a factor of 3 5 times higher stress drops for strike slip earthquakes and also find a factor of 2 times higher stress drops for intraplate earthquakes compared to interplate earthquakes

spatial and temporal stress drop variations in small earthquakes near parkfield california 1 we estimate source parameters from spectra of 42367 earthquakes between 1984 and 2005 that occurred in the parkfield segment of the san andreas fault in central california we use a method that isolates the source term of the displacement spectra based on a convolutional model and correct the observed p wave source spectra with a spatially varying empirical green s function egf our brune type stress drop estimates vary from 0 1 to over 100 mpa with a median value of 6 75 mpa which is nearly constant with moment implying self similarity over the ml 0 5 to 3 0 range of our data the corner frequency decreases for earthquakes at shallower depths consistent with slower rupture velocities and reduced shear wave velocities in local velocity models the estimated median stress drops show significant lateral variations we find lower stress drops in the middle mountain asperity and along the creeping fault section and higher stress drops in the hypocentral region of the 2004 m6 0 parkfield earthquake the main shock did not alter the overall pattern of high and low stress drop regions however a statistical test reveals areas with significant changes in computed stress drops after the main shock which we compare to estimated absolute shear stress changes from a main shock slip model by calculating t from the spectral egf ratio we also identify areas with increased attenuation after the main shock and we are able to distinguish source effects and near source attenuation effects in the spectral analysis these results are confirmed independently from spectral ratios of repeating microearthquake clusters

the transition of dynamic rupture styles in elastic media under velocity weakening friction although kinematic earthquake source inversions show dominantly pulse like subshear rupture behavior seismological observations laboratory experiments and theoretical models indicate that earthquakes can operate with different rupture styles either as pulses or cracks that propagate at subshear or supershear speeds the determination of rupture style and speed has important implications for ground motions and may inform about the state of stress and strength of active fault zones we conduct 2d in plane dynamic rupture simulations with a spectral element method to investigate the diversity of rupture styles on faults governed by velocity and state dependent friction with dramatic velocity weakening at high slip rate our rupture models are governed by uniform initial stresses and are artificially initiated we identify the conditions that lead to different rupture styles by investigating the transitions between decaying steady state and growing pulses cracks sub shear and super shear ruptures as a function of background stress nucleation size and characteristic velocity at the onset of severe weakening our models show that small changes of background stress or nucleation size may lead to dramatic changes of rupture style we characterize the asymptotic properties of steady state and self similar pulses as a function of background stress we show that an earthquake may not be restricted to a single rupture style but that complex rupture patterns may emerge that consist of multiple rupture fronts possibly involving different styles and back propagating fronts we also demonstrate the possibility of a super shear transition for pulse like ruptures finally we draw connections between our findings and recent seismological observations

calcium carbonate precipitation mediated by bacterial carbonic anhydrase in a karst cave crystal morphology and stable isotopic fractionation abstract stable oxygen 18o and carbon 13c isotopes of speleothems are widely used as important proxies for paleoclimatic and paleoenvironment reconstructions however the influence of microbial activity on carbon and oxygen isotope fractionation during speleothem precipitation remains unclear bacterial carbonic anhydrase ca can promote calcium carbonate precipitation to catalyze the mutual transformation between co2 and hco3 ca producing bacteria lysinibacillus sp strain lhxy2 were separated in the xueyu cave chongqing sw china and used in laboratory and cave in situ models to investigate their influence on the precipitation amount mineral components crystal morphology and carbon and oxygen isotope fractionation of caco3 a ca activity gradient was applied in the laboratory model by considering various ca inhibitor acetazolamide az concentrations which showed that the ca activity could substantially enhance precipitation alter the mineral components and morphology and reduce the 13c and 18o values of the caco3 formed most importantly the laboratory and in situ model results revealed approximately 7 and 1 4 13c shifts respectively compared to the bacteria free model results which indicated that microbial driven carbon isotopic fractionation can cause great uncertainties in paleoclimate and paleoenvironment reconstructions

elastodynamic analysis for slow tectonic loading with spontaneous rupture episodes on faults with rate and state dependent friction we present an efficient and rigorous numerical procedure for calculating the elastodynamic response of a fault subjected to slow tectonic loading processes of long duration within which there are episodes of rapid earthquake failure this is done for a general class of rate and state dependent friction laws with positive direct velocity effect the algorithm allows us to treat accurately within a single computational procedure loading intervals of thousands of years and to calculate for each earthquake episode initially aseismic accelerating slip prior to dynamic rupture the rupture propagation itself rapid post seismic deformation which follows and also ongoing creep slippage throughout the loading period in velocity strengthening fault regions the methodology is presented using the two dimensional 2 d antiplane spectral formulation and can be readily extended to the 2 d in plane and 3 d spectral formulations and with certain modifications to the space time boundary integral formulations as well as to their discretized development using finite difference or finite element methods the methodology can be used to address a number of important issues such as fault operation under low overall stress interaction of dynamic rupture propagation with pore pressure development patterns of rupture propagation in events nucleated naturally as a part of a sequence the earthquake nucleation process earthquake sequences on faults with heterogeneous frictional properties and or normal stress and others the procedure is illustrated for a 2 d crustal strike slip fault model with depth variable properties for lower values of the state evolution distance of the friction law small events appear the nucleation phases of the small and large events are very similar suggesting that the size of an event is determined by the conditions on the fault segments the event is propagating into rather than by the nucleation process itself we demonstrate the importance of incorporating slow tectonic loading with elastodynamics by evaluating two simplified approaches one with the slow tectonic loading but no wave effects and the other with all dynamic effects included but much higher loading rate

the seismic radiation from composite models of faulting abstract the failure of an asperity i e the dynamic rupture of a small fault area with finite stress drop surrounded by a broken or weak fault area which has no stress drop but which slips after the asperity fails is proposed as a model for the rupture process of a subevent in a composite earthquake the rupture area of the composite earthquake surrounding the subevent is modeled by the weak fault area surrounding the asperity in the subevent model the resulting seismic moment of the subevent is proportional to the stress drop and the rupture area of the subevent as well as the radius of the composite earthaquake by setting the stress drops of the asperity models equal to the dynamic stress drops of the subevents the composite earthquake can be modeled as the sum of a set of subevents which cover the rupture area of the composite earthquake the scaling of the high and low frequency radiation from composite earthquakes composed of asperities is commensurate with generally observed spectral scaling laws in contrast to composite earthquakes composed of cracks or smaller earthquakes a simple filtering strategy is proposed for filtering the waveforms radiated by cracks to approximate the waveforms radiated by asperities the p and s waves radiated by an m l 5 2 earthquake which occurred on 9 may 1983 at coalinga california are simulated using the p and s waves radiated by an m l 3 6 aftershock the aftershock waveforms are first filtered to approximate the radiation from asperities with the appropriate rupture areas and then the waveforms of 12 asperity subevents are summed together to simulate the waveforms and spectra of the composite earthquake

review of aragonite and calcite crystal morphogenesis in thermal spring systems abstract aragonite and calcite crystals are the fundamental building blocks of calcareous thermal spring deposits the diverse array of crystal morphologies found in these deposits which includes monocrystals mesocrystals skeletal crystals dendrites and spherulites are commonly precipitated under far from equilibrium conditions such crystals form through both abiotic and biotic processes many crystals develop through non classical crystal growth models that involve the arrangement of nanocrystals in a precisely controlled crystallographic register calcite crystal morphogenesis has commonly been linked to a driving force which is a conceptual measure of the distance of the growth conditions from equilibrium conditions essentially this scheme indicates that increasing levels of supersaturation and various other parameters that produce a progressive change from monocrystals and mesocrystals to skeletal crystals to crystallographic and non crystallographic dendrites to dumbbells to spherulites despite the vast amount of information available from laboratory experiments and natural spring systems the precise factors that control the driving force are open to debate the fact that calcite crystal morphogenesis is still poorly understood is largely a reflection of the complexity of the factors that influence aragonite and calcite precipitation available information indicates that variations in calcite crystal morphogenesis can be attributed to physical and chemical parameters of the parent water the presence of impurities the addition of organic or inorganic additives to the water the rate of crystal growth and or the presence of microbes and their associated biofilms the problems in trying to relate crystal morphogenesis to specific environmental parameters arise because it is generally impossible to disentangle the controlling factor s from the vast array of potential parameters that may act alone or in unison with each other

rupture dynamics and ground motion from 3 d rough fault simulations 1 we perform three dimensional 3 d numerical calculations of dynamic rupture along non planar faults to study the effects of fault roughness on rupture propagation and resultant ground motion the fault roughness model follows a self similar fractal distribution over length scales spanning three orders of magnitude from 102 to 105 m the fault is governed by a strongly rate weakening friction and the bulk material is subject to drucker prager viscoplasticity fault roughness promotes the development of self healing rupture pulses and a heterogeneous distribution of fault slip at the free surface and at depth the inelastic deformation generated by the large dynamic stress near rupture fronts occurs in a narrow volume around the fault with heterogeneous thickness correlated to local roughness slopes inelastic deformation near the free surface however is induced by the stress waves originated from dynamic rupture at depth and spreads to large distances 10 km away from the fault the present simulations model seismic wave excitation up to 10 hz with rupture lengths of 100 km permitting comparisons with empirical studies of ground motion intensity measures of engineering interest characteristics of site averaged synthetic response spectra including the distance and period dependence of the median values absolute level and intra event standard deviation are comparable to appropriate empirical estimates throughout the period range 0 1 3 0 s this class of model may provide a viable representation of the ground motion excitation process over a wide frequency range in a large spatial domain with potential applications to the numerical prediction of source and path specific effects on earthquake ground motion

microseismicity simulated on asperity like fault patches on scaling of seismic moment with duration and seismological estimates of stress drops observations show that microseismic events from the same location can have similar source durations but different seismic moments violating the commonly assumed scaling we use numerical simulations of earthquake sequences to demonstrate that strength variations over seismogenic patches provide an explanation of such behavior with the event duration controlled by the patch size and event magnitude determined by how much of the patch area is ruptured we find that stress drops estimated by typical seismological analyses for the simulated sources significantly increase with the event magnitude ranging from 0 006 to 8 mpa however the actual stress drops determined from the on fault stress changes are magnitude independent and 3 mpa our findings suggest that fault heterogeneity results in local deviations in the moment duration scaling and earthquake sources with complex shapes of the ruptured area for some of which stress drops may be significantly 100 1 000 times underestimated by the typical seismological methods

pulse like ruptures induced by low velocity fault zones low velocity fault zones lvfzs are found in most mature faults they are usually 100 400 m wide and have 20 60 wave velocity reductions relative to the country rock to study the effect of lvfzs on earthquake rupture and the radiated wavefield we conducted two dimensional 2 d simulations of dynamic rupture on faults that bisect a lvfz considering a range of velocity reductions and widths most earthquakes apparently have slip rise times much shorter than their overall rupture duration a number of dynamic mechanisms for such pulse like ruptures have been proposed including frictional self healing fault strength heterogeneities and bimaterial effects we find that ruptures in lvfzs with strong enough wave velocity contrast behave as pulses these pulses are generated by fault locking induced by waves reflected from the boundaries of the lvfz this mechanism of pulse generation is robust to variations of initial stress smoothness of the lvfz structure rupture mode and exclusion of frictional healing moreover we find that lvfzs can generate complex rupture patterns lvfzs with low velocity reduction induce multiple rupture fronts involving coexisting pulses and cracks lvfzs with certain widths can accelerate the transition to supershear rupture speed these additional effects of lvfzs on dynamic rupture can contribute to the complexity of high frequency ground motions

three dimensional finite difference simulation of fault dynamics rectangular faults with fixed rupture velocity we analyze three dimensional finite difference solutions for a simple shear crack model of faulting to determine the effects of fault length and width on the earthquake slip function the fault model is dynamic with only rupture velocity fault dimensions and dynamic stress drop prescribed the numerical solutions are accurate for frequencies up to 5 hz and are combined with asymptotic results for shear cracks in order to characterize the slip function at higher frequencies near the hypocenter the slip velocity exhibits a square root singularity whose intensity increases with hypocentral distance at distances greater than the fault width w growth of the velocity intensity ceases and the slip function becomes nearly invariant with distance along the fault length closed form expressions are developed for the dependence of static slip s slip rise time tr and slip velocity intensity v on fault geometry along the center line of a long narrow fault at hypocentral distances exceeding w these expressions reduce to s w tr 0 5 w vr and v w 2 vr where is the dynamic stress drop the shear modulus and vr the rupture velocity the numerical results imply that uniform dislocation kinematic earthquake models in which slip is represented by a ramp time function will underpredict high frequency ground motion relative to low frequency ground motion a further implication of the numerical solutions is that the nature of inelastic processes at the advancing edge of a long fault will depend on fault width but will be independent of rupture length