synorogenic melting of mafic lower crust constraints from geochronology petrology and sr nd pb and o isotope geochemistry of quartz diorites damara orogen namibia quartz diorites represent the earliest ca 540 ma and most primitive plutonic rocks in the pan african damara belt and they pre date the main phase of high t regional metamorphism two suites of synorogenic quartz diorites are unusual among damaran intrusive rocks in their elemental and isotopic features comparison of the diorite compositions with melts from amphibolite dehydration melting experiments points to a garnet bearing meta tholeiite probably enriched in k2o as a likely source rock partial melting processes generated mafic ca 50 wt sio2 quartz diorites in the deep crust at temperatures of between 1 000 and 1 100 c based on comparison with experimental results and similar temperature estimates based on p2o5 solubility in mafic rocks subsequently the quartz diorites evolved by multistage polybaric differentiation processes including fractional crystallization of mainly hornblende and plagioclase and assimilation of felsic basement gneisses although their chemical characteristics high lile low hfse resemble those of other quartz diorites with calc alkaline affinities they differ in their enriched sr initial 87sr 86sr 0 70943 0 71285 nd initial e nd 9 1 to 15 2 and o 18o 6 8 8 1 isotope compositions neodymium model ages tdm that range from 1 7 to 2 2 ga and large variation in 207pb 204pb relative to 206pb 204pb indicates involvement of ancient crustal material lead 206pb 204pb 17 08 17 23 207pb 204pb 15 53 15 62 208pb 204pb 37 71 38 16 isotope compositions are strongly retarded indicating that the source underwent a pre pan african u pb fractionation and u depletion it is proposed that the quartz diorites originated by synorogenic high temperature melting of mafic lower crust this contrasts with previous suggestions favouring an origin of these rocks by melting of an enriched mantle during pan african times with characteristics modified by subduction of oceanic crust and sedimentary rocks

characterization of nucleation during laboratory earthquakes 1 we observe the nucleation phase of in plane ruptures in the laboratory we show that the nucleation is composed of two distinct phases a quasi static and an acceleration stage followed by dynamic propagation we propose an empirical model which describes the rupture length evolution the quasi static phase is described by an exponential growth while the acceleration phase is described by an inverse power law of time the transition from quasi static to accelerating rupture is related to the critical nucleation length which scales inversely with normal stress in accordance with theoretical predictions and to a critical surfacic power which may be an intrinsic property of the interface finally we discuss these results in the frame of previous studies and propose a scaling up to natural earthquake dimensions

roughness of natural fault surfaces the roughness of fault surfaces is important in the mechanics of fault slip and could play a role in determining whether sliding occurs via earthquakes or fault creep we have made preliminary measurements of the power spectral density of several fault surfaces over the wavelength range from 10 5 to 1 m using field and laboratory scale profilimeters the fault surfaces are strongly anisotropic profiles parallel to the slip direction have amplitudes about one order of magnitude lower than those perpendicular to the slip direction over most of the wavelength interval measured fault roughness perpendicular to the slip direction is similar to the roughness of natural joints the greater smoothness in the slip direction presumably represents wear resulting from slip combining our data with previous measurements of the roughness spectrum of the san andreas fault shows that fault surfaces are fractal over nearly eleven orders of magnitude in wavelength

a spatial random field model to characterize complexity in earthquake slip 1 finite fault source inversions reveal the spatial complexity of earthquake slip over the fault plane we develop a stochastic characterization of earthquake slip complexity based on published finite source rupture models in which we model the distribution of slip as a spatial random field the model most consistent with the data follows a von karman autocorrelation function acf for which the correlation lengths a increase with source dimension for earthquakes with large fault aspect ratios we observe substantial differences of the correlation length in the along strike a x and downdip a z directions increasing correlation length with increasing magnitude can be understood using concepts of dynamic rupture propagation the power spectrum of the slip distribution can also be well described with a power law decay i e a fractal distribution in which the fractal dimension d remains scale invariant with a median value d 2 29 0 23 while the comer wave number k c which is inversely proportional to source size decreases with earthquake magnitude accounting for larger slip patches for large magnitude events our stochastic slip model can be used to generate realizations of scenario earthquakes for near source ground motion simulations

correlation of earthquake source parameters inferred from dynamic rupture simulations 1 we analyzed 315 dynamic strike slip rupture models computed up to 5 0 hz to get a quantitative understanding of the correlation and amplitude distributions of parameters describing the earthquake source such as slip and rupture velocity to account for the epistemic uncertainty of the problem we constructed a database of dynamic ruptures computed by ourselves and other authors this database contains ruptures computed using different models of initial stress peak stress and critical slip weakening distance using the set of computed ruptures we constructed probability density functions pdfs for the amplitude distributions of the source parameters and for the correlation between the source parameters we tried to extract parameter pairs that showed a small variability in the spatial correlation given the large epistemic uncertainty in the input we only analyzed the areas on the fault with subshear propagation speed the principal findings are as follows 1 final slip amplitude does not show correlation with the local rupture velocity 2 final slip amplitude correlates well with risetime 3 rupture velocity correlates well with peak slip rate and the duration of the impulsive part of the slip rate function 4 the pdf of rupture velocity risetime and peak slip rate depends on the distance from the nucleation zone 5 fracture energy is not the single controlling factor for the rupture velocity the slope of the linear slip weakening curve has a significant effect on the rupture velocity 6 the crack length length that is slipping at a given time decreases with the distance from the nucleation zone

petrology of an intrusion related high grade migmatite implications for partial melting of metasedimentary rocks and leucosome forming processes intrusion related migmatites comprise a substantial part of the high grade part of the southern damara orogen namibia which is dominated by al rich metasedimentary rocks and various granites migmatites consist of melanosomes with biotite sillimanite garnet cordierite hercynite and leucosomes are garnet and cordierite bearing metamorphic grade throughout the area is in the upper amphibolite to lower granulite facies 5 6 kbar at 730 750 c field evidence petrographic observations chemical data and mass balance calculations suggest that intrusion of granitic magmas and concomitant partial melting of metasedimentary units were the main processes for the generation of the migmatites the intruding melts were significantly modified by magma mixing with in situ partial melts accumulation of mainly feldspar and contamination with garnet from the wall rocks however it is suggested that these melts originally represented disequilibrium melts from a metasedimentary protolith the occurrence of lile hfse and lree enriched and depleted residues within the leucosomes implies that both quartzo feldspathic and pelitic rocks were subjected to partial melting isotope ratios of the leucosomes are rather constant 143nd 144nd 500 ma 0 511718 0 511754 e nd 500 ma 3 54 to 5 11 and sr 87sr 86sr 500 ma 0 714119 0 714686 the metasedimentary units have rather constant nd isotope ratios 143nd 144nd 500 ma 0 511622 0 511789 e nd 500 ma 3 70 to 6 93 but variable sr isotope ratios sr 87sr 86sr 500 ma 0 713527 0 722268 the most restitic melanosome mel 4 has a sr isotopic composition of 87sr 86sr 500 ma 0 729380 oxygen isotopes do not mirror the proposed contamination process due to the equally high 18o contents of metasediments and crustal melts however the most lile depleted residue mel 4 shows the lowest 18o value 10 mass balance calculations suggest high degrees of partial melting 20 40 it is concluded that partial melting was promoted by heat transfer and release of a fluid phase from the intruding granites high degrees of partial melting can be reached as long as the available h2o derived from the crystallization of the intruding granites is efficiently recycled within the rock volume due to the limited amounts of in situ melting it seems likely that such regional migmatite terranes are not the sources for large intrusive granite bodies the high geothermal gradient inferred from the metamorphic conditions was probably caused by exhumation of deep crustal rocks and contemporaneous intrusion of huge masses of granitoid magmas the davetsaub area represents an example of migmatites formed at moderate pressures and high temperatures and illustrates some of the reactions that may modify leucosome compositions the area provides constraints on melting processes operating in high grade metasedimentary rocks

stress field associated with the rupture of the 1992 landers california earthquake and its implications concerning the fault strength at the onset of the earthquake we investigate the space and time history of the shear stress produced on the fault during the 1992 landers earthquake the stress is directly calculated from the tomographic image of slip on the fault derived from near source strong motion data the results obtained shed some light on why the earthquake rupture cascaded along a series of previously distinct fault segments to produce the largest earthquake in california in over 40 years rupture on the 30 km long northernmost segment of the fault was triggered by a large dynamic increase of the stress field of the order of 20 to 30 mpa produced by the rupturing of the adjacent fault segments such a large increase was necessary to overcome the static friction on this strand of the fault unfavorably oriented in today s tectonic stress field this misorientation eventually led to the arrest of rupture the same mechanism explains why rupture broke only a small portion of the johnson valley fault on which the earthquake originally started before jumping to an adjacent fault more favorably oriented we conclude from these results that the dynamic stress field could not sustain and drive the rupture along the strongly misoriented nw se strands of the preexisting fault system instead the dynamic stress field produced new fractures favorably oriented in a n s direction and connecting parts of the old fault system

effect of water and rock composition on re strengthening of cohesive faults during the deceleration phase of seismic slip pulses abstract the elastic strain energy release rate and seismic waves emitted during earthquakes are controlled by the on fault temporal evolution of the shear stress during rupture propagation high velocity friction experiments highlighted that shear stress on the fault surface evolves rapidly during seismic slip pulses this temporal evolution of shear stress is controlled by both fault weakening at seismic slip initiation and re strengthening rate towards the end of slip while numerous studies focused on fault weakening less attention was given to co seismic re strengthening processes here we performed 53 friction experiments normal stress 30 mpa slip rate 6 5 m s 1 imposing constant slip acceleration and deceleration 7 8 m s 2 on cohesive carrara marble 99 calcite and micro gabbro silicate built rock under dry vacuum and water pressurized conditions microstructural observations showed that micro gabbro accommodated seismic slip by bulk melting of the sliding surfaces whereas carrara marble by coupled decarbonation and grain size dependent crystal plastic processes under room humidity conditions and low imposed power density i e product of normal stress per slip rate re strengthening rate during the deceleration stage was up to 17 times faster in marble than in micrograbbro in the latter the re strengthening rate increased slightly with the power density the presence of water enhanced further this trend on the contrary in marbles the re strengthening rate decreased drastically with power density and in the presence of water our experimental observations highlighted the first order importance of the mineralogy and rheology of the slip zone materials and to a second order of the presence of water in controlling co seismic re strengthening of faults during seismic slip deceleration

slow slip events on the whillans ice plain antarctica described using rate and state friction as an ice stream sliding law the whillans ice plain wip antarctica experiences twice daily tidally modulated stick slip cycles slip events last about 30 minutes have sliding velocities as high as 0 5 mm s 15 km yr and have total slip 0 5 m slip events tend to occur during falling ocean tide just after high tide and just before low tide to reproduce these characteristics we use rate and state friction which is commonly used to simulate tectonic faulting as an ice stream sliding law this framework describes the evolving strength of the ice bed interface throughout stick slip cycles we present simulations that resolve the cross stream dimension using a depth integrated treatment of an elastic ice layer loaded by tides and steady ice inflow steady sliding with rate weakening friction is conditionally stable with steady sliding occurring for sufficiently narrow ice streams relative to a nucleation length stick slip cycles occur when the ice stream is wider than the nucleation length or equivalently when effective pressures exceed a critical value ice streams barely wider than the nucleation length experience slow slip events and our simulations suggest that the wip is in this slow slip regime slip events on the wip show a sense of propagation and we reproduce this behavior by introducing a rate strengthening region in the center of the otherwise rate weakening ice stream if pore pressures are raised above a critical value our simulations predict that the wip would exhibit quasi steady tidally modulated sliding as observed on other ice streams this study validates rate and state friction as a sliding law to describe ice stream sliding styles

effective friction law for small scale fault heterogeneity in 3d dynamic rupture 1 we address the problem of modeling dynamic rupture on multiscale heterogeneous faults in 3d under the assumption of slip weakening friction we numerically construct effective friction laws that integrate the effects of small scale heterogeneity during the rupture this homogenization process is based on the description of the initial phase of the rupture by the dominant unstable spectral mode its dynamics is influenced by the geometry of the fault the static friction heterogeneities and the friction law we first define a periodic small scale heterogeneous model introducing heterogeneity in the distribution of the static friction coefficient we then describe a method for constructing this effective friction law applying this new law homogeneously on the fault permits to reproduce the dynamic evolution of the heterogeneous fault furthermore we show that the effective friction law can be used to replace small scale heterogeneities in two scale heterogeneous models while preserving their effects we study three kinds of two scale models with growing complexity first periodic at both scales then periodic only at small scale and finally irregular at both scales this homogenization method can be adapted to the case where the heterogeneity is introduced in the initial stress rather than in the static friction value finally we show in a simple example that the effective friction law permits to reproduce the transition between subshear and supershear rupture propagation originally produced by heterogeneities on the fault

dynamic modeling of the 1992 landers earthquake we have used observed band pass filtered accelerograms and a previously determined slip distribution to invert for the dynamic rupture propagation of the 1992 landers earthquake in our simulations dynamic rupture grows under the simultaneous control of initial stress and rupture resistance by friction which we modeled using a simple slip weakening law we used a simplified landers fault model where the fault segments were combined into a single vertical planar fault by trial and error we modified an initial stress field inferred from the kinematic slip distribution proposed by wald and heaton 1994 until dynamic rupture generated a rupture history and final slip distribution that approximately matched those determined by the kinematic inversion we found that rupture propagation was extremely sensitive to small changes in the distribution of prestress and that a delicate balance with energy release rate controls the average rupture speed for the inversion we generated synthetic 0 5 hz ground displacements using an efficient green s function propagator method axitra this method enables us to propagate the radiation generated by the dynamic rupture to distances greater than those feasible using the finite difference method the dynamic model built by trial and error inversion provides a very satisfactory fit between synthetics and strong motion data we validated this model using records from stations used in the slip inversion as well as some which were not included we also inverted for a complementary model that fits the data just as well but in which the initial stress was perfectly uniform while rupture resistance was heterogeneous this demonstrates that inversion of ground motion is nonunique

faulting characteristics of supershear earthquakes article i nfo recent observations of large continental strike slip earthquakes show that different fault segments may rupture at different speeds and that rupture may propagate faster than the shear wave velocity of surrounding rocks we report that all the documented occurrences of supershear rupture are associated with faults which have simple geometry the surface trace of these faults is described in the field or seen on satellite images as remarkably linear continuous and narrow segmentation features along these segments are small or absent and the deformation is highly localized as theoretically predicted supershear is clearly associated with mode ii rupture

stress breakdown time and slip weakening distance inferred from slip velocity functions on earthquake faults we estimate the critical slip weakening distance on earthquake faults by using a new approach which is independent of the estimate of fracture energy or radiated seismic energy the approach is to find a physically based relation between the breakdown time of shear stress tb the time of peak slip velocity tpv and the slip weakening distance dc from the time histories of shear stress slip and slip velocity at each point on the fault which can be obtained from dynamic rupture calculations using a simple slip weakening friction law numerical calculations are carried out for a dynamic shear crack propagating either spontaneously or at a fixed rupture velocity on a vertical fault located in a 3d half space and a more realistic horizontally layered structure with finite difference schemes the results show that tpv is well correlated with tb for faults even with a heterogeneous stress drop dis tribution except at locations near strong barriers and the fault edges we also inves tigate this relation for different types of slip weakening behavior we have applied the method to two recent strike slip earthquakes in western japan the 2000 tottori and the 1995 kobe events we integrated the slip velocity functions on the vertical fault obtained from kinematic waveform inversion of strong motion and teleseismic records from the arrival time of rupture tr to the time of the peak slip velocity tpv and we then corrected the slip obtained at tpv for the errors expected from the dynamic calculations it was found that the slip weakening dis tance d c estimated in the frequency window between 0 05 and 0 5 hz ranges between 40 and 90 cm on the two earthquake faults however if we consider the limited frequency resolution of the observed waveforms probable time errors in the slip velocity functions obtained from kinematic inversion and the uncertainty of the slip weakening behavior the above estimates may be those located between the minimum resolvable limit and the upper bound of their real values the estimated dc values do not necessarily seem to indicate larger values in the shallower part and smaller values in the deeper part of the fault but rather a spatially heterogeneous distribution that appears to be dependent on the local maximum slip this possible dependence might be interpreted by the frictional properties of the fault such as the degree of roughness or the thickness of gouge layers in addition to stress heterogeneities

high resolution 3d laser scanner measurements of a strike slip fault quantify its morphological anisotropy at all scales 1 the surface roughness of a recently exhumed strike slip fault plane has been measured by three independent 3d portable laser scanners digital elevation models of several fault surface areas from 1 m2 to 600 m2 have been measured at a resolution ranging from 5 mm to 80 mm out of plane height fluctuations are described by non gaussian distribution with exponential long range tails statistical scaling analyses show that the striated fault surface exhibits self affine scaling invariance with a small but significant directional morphological anisotropy that can be described by two scaling roughness exponents h1 0 7 in the direction of slip and h2 0 8 perpendicular to the direction of slip

characterization of fault roughness at various scales implications of three dimensional high resolution topography measurements accurate description of the topography of active fault surfaces represents an important geophysical issue because this topography is strongly related to the stress distribution along fault planes and therefore to processes implicated in earthquake nucleation propagation and arrest to date due to technical limitations studies of natural fault roughness either performed using laboratory of field profilometers were obtained mainly from 1 d profiles with the recent development of light detection and ranging lidar apparatus it is now possible to measure accurately the 3 d topography of rough surfaces with a comparable resolution in all directions both at field and laboratory scales in the present study we have investigated the scaling properties including possible anisotropy properties of several outcrops of two natural fault surfaces vuache strike slip fault france and magnola normal fault italy in limestones at the field scale digital elevation models of the fault roughness were obtained over surfaces of 0 25 m2 to 600 m2 with a height resolution ranging from 0 5 mm to 20 mm at the laboratory scale the 3 d geometry was measured on two slip planes using a laser profilometer with a spatial resolution of 20 m and a height resolution less than 1 m

heterogeneous distribution of the dynamic source parameters of the 1999 chi chi taiwan earthquake 1 the spatial and temporal distribution of the stress on the fault plane of the 1999 chi chi taiwan earthquake is calculated from kinematic inversion results using a three dimensional finite difference method for solving the elastodynamic equations we analyze the relations between stress and slip for all grid positions on the fault and use these relations to infer the friction law for the rupture the dynamic source parameters were also determined our results show that for most of the points on the fault the relation between stress and slip was consistent with the slip weakening law during the rupture process especially for those points with large slip however consistency with the velocity weakening law is not clear from the observed relation between stress and slip velocity the distributions of the dynamic parameters on the fault are very heterogeneous the peak value of the static stress drop is 35 mpa in general high stress drop occurred in the areas with large slip the estimated strength excesses are generally small suggesting that the tectonic shear stress had reached the level of the fault strength before the main shock the slip weakening distance dc and the fracture energy gc are proportional to the final slip the aftershock activity correlates with the spatial distribution of dynamic source parameters usually the aftershocks near the fault plane are concentrated in regions with small or negative static stress drop and there were few aftershocks in regions which had large values of critical slip weakening distance dc

sensitivity of high frequency ground motion to kinematic source parameters empirical ground motion prediction equations are calibrated from past earthquake seismic recordings although they are often used to predict peak ground acceleration pga and its variability the use of these equations to predict near fault pga remains questionable due to the scarcity of near fault recordings for large earthquakes e g mai encyclopedia of complexity and systems science pp 4435 4474 new york springer https doi org 10 1007 978 0 387 30440 3 263 2009 the simulation of strong ground motion offers an attractive alternative for the assessment of near fault seismic hazards but the a priori choice of the source parameters used to describe the fault rupture process remains a complex issue in order to better understand the effects of rupture parameters on surface ground motion and to capture the key source ingredients that impact ground motion variability we simulated ground motions produced by various m7 strike slip rupture earthquake scenarios on vertical faults we computed ground motion up to 5 hz using the far field approximation as well as at the near field stations located at 5 km 25 km and 70 km from the fault assuming a visco elastic medium the kinematic rupture parameters are modeled using a statistical rupture model generator as proposed by song et al geophysical journal international 196 3 1770 1786 2014 our work demonstrates that pga is mostly generated by abrupt changes in the rupture propagation e g stopping phases at the fault boundaries or strong heterogeneities of rupture speed along the fault we observed that pga is mostly controlled by average rupture speed and average stress drop in the far field and to a lesser extent by the standard deviation of the rupture speed it is worth noting that for the set of stations in study the correlation between source parameters and spatial correlation length does not affect average pga and related variability significantly

a new multilayered visco elasto plastic experimental model to study strike slip fault seismic cycle nowadays technological advances in satellite imagery measurements as well as the development of dense geodetic and seismologic networks allow for a detailed analysis of surface deformation associated with active fault seismic cycle however the study of earthquake dynamics faces several limiting factors related to the difficulty to access the deep source of earthquake and to integrate the characteristic time scales of deformation processes that extend from seconds to thousands of years to overcome part of these limitations and better constrain the role and couplings between kinematic and mechanical parameters we have developed a new experimental approach allowing for the simulation of strike slip fault earthquakes and analyze in detail hundreds of successive seismic cycle model rheology is made of multilayered visco elasto plastic analog materials to account for the mechanical behavior of the upper and lower crust and to allow simulating brittle ductile coupling postseismic deformation phase and far field stress transfers the kinematic evolution of the model surface is monitored using an optical system based on subpixel spectral correlation of high resolution digital images first results show that the model succeed in reproducing the deformation mechanisms and surface kinematics associated to the main phases of the seismic cycle indicating that model scaling is satisfactory these results are comforted by using numerical algorithms to study the strain and stress distribution at the surface and at depth along the fault plane our analog modeling approach appears then as an efficient complementary approach to investigate earthquake dynamics

scaling of the shear rupture process from nucleation to dynamic propagation implications of geometric irregularity of the rupturing surfaces a series of systematic high resolution laboratory experiments have been performed on the nucleation of propagating slip failure on preexisting faults having different surface roughnesses to demonstrate how the size scale and duration of shear rupture nucleation are affected by geometric irregularity of the rupturing surfaces on the basis of the experimental results it has been discussed theoretically how consistently scale dependent physical quantities inherent in shear rupture are scaled the experiments led to conclusive results that the nucleation process consists of two phases phase i an initial quasi static phase and phase ii a subsequent accelerating phase and that the nucleation process is greatly affected by geometric irregularities on the rupturing surfaces in phase i the rupture grows at a slow steady speed which is independent of the rupture growth length l in contrast during phase ii the rupture develops at accelerating speeds v which increase with an increase in l obeying a power law v vs l c n where vs is the shear wave velocity c is the characteristic length representing the geometric irregularity of the fault surfaces and and n are constants 8 87 10 29 and n 7 31 scale dependency of scale dependent physical quantities including the nucleation zone size and its duration is commonly ascribed to scale dependency of the slip dependent constitutive law parameter dc which is in turn governed by c it has been discussed that a unified comprehension can be provided for shear rupture of any size scale if the constitutive law for shear rupture is formulated as a slip dependent law

nucleation and early seismic propagation of small and large events in a crustal earthquake model 1 earthquake nucleation and early seismic propagation are studied in a two dimensional strike slip fault model with depth variable properties the fault is governed by the dieterich ruina rate and state friction law we use an efficient and rigorous numerical procedure for elastodynamic analysis of earthquake sequences on slowly loaded faults developed by lapusta et al 2000 we find that for decreasing values of the characteristic slip distance of the friction law small events appear at the transition from the locked to creeping behavior toward the bottom of the seismogenic zone small and large events have very similar nucleation phases in our simulations here by nucleation phase we mean gradually accelerating aseismic slip in a small slowly expanding zone before the breakout of the dynamic seismically detectable event moment acceleration to which velocity seismograms are proportional in early stages of seismic propagation exhibits irregular fluctuations in the form of speedups and slowdowns in the moment release rate consistently with observations as reported by ellsworth and beroza 1995 our simulations show that such irregular moment acceleration can at least in part be due to the heterogeneous stress distribution imprinted on the fault by the arrest of previous small events and by stress concentrations at the borders of creeping regions and to partial arrest of the rupture in velocity strengthening fault regions which inhibit seismic slip index terms 7209 seismology earthquake dynamics and mechanics 7260 seismology theory and modeling 3220 mathematical geophysics nonlinear dynamics 7230 seismology seismicity and seismotectonics 3230 mathematical geophysics numerical solutions 8164 tectonophysics stresses crust and lithosphere keywords earthquake nucleation phase event clustering irregular moment release stress concentrations rate and state friction earthquake sequences

slip weakening distance in dynamic rupture of in slab normal faulting earthquakes we apply the above method to three large in slab normal faulting earthquakes in the mexican subduction zone to do this we calculate the spatial distribution of slip velocity functions and final slip from kinematic waveform inversion of strong motion and teleseismic records and the stress history and final stress change from dynamic rupture calculations by integrating the slip velocity functions obtained from the inversion from the rupture arrival time to the time of peak slip velocity we obtain slip dat t pv and then correct it for dc at t b through dynamic calculations we also estimate the lowest resolvable limit and probable errors of dc from the slip velocity functions and its upper bound from a theoretical constraint between the dynamic stress drop and dc we found that the slip weakening distance dc estimated in the frequency band between 0 05 and 0 5 hz ranges between 40 and 120 cm on the in slab fault of the 1999 oaxaca earthquake mw 7 5 the largest dc is detected in the central fault and in part of the deeper sections and dc in the zone around the hypocentre ranges between 50 and 70 cm the estimated dc values appear to be less depth dependent but are rather more dependent on the local maximum slip this possible slip dependence might be interpreted by the degree of fault roughness in addition to stress heterogeneities the fracture energy g in the central section and in the hypocentral zone are roughly estimated to be of the order of 10 15 and 5 8 mj m 2 respectively both of the estimated dc and g values are somewhat larger than those on the vertical fault of two recent shallow strike slip earthquakes in western japan

on relations between earthquake population and asperity population on a fault data were compiled on the trend of teleseismic short period t 1 4 s peak amplitude and spectral level vs m 0 for log m 0 26 slopes in log log scale of these trends were estimated as b 0 35 and 0 39 respectively for a similar trend of seismogram peak factor peak to rms amplitude ratio the slope estimate is p 0 13 0 39 disagrees with the 752 spectral model but can be explained by the multiasperity fault model of gusev 1989 if the typical asperity size 2r a is assumed to grow slowly with m 0

determination of constitutive relations of fault slip based on seismic wave analysis constitutive laws define the boundary conditions on fault plane and govern many aspects of earthquake failure although several constitutive laws have been formulated based on laboratory rock experiments and applied to theoretical studies in various fields no actual relation during a natural earthquake has been determined the 1995 kobe earthquake is suitable for detailed kinematic analysis and this enables the first evaluation of constitutive relations for a natural earthquake in this study we determine spatiotemporal slip distribution on an assumed fault plane of the 1995 kobe earthquake by waveform inversion and then solve elastodynamic equations using a finite difference method to determine the stress distribution and constitutive relations on the fault plane an inversion method based on bayes theorem is employed to obtain a spatiotemporal slip distribution and enables us to ensure the objective uniqueness of the solution with numerous parameters and smoothing constraints this slip distribution is then used as part of the boundary condition in the finite difference calculation the time histories of slip and shear stress obtained then provide a constitutive relation at each point on the fault plane they show slip weakening relations almost everywhere on the fault plane while slip rate dependency is not clear the slip weakening behavior has a clear depth dependency indicating that the slip weakening rate d du is smaller in the shallow crust than that in the deep crust this may be associated with the paucity of shallow seismicity observed in the source region of this earthquake as reported for many mature fault systems

direct seismic energy modeling and application to the 1979 imperial valley earthquake 1 the seismic energy associated with an earthquake has two representations the work of the seismic waves done against a distant surface or a fault representation for a fault subject to slip weakening friction the energy density is the difference between an elastostatic work and a work density spent in fracture and relaxation we apply this to a dynamic simulation of the 1979 imperial valley earthquake whose initial conditions are inspired by previous kinematic studies a large area of the fault has a negative energy density and the emission of energy is roughly confined to small parts of the fault with large positive energy density we compute the work of the seismic waves against the surface of a sphere enclosing the source and we find the same amount of energy we produce a map of energy directivity that shows that 40 of the energy passes through only 6 5 of the sphere

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

dependency of supershear transition and ground motion on the autocorrelation of initial stress abstract theoretical and observational studies show that earthquakes on strike slip faults can have rupture speeds exceeding the shear wave speed due to the close relationship between the rupture velocity and the radiated wave field it is important to understand the conditions leading to supershear ruptures and their effect on the resulting ground motion we compute dynamic strike slip ruptures in a 3d elastic half space using heterogeneous frictional properties on faults that are 60 km long we use a grid spacing of 60 m allowing us to compute ground motion for frequencies from 0 to 5 hz we analyze the resulting ground motion using isochrones to explain phenomena we observe we model the amplitudes of the initial shear stress as a self similar random field with cauchy distributed amplitudes the wavenumber amplitude spectrum of initial stress decays as a power law with exponent that controls the decay and the spatial correlation of the initial stress the faster the decay corresponding to larger value of the more correlated is the stress on the fault i e the stress field appears spatially smoother the strength on the fault is computed under the assumption of a constant s factor where s is the ratio of strength excess over stress drop on a fault with uniform strength and stress drop the s factor has to be less than a critical value for the supershear transition to occur for models with heterogeneous initial stress we find that both the s factor and the value of the spectral decay constant affect the occurrence of supershear rupture we observe that for a given but small enough s factor a smooth model 2 can run at supershear speed while a rough model 1 will rupture at subshear speeds for the same s factor based on the theory of fracture a non dimensional number was introduced to quantify the condition when a transition to supershear rupture velocity can occur during an earthquake transition will occur when exceeds a critical value we introduce a modified dimensionless parameter ac that is based on the original parameter the parameter ac incorporates a length scale w ac that reflects the degree of the autocorrelation of the stress field we compute ac for a large number of available dynamic ruptures that propagate at subshear and supershear speeds and find i there is a critical value ac c below which all ruptures propagate subshear ii for values larger than ac c there is only a finite probability that the rupture goes supershear i e it is a necessary but not a sufficient condition for the occurrence of supershear rupture propagation

dynamics of a powerful deep submarine eruption recorded in h2o contents and speciation in rhyolitic glass the 2012 havre eruption constraining the syn eruptive volatile contents of magmatic melt is critical to understanding the intensities and styles of deep submarine volcanic eruptions for which direct observations are scarce quantifying residual magmatic water contents in volcanic glass is complicated by rehydration i e late stage addition of molecular water the 2012 deep submarine silicic eruption of havre volcano provides an unusual opportunity to quantify glass water contents from a recent well sampled stratigraphic sequence fourier transform infrared and microraman spectroscopy measurements of water concentration and water speciation across the havre 2012 eruptive sequence reveal an unanticipated range of excess molecular water within pumice this excess water requires rapid timescales of diffusion that are inconsistent with our current understanding of low temperature secondary rehydration in both subaerial and subaqueous eruptive products diffusion models applied to enrichment profiles at vesicle edges confirm that low temperature rehydration is an unlikely cause we instead support higher temperature syn eruptive pumice rehydration by condensed magmatic water and seawater in a submarine plume hydroxyl concentrations suggest shallow quenching depths of havre pumice hundreds of meters above the 900 meter deep main vent our data also support the presence of a vapor rich plume and consequent modification of ocean pressure above the vent we combine this novel volatile data with textural information and cooling rate calculations to explore the conditions that would cause slower shallow cooling of clasts from a deep submarine eruption by exploring the physical conditions for the interaction between pumice and submarine plumes we emphasize fundamental differences between subaerial and submarine clast producing eruptions

petrology of the chilliwack batholith north cascades washington generation of calc alkaline granitoids by melting of mafic lower crust with variable water fugacity calc alkaline granitoid rocks of the oligocene pliocene chilliwack batholith north cascades range from quartz diorites to granites 57 78 sio2 and are coeval with small gabbroic stocks modeling of major element trace element and isotopic data for granitoid and mafic rocks suggests that 1 the granitoids were derived from amphibolitic lower crust having ree rare earth element and sr nd isotopic characteristics of the exposed gabbros 2 lithologic diversity among the granitoids is primarily the result of variable water fugacity during melting the main effect of fh 2 o variation is to change the relative proportions of plagioclase and amphibole in the residuum the ree data for intermediate granitoids quartz diorite granodiorite eu eu 0 84 0 50 are modeled by melting with fh 2 o 1 kbar leaving a plagioclase pyroxene residuum in contrast data for leucocratic granitoids leuco granodiorites and granites eu eu 1 0 0 54 require residual amphibole in the source and are modeled by melting with fh 2 o 2 3 kbar consistent with this model isotopic data for the granitoids show no systematic variation with rock type 87sr 86sri 0 7033 0 7043 end 0 3 3 to 5 5 and overlap significantly with data for the gabbroic rocks 87sr 86sri 0 7034 0 7040 end 0 3 3 to 6 9 the fh 2 o variations during melting may reflect additions of h2o to the lower crust from crystallizing basaltic magmas having a range of h2o contents chillwack gabbros document the existence of such basalts one dimensional conductive heat transfer calculations indicate that underplating of basaltic magmas can provide the heat required for large scale melting of amphibolitic lower crust provided that ambient wallrock temperatures exceed 800 c based on lithologic and geochemical similarities this model may be applicable to other cordilleran batholiths