a kinematic model for deformation of the lithosphere at subduction zones a subduction model that interprets the whole pattern of topography and gravity anomalies across the island arc trench system has been constructed on the basis of dislocation theory we model the lithosphere asthenosphere system by a gravitating stratified half space which consists of an elastic surface layer an intervening layer with maxwell viscoelasticily and an elastic substratum the steady subduction of the oceanic plate beneath the continental plate is represented by uniform slip at a constant rate over the plate interface which divides the elastic viscoelastic half space into two blocks using the limiting value theorem of the laplace transform we can show that the steady slip on the interface deeper than the lithosphere asthenosphere boundary does not contribute to surface deformation in the steady state accordingly the pattern of surface deformation associated with the steady state subduction depends only on the thickness of the lithosphere and the geometry of the plate interface shallower than the lithosphere asthenosphere boundary numerical results show that the pattern of vertical motion at subduction zones is characterized by steep uplift on the continental side sharp subsidence at the plate boundary and gentle uplift on the oceanic side this pattern bears a striking resemblance to the general pattern of topography across island arc trench systems the whole pattern of topography and gravity anomalies across the southern kurile arc is well matched by the subduction model with a lithosphere thickness of 50 km and a dip angle of 30 at depths

self consistent thermodynamic description of silicate liquids with application to shock melting of mgo periclase and mgsio3 perovskite summary we develop a self consistent thermodynamic description of silicate liquids applicable across the entire mantle pressure and temperature regime the description combines the finite strain free energy expansion with an account of the temperature dependence of liquid properties into a single fundamental relation while honouring the expected limiting behaviour at large volume and high temperature we find that the fundamental relation describes well previous experimental and theoretical results for liquid mgo mgsio3 m g2sio4 and sio2 we apply the description to calculate melting curves and hugoniots of solid and liquid mgo and mgsio3 for periclase we find a melting temperature at the core mantle boundary cmb of 7810 160 k with the solid hugoniot crossing the melting curve at 375 gpa 9580 k and the liquid hugoniot crossing at 470 gpa 9870 k for complete shock melting of periclase we predict a density increase of 0 14 g cm 3 and a sound speed decrease of 2 2 km s 1 for perovskite we find a melting temperature at the cmb of 5100 100 k with the perovskite section of the enstatite hugoniot crossing the melting curve at 150 gpa 5190 k and the liquid hugoniot crossing at 220 gpa 5520 k for complete shock melting of perovskite along the enstatite principal hugoniot we predict a density increase of 0 10 g cm 3 with a sound speed decrease of 2 6 km s 1

stressing of locked patches along a creeping fault an analysis is presented of the stressing of locked patches along a fault zone which is creeping elsewhere the model consists of strike slip faulted elastic lithospheric plates loaded in a manner equivalent to imposition of a remotely uniform tectonic shear stress the fault zone has an inhomogeneous strength distribution both depth wise and along strike it is modeled as being composed of locked patches and freely slipping parts treated as cracks the solution is given with the use of the line spring model which analyzes the problem by thickness averaged plane stress theory for lithospheric plates which slip along a discontinuity cut at the plate boundary as a boundary condition thickness averaged stress and slip at each local section along the cut was related to one another by the result of an antiplane strain analysis of slip for the crack or crack pair which describes the slipping and locked depth ranges at that section the analysis indicates that the slip distribution along creeping parts of the fault as well as the stress distribution along locked patches depends strongly on the geometry of these zones the model is used to examine stress concentrations associated with a slip deficient seismic gap along strike and to study the effect of local irregularities in the margin of a locked region it is also used to simulate slip and stressing processes associated with the creeping portion of the san andreas fault in central california between the presently locked zones of the great 1906 and 1857 ruptures and to constrain the nature of an apparently locked zone at the southeastern end which ruptures in characteristic parkfield earthquakes near fault creep and broadscale displacement data along the fault since the 1966 parkfield earthquake and inferences from seismicity distributions are used limitations of the modeling procedure at short spatial wavelengths prohibit an accurate description of the parkfield locked patch but results suggest that it may be localized and occupy a small fraction of area of the normal seismogenic zone an effective remote stressing rate of order 0 3 10 6 shear modulus yr is inferred together with a less well constrained 30 to 40 km lithospheric thickness for consistency with the displacement data results enable estimates of stress accumulation along the locked 1857 rupture zone and the build up of fracture energy release capability of order 107 j m2 in 150 yr at its lower margin

strike slip earthquakes on quasi vertical transcurrent faults inferences for general scaling relations the recent occurrence of several large strike slip earthquakes provides the opportunity to review and complement available data on the scaling of seismic moment mo with length of rupture l for large earthquakes depending on their tectonic setting and mechanism for strike slip earthquakes on quasi vertical transcurrent faults the mo versus l relation has a significant change of slope around mo 0 6 0 8 1020 n m and for larger earthquakes mo scales linearly with l this is compatible with models where slip is controlled by the width of the fault also it appears to be easier to categorize large earthquakes by their mechanism strike slip on vertical transcurrent fault versus pure thrust normal than their tectonic setting interplate intraplate

earthquake scaling and the strength of seismogenic faults 1 two important and unresolved issues in tectonics and earthquake mechanics are the strength of seismogenic faults and scaling relationships between the seismic moment of an earthquake and the area or length of the rupture these two issues usually treated separately are shown here to be fundamentally related it is shown that the reported scatter in moment area and moment length data of strike slip and dip slip earthquakes is not scatter but instead reflects the strength of the fault that failed relationships that exhibit continuous scaling between small and large earthquakes are derived and demonstrate that fault zone pore pressure is the scaling parameter that collapses the combined catalogs of strike slip and dip slip earthquakes to a single function it is shown that for large earthquakes overpressures vary continuously between hydrostatic and near lithostatic above about 15 km with evidence for a clear transition to near lithostatic pore pressures below this depth these results have significant implications for plate tectonics earthquake source physics and mechanistic seismic hazard assessment

roughness at the base of the seismogenic zone contributing factors the cutout depth of microseismic activity in continental fault zones appears to correspond to the onset of greenschist metamorphic conditions at about 300 c it can generally be modeled as the transition from frictional to quasi plastic behavior in quartzofeldspathic crust shear resistance increases with depth through the frictional regime to peak at the transition beneath which it falls off exponentially with increasing temperature larger earthquake ruptures ml 5 5 nucleate around this transition depth where the highest concentrations of strain energy may accumulate varying depth and amplitude of the peak shear resistance along strike induce fluctuations in strain energy concentration at the base of the seismogenic zone factors affecting the depth of the transition include crustal composition geometry and mode of faulting fluid pressure levels in the frictional regime and water content in the quasi plastic regime quasi plastic strain rate and geothermal gradient evaluation of their relative importance is complicated because several are interdependent however compositional change may cause abrupt irregularities in seismogenic depth and peak shear resistance while regional variations in heat flow look to be particularly effective in creating long wavelength heterogeneities in strain energy concentration affecting faulting style

shear viscosity and diffusion in liquid mgsio3 transport properties and implications for terrestrial planet magma oceans molecular dynamics simulations using a pair wise additive potential are implemented to investigate self diffusion mg si and o and shear viscosity of liquid mgsio 3 in the density temperature pressure range 2350 5300 kg m 3 2500 5000 k and 0 140 gpa respectively self diffusivity and shear viscosity are described by modified arrhenian expressions which feature a pressure dependent activation volume activation energies for self diffusion mg si and o and viscous flow are 99 6 109 3 97 4 and 95 3 kj mol respectively evidently oxygen mobility dominates liquid dynamics activation volumes for self diffusion and shear viscosity at low 2 5 gpa pressure are 1 cm 3 mol with self diffusion decreasing and shear viscosity increasing as pressure increases although there is a small interval near zero pressure within which diffusivity increases slightly with increasing pressure shear viscosity increases by a factor of 75 along the 3000 k isotherm from the top of the mantle to the core mantle boundary along the 3000 k isentrope relevant to terrestrial magma ocean convection shear viscosity increases by about a factor of three the equivalence conditions between the stokes einstein and eyring transport models are derived the eyring model provides information on the size of the activated complex associated with viscous flow across the range in pressures relevant to the earth s mantle and suggests that the number of atoms in the activated complex associated with shear flow decreases from 8 atoms at low pressure to 4 atoms at high pressure at 4500 k

thermodynamics of silicate liquids in the deep earth article i nfo we discuss the geophysical implications of recent first principles molecular dynamics simulations of mgsio3 liquid in particular the findings that the gruneisen parameter increases by a factor of three on two fold compression and the predicted melting curve the predicted melting temperature of mgsio3 perovskite at 136 gpa is 5400 600 k which if lowered by freezing point depression by 1300 k yields a mantle solidus temperature of 4100 k identical to recent estimates of the temperature at the base of the mantle we argue on this basis that partial melting at the base of the mantle is plausible while mgsio3 perovskite is denser than the isochemical liquid reasonable values of iron partitioning and bulk iron contents leads to the conclusion that a melt at the base of the multi component mantle would be denser than its surroundings and therefore buoyantly stable we predict the bulk sound velocity of this melt to be 10 9 km s 1 less than that of ultra low velocity zones and consistent with the explanation of these regions as being due to partial melting the increase on compression of the gruneisen parameter in the liquid state yields isentropes that are much hotter than previously thought a potential temperature of only 2450 k is sufficient to melt the entire mantle and a magma ocean will begin crystallization at mid mantle depths rather than at the base of the mantle

viscoelastic gravitational deformation by a rectangular thrust fault in a layered earth previous papers in this series have been concerned with developing the numerical techniques required for the evaluation of vertical displacements which are the result of thrust faulting in a layered elastic gravitational earth model this paper extends these methods to the calculation of fully time dependent vertical surface deformation from a rectangular dipping thrust fault in an elastic gravitational layer over a viscoelastic gravitational half space the elastic gravitational solutions are used together with the correspondence principle of linear viscoelasticity to give the solution in the laplace transform domain the technique used here to invert the displacements into the time domain is the prony series technique wherein the transformed solution is fit to the transformed representation of a truncated series of decaying exponentials purely viscoelastic results obtained are checked against results found previously using a different inverse transform method and agreement is excellent the major advantage in using the prony series technique is that deformations can be computed for arbitrary time intervals a series of results are obtained for a rectangular 30 dipping thrust fault in an elastic gravitational layer over viscoelastic gravitational half space time dependent displacements are calculated out to 50 half space relaxation times a or 100 maxwell times 2 m a significant effects due to gravity are shown to exist in the solutions as early as several a the difference between the purely viscoelastic solution and the viscoelastic gravitational solutions grows as time progresses typically the solutions with gravity reach an equilibrium value after 10 20 relaxation times when the purely viscoelastic solutions are still changing significantly additionally the length scaling which was apparent in the purely viscoelastic problem breaks down in the viscoelastic gravitational problem two independent length scales one of which changes with time are now seen to characterize the problem

regional difference in scaling laws for large earthquakes and its tectonic implication we compiled 67 large earthquakes which occurred at and around plate boundaries for the last 140 yrs and classified them into four groups interplate strike slip events intraplate strike slip events underthrust events at island arc subduction zones and underthrust events at continental margin subduction zones for each group of earthquakes we examined relations between seismic moment m 0 fault length l fault width w and average fault slip d and found the following scaling laws in the case of interplate strike slip events the well known l cubed dependence of seismic moment breaks down when l exceeds 30 km because the extent of the seismogenic zone is limited in depth 12 km for large events l 30 km d and m 0 increase with l as d overline delta tau l mu left alpha l beta right and m 0 overline delta tau w l 2 left alpha l beta right respectively where the mean fault width bar w is 12 km and the mean stress drop overline delta tau is 1 8 mpa here and are structural parameters for intraplate strike slip events we obtained nearly the same relations except for significantly higher stress drop 3 1 mpa the difference in stress drop between interplate and intraplate events may be ascribed to the difference in stress accumulation rates and thus the recurrence time of earthquakes in the case of underthrust events at island arc subduction zones we also found the saturation of fault width bar w 120km and the breakaway from the l cubed dependence of m 0 for events larger than l 200 km if we consider the average dip angle of plate boundaries at island arc subduction zones to be 20 30 this indicates that the extent of the seismogenic zone in depth is limited to 40 60 km in the case of continental margin subduction zones on the other hand we could not find the saturation of fault width nor the breakaway from the l cubed dependence of m 0 from the analysis of the present data set w 200 km l 1000 km for sufficiently large earthquakes in general the downward rupture growth is limited to a certain depth due to the existence of a ductile unstressed region which extends under the brittle seismogenic zone since the brittle ductile transition occurs at 300 400 c the difference in the lower limit of the seismogenic zones between tectonically different regions may be attributed to the difference in thermal state there

constitutive relations between dynamic physical parameters near a tip of the propagating slip zone during stick slip shear failure abstract constitutive relations between physical parameters in the cohesive zone during stick slip shear failure are experimentally investigated stick slip was generated along a 40 cm long precut fault in tsukuba granite samples using a servocontrolled biaxial loading apparatus dynamic behavior during local breakdown processes near a tip of the slipping zone is revealed the slip velocity and acceleration are given as a function of the slip displacement and the cohesive or breakdown shear stress as a function of the slip velocity a cycle of the breakdown and restrengthening process of stick slip is composed of five phases characterized in terms of the cohesive strength and the slip velocity the cohesive strength can degrade regardless of the slip velocity during slip instabilities the maximum slip acceleration u max and the maximum slip velocity u max are obtained experimentally as u max 2 u c u max 2 and u max b g v where u c is the critical displacement b the breakdown stress drop g the rigidity and v the rupture velocity these relations are consistent with ida s theoretical estimation based on the cohesive zone model the above formula gives good estimates for the maximum slip acceleration of actual earthquakes the cutoff frequency max of the power spectral density of the slip acceleration increases with increasing normal stress in particular max is found to be directly proportional to the normal stress n within the normal stress range less than 17 mpa as max khz 4 0 n mpa n max increase with an increase in u max or u max all these results lead to the conclusion that u max u max and max increase with increasing normal stress this is consistent with a previous observation that b increases with increasing normal stress the above empirical linear relation between max and n can be explained by a linear dependence of b on n the size scale dependence of physical parameters is discussed and such size scale dependent parameters as u max and apparent fracture energy are scaled to the breakdown zone size regarded as a characteristic length to extend the results obtained in the laboratory to an earthquake failure in the earth

surface rupture effects on earthquake moment area scaling relations empirical earthquake scaling relations play a central role in fundamental studies of earthquake physics and in current practice of earthquake hazard assessment and are being refined by advances in earthquake source analysis a scaling relation between seismic moment m0 and rupture area a currently in use for ground motion prediction in japan features a transition regime of the form m0 a2 between the well recognized small self similar and very large w model earthquake regimes which has counterintuitive attributes and uncertain theoretical underpinnings here we investigate the mechanical origin of this transition regime via earthquake cycle simulations analytical dislocation models and numerical crack models on strike slip faults we find that even if stress drop is assumed constant the properties of the transition regime are controlled by surface rupture effects comprising an effective rupture elongation along dip due to a mirror effect and systematic changes of the shape factor relating slip to stress drop based on this physical insight we propose a simplified formula to account for these effects in m0 a scaling relations for strike slip earthquakes

magma ocean formation due to giant impacts current understanding of the last stages of planetary accretion suggests that mass and energy accumulation are dominated by a few large impacts an important thermal consequence of such impacts is melting and formation of a large melt pond if the planet s isostatic adjustment time scale is short compared to the magma pond s cooling time scale the melt may be extruded onto the surface and form a magma ocean of approximately uniform depth although a giant impact striking at 10 15 km s 1 deposits enough energy to melt the entire planet the distribution of that energy is important in determining the thermal outcome of the collision we examine the thermal effects of giant impacts by estimating the melt volume generated by the initial shock wave and corresponding magma ocean depths additionally we examine the effects of the planet s initial temperature on the generated melt volume the hugoniot curve plotted in pressure entropy space is used to determine the shock pressure required to completely melt the material for room temperature dunite this pressure is about 150 gpa and the partial melt region is narrow for dunite initially at the solidus temperature this pressure is about 115 gpa the partial melt region extends throughout the planet once the melting pressure is known an impact melting model based on the second hugoniot equation the linear shock particle velocity relationship and the empirical particle velocity distance relationship is used to estimate the radial distance melting occurred from the impact site once the distance is found the melt region s geometry determines the associated melt volume partial melt volume is also estimated the melt fraction that is not excavated during crater formation is estimated and magma ocean depths resulting from both excavated and retained melt are calculated the model is also used to estimate the fraction of a planet melted by the initial shock wave nominal conditions of the moon forming giant impact projectile planet mass 0 14 impact speed 15 km s 1 generate melting of 30 65 of the planet depending on its initial temperature whole planet melting requires projectile planet mass ratios of 0 4 for a 15 km s 1 impact if the planet was near its solidus before the impact isostatic relaxation may generate a significant volume of additional melting

the mw 9 0 northeast japan earthquake total rupture of a basement asperity summary the mw 9 0 off northeast japan tohoku oki earthquake occurred on 2011 march 11 at the interface between the north american na and pacific pa plates the occurrence of interplate earthquakes can be regarded as the sudden release of tectonic stress accumulated by the interseismic gradual increase of slip deficit in source regions the inversion analysis of gps velocity data for a seismically calm period 1996 2000 before the tohoku oki earthquake has revealed the existence of five remarkable slip deficit zones distributed on the na pa plate interface along the southern kuril japan trench we analysed coseismic gps displacement data for the tohoku oki earthquake with the same inversion method and obtained the bimodal distribution of coseismic slip spreading over the southern two miyagi oki and fukushima oki interseismic slip deficit zones the maximum slip is 32 m for the miyagi oki slip deficit zone but only 7 m for the fukushima oki slip deficit zone the extraordinarily large coseismic slip in the miyagi oki slip deficit zone where ordinarily large earthquakes with about 3 m coseismic slips have repeated every 40 yr in the past two centuries suggests the total rupture of a 300 km long basement asperity underlying much smaller scale local asperities

physical state of an early magma ocean constrained by the thermodynamics and viscosity of iron silicate liquid abstract the initial cooling stage and crystallization of a magma ocean were significantly affected by the thermodynamics and viscosity of iron silicate liquid here we use first principles molecular dynamics based on density functional theory plus the hubbard u method to study the structures thermodynamics and viscosities of fe2sio4 liquid at 3000 6000 k under pressure conditions spanning the entire mantle our calculations show that the compressibility of fe2sio4 liquid is weakened at pressures above 50 gpa the densification of fe2sio4 liquid under compression is mainly manifested by a decrease in the distance among si o polyhedra and an increase in the cation anion coordination number we find that the viscosity of the fe2sio4 liquid has a positive pressure dependence and the effect of pressure on viscosity decreases with increasing temperature the predicted behaviour of viscosity coefficients of the fe2sio4 liquid at different p t conditions can be described well as p t exp 7 89 0 0042 p 0 0000632 p 2 3800 61 6 p 0 18 p 2 t 1000 compared to mg2sio4 liquid the viscosity of fe2sio4 liquid is lower under the pressure of the lower mantle along isotherms we calculate the adiabat of the fe2sio4 liquid in a magma ocean and the results show that the iron content has little effect on the adiabats of mg fe 2sio4 liquid in the magma ocean combining our calculated thermodynamic properties and viscosities with those of previous studies the physical properties of an early magma ocean were constrained the upper bound of the potential temperature for magma ocean crystallization is 3250 k we constructed the range of the viscosity profile of a magma ocean and found that the lower viscosity of iron rich silicate liquid would maintain the viscosity of an early magma ocean in the range of several mpa s as the magma ocean starts to crystallize the lower bound of the viscosity at the surface and the core mantle boundary are 0 0020 pa s and 0 0068 pa s respectively the weakening of the viscosity of the iron silicate liquids would have a significant impact on the evolution of the magma ocean

slip dependent friction law and nucleation processes in earthquake rupture abstract matsu ura m kataoka h and shibazaki b 1992 slip dependent friction law and nucleation processes in earthquake rupture in t mikumo k aki m ohnaka l j ruff and p k p spudich editors earthquake source physics and earthquake precursors tectonophysics 211 135 148 we developed a physical model that interprets slip strengthening and slip weakening processes in brittle shear fracture by considering the microscopic interaction between statistically self similar fault surfaces our model successfully describes general features of the constitutive behaviour observed in laboratory experiments of stick slip with the progress of fault slip frictional stress first increases rapidly up to a peak value and then decreases gradually to a constant level the first slip strengthening process can be explained by the increase of frictional resistance in transition from the in phase contact to the random phase contact of fault surfaces the latter slip weakening process can be explained by the decrease of frictional resistance due to the abrasion of surface asperities the trade off between these two processes determines the peak stress and the critical displacement over which the slip weakening proceeds we examined the nucleation process proceeding in a seismogenic zone with the increase of external shear stress through numerical simulations in our model the seismogenic zone is represented by a broad weak zone with a locally strong part asperity on a fault plane the basic equations governing the nucleation process are the equation of equilibrium and the constitutive relation between frictional stress and fault slip we obtained the following results the nucleation process first proceeds quasi statically at the weak portions with the increase of external shear stress then if the constitutive relation at the asperity has a high and narrow peak of stress brittle dynamic rupture occurs in a limited area around the asperity when the constitutive relation has a low and broad peak the dynamic rupture of the asperity does not occur the process is completely aseismic when the peak of stress is high and broad the dynamic rupture of the asperity leads to the catastrophic rupture which extends over the whole region from these results it is concluded that diversity in the nucleation process can be ascribed to difference in the variation of constitutive behaviour along the fault

3 d simulation of tectonic evolution of the mariana arc back arc system with a coupled model of plate subduction and back arc spreading abstract we developed a mechanical model for the nonlinear coupled system of plate subduction and back arc spreading on the basis of mathematical formulation for internal deformation due to a moment tensor in an elastic viscoelastic layered half space under gravity in our modeling the plate subduction and the back arc spreading are rationally represented by the increase of tangential displacement discontinuity at the plate interface and normal displacement discontinuity at the spreading center respectively through 3 d numerical simulation with this model we obtained a possible scenario for the tectonic evolution of back arc basins as follows at the first stage steady plate subduction gradually forms tensile stress fields in the back arc region when the accumulated tensile stress reaches a critical level back arc spreading starts at a structurally weak portion of the overriding plate the back arc spreading pushes out the frontal part of the overriding plate toward the plate boundary and leads to the increase of slip rates at the plate interface the local increase of slip rates at the plate interface produces additional tensile stress in the back arc region the incremental tensile stress is canceled out by further back arc spreading such a feedback mechanism is necessary to maintain steady back arc spreading the long duration of slip rate excess due to back arc spreading leads to the gradual protrusion of the plate boundary toward the descending plate trench retreat as the plate boundary moves away from the back arc spreading center the accumulation rate of tensile stress at the spreading center gradually decreases and the slip rate excess at the plate interface due to back arc spreading also decreases then the original back arc spreading center becomes less effective in releasing the tectonic tensile stress and new active back arc spreading will start somewhere closer to the plate boundary such a qualitative scenario accords with the evolution history of back arc basins in the mariana region we obtained the slip rate excess of 7 mm year at the plate interface and the 20 km trench retreat for the last 4 5 myr these simulation results are significantly smaller than observations in the mariana region the discrepancy between simulation results and observations can be ascribed to the effect of the negative buoyancy acting on cold descending slab which advances spontaneous plate subduction and directly increases the slip rate excess and the trench retreat in our model

rheology of crystal bearing silicate melts an experimental study at high viscosities the viscosity of partially crystallized mg3al2si3o12 melts has been measured under uniaxial compression in the interval 1010 1013 poise as a function of the volume fraction of crystals these inclusions are well rounded spherulites of aluminous enstatite having the same composition as the melt and whose growth rate is negligible at the temperature of the measurements the viscosity increases by less than 1 order of magnitude for crystal fractions of 40 vol and remains newtonian up to the maximum stress exerted namely 1 kbar the einstein roscoe equation 0 1 m n provides very good fits to the measurements only if either the m or n parameter is allowed to depend on temperature for modeling of magmatic processes however the widely recommended constant values m 0 6 and n 2 5 should be adequate the rheology changes abruptly when the clustered spherulites begin to oppose shear deformation at a crystal fraction of about 40 vol the viscosity becomes non newtonian with yield strengths of a few tens of bars at temperatures at which the viscosity of the melt is higher than 1010 poise as long as the crystal fraction remains lower than 70 vol the deformation proceeds in an irregular manner with a nonuniform distribution of crystals and melt the deformation becomes again regular at low stresses with lower melt fractions but samples undergo extensive fracturation along the direction of uniaxial stress similar rheology changes have been observed during the isothermal crystallization of li2si2o5 melts which produces small ellipsoidal inclusions these results suggest that the influence of solid suspensions on the rheology of magmas is primarily determined by the crystal fraction even though additional measurements would be useful to determine the possible influence of other factors such as the size distribution or the shape of the inclusions

faulting processes controlled by the nonuniform thermal structure of the crust and uppermost mantle beneath the northeastern japanese island arc 1 we performed a finite element analysis taking into account nonlinear viscoelasticity and plasticity to construct a two dimensional model of the deformation and faulting processes that occur in the deeper parts of the seismogenic zone beneath northeastern japan our finite element code was developed on the basis of the geofem parallel finite element code using plug ins to adopt several nonlinear functions an extensive onshore offshore wide angle seismic expedition conducted across northeastern japan in 1997 revealed a detailed image of the deep crust and uppermost mantle structures in modeling the deformation and faulting beneath the ou backbone range and dewa hill northeastern japan we consider a realistic crust and uppermost mantle structure revealed by the 1997 seismic expedition and the existence of the two hot regions revealed by geothermal observations in a compressional tectonic setting the numerical results reveal that shortening deformation due to nonlinear viscous flow occurs in the hot region in the lower crust and the uppermost mantle resulting in shear faulting in the upper crust our model reproduces three reverse fault zones that are consistent with those observed we investigate the stress accumulation process over a period approximately corresponding to the earthquake recurrence interval by prohibiting plastic faulting and found that the stress is loaded along the fault zone at magnitudes much lower than the absolute stress level the results indicate that the loading processes of large inland earthquakes in northeastern japan are determined by the nonuniform thermal structure in the deeper crust and uppermost mantle

scaling of earthquake rupture growth in the parkfield area self similar growth and suppression by the finite seismogenic layer 1 we propose a new framework on the scaling of earthquake rupture growth time history and we scale the moment rate and the cumulative moment functions of earthquakes over a wide magnitude range mw 1 7 6 0 in parkfield california the moment rate and the cumulative moment functions of the small and medium earthquakes mw 1 7 4 6 are derived by slip inversion analyses with the empirical green s function technique the moment rate functions of the investigated earthquakes except the mw 6 0 event are similar to each other increasing rapidly in the first half growth stage and decelerating in the latter half decline stage in the growth stage the cumulative moment functions are approximated by mo t nm 2 1017 t s 3 independent of the final size of the earthquakes the proportionality of the cumulative moment to the cube of time implies self similarity during earthquake rupture growth in the decline stage the cumulative moment function veers off the common rupture curve the mw 6 0 event also grows along the same rupture curve until 1 s after which the cumulative moment function is proportional to time from the onset itself this is because the finite seismogenic layer limits the vertical extent of dynamic rupture our method and results contribute to our understanding of earthquake source physics especially on earthquake rupture growth processes which may help to improve earthquake early warning techniques

hard turbulent thermal convection and thermal evolution of the mantle this article summarizes the results of hard turbulent convection obtained in laboratory experiments and numerical simulations its applications to mantle convection are illustrated by two dimensional numerical solutions to 1 newtonian 2 non newtonian convection and 3 newtonian convection with multiple phase transitions in newtonian mantle convection the transition from soft to hard turbulence is marked by the appearance of disconnected plumes spectral analysis of the time series of the nusselt number reveals the presence of a spectral scaling subrange for hard turbulence but not for soft turbulence in hard turbulence there is correspondence between the spectra in frequency and wavenumber domains the slope of the seismic wave spectra measured from seismology suggests that the mantle convection today is strongly time dependent the transition to hard turbulence takes place at much lower nusselt numbers for non newtonian than for newtonian rheology for the mantle this would have important ramifications non newtonian plumes behave quite differently from newtonian ones in that large curvatures are developed in their trajectories in the hard turbulent regime mantle convection with phase transitions tends to become more layered with increasing rayleigh numbers the style of mantle convection might have changed from a layered to a more whole mantle type of flow with time catastrophic overturns associated with strong gravitational instabilities in the transition zone could be responsible for superplume events

dynamics of metal silicate separation in a terrestrial magma ocean in a terrestrial magma ocean the metal silicate separation involved small metal droplets our goal is to better understand the dynamics of the metal droplet scenario the mechanism of sedimentation in a vigorously convecting and strongly rotating magma ocean may differ significantly from settling droplets in a still fluid in order to systematically study the parameter dependence on the style of motion we utilize two dimensional and three dimensional numerical convection models combined with a tracer based sedimentation method we investigate the characteristic flow patterns resulting from the competing effects of convection and droplet settling and find three styles of motion a temperature dominated style where most droplets remain suspended a droplet dominated style where the droplets separate from the fluid and a style of repetitive motion we find that the droplet dominated style is relevant to the magma ocean in this scenario the droplets settle and form a dense bottom layer one of the key findings of this work is that the formation of the dense bottom layer and therefore the separation of metal droplets from the liquid silicate occurs on a characteristic timescale which is identical with the stokes settling time finally we study the chemical interaction of settling metal droplets and liquid silicate and discuss how accurately a simple parameterized model can describe the chemical equilibration in the metal rain scenario of a terrestrial magma ocean we find agreement between the parameterized model and our two dimensional model our simulations which include thermal convection into the metal rain model confirm the fundamental observation that metal droplets are not permanently suspended in the convecting silicate melt but that they sink and rapidly form a dense layer at the base of the magma ocean

thermal conductivity of mgo periclase at high pressure implications for the d region abstract the thermal conductivity of the lowermost mantle determines the rate at which heat flows across the core mantle boundary and consequently plays a central role in the thermal evolution of both the mantle as well as the core in an effort to test and improve model estimates of thermal conductivity in the deep mantle we perform first principles computations of the lattice conductivity for mgo periclase the method uses the peierls boltzmann transport equation via a combination of first principles molecular dynamics and first principles lattice dynamics phonon lifetimes are found to be inversely proportional to temperature and increases 3 fold as the density is increased from 3 37 to 5 49 g cm 3 thermal conductivities increase nearly 6 fold over the same density interval and show excellent agreement with the available experimental measurements we use these results to assess how conductivity measurements of mantle minerals can be reliably extrapolated to conditions characteristic of the lowermost mantle and find debye theory to be superior for this task we then apply this insight to estimate the conductivity of mgsio 3 perovskite in the lowermost mantle and combine this with our computational results for mgo periclase to construct a model estimate for a representative lower mantle assemblage we find the mantle conductivity to be 5 9 0 6 w m k at the top of the thermal boundary layer and 4 0 0 5 w m k at its base implying core mantle boundary heat flux values at the lower end of geophysical estimates

self diffusion and chemical diffusion in peridotite melt at high pressure and implications for magma ocean viscosities abstract self diffusion coefficients of si o mg and ca and chemical diffusion coefficients of ni and co have been determined experimentally up to 24 gpa and 2623 k in anhydrous peridotite liquid using a multi anvil press each diffusion couple consisted of a cylinder of isotopically natural peridotite enriched in 1 wt coo that was mated to a cylinder of chemically similar peridotite enriched in 18o 30si 25mg 44ca and 1 wt nio isotope abundance 18o 30si 25mg 44ca profiles along each sample length and perpendicular to the diffusion interface were analyzed by secondary ion mass spectrometry and ni and co concentration profiles were measured by electron microprobe analysis the rates of self diffusion of si o mg ca and chemical diffusion of ni and co decrease with increasing pressure from 4 to 8 gpa where diffusivity reaches a minimum and then increase with a further pressure increase to reach a maximum at 12 gpa the observed change in the pressure dependence at 8 10 gpa is likely caused by pressure induced structural changes and the formation of high coordinated intermediate species above 12 gpa diffusivities again decrease weakly with increasing pressure most likely as a result of further melt compaction when the coordination changes are complete predicted viscosities from self diffusion coefficients for oxygen obtained using the eyring equation are similar to viscosities measured by falling sphere viscometry including the observed changes of the pressure dependence the effect of pressure on diffusion and viscosity in peridotite melt is small compared with the effect of temperature indicating that the viscosity along the melting curve decreases with depth diffusion parameters determined in this study are used to estimate the viscosity of a magma ocean with a depth of 700 km the results indicate that the viscosity increases from 10 mpa s near the surface to a reach a maximum of 50 mpa s at a depth of 250 km at higher pressures the viscosity decreases to 10 mpa s at a depth of 300 km below which it remains almost constant

a dislocation model for the earthquake cycle at convergent plate boundaries summary a kinematic model for the earthquake cycle at convergent plate boundaries has been constructed on the basis of dislocation theory we model the lithosphere asthenosphere system by a stratified semi infinite medium under gravity consisting of an elastic surface layer an intervening layer with maxwell viscoelasticity and an elastic substratum the steady motion of plate convergence is naturally represented by uniform slip at a constant rate on the upper boundary of the descending oceanic plate the occurrence of interplate earthquakes is regarded as a perturbation of the steady state plate motion and represented by a periodic sequence of step slips on a finite seismic zone of the plate interface based on dislocation theory we can show that the steady slip on the interface deeper than the lithosphereasthenosphere boundary does not contribute to surface deformation in the steady state accordingly the surface deformation associated with the earthquake cycle is given by the superposition of viscoelastic responses to the steady slip on the interface shallower than the lithosphere asthenosphere boundary the steady backslip on the seismic zone and the periodic sequence of seismic slips we have computed cyclic patterns of vertical displacements at the free surface for two representative cases taking account of gravity effects the patterns of vertical displacements differ notably in the latter stage of the cycle depending on whether or not the seismic zone extends through the entire thickness of the lithosphere after the completion of one earthquake cycle our model yields a certain amount of permanent deformation resulting from the steady plate convergence the pattern of the permanent deformation that is characterized by steep uplift on the continental side sharp subsidence at the plate boundary and gentle uplift on the oceanic side is irrespective of the cyclic process of stress accumulation and release repeated on the seismic zone the earthquake cycle model developed here provides a possible explanation for the formation of earthquake origin marine terraces

phase transitions and equation of state of forsterite to 90 gpa from single crystal x ray diffraction and molecular modeling forsterite mg2sio4 the magnesian end member of the olivine system is the archetypal example of an orthosilicate structure we have conducted synchrotron based single crystal x ray diffraction experiments to 90 gpa on synthetic end member forsterite to study its equation of state and phase transitions upon room temperature compression the forsterite structure is observed to 48 gpa by fitting a third order birch murnaghan equation of state to our compression data we obtain the zero pressure isothermal bulk modulus k 0t 130 0 9 gpa and its pressure derivative k 0t 4 12 7 for a fixed room pressure volume v 290 1 1 a3 in good agreement with earlier work at 50 gpa a phase transition to a new structure forsterite ii occurs followed by a second transition to forsterite iii at 58 gpa forsterite iii undergoes no additional phase transitions until at least 90 gpa there is an 4 8 volume reduction between forsterite and forsterite ii and a further 4 2 volume reduction between forsterite ii and iii on decompression forsterite iii remains until as low as 12 gpa but becomes amorphous at ambient conditions using our x ray diffraction data together with an evolutionary crystal structure prediction algorithm and metadynamics simulations we find that forsterite ii has triclinic space group p 1 and forsterite iii has orthorhombic space group cmc 21 both high pressure phases are metastable metadynamics simulations show a stepwise phase transition sequence from 4 coordinated si in forsterite to mixed tetrahedral and octahedral si as in forsterite ii and then fully sixfold coordinated si as in forsterite iii occurring by displacement in 001 100 the forsterite iii structure is a member of the family of post spinel structures adopted by compositions such as cafe2o4 and cati2o4

melting of forsterite mg2sio4 up to 15 gpa the melting curve of forsterite has been studied by static experiment up to a pressure of 15 gpa forsterite melts congruently at least up to 12 7 gpa the congruent melting temperature is expressed by the kraut kennedy equation in the following form tm k 2163 1 3 0 v0 v v0 where the volume change with pressure was calculated by the birch managhan equation of state with the isothermal bulk modulus k0 125 4 gpa and its pressure derivative k 5 33 the triple point of forsterite mg2sio4 liquid will be located at about 2600 c and 20 gpa assuming that congruent melting persists up to the limit of the stability field of forsterite the extrapolation of the previous melting data on enstatite and periclase indicates that the eutectic composition of the forsterite enstatite system should shift toward the forsterite component with increasing pressure and there is a possibility of incongruent melting of forsterite into periclase and liquid at higher pressure although no evidence on incongruent melting has been obtained in the present experiment

early evolution of the earth accretion atmosphere formation and thermal history atmospheric and thermal evolution of the earth growing by planetesimal impacts was modeled by taking into account the blanketing effect of an impact induced h2o atmosphere and the temperature dependence of h2o degassing when the water content of planetesimals is larger than 0 1 by weight and the accretion time of the earth is less than 5 107 years the surface of the accreting earth melts and thus a magma ocean forms and covers the surface the formation of a magma ocean will result in the initiation of core mantle separation and mantle differentiation during accretion once a magma ocean is formed the surface temperature the degree of melting in the magma ocean and the mass of the h2o atmosphere are nearly constant as the protoplanet grows further the final mass of the h2o atmosphere is about 1021 kg a value which is insensitive to variations in the model parameter values such as the accretion time and the water content of planetesimals that the final mass of the h2o atmosphere is close to the mass of the present oceans suggests an impact origin for the earth s hydrosphere on the other hand most of the h2o retained in planetesimals will be deposited in the solid earth free water within the proto earth may affect differentiation of the proto mantle in particular the mantle feo abundance and the incorporation of a light element in the outer core

a reappraisal of large earthquake scaling abstract twelve years ago i pointed out that observations indicate that the slip in large earthquakes scales with their length rather than their width as expected from the canonical model romanowicz 1992 has recently argued that more recent data show that the opposite is true which has obliged me to re examine the question i point out here a defining flaw in her analysis in that she allowed mo the moment at the cross over from small to large earthquakes to be a free variable in her curve fitting whereas this parameter can be defined independently when this parameter is independently fixed i find that the up dated data set confirms my earlier conclusion that for large crustal earthquakes m0 scales with l 2 a little over a decade ago i pointed out that obser vations indicate that the slip in large earthquakes scales with their rupture length scholz 1982 several sub sequent papers provided additional data supportive of this view chen and molnar 1983 shimazaki 1986 scholz et al 1986 large earthquakes are defined in this con text as those that rupture the entire seismogenic thick ness w0 and are thus constrained to propagate farther in a horizontal direction only for crustal earthquakes w0 is nearly constant 15 km so this scaling conflicts with conventional models of earthquakes such as dislocation models because they predict that slip scales with width which is invariant for these earthquakes i offered two alternative ways to interpret these observations one is that such conventional w models are correct but that stress drop could no longer be regarded as scale invariant but must scale with fault length as an alternative i sug gested the possibility of what i termed an l model in which slip intrinsically scales with fault length this created a minor crisis in seismology which has yet to be resolved it is no exaggeration to say that my l model suggestion has not attracted a noticeable coterie of admirers nor has my other suggestion and there has been no other model proposed in the interim that ex plains the observed l scaling although heaton 1990 has suggested a way in which length may scale with stress drop a variation of my w model scaling alternative in the face of this an alternative is to question the obser vations which is what romanowicz 1992 has recently chosen to do in her interpretation of an updated data set she concluded that seismic moment m0 scales lin early with rupture length l for large earthquakes which is consistent with w models and implies that slip u is scale invariant for large crustal earthquakes this great discrepancy with the earlier result she implies is due to the presence of superior modern measurements in the updated data set this issue has major implications both practical and theoretical and merits some debate here i present my own reappraisal of the data in which the conclusions are very different reappraisal of the data romanowicz s conclusions were based on a log log plot of m0 versus l for a data set of strike slip earth quakes she showed that the data in this figure could be better fit by two straight lines one with slope 3 in the lower scale range and one with slope 1 in the upper scale range than with a single line of slope 2 for small earth quakes which grow in both dimensions with l w m0 should scale with l 3 for large earthquakes where w has saturated at w0 and growth only occurs in the l di rection m0 should scale with l according to conven tional models hence the problem produced by my ob servation that m0 scales with l 2 for those events superficially then it appears that she has resolved the issue the problem however is that she has allowed the cross over length l which separates small from large earthquakes to be a free variable in her curve fitting ex ercise she thus obtains a cross over moment of 0 6 to 0 8 x 1020 n m which is appropriate for a rupture length of 60 to 70 km by adding an additional free parameter to the curve fitting one would expect a much better fit to be achieved the question is whether such a step is justified if small earthquakes grow with l w then the transition to large earthquakes defined as an event that ruptures the entire seismogenic thickness would be l w0 10 to 20 km for the data being studied this may be checked observationally because large earth quakes almost invariably nucleate near the base of the seismogenic layer das and scholz 1983 it follows that the transition to large earthquakes is at the length at which one begins to consistently see surface ruptures inspec tion of the earthquakes in romanowicz s 1992 figure 215

3 d simulation of earthquake generation cycles and evolution of fault constitutitve properties the earthquake generation cycle consists of tectonic loading quasi static rupture nucleation dynamic rupture propagation and stop and subsequent stress redistribution and fault restrengthening from a macroscopic point of view the entire process of earthquake generation cycles should be consistently described by a coupled nonlinear system of a slip response function a fault constitutive law and a driving force on the basis of such a general idea we constructed a realistic 3 d simulation model for earthquake generation cycles at a transcurrent plate boundary by combining the viscoelastic slip response function derived for a two layered elastic viscoelastic structure model the slip and time dependent fault constitutive law that has an inherent mechanism of fault restrengthening and the steady relative plate motion as a driving force into a single closed system with this model we numerically simulated the earthquake generation cycles repeated in a seismogenic region on a plate interface and examined space time changes in shear stress slip deficits and fault constitutive properties during one complete cycle in detail the occurrence of unstable dynamic slip brings about decrease both in fault strength and shear stress to a constant residual level after the arrest of dynamic slip the breakdown strength drop p of fault is restored rapidly and the process of stress accumulation resumes in the seismogenic region on the other hand the restoration of the critical weakening displacement d c proceeds gradually with time through the interseismic period the restoration of d c can be regarded as the macroscopic manifestation of the microscopic recovery process of fractal fault surface structure through numerical simulation with a multi segmented fault model we examined the effects of viscoelastic faultto fault interaction the effect of transient viscoelastic stress transfer through the asthenosphere is significant as well as the direct effect of elastic stress transfer and it possibly explains the time lag of the sequential occurrence of large events along a plate boundary

application of linked stress release model to historical earthquake data comparison between two kinds of tectonic seismicity the linked stress release model incorporating a slow buildup of stress within a seismic region its stochastic release through earthquakes and transfer between seismic regions is applied to fit historical data from two typical kinds of seismicity earthquakes occurring in intraplate north china and plate boundary new zealand regions the best model among different modifications of the basic model which may reflect on a possible geophysical mechanism for earthquake occurrences is obtained in terms of akaike information criterion for both tectonic regions studied the linked stress release model fits the new zealand data better than a collection of independent simple models but is nearly indistinguishable from the simple stress release model in the case of north china the seismicity in a plate boundary region due to subduction is more active and complex than that in an intraplate region due to collision between tectonic plates the results highlight the major differences in tectonic seismicity especially the heterogeneities of tectonic stress fields and dynamic triggering mechanism with evidence that the crust may lie in a near critical state

loading mechanism and scaling relations of large interplate earthquakes we have done a numerical simulation of tectonic loading at transform plate boundaries with a lithosphere asthenosphere coupling model subject to steady relative plate motion in this model a seismic fault is represented by a locked patch with a finite length on an infinitely long vertical dislocation surface cutting the entire lithosphere through the numerical simulation we have obtained the following results stress accumulation on the fault is partly due to viscous drag at the base of the lithosphere base loading and partly due to dislocation pile ups at horizontal edges of the fault edge loading if the viscosity of the asthenosphere is less than 1018 pa s the base loading is not effective since its rate exponentially decays very soon if the viscosity of the asthenosphere is greater than 1020 pa s both types of loading are effective and then the stress accumulation rate in the early stage of loading is formally written as d dt vpl a bl where vpl is a rate of relative plate motion and l is a fault length when the fault length l is small the effect of edge loading the second term is dominant and the stress accumulation rate is in proportion to the inverse of l when the fault length l is large the effect of base loading the first term becomes dominant and the stress accumulation rate is independent of l it is well known that the general l cubed dependence of seismic moment m0 breaks for large interplate earthquakes this break in the moment length relation can be ascribed to difference in loading mechanism between small and large earthquakes from the results of numerical computation if interplate earthquakes have the same stress drop regardless of their fault lengths we may derive a l squared dependence of m0 for large interplate earthquakes and a linear l dependence of m0 for very large interplate earthquakes

preseismic rupture progression and great earthquake instabilities at plate boundaries we present a procedure for modeling the initially quasi static upward progression of a zone of slip from some depth in the lithosphere toward the earth s surface along a transform plate margin culminating in a great crustal earthquake stress transmission in the lithosphere is analyzed with a generalized elsasser model in which elastic lithospheric plates undergo plane stress deformation and are coupled by an elementary foundation model to a maxwellian viscoelastic asthenosphere upward progression of rupture over a finite length of plate boundary corresponding to a seismic gap along strike is analyzed by a method based on the line spring concept whereby a two dimensional antiplane analysis of the upward progression provides the relation between lithospheric thickness averaged stress and slip used as a boundary condition in the generalized elsasser plate model the formulation results in a nonlinear integral equation for the rupture progression as a function of time and distance along strike a simpler approximate single degree of freedom analysis procedure is described and shown to lead to instability results that can be formulated in terms of the slip softening slope at the boundary falling below the elastic unloading stiffness of the surroundings the results also indicate a delay of ultimate seismic instability due to the stiffer short versus long time asthenospheric response and predict a final period of self driven creep toward instability the procedures for prediction of rupture progression and instability are illustrated in detail for an elastic brittle crack model of slip zone advance and parameters of the model are chosen consistently with great earthquake slips and stress drops for example an effective crack fracture energy of the order 4 106 j m2 at the peak 7 to 10 km below surface of a gaussian bell shaped distribution of fracture energy with depth with variance of the order 5 km simulating strength build up in a seismogenic layer leads to prediction of nominal seismic stress drops of 30 to 60 bars and slips of 2 to 5 m in great strike slip earthquake ruptures breaking 100 to 400 km along strike precursory surface straining in the self driven stage is predicted to proceed at a distinctly higher rate over time intervals beginning 3 to 10 months before such an earthquake this interval being greater for longer distances along strike over which the preseismic upward rupture progression takes place

3 d physical modelling of stress accumulation processes at transcurrent plate boundaries we constructed a 3 d physical model of tectonic loading at transcurrent plate boundaries by considering viscoelastic stress relaxation in the asthenosphere and spatial variation in frictional properties peak strength and critical weakening displacement of faults with this model we simulated the process of stress accumulation and release at a seismogenic region with relatively high strength on the plate interface in low strength regions surrounding the seismogenic region quasi static fault slip gradually proceeds with the progress of relative plate motion the increase of slip deficits in the seismogenic region brings about stress concentration at its margin the stress accumulation rate is roughly proportional to the inverse of the effective fault length the accumulated stress is released by unstable dynamic rupture if the critical weakening displacement d c is small and by stable fault slip if d c is very large when a fault system consists of two adjacent seismogenic regions sudden stress release in one region accelerates the stress accumulation process in another region through transient viscoelastic stress transfer as well as instantaneous elastic stress transfer this indicates the importance of elastic and viscoelastic interaction between adjacent seismic faults even in stress accumulation processes

scaling relations of strike slip earthquakes with different slip rate dependent properties at depth abstract empirical observations suggest that earthquake stress drop is generally constant to investigate the effect of rupture width on earthquake scaling relations we analyze synthetic seismicity produced by a 3d vertical strike slip fault model using two different profiles of frictional slip rate behavior below the seismogenic zone within the rate and state framework a relatively abrupt transition of the a b profile from velocity weakening to strengthening at the base of the seismogenic crust produces increasing slip and stress drop with increasing event size choosing a smoother transition allows large earthquakes to propagate deeper leading to similar slip length scaling but constant stress drop scaling our numerical experiments support the idea that the maintenance of constant stress drop across the entire range of observed earthquake magnitudes may be achieved by allowing coseismic slip to rupture to depths below the seismogenic layer

modeling earth materials from crustal to lower mantle conditions a transferable set of interaction potentials for the cmas system abstract a fully flexible ionic interaction model aspherical ion model aim is presented and applied to various relevant minerals and melts of the ca mg al si o cmas system the model reproduces accurately lattice parameters and thermoelastic properties of minerals in a wide range of compositions furthermore its transferability range extends from the pressure and temperature conditions of the earth s crust to the lower mantle thus the aim extends greatly the applicability of classical models in nanoscale computer simulations of earth materials the increased transferability compared to other interatomic potentials and the much more efficient calculation of interaction energies compared to first principles electronic structure calculations will allow larger scale simulations the potential applications of the aim to new fields of atomistic modeling in earth sciences is discussed

thermal and chemical evolution of the terrestrial magma ocean abstract the earth is likely to have experienced a magma ocean stage during accretion thermal and chemical evolution of magma ocean is investigated based on a one dimensional two phase flow heat and mass transfer model differentiation at lower mantle pressure depends on the type of magma ocean and surrounding atmosphere if the magma ocean is formed by the blanketing effect of a solar type proto atmosphere extensive differentiation proceeds at lower mantle pressure if the magma ocean is formed by the blanketing effect of an impact induced steam atmosphere no differentiation at lower mantle pressure is likely if a very deep magma ocean is formed by a giant impact whether differentiation proceeds at lower mantle pressure or not depends on grain size viscosity of melt and or properties of a transient atmosphere on the contrary chemical differentiation likely proceeds at upper mantle pressure irrespective of magma ocean type a shallow magma ocean can remain for 100 200 my without any heating processes

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

simulation of the transition of earthquake rupture from quasi static growth to dynamic propagation we have simulated a rupture transition from quasi static growth to dynamic propagation using the boundary integral equation method in order to make a physically reasonable model of earthquake cycle we have to evaluate the dynamic rupture propagation in the context of quasi static simulation we used a snapshot of the stress distribution just before the earthquake in the quasi static simulation the resultant stress will be fed back to the quasi static simulation since the quasi static simulation used the slip and time dependent constitutive relation the friction law itself evolves with time thus we used the slip weakening constitutive relation for dynamic rupture propagation consistent with that used for the quasi static simulation we modeled a san andreas type strike slip fault in which two different size asperities existed

development of multiscale slip inversion method and its application to the 2004 mid niigata prefecture earthquake 1 we present a multiscale slip inversion method for earthquakes as a first attempt to analyze an initial rupture process on a small scale and a whole one on a large scale a multiscale source model is constructed by renormalizing slip rate distributions on different scales a multiscale observation equation includes a renormalized kernel matrix using the new method and employing theoretical and empirical green s functions with two small events mw 2 3 and 3 3 we analyze the 2004 mid niigata prefecture earthquake mw 6 6 following a preliminary deconvolution analysis suggesting a complexity of the initial phase the multiscale analysis reveals details of the initial stage of the rupture process the first 1 s successfully in the multiscale model the estimated source process is consistent for all scales while independent slip inversion analyses on three scales monoscale analysis result in inconsistent slip distributions with large errors the maximum slip rate is about 1 0 m s and the rupture velocity is 2 5 3 0 km s in the initial rupture process four stages of rupture growth with different rupture directivities are found the first 0 4 s with northeastward directivity from 0 6 s to 1 0 s with southward directivity until 2 0 s with northeastward directivity again and after 2 0 s with southwestward directivity these stages may represent cascading ruptures evolving into a large earthquake the image of the whole rupture process implies self similarity of the dynamic rupture process and is a breakthrough in the complete realization of earthquake source scaling

transport properties of mg2sio4 liquid at high pressure physical state of a magma ocean abstract we use a flexible potential model to perform large scale molecular dynamics simulations on self diffusivity and viscosity of mg 2 sio 4 melt up to pressures of 32 gpa and over a temperature range of 2600 to 3200 k we find that self diffusivity decreases and viscosity increases uniformly with pressure the latter from values of 10 2 pa s at 0 gpa to 10 1 pa s at 32 gpa 2600 k both transport properties can be readily fit with a closed arrhenius expression over the whole pressure and temperature range considered independent estimates of self diffusivities and viscosity allow us to examine their relation through the stokes einstein and the eyring equations while at low pressures the sio 4 tetrahedron seems to be the viscous flow unit bare ion diffusion becomes more dominant at high pressure combining previous simulation results on thermodynamic properties with the current viscosity simulations we compute a magma ocean adiabat and the associated viscosity profile we find that viscosity in the magma ocean is 2 10 2 pa s near the surface and that it increases by less than 0 5 log unit up to 35 gpa combining scenarios for magma ocean dimensions in the young earth with thermodynamic properties and viscosity of mg 2 sio 4 melt we compute a magma ocean rayleigh number ra in the range of 10 28 and 10 29 putting the magma ocean in the dynamic regime of hard turbulence using scaling relations for the nusselt number nu at very high ra we estimate the heat flux of the magma ocean to be in the range of 10 18 to 10 19 w

suspension in convective layers and style of differentiation of a terrestrial magma ocean recent physical theories for the formation of the earth suggest that about 4 5 b y ago the mantle of the earth was partially or completely molten fractional crystallization of this hypothetical magma ocean would result in a strong chemical stratification of the earth s mantle such a scenario is controversial from the geochemical point of view however it has been noted that the simple scenario of fractional crystallization could be avoidable in a convective magma ocean if crystals remain suspended in this paper the problem of suspension is developed with the help of an energetic approach convection must do some work against gravitational settling we distinguish three regimes of convective suspensions absolute or complete sedimentation occurs when the energy dissipation due to the settling exceeds the heat loss from the convective layer this is possible only in large scale systems like magma oceans and implies that cooling can proceed only together with sedimentation crystallization and a decrease in the liquidus temperature at a constant pressure a regime of partial differentiation occurs when the energy dissipation due to the settling is less than the total heat loss but larger than the power which can be spent by convection on the crystal reentrainment process the differentiation is not complete and a competition between the rate of cooling the rate of sedimentation and the rate of turbulent diffusion determines the degree of differentiation the third regime is an absolute suspension which could be sustained for an indefinitely long time in this case sedimentation starts only when the crystal fraction reaches the maximum packing value when the viscosity of the magma rapidly increases the power which can be spent by convection on reentrainment is equal to e gd cp of the total energy supply to the convective layer where e 15 gpa or 10 3 10 1 cm during crystallization of shallow layers the first regime fractional crystallization is unavoidable the estimates depend on various poorly constrained parameters and processes such as heat flux viscosity thermodynamical disequilibrium and highly variable viscosity convection for absolute suspension the crystal size must be at least e times less or 10 3 10 1 cm and 10 4 10 2 cm respectively if e 0 01 the partial differentiation occurs in a narrow one decade range between these two regimes the radius of about 1 cm must be considered as an absolute upper bound above which fractional differentiation is guaranteed these estimates for the critical crystal size are orders of magnitude lower than suggested previously and thus the problem of crystal sizes becomes a central one for magma oceans a necessary condition for reentrainment is the existence of local mechanisms the absence of such mechanisms to reentrain the particles from the bottom would mean that an absolute suspension is impossible even if the energetics allows it turbulence is considered as a possible important factor a simple model of convection predicts a strong turbulence provided the viscosity is less than 10 9 10 10 p rotation reduces this critical viscosity to 10 5 10 8 p but this is still sufficiently large and is reached only near the maximum packing crystal fraction power law or bingham rheology of partial melts can exclude any turbulence already at 20 30 of crystal fraction we also show that the energetic criterion for the absolute suspension with e 1 coincides with the condition that the particle concentration gradient suppresses the turbulence

high pressure equation of state of molten anorthite and diopside new hugoniot equation of state data for molten diopside at 1773 k and molten anorthite at 1923 k are reported to 38 and 35 gpa respectively the diopside data initial density 2 61 mg m 3 are described by a straight line fit to the shock velocity particle velocity results of u s 3 30 1 44 u p km s 1 and our preferred fit to the anorthite data initial density 2 55 mg m 3 is given by u s 2 68 1 42 u p km s 1 reduction of the data to a third order birch murnaghan isentrope assuming the gruneisen ratio times the density is a constant and the mie gruneisen equation of state gives k 0s 22 4 gpa and k s 6 9 for diopside for anorthite we calculate k 0s 17 9 gpa and k s 5 3 the present data for diopside are used to calculate the diopside solidus at high pressures we expect the solidus to be shallow above 10 gpa but the lack of data on the variation of either the gruneisen parameters of the liquid and crystal or the heat capacity and thermal expansion at elevated pressures makes extrapolation of fusion curves uncertain solidus temperatures of 2400 2500 k and 2560 2705 k for diopside are calculated at 10 and 20 gpa respectively the new data are combined with those of rigden et al 1988 for the di 0 64 a 0 36 eutectic composition to examine the degree to which such liquids mix ideally with respect to volume up to 25 gpa for the eutectic composition at 1400 c we calculate the volumes of the an and di mix nearly ideally to 25 gpa we find that the ratio of the partial molar volumes of the oxides in silicate melts to that of the crystal oxides at 1673 k and 1 atm is 1 0 0 1 for a wide range of oxide components for the low pressure tetrahedrally coordinated oxides e g sio 2 al 2o 3 fe 2o 3 the ratio is 1 3 with respect to oxides such as stishovite corundum and hematite in which the cations are octahedrally coordinated by oxygens if changes in coordination of al and si from tetrahedral at low pressures to octahedral at high pressures occur in melts they do so gradually over an interval of 40 gpa although 1 atm bulk moduli for a wide compositional range of silicate melts are similar the differences in integrated compression to mixed oxide like high pressure configurations are reflected mainly by variations in k t k t is found to vary inversely with fraction of network forming initially tetrahedrally coordinated cations e g al 3 si 4 thus k t which may be uncertain by 1 5 is estimated to vary from 7 for molten anorthite enstatite and diopside to 8 for molten ferrosilite to 10 for molten forsterite and to 11 for molten fayalite

melting of forsterite mg2sio4 from 9 7 to 16 5 gpa a multianvil apparatus has been used to determine the pressure temperature melting curve of forsterite from 9 7 to 16 5 gpa at 10 1 gpa a singular point occurs that marks the change from congruent melting at lower pressures to incongruent melting forsterite periclase liquid at higher pressures the melting curve also passes through two invariant points at one 15 6 gpa 2310 c the phases forsterite periclase anhydrous b and liquid coexist and the melting reaction changes from forsterite periclase liquid at lower pressures to forsterite anhydrous b liquid at higher pressures at the other 16 7 gpa 2315 c the phases forsterite modified spinel anhydrous b and liquid coexist and the melting reaction changes from forsterite anhydrous b liquid at lower pressures to modified spinel anhydrous b liquid at higher pressures the simon equation p gpa 2 44 t k 2171 11 4 1 fits both our melting curve data and the lower pressure data of davis and england 1964 at low pressures the melting curve of forsterite lies at higher temperatures than that of enstatite but the two curves cross at 13 3 gpa because of the lower dt dp slope of the forsterite melting curve this causes the forsterite enstatite eutectic to shift toward forsterite as pressure increases but our data are consistent with earlier findings that the shift is not sufficient to support an origin for the mantle by eutectic like melting at high pressures

the equation of state of a molten komatiite 2 application to komatiite petrogenesis and the hadean mantle new experimental data for the equation of state of a komatiitic liquid were used to model adiabatic melting in a peridotitic mantle if komatiites are formed by 30 partial melting of a peridotitic mantle then komatiites generated by adiabatic melting come from source regions that began their unmelted ascent in the lower transition zone 500 670 km or the lower mantle 670 km the great depth of incipient melting implied by this model suggests that komatiitic liquids may form in a pressure regime where they are denser than their coexisting crystals possibly the bulk mantle although komatiitic magmas are thought to separate from residual crystals in the mantle at a temperature 200 c greater than modem mid ocean ridge basalts morbs their ultimate sources are predicted to be diapirs that if adiabatically decompressed from initially solid mantle were more than 700 c hotter than the sources of morbs and were derived from great depth we also studied the evolution of an initially molten mantle i e a magma ocean our model considers the thermal structure of the magma ocean density constraints on crystal segregation and approximate phase relationships for a nominally chondritic mantle crystallization will begin at the core mantle boundary perovskite buoyancy at 70 gpa may lead to a compositionally stratified lower mantle with iron enriched magnesiowustite content increasing with depth large convective velocities in the magma ocean would prohibit crystal liquid fractionation by settling or flotation until quiescent boundary layers form such boundary layers could form when the crystal content of the magma reaches a critical value near 44 vol and in the late stages of crystallization around unmelted blocks of foundered protocrust matrix compaction and diapirism could also lead to fractionation effects the upper mantle could be depleted or enriched in perovskite components relative to the bulk mantle olivine neutral buoyancy may lead to the formation of a dunite septum in the upper mantle partitioning the ocean into upper and lower reservoirs but this septum must be permeable

slip sequences in laboratory experiments resulting from inhomogeneous shear as analogs of earthquakes associated with a fault edge faults are intrinsically heterogeneous with common occurrences of jogs edges and steps we therefore explore experimentally and theoretically how fault edges may affect earthquake and slip dynamics in the presented experiments and accompanying theoretical model shear loads are applied to the edge of one of two flat blocks in frictional contact that form a fault analog we show that slip occurs via a sequence of rapid rupture events that initiate from the loading edge and are arrested after propagating a finite distance each successive event extends the slip size transfers the applied shear across the block and causes progressively larger changes of the contact area along the contact surface resulting from this sequence of events a hard asperity is dynamically formed near the loaded edge the contact area beyond this asperity is largely reduced these sequences of rapid events culminate in slow slip events that precede a major unarrested slip event along the entire contact surface we suggest that the 1998 m5 0 sendai and 1995 off etorofu earthquake sequences may correspond to this scenario our work demonstrates qualitatively how the simplest deviation from uniform shear loading may significantly affect both earthquake nucleation processes and how fault complexity develops