is the transition zone an empty water reservoir inferences from numerical model of mantle dynamics abstract water is probably present everywhere in the earth s mantle today with abundances ranging between scales of percent to the parts per million ppm mantle total water content is estimated to be between 10 to several times that of the present day hydrosphere numerous studies have been devoted to the determination of water solubility in mantle material d r bell g r rossmann science 255 1992 1391 1397 j ingrin h skogby eur j mineral 12 2000 543 570 they all show strong solubility variations from one mineral phase to another principally water partitioning has made the transition zone a probable trap for water from the earth s mantle n bolfan casanova et al earth planet sci lett 182 2000 209 221 d l kohlstedt et al contrib mineral petrol 123 1996 345 357 nevertheless water distribution within the mantle is still debated we have studied the role of mantle dynamics in water distribution by modeling water transport and mantle convection in a two dimensional 2 d cartesian geometry the model takes into account water partitioning between the mantle s transition zone and the upper mantle of 10 1 and between the lower mantle and the transition zone of 1 100 i e respectively between olivine and spinel and spinel and post spinel we have modeled the mantle temperature field using depth dependent viscosity and plate like surface conditions water injection at the trench has also been simulated our numerical experiments suggest that diffusivity of water has to be very high at least two orders of magnitude higher than the one experimentally determined d r bell g r rossmann science 255 1992 1391 1397 j ingrin h skogby eur j mineral 12 2000 543 570 to significantly influence water distribution in earth s mantle in fact the diffusion process is not efficient enough to balance the mixing due to mantle dynamics and to force water into the transition zone we show that the distribution of water should be quite homogeneous throughout the mantle if advection and diffusion are the only processes involved in water transport in the mantle this homogeneity implies that water below the transition zone could be in excess according to the lower mantle rocks solubility this addresses the question of stability of free water in the lower mantle and its mobility by percolation process which could be a very efficient transport process previously unconsidered in this field of research

a geodynamic model of mantle density heterogeneity using cenozoic and mesozoic plate motion reconstructions we derive a model of present day mantle density heterogeneity under the assumption that subducted slabs sink vertically into the mantle the thermal buoyancy of these slabs is estimated from the observed thermal subsidence cooling of oceanic lithosphere slab velocities in the upper mantle are computed from the local convergence rate we assume that slabs cross the upper lower mantle interface and continue sinking into the lower mantle with a reduced velocity for a velocity reduction factor between 2 and 5 our slab heterogeneity model is as correlated with current tomographic models as these models are correlated with each other we have also computed a synthetic geoid from our density model for a viscosity increase of about a factor of 40 from the upper to lower mantle our model predicts the first 8 spherical harmonic degrees of the geoid with statistical confidence larger than 95 and explains 84 of the observed geoid assuming that the model c21 and s21 terms are absent due to a long relaxation time for earth s rotational bulge otherwise 73 of the geoid variance is explained the viscosity increase is consistent with our velocity reduction factor for slabs entering the lower mantle since downwelling velocities are expected to scale roughly as the logarithm of viscosity loge 40 3 7 these results show that the history of plate tectonics can explain the main features of the present day structure of the mantle the dynamic topography induced by this heterogeneity structure consists mainly of about 1 km amplitude lows concentrated along the active continental margins of the pacific basin our model can also be used to predict the time variation of mantle heterogeneity and the gravity field we find that the age of the geoid defined as the time in the past before which the geoid becomes uncorrelated with the present geoid is about 50 m y our model for the history of the degree 2 geoid which is equivalent to the history of the inertia tensor should give us a tool to study the variations in earth s rotation pole indicated in paleomagiietic studies

mesozoic plate motion history below the northeast pacific ocean from seismic images of the subducted farallon slab the high resolution seismic imaging of subducted oceanic slabs1 2 has become a powerful tool for reconstructing palaeogeography3 the images can now be interpreted quantitatively by comparison with models of the general circulation of the earth s mantle4 here we use a three dimensional spherical computer model of mantle convection5 6 to show that seismic images of the subducted farallon plate provide strong evidence for a mesozoic period of low angle subduction under north america such a period of low angle subduction has been invoked independently to explain rocky mountain uplift far inland from the plate boundary during the laramide orogeny7 the computer simulations also allow us to locate the largely unknown kula farallon spreading plate boundary the location of which is important for inferring the trajectories of suspect terrain across the pacific basin8

lu hf and pbsl geochronology of apatites from proterozoic terranes a first look at lu hf isotopic closure in metamorphic apatite abstract the mineral apatite is characterized by elevated and highly variable lu hf ratios that in some cases allow for single crystal dating by the lu hf isotopic system apatites from the adirondack lowlands and otter lake area in the grenville province and from the black hills south dakota yield lu hf ages that are consistently older than their respective pb step leaching ages isotopic closure for the lu hf system therefore occurs before u pb system closure in this mineral in the adirondack lowlands where h2o activity was low lu hf systematics of cm sized apatite crystals remained undisturbed during upper amphibolite facies metamorphism 700 to 675 c at 1170 1130 ma the relatively old lu hf ages of 1270 and 1230 ma observed for these apatites correlate with decreasing crystal size in contrast apatite from the fluid rich otter lake area and black hills yields unrealistically low apparent lu hf closure temperatures implying that in these apatites fluids facilitated late exchange the lu hf ages for the metamorphic apatites were thus controlled either by the prevailing temperature and grain size or by fluid activity

tomographic images of a mantle circulation model sampling convection in the earth s mantle by seismic tomography is difficult as evidenced by the uneven distribution of seismic stations and events with some regions being well imaged compared to others here we quantitatively explore tomographic filtering on earth structure by tracing isc p body wave data through a computer simulation of mantle circulation which accounts for internal heating of the mantle by radioactive decay heatflux from the core a depthwise increase in viscosity and plate motion history of the past 120 million years the travel time residuals are inverted by solving jointly for structure and hypocentral parameters with explicit damping and smoothing we recover the farallon and tethys slabs as well as some low velocity anomalies associated with hot upwelling flow suggesting that tomographic filtering is probably minor in areas of high ray density

mountain belt growth inferred from histories of past plate convergence a new tectonic inverse problem past plate motions display a range of variability including speedups and slowdowns that cannot easily be attributed to changes in mantle related driving forces one key controlling factor for these variations is the surface topography at convergent margins as previous modeling shows that the topographic load of large mountain belts consumes a significant amount of the driving forces available for plate tectonics by increasing frictional forces between downgoing and overriding plates here we use this insight to pose a new tectonic inverse problem and to infer the growth of mountain belts from a record of past plate convergence we introduce the automatic differentiation method which is a technique to produce derivative code free of truncation error by source transformation of the forward model we apply the method to a publicly available global tectonic thin shell model and generate a simple derivative code to relate nazca south america plate convergence to gross topography of the andes mountain belt we test the code in a search algorithm to infer an optimal paleotopography of the andes 3 2 m y ago from the well known history of nazca south america plate convergence our modeling results are in excellent agreement with published estimates of andean paleotopography and support the notion of strong feedback between mountain belt growth and plate convergence 2007 elsevier b v all rights reserved

haskell 1935 revisited the haskell 1935 value of 1021 pa s for mantle viscosity is a classic and enduring constraint on the rheology of the earth s interior we revisit this inference using spherically symmetric self gravitating maxwell viscoelastic earth models our inference is based on both forward and inverse analyses of decay times associated with uplift at two sites considered by haskell angerman river sweden and oslo norway rather than the raw relative sea level rsl data at these sites we demonstrate that predictions of the decay time associated with the angerman river data are insensitive to variations in both the late pleistocene ice load history and the lithospheric thickness of the earth model the predictions at oslo are sensitive to both these inputs and hence decay times at this site provide a remarkably robust constraint on mantle viscosity we derive a constraint on the average viscosity of the mantle of 0 65 1 10 1021 pa s where the average resolved by the data encompasses a region which extends from the base of the lithosphere to a depth of near 1400 km this indicates that many previous analyses which have invoked the haskell value of 1021 pa s as a constraint on the average upper mantle i e above 670 km depth viscosity alone have misinterpreted the resolving power of the inference furthermore our analysis indicates that a number of apparently contradictory inferences of viscosity based on fennoscandian data satisfy the new rigorous interpretation of the haskell constraint finally we demonstrate how the ambiguity in the upper mantle lower mantle viscosity contrast associated with the haskell average may be reduced by invoking decay time constraints estimated from rsl curves in hudson bay a preliminary inversion of decay times at angerman river and richmond gulf in hudson bay suggests a contrast of approximately an order of magnitude between the average viscosities of the upper mantle and the top 1000 km of the lower mantle however a conclusive analysis in this regard must await the determination of consistent decay time estimates for the hudson bay region

simultaneous inversion of mantle properties and initial conditions using an adjoint of mantle convection through the assimilation of present day mantle seismic structure adjoint methods can be used to constrain the structure of the mantle at earlier times i e mantle initial conditions however the application to geophysical problems is restricted through both the high computational expense from repeated iteration between forward and adjoint models and the need to know mantle properties such as viscosity and the absolute magnitude of temperature or density a priori we propose that an optimal first guess to the initial condition can be obtained through a simple backward integration sbi of the governing equations thus lessening the computational expense given a model with known mantle properties we show that a solution based on an sbi generated first guess has smaller residuals than arbitrary guesses mantle viscosity and the effective rayleigh number are crucial for mantle convection models neither of which is exactly known we place additional constraints on these basic mantle properties when the convection induced dynamic topography on earth s surface is considered within an adjoint inverse method besides assimilating present day seismic structure as a constraint we use dynamic topography and its rate of change in an inverse method that allows simultaneous inversion of the absolute upper and lower mantle viscosities scaling between seismic velocity and thermal anomalies and initial condition the theory is derived from the governing equations of mantle convection and validated by synthetic experiments for both one layer viscosity and two layer viscosity regionally bounded spherical shells for the one layer model at any instant of time the magnitude of dynamic topography is controlled by the temperature scaling while the rate of change of topography is controlled by the absolute value of viscosity for the two layer case the rate of change of topography constrains upper mantle viscosity while the magnitude of dynamic topography determines the temperature scaling lower mantle viscosity when upper mantle lower mantle density anomaly dominates the flow field this two stage scheme minimizes the tradeoff between temperature and lower mantle viscosity for both cases we show that the theory can constrain mantle properties with errors arising through the adjoint recovery of the initial condition for the two layer model this error is manifest as a tradeoff between the temperature scaling and lower mantle viscosity

variational assimilation of geosat data into an eddy resolving model of the gulf stream extension area abstract a variational inverse technique is applied to assimilate sea surface height ssh measurements into a simple eddy resolving quasigeostrophic ocean model the data used were measured by geosat in the spring of 1987 in an area in the gulf stream extension the assimilation technique minimizes the weighted least squares difference between model and observations while the dynamical model equations are satisfied exactly fitting the model to data by applying the adjoint technique allows us not only to solve for the best model trajectory in phase space but also the wind forcing and internal model parameters describing for example diffusion or stratification the method is first tested systematically by performing a number of identical twin experiments with model produced observations a hierarchy of ocean models is then applied to test their performance in assimilating two repeat cycles of geosat sea surface height ssh measurements the most successful model is nonlinear and baroclinic it can f

role of a low viscosity zone in stabilizing plate tectonics implications for comparative terrestrial planetology 1 earth s near surface layer its lithosphere is broken into quasi rigid plates that form the upper thermal boundary layer for mantle convection since the discovery of plate tectonics it has been widely conjectured but only recently demonstrated that this peculiar style of convection may be facilitated by an upper mantle low viscosity zone lvz over which the plates glide easily the lvz or asthenosphere concept dates from 19th century investigations of isostatic support of mountain belts and is supported by modern evidence for a seismic low velocity zone and by studies of postglacial rebound and dynamic compensation of the earth s gravity field here we show in both two dimensional 2 d cartesian and 3 d spherical earth models that combining a pronounced lvz and a plastic yield stress to allow localized weakening of the cold thermal boundary layer results in a distinctly plate tectonic style of convection with 30 toroidal surface motion for the 3 d case recycling of water into the upper mantle at subduction zones is a plausible cause of earth s lvz whereas venus is dry and lacks both an lvz and plate tectonics

polar wandering in mantle convection models we calculate polar motion in models of 3 d spherical mantle convection at rayleigh numbers up to 108 which include internal heating radial viscosity variations and an endothermic phase change isoviscous models yield rapid polar motion of order 3 myr but a factor of 30 increase in viscosity with depth reduces the rate of polar motion to about 0 5 myr due to stabilization of the large scale pattern of convection avalanching due to an endothermic phase change causes pulsating inertial interchange polar excursions of order 80 110 and of duration 20 70 myr a layered viscosity model with an endothermic phase change yields only one inertial interchange event in 600 million years these models show that the slow observed rate of post paleozoic true polar wander is not incompatible with higher rates inferred for earlier times

reconstructing farallon plate subduction beneath north america back to the late cretaceous using an inverse mantle convection model that assimilates seismic structure and plate motions we reconstruct farallon plate subduction back to 100 million years ago models consistent with stratigraphy constrain the depth dependence of mantle viscosity and buoyancy requiring that the farallon slab was flat lying in the late cretaceous consistent with geological reconstructions the simulation predicts that an extensive zone of shallow dipping subduction extended beyond the flat lying slab farther east and north by up to 1000 kilometers the limited region of flat subduction is consistent with the notion that subduction of an oceanic plateau caused the slab to flatten the results imply that seismic images of the current mantle provide more constraints on past tectonic events than previously recognized

shear zone model for the origin of metamorphic core complexes core complex tectonite results from simple shear rotational strain within regional ductile shear zones that have accommodated a tertiary crustal stretching the emplacement of younger and or upper level nontectonite rocks on older and or deeper level tectonites is the ordinary and predictable result of normal slip translation along shear zones that cut upward through the local geologic column progressive deformation produces a structural stratigraphy marked from bottom to top by normal country rock protolith mylonitic gneiss tectonite carapace microbrecciated tectonite microbreccia decollement and upper plate detachment rocks as young as mid miocene the reconstructions suggest that local regional crustal stretching locally exceeded 100

mantle circulation models with variational data assimilation inferring past mantle flow and structure from plate motion histories and seismic tomography summary mantle convection models require an initial condition some time in the past because this initial condition is unknown for earth we cannot infer the geological evolution of mantle flow from forward mantle convection calculations even for the most recent mesozoic and cenozoic geological history of our planet here we introduce a fluid dynamic inverse problem to constrain unknown mantle flow back in time from seismic tomographic observations of the mantle and reconstructions of past plate motions using variational data assimilation we derive the generalized inverse of mantle convection and explore the initial condition problem in high resolution 3 d spherical mantle circulation models for a time period of 100 myr roughly comparable to half a mantle overturn we present a synthetic modelling experiment to demonstrate that mid cretaceous mantle structure can be inferred accurately from fluid dynamic inverse modelling assuming present day mantle structure is well known even if an initial first guess assumption about the mid cretaceous mantle involved only a simple 1 d radial temperature profile we also demonstrate that convecting present day mantle structure back in time by reversing the time stepping of the energy equation is insufficient to model the mantle structure of the past the difficulty arises because such backward convection calculations ignore thermal diffusion effects and therefore cannot account for the generation of thermal buoyancy in boundary layers as we go back in time inverse mantle convection modelling should make it possible to infer a number of flow parameters from observational constraints of the mantle

three dimensional forward and backward numerical modeling of mantle plume evolution effects of thermal diffusion we investigate the effects of thermal diffusion on the evolution of mantle plumes by means of three dimensional numerical modeling forward and backward in time mantle plumes are fed by a hot low viscous material from the thermal boundary layer the material of the plumes is mainly advected toward the earth s surface with some effects of thermal diffusion however the feeding can become weaker with time and then thermal diffusion can take over and control the evolution of the plumes numerical experiments forward in time show that a week feeding of mantle plumes by the hot material from the boundary layer results in the diffusive disappearance of plume tails first and plume heads later this is the most likely explanation for the seismically detected low velocity mantle structures mantle plumes with prominent heads and almost invisible tails at midmantle depths we develop restoration models backward in time to recover strong features of mantle plumes in the geological past after they have dissipated due to thermal diffusion and analyze effects of thermal diffusion and temperature dependent viscosity on the reconstruction of the mantle plumes we investigate the impact of thermal diffusion on the performance of our restoration variational data assimilation algorithm for a given range of rayleigh number ra and two values of the viscosity ratio r between the upper and lower boundaries of the model domain we show that 1 the residuals between the temperature predicted by the forward model and that reconstructed by the backward modeling become larger and 2 the restoration process becomes poorer as ra decreases and r increases we assimilate temperature obtained from high resolution seismic tomography data for the southeastern carpathians and show that present diffused mantle structures can be restored to their prominent state in the miocene times we discuss the problems of smoothness of model input and output data errors associated with the modeling and some other challenges in the data assimilation for thermoconvective flow in the mantle

lower mantle convection and geomagnetism the statistical properties of recent marine magnetic anomaly time scales covering the period from 165 ma to the present are analyzed via the methods presented in the companion paper mcfadden this issue the data no longer support the hypothesis that during the last 86 ma there were two periods separated by a discontinuity at about 45 ma when the properties were stationary instead there is strong evidence that the rate of reversals decreased in an approximately linear manner with time from 165 ma until it reached zero resulting in the cretaceous normal polarity interval at about 86 ma ago the process of reversals began again and the rate of reversals increased linearly with time there is a slight indication that the rate of reversals reached a maximum about 10 ma ago and is again decreasing analysis of the reversal sequences shows there is no good evidence for the concept of differences in the relative stabilities of the two polarity states nor need such a concept be invoked to explain long intervals without reversals such as the cretaceous normal polarity interval quite clearly there has been some form of thermal perturbation at the base of the mantle with a characteristic time of the order of 108 years our interpretations require convection deep within the mantle and suggest that the temperature at the base of the mantle attains a maximum during long magnetic quiet intervals

three dimensional spherical models of convection in the earth s mantle three dimensional spherical models of mantle convection in the earth reveal that upwelling cylindrical plumes and downwelling planar sheets are the primary features of mantle circulation thus subduction zones and descending sheetlike slabs in the mantle are fundamental characteristics of thermal convection in a spherical shell and are not merely the consequences of the rigidity of the slabs which are cooler than the surrounding mantle cylindrical mantle plumes that cause hotspots such as hawaii are probably the only form of active upwelling and are therefore not just secondary convective currents separate from the large scale mantle circulation active sheetlike upwellings that could be associated with mid ocean ridges did not develop in the model simulations a result that is in agreement with evidence suggesting that ridges are passive phenomena resulting from the tearing of surface plates by the pull of descending slabs

inverse problem of thermal convection numerical approach and application to mantle plume restoration abstract modern seismic tomographic images of the earth s interior facilitate the inference of the complex trajectories of present day convective flow in the upper mantle quantitative reconstruction of both the observed mantle structure and temperature field backwards in time requires a numerical tool for solving the inverse problem of thermal convection at infinite prandtl number in this paper we present a variational approach to three dimensional numerical restoration of thermoconvective mantle flow with temperature dependent viscosity this approach is based on a search for the mantle temperature and flow in the geological past by minimizing differences between present day mantle temperature derived from seismic velocities or their anomalies and that predicted by forward models of mantle flow for an initial temperature guess the past mantle temperatures so obtained can be employed as constraints on forward models of mantle dynamics to demonstrate the applicability of this technique we restore numerically a fluid dynamic model of the evolution of upper mantle plumes and show that the initial shape of the plumes can be accurately reconstructed we then model the evolution of the plumes forward in time plume upbuilding starting from the restored state to the state they were before the restoration and demonstrate the high accuracy of the model predictions we also show that the neglect of thermal diffusion in the backward modeling of thermal plumes in order to simplify the numerical procedure results in erroneous restorations of the plumes

nd isotope mapping of a pinwarian age composite arc belt in the quebecia terrane of the central grenville province canada abstract there continues to be confusion in the geological community concerning the ages of crustal formation and crustal accretion within the central grenville province of quebec to clarify the geological history of crustal growth in the eastern part of the quebecia terrane sixty new nd isotope analyses are presented from a 60 000 km2 area northwest of baie comeau most samples yield pinwarian nd model ages that suggest them to be derived from juvenile oceanic arc terranes however two large slivers with paleoproterozoic tdm ages attest to the existence of hidden blocks of old crust which divide the area of juvenile pinwarian crust into a composite arc belt of smaller accreted terranes the old crustal blocks probably do not reach the present surface but represent an igneous crustal protolith of younger i type magmatism by comparison with a mesozoic tectonic analogue it is proposed that accreted juvenile arc crust with attached slivers of older crust were rifted away from an active margin to the west and translated eastwards until blocked by the previously accreted labradoria terrane although the quebecia composite arc belt consists of over 95 of pinwarian juvenile arc crust the age of arc accretion was post pinwarian the proposed oblique nature of the accretion process may explain the lack of a major collisional orogen at that time this paper shows the usefulness of large scale nd isotope mapping of precambrian crustal terranes to clarify complex processes of crustal formation and arc accretion

the detachment era 1977 1982 and its role in revolutionizing continental tectonics after the discovery of thrust and nappe structure near the turn of the twentieth century mountain belts were viewed as a direct expression of horizontal shortening of the continental crust and continental rifting was viewed as a phenomenon distinct from it by mid century broad consensus had emerged mainly on the basis of physical reasoning that thrust and nappe structure instead reflected gravity sliding secondary to vertical motions of the crust as embodied in the influential stockwerk folding hypothesis in a noteworthy period from 1977 to 1982 informally referred to here as the detachment era not only did the last vestiges of support for the stockwerk hypothesis evaporate but large magnitude extension was discovered throughout the cordillera manifest primarily by extensional detachments and metamorphic core complexes soon afterward extensional detachments were recognized as a global phenomenon forcing first order reinterpretation of field relations in most orogens although plate tectonics is indisputably the most profound discovery in earth sciences in the twentieth century the detachment era arguably had commensurate impact on field based interpretations of continental tectonics three decades later controversy persists over the origin of metamorphic tectonites in core complexes and over the existence and mechanics of slip on shallowly dipping extensional detachments

fault and fault rock characteristics associated with cenozoic extension and core complex evolution in the catalina rincon region southeastern arizona cenozoic extensional deformation in southern arizona included 1 a neogene phase of basin and range deformation recorded by high angle normal faults and 2 an earlier phase of detachment faulting and brittle ductile crustal shearing associated with tectonic denudation of metamorphic core complexes in the catalina rincon region exposed fault zones produced at different crustal depths during successive extensional episodes display differing fault geometries and types of fault rocks formed during progressive crustal extension detachment faults are associated with both mylonites produced by ductile shear and cataclasites produced by brittle shear younger faults formed at shallower depths are associated with less intense cataclastic deformation and with brittle fracturing that includes transtensile phenomena at the shallowest crustal levels represented qualitative measures of net displacement along individual fault zones are provided by 1 the nature of contrasts among successively overprinted fabrics and internal structures in the footwall and 2 the degree of contrast between fabrics and structures of footwall and hanging wall rocks footwalls of the oldest structures display varied brittle overprints of ductile fabrics and are juxtaposed across gouge zones along detachment surfaces with stratal successions cut by multiple brittle shear surfaces footwalls of younger structures formed at shallower depths display multiple generations of cataclastic features including brecciation of variable intensity and cataclasite dikes but are juxtaposed against hanging wall strata that are only moderately deformed by subsidiary faults the shallowest fault zones lack either structural overprints in their footwalls or any significant contrasts between footwall and hanging wall deformation exposures of mid crustal rocks within the core complexes reflect successive exhumation and uplift of fault footwalls during sequential episodes of deformation the present high elevation of mylonitic rocks in the catalina rincon metamorphic core complex reflects dip slip and isostatic footwall flexure during basin and range deformation as well as tectonic denudation during detachment faulting net uplift of core rocks resulted from multiple phases of deformation

sea level change glacial rebound and mantle viscosity fornorthern europe northwestern europe remains a key region for testing models of glacial isostasy because of the good geological record of crustal response to the glacial unloading since the time of the last glacial maximum models for this rebound and associated sea level change require a detailed knowledge of the ice sheet geometry including the ice thickness through time existing ice sheet reconstructions are strongly model dependent and inversions of sea level data for the mantle response may be a function of the model assumptions thus inverse solutions for the sea level data are sought that include both ice and earth model parameters as unknowns sea level data from fennoscandia the north sea the british isles and the atlantic and english channel coasts have been evaluated and incorporated into the solutions the starting ice sheet for fennoscandia is based on a reconstruction of a model by denton hughes 1981 that is characterized by quasi parabolic cross sections and symmetry about the load centre both global northwestern europe as a whole and regional subsets of the data solutions have been made for earth model parameters and ice height scaling parameters the key results are as follows 1 the response of the upper mantle to the changing ice and water loads is spatially relatively homogenous across scandinavia the north sea and the british isles 2 this response can be adequately modelled by an effective elastic lithosphere of thickness 65 85 km and by an effective upper mantle viscosity from the base of the lithosphere to the 670 km depth seismic discontinuity of about 3 4 1020 pa s the effective lower mantle viscosity is at least an order of magnitude greater 3 the ice thickness over scandinavia at the time of maximum glaciation was only about 2000 m much less than the 3400 m assumed in the denton hughes model 4 the ice profiles are asymmetric about the centre of the ice sheet with those over the western part being consistent with quasi parabolic functions whereas the ice heights over the eastern and southern regions increase much more slowly with distance inwards from the ice margin

variational coupling of plinian column models and data application to el chichon volcano abstract many efforts have been done in the modelling of plinian columns however until now the inverse problem of the reconstruction of a plinian event from observed data has been only roughly tackled this paper discusses the efficient variational data assimilation vda that manages the optimization iterate sequence by means of gradient computations theoretical developments of vda are presented for both the woods equations and a generic system allowing for the modelling of the navier stokes equations two and three dimensional unsteady plinian models being based on the latters vda could be clearly performed on their differentiable subset of equations although no column data are available for the 1982 el chichon eruptions identical twin experiments were used to check the abilities of the vda approach vda experiments coupled with a tephra tephra fall model could be used to obtain isopach and isopleth maps of past eruptions performing vda experiments with a plinian model coupled to a tephra fall model could be an interesting solution to exploit isopach and isopleth maps of the past eruptions of el chichon some of the numerical experiments presented in this paper are downloadable in the pliniad package which is freely available from the author s webpage

normal mode and free air gravity constraints on lateral variations in velocity and density of earth s mantle with the use of a large collection of free oscillation data and additional constraints imposed by the free air gravity anomaly lateral variations in shear velocity compressional velocity and density within the mantle dynamic topography on the free surface and topography on the 660 km discontinuity and the core mantle boundary were determined the velocity models are consistent with existing models based on travel time and waveform inversions in the lowermost mantle near the core mantle boundary denser than average material is found beneath regions of upwellings centered on the pacific ocean and africa that are characterized by slow shear velocities these anomalies suggest the existence of compositional heterogeneity near the core mantle boundary

the modern geoid and ancient plate boundaries abstract the non hydrostatic geoid is dominated by three large anomalies an area of high gravity potential in the equatorial pacific another stretching from greenland through africa to the southwest indian ocean and a semi continuous low region passing from hudson s bay through siberia to india and on to antarctica none of these three high amplitude greater than 60 m and long wavelength anomalies corresponds to present day plate boundaries however if the modern geoid is plotted over the positions of continents and plate boundaries at 125 ma b p reconstructed relative to hotspots a strong correlation emerges the modern geoidal low corresponds in position to the areas of subduction surrounding the pacific 125 ma ago the geoidal high now centered on africa is entirely contained within ancient pangaea and the equatorial pacific high overlies the location of the spreading centers preserved in the magnetic anomalies of the central pacific the most plausible cause of the large geoidal undulations is lower mantle convection only weakly coupled to plate motions the correspondence between modern geoid and ancient plate boundaries implies either that the coupling was much more intimate in the past or that there is a lag of at least 100 ma in response of the lower mantle to upper mantle conditions

phanerozoic marine inundation of continents driven by dynamic topography above subducting slabs a spherical model of mantle flow constrained by the locations of trenches can be used to predict the dynamic topography of the earth s surface and hence the marine inundation of continents for past periods of high sea level the predicted geographical pattern of flooding correlates well with the geological record the high spatial correlation may result from increased plate velocities at these times leading to increased rates of subduction subsidence and inundation at convergent margins

fault zone reactivation kinematics and mechanisms the kinematics and mechanisms of fault zone reactivation are reviewed reactivation is dependent upon fault zone orientation and the existence of weak mylonites along these zones the recognition of reactivation within mylonite zones and the softening processes that first concentrate deformation into these and secondly provide a weak medium for reactivation are discussed attention is given to the darling mobile zone western australia and the redbank zone see obee white this symposium as examples of reactivated zones

field tests of rolling hinges existence mechanical types and implications for extensional tectonics in rolling hinge models a locus of isostatic footwall uplift migrates together with the withdrawing hanging wall of a large displacement tens of kilometers normal fault a fault bend fold that migrates through the footwall results causing progressive deactivation of the updip part of the fault as it is tilted to a lower dip rolling hinge migration should leave a discernible geologic record but compelling tests are difficult to design because predictions of rolling hinge models are nonunique and alternative models commonly can explain individual data sets field tests based on thermochronology paleomagnetism and structural analysis are typically applied to footwall rocks whereas sedimentology geochronology of volcanic rocks and structural analysis are typically applied to upper plate rocks we review existing theoretical models and case studies in 14 detachment terranes some negative results are reasonably compelling but positive tests as yet tend to permit rather than demand a rolling hinge locally both positive and negative conclusions have been reached about the passage of a hinge within the same terrane such differences in interpretation may depend more on the scale of observation or on the specific model considered than on the geological development of the area subvertical simple shear and flexural failure mechanisms with or without significant induced flow of lower crustal material are thought to dominate hinge related footwall deformation in individual sites although rolling hinge models offer an alternative to low initial fault dips hinge related deformation does not demand a steep initial fault dip few areas in which rolling hinge tectonics are permissible had initially steep faults 35 rather where the evidence most strongly favors a rolling hinge detachment faults had initial dips 35 in the future conclusive results are most likely to be obtained if diverse tests are applied to both the upper and lower plates of detachment terranes where other geological sources of ambiguity are minimal at best the rolling hinge mechanism does not universally explain the observation that earthquakes are rare on low angle normal faults nor solve the mechanical problems of frictional slip on such faults

the petrogenesis of mafic minor intrusions and volcanics of the central metasedimentary belt grenville province canada morb and oib sources abstract numerous separate suites containing mafic igneous rocks each characterized by its own trace element signature have been identified and described in the western part of the elzevir terrane of the central metasedimentary belt of the grenville province in canada the average compositions of the mafic rocks from the tudor and turriff volcanics and the low zirconium lzs intermediate zirconium izs high zirconium hzs calc alkaline cas highly fractionated tholeiite hft and ultra potassic uks suites of minor intrusions all show negative nb and ti anomalies on chondrite normalized multi element plots this series of rock suites with their characteristic anomalies have been interpreted as being emplaced in a marginal basin formed on attenuated continental crust similarities in multi element plots and the results of petrogenetic calculations suggest that the turriff lavas lzs izs and tudor lavas and hzs suites were all formed from melts derived from the same spinel lherzolite source the composition of this source is considered to be similar to that from which mid ocean ridge basalts are derived modified by crustal contamination the hft cas and uks rocks were formed from melts derived from various garnet lherzolite sources these sources may be modelled as having a trace element composition similar to that from which ocean island basalts are derived modified to different extents by subduction derived components

true polar wander abstract a re evaluation of the existence of true polar wander tpw since the late cretaceous and a comparison among the various approaches are made using updated paleomagnetic hotspot and relative motion datasets previous attempts to determine the existence of tpw had resulted in different conclusions comparison of hotspot locations and paleomagnetic poles required significant pole motion although lithospheric plate displacement analysis yielded insignificant motion however these earlier determinations cannot be directly compared to find the reason for the discrepancies because each used different datasets for this study the different approaches are applied to a single updated model with three alternative relative motions of east and west antarctica although the results are model dependent in general there was not significant motion of the pole relative to the lithosphere 1 5 since the early tertiary but a large motion 10 12 relative to the hotspot framework it is unlikely that errors in the determinations could account for this disagreement the a95 of the plate reconstruction is about 3 the uncertainty in antarctica motion is estimated to no larger than 3 and cumulative errors in the relative plate motions may also amount to 3 only if all these errors are present in the maximum estimated amount and in the same direction could they account for the 10 12 gap between the two approaches this conclusion of pole motion relative to the hotspots but not the lithosphere may indicate an independent shift of the mesosphere relative to the lithosphere or mantle roll of hargraves and duncan

steady plumes produced by downwellings in earth like vigor spherical whole mantle convection models if mantle thermal upwellings plumes are the cause of volcanic hot spots then observations suggest that plumes are relatively fixed with nonuniform distribution and limited lifetimes to date fixity of upwellings has only been shown in models of convection at either low vigor or with layering though studies where the lower mantle has high viscosity do frequently show upwellings with much lower drift velocities than the surface velocity since more vigorous convection traditionally shows more time dependence fixity of upwellings has not been expected for nonlayered convection at earth like vigor rather we might expect slow but increasing drift velocities i have undertaken numerical models of whole mantle convection in three dimensional spherical geometry at approaching earth like vigor surprisingly these simulations show prominent steady virtually fixed plumes arising from self organization controlled by the smaller but numerous cold downwellings if downwelling subduction dominates earth s interior dynamics then this work suggests that plume fixity need not require layering the regular spacing and permanence of model upwellings contrast with observations of hot spots though in these models which do not simulate plates the fixity and regular spacing result from the freedom of downwellings to occur everywhere except where plumes reach the surface i suggest that on earth this feedback is weakened by the presence of plates but that whole mantle thermal convection can still produce relatively fixed plumes though we might expect them to be weaker more mobile and transient

geochemistry of two metavolcanic arc suites from the central metasedimentary belt of the grenville province southeastern ontario canada samples of two subalkaline metavolcanic suites the tudor formation ca 1 28 ga and the overlying kashwakamak formation have been analysed for major elements and 27 trace elements including rare earth elements the tudor formation is tholeiitic and contains mainly basaltic flows whereas the kashwakamak formation is calc alkaline and contains mainly andesitic rocks with minor felsic rocks the succession has been regionally metamorphosed to upper greenschist lower amphibolite facies trace element abundances and ratios indicate that rocks of the tudor and kashwakamak formations are island arc type geochemical modelling using rare earth elements zr ti and y indicates that the tudor volcanic rocks are not derived from a single parental magma through simple fractional crystallization equilibrium partial melting of a heterogeneous proterozoic upper mantle can explain the trace element abundances and ratios of tudor formation volcanic rocks the intermediate to felsic rocks of the kashwakamak formation appear to have been derived from a separate partial melting event the data are consistent with an origin of the arc either on oceanic crust or on thinned continental crust and with accretion of the arc to a continental margin between the time of extrusion of tudor volcanic rocks and that of kashwakamak volcanic rocks

tidal currents on the central oregon shelf models data and assimilation 1 measurements of tidal currents on the central oregon shelf are available from several sources including recent high frequency hf coastal radar and acoustic doppler profiler adp deployments and historical current moorings in this paper we use a generalized inverse gi approach to compare these data to and then assimilate them into numerical models for the barotropic tides harmonic analysis of the data in short time windows using a modified admittance approach reveals that tidal currents on the oregon shelf are highly variable in time and can contain significant baroclinic components data from the winter months when waters on the shelf are only weakly stratified are found to be most nearly barotropic and thus most reasonable for assimilation into the shallow water equations model the various data sources are used in several different combinations for assimilation and validation forcing the prior forward model with normal flow open boundary conditions obtained from a regional barotropic inverse model results in semidiurnal barotropic currents that are consistent within estimated error limits with all available data in contrast diurnal currents on the shelf are very sensitive to details of the model configuration and are significantly improved by data assimilation very similar solutions result from assimilation of either the hf radar or adp data sets the high sensitivity of the diurnal band currents can be understood dynamically in terms of trapped shelf waves a short 85 km long section of shelf off the central oregon coast is wide enough to allow first mode barotropic shelf waves at the subinertial diurnal frequencies this results in locally resonant large amplitude diurnal tidal currents that are very sensitive to details in the local forcing and hence quite variable in time

jurassic and cretaceous plate tectonic reconstructions abstract five plate tectonic reconstructions are presented illustrating the breakup of pangea and the evolution of the world s ocean basins during the early jurassic pliensbachian late jurassic volgian early cretaceous aptian late cretaceous cenomanian and latest cretaceous maestrichtian indicated on the maps are the location of the spreading centers intracontinental rifts subduction zones and transform faults which were active during each interval

on convection in the earth s core driven by lateral temperature variations in the lower mantle summary lateral variations in heat flux or temperature in the lowermost mantle associated with mantle convection will drive fluid flow in the liquid core the effect is modelled by a rotating spherical shell with uniform lower boundary temperature and a laterally varying upper surface temperature and the solutions found by numerical calculation some for a density stratified fluid the problem depends upon two dimensionless numbers a horizontal rayleigh number and a stratification parameter the calculations are restricted to surface temperatures which are symmetric about the equator and steady solutions are found induced toroidal flows near the surface are closely linked with the applied temperature profile through the thermal wind equation and coriolis forces make the convection penetrate into the shell stratification acts mainly to suppress radial flow but the surface toroidal flow is relatively unaffected the results illustrate the powerful influence exerted by the surface temperature but are difficult to apply directly to the earth s core because molecular values of the thermal diffusivity entail a very long time scale assuming a turbulent thermal diffusivity equal to the magnetic diffusivity gives a more realistic time scale and it is possible to recover for specific simple imposed temperature profiles flows similar to those found in the earth s core from inversion of geomagnetic secular change

effects of multiple phase transitions in a three dimensional spherical model of convection in earth s mantle numerical models of mantle convection that incorporate the major mantle phase changes of the transition zone reveal an inherently three dimensional flow pattern with cylindrical features and linear features that behave differently in their ability to penetrate the 670 km discontinuity the dynamics are dominated by accumulation of cold linear downwellings into rounded pools above the endothermic phase change at 670 km depth resulting in frequent avalanches of upper mantle material into the lower mantle the effect of the exothermic phase transition at 400 km depth is to reduce the overall degree of layering by pushing material through the 670 km phase change resulting in smaller and more frequent avalanches and a wider range of morphologies large quantities of avalanched cold material accumulate above the coremantle boundary cmb resulting in a region of strongly depressed mean temperature at the base of the mantle the 670 km phase change has a strong effect on the temperature field with three distinct regions being visible 1 the upper mantle containing linear downwellings and pools of cold material in the transition zone and characterized by a high amplitude long wavelength spectrum 2 the midmantle containing quasi cylindrical avalanche conduits and characterized by a low amplitude broad spectrum and 3 the deep mantle containing large pools of cold avalanched material and characterized by a high amplitude ultra red i e long wavelength spectrum the effect on the velocity field is very different flow penetration across the 670 km phase change is strongly wavelength dependent with easy penetration at long wavelengths but strong inhibition at short wavelengths thus when comparing numerical models with long wavelength seismic tomography diagnostics based on the density field such as the radial correlation function are much more sensitive to the effects of phase transitions than those based on the velocity field the amplitude of the geoid is not significantly affected by the partial layering because the contribution from the strong heterogeneity in the transition zone is almost perfectly balanced by the contribution from deflection of the 670 km discontinuity avalanches are associated with geoid lows however a more complex viscosity structure is required to correctly match the sign of the geoid over slabs in earth

isostatic deformations and polar wander induced by redistribution of mass within the earth the effects at the surface of the earth of time dependent mantle mass anomalies are analyzed within the framework of a viscoelastic mantle with maxwell rheology the implications for the earth s rotation are developed using the linearized liouville equations valid for small polar displacements our approach is appropriate for a simplified modeling of subduction the displacement of the earth s axis of rotation called true polar wander is very sensitive to the viscosity profile of the mantle and to the nature of the 670 km seismic discontinuity phase change models generally yield a huge amount of polar wander except for large viscosity increases for chemically stratified models true polar wander is drastically reduced as a consequence of dynamic compensation of the mass anomalies at the upper lower mantle interface when the source is embedded in the upper mantle in the proximity of the chemical density jump the polar wander stops after a finite time controlled by the slowest isostatic mode

a simple global model of plate dynamics and mantle convection cooling and thickening of lithospheric plates with age and subduction result in large scale horizontal density contrasts tending to drive plate motions and mantle flow we quantify the driving forces associated with these density contrasts to determine if they can drive the observed plate motions first two dimensional models are computed to evaluate the effects of assumed rheologies and boundary conditions we are unable to obtain platelike behavior in viscous models with traction free boundary conditions the piecewise uniform velocities distinctive of plate motion can be imposed as boundary conditions and the dynamic consistency of the models evaluated by determining if the net force on each vanishes if the lithosphere has a newtonian viscous rheology the net force on any plate is a strong function of the effective grid spacing used leading to ambiguities in interpretation incorporating a rigid plastic lithosphere which fails at a critical yield stress into the otherwise viscous model removes these ambiguities the model is extended to the actual three dimensional spherical plate geometry the observed velocities of rigid plastic plates are matched to the solution of the viscous stokes equation at the lithosphere asthenosphere boundary body forces from the seismically observed slabs from the thickening of the lithosphere obtained from the actual lithospheric ages and from the differences in structure between continents and oceans are included interior density contrasts such as those resulting from upwellings from a hot bottom boundary layer are assumed to occur on a scale small compared to plate dimensions and are not included the driving forces from the density contrasts within the plates are calculated and compared to resisting forces resulting from viscous drag computed from the three dimensional global return flow and resistance to deformation at converging boundaries the rms residual torque is 30 of the driving torque the density contrasts within the plates themselves can reasonably account for plate motions body forces from convection in the interior may provide only a small net force on the plates at converging boundaries the lithosphere has a yield stress of 100 bars drag at the base of the plates is 5 bars and resists plate motion the net driving forces from subducting slabs and collisional resistance are localized and approximately balance driving forces from lithospheric thickening are distributed over the areas of the plates as is viscous drag the approximate balance of these two forces predicts plate velocities uncorrelated with plate area as observed the model represents a specific case of boundary layer convection the dynamical results are consistent with either upper mantle or mantle wide convection

stress state and fluid pressure level along the whipple detachment fault california brittle structures in the upper 200 m of the footwall of the whipple detachment fault are used to characterize the state of stress under which the detachment slipped they are younger than or coeval with chloride brecciation and those that record shear typically are either moderately northeast dipping normal structures or steep northwest striking southwest down structures that we interpret as conjugate shears from this we infer that the maximum principal stress was oriented 55 80 from the detachment while they were active the angle between the conjugate faults averages about 30 indicating failure in the transtensional regime during conjugate faulting the effective least principal stress was nearly equal to the tensile strength the whipple fault probably had a normal coefficient of static friction and it slipped under hydrostatic to only moderately elevated fluid pressure rapid mineralization in the surroundings of major fault zones allows transtensional failure there and permits differential stress to be higher than if cohesionless friction limits strength this causes resolved shear stress sufficient for slip on faults severely misoriented relative to the maximum principal stress

reconstructing the cenozoic evolution of the mantle implications for mantle plume dynamics under the pacific and indian plates article history the lack of knowledge of the initial thermal state of the mantle in the geological past is an outstanding problem in mantle convection the resolution of this problem also requires the modelling of 3 d mantle evolution that yields maximum consistency with a wide suite of geophysical constraints quantifying the robustness of the reconstructed thermal evolution is another major concern to solve and estimate the robustness of the time reversed inverse problem of mantle convection we analyse two different numerical techniques the quasi reversible qrv and the backward advection bad methods our investigation extends over the 65 myr interval encompassing the cenozoic era using a pseudo spectral solution for compressible flow thermal convection in 3 d spherical geometry we find that the two dominant issues for solving the inverse problem of mantle convection are the choice of horizontally averaged temperature i e geotherm and mechanical surface boundary conditions we find in particular that the inclusion of thermal boundary layers that yield earth like heat flux at the top and bottom of the mantle has a critical impact on the reconstruction of mantle evolution we have developed a new regularisation scheme for the qrv method using a time dependent regularisation function this revised implementation of the qrv method delivers time dependent reconstructions of mantle heterogeneity that reveal 1 the stability of pacific and african large low shear velocity provinces llsvp over the last 65 myr 2 strong upward deflections of the cmb topography at 65 ma beneath the north atlantic the south central pacific the east pacific rise epr and the eastern antarctica 3 an anchored deep mantle plume ascending directly under the epr easter and pitcairn hotspots throughout the cenozoic era and 4 the appearance of the transient reunion plume head beneath the western edge of the deccan plateau at 65 ma our reconstructions of cenozoic mantle evolution thus suggest that mantle plumes play a key role in driving surface tectonic processes and large scale volcanism 2014 elsevier b v all rights reserved

localization control for chlorite breccia deformation beneath catalina detachment fault rincon mountains tucson arizona abstract the structural location of an approximately 3 km stretch of the catalina detachment fault zone appears to have been controlled by an ultramylonite shear zone within mylonites of the catalina rincon metamorphic core complex the catalina detachment fault zone consists of the detachment fault surface a 3 5 m interval of cataclasite and ultracataclasite up to 50 m of chlorite breccia and a discrete subdetachment fault beneath the subdetachment fault is a km scale thickness of mylonites progressive ductile to brittle shear zone evolution of the fault rock stratigraphy started with mylonitization was followed by overprinting of mylonites by chlorite brecciation and culminated in the formation of the catalina detachment fault and associated ultracataclasites the detachment fault is cospatial with and subparallel to the zone of chlorite breccia the subdetachment fault is subparallel to the interval of chlorite brecciation and to the detachment fault the plane of projection of the approximately 30 m thick ultramylonite shear zone within the mountain of mylonite when followed downdip coincides with the base of the chlorite breccia brittle shear zone ultramylonite is preserved in places in the immediate lower plate of the subdetachment fault the position and orientation of the subdetachment fault appears to have been controlled by an ultramylonite shear zone within the lower plate mylonites the rheological properties and orientation of this ultramylonite shear zone favored its reactivation as the brittle sole fault of the zone of chloritic brecciation

imaging 3 d spherical convection models what can seismic tomography tell us about mantle dynamics we assess whether current global seismic tomography can resolve parameters characterizing mantle dynamics in particular 1 a viscosity increase from the upper to the lower mantle 2 an endothermic phase transition at the 670 km discontinuity 3 heat flux across the core mantle boundary and 4 the effect of the motion of rigid surface plates on the convection planform we apply a linear seismic filter to numerical convection models that incorporate the desired physical parameters assuming that the shear velocity perturbations depend only on the convectively induced temperature variations we show that the differences between the characteristic spectral patterns of convection models are preserved by the filtering process comparison with actual 3d seismic mantle models indicates that the effect of rigid plates dominates the spectral characteristics of the models we estimate the effect of spatial aliasing of higher order structure into a lower order model and find that the structure retrieved by inversion is more distorted by the effects of the aliasing than by those due to uneven ray coverage this effect is strongest at shorter wavelengths and near the core mantle boundary we also find that the proper choice of radial smoothing parameters is crucial for detecting subtle signatures such as that of an endothermic phase transition at the 670 km discontinuity

nd isotope mapping of the dysart gneiss complex evidence for a rifted block within the central metasedimentary belt of the grenville province abstract more than 65 new nd isotope analyses are presented for the vicinity of the central metasedimentary belt boundary zone cmbbz near haliburton in the grenville province of ontario canada they fall into two well defined groups with distinct ranges of tdm model ages these two groups comprise the cmbbz with an average tdm age 1 46 ga and rocks of the central metasedimentary belt cmb with an average tdm age of 1 28 ga however a distinct block of crust within the cmb comprising the dysart gneiss complex has an older model age signature tdm age 1 40 ga resembling the cmbbz rather than the rift zone the dysart complex is surrounded by marble tectonites interspersed with elongate bodies of orthogneiss that yield young nd model ages typical of the cmb however it is argued that the development of the dysart complex as a distinct crustal block predates ductile deformation during the grenville orogeny instead the dysart block is thought to have rifted away from the central gneiss belt to the northwest during the formation of the cmb as an ensimatic back arc rift zone isotopic mapping of the dysart block along with the previously discovered elzevir block provides evidence for the geometry of the rifting process and also has important implications for the structure of grenville basement in eastern north america

stationary and nonstationary behaviour within the geomagnetic polarity time scale we analyse the geomagnetic polarity time scale gpts since the upper jurassic by displaying the successive lengths of polarity intervals as a function of their order of occurrence the sequence consists of three segments between the upper jurassic and the lower cretaceous segment a comprises intervals of short duration with a mean duration of about 0 29 my and no clear long term evolution segment b begins around 130 ma displays a sudden increase of the duration of the magnetic intervals an interval of maximum duration the normal cretaceous superchron and a long and erratic sequence of intervals with decreasing average duration between 85 ma and about 25 ma from 25 ma to the present segment c consists of intervals of short duration with a mean value of 0 23 my this description suggests that the earth s magnetic field could have experienced a fairly stationary regime until slightly before the onset of the cretaceous superchron when the regime has been rapidly and strongly perturbed before progressively returning to another stationary regime about 25 ma ago a geophysical explanation for this sequence of events could be that the geodynamo has been perturbed by the arrival of some cold material at the core mantle boundary as this material would have heated up the geodynamo would have been brought back to its stationary regime

efficient sensitivity analysis for flow and transport in the earth s crust and mantle summary this paper focuses on the role of sensitivity analysis in studies of water transport in the environmental and geophysical sciences sensitivity analysis is useful in model development to determine how changes in parameter input will affect a model s response it is also used in data assimilation to incorporate observations into a model the adjoint method allows an efficient calculation of a model s sensitivity when the number of parameters exceeds the number of observations in this paper we present studies demonstrating the use of the adjoint method for modelling water transport in both the earth s crust and mantle

global paleo lithospheric models for geodynamical analysis of plate reconstructions we present a general framework to generate time dependent global subduction history models from kinematic plate reconstructions and explore their associated coupled plate mantle dynamic behaviour slabs are constructed by advecting material into the mantle by prescribing its radial velocity and following the absolute tangential motion of the subducting plate a simple geodynamic scenario where plates and slabs define isopycnic and isoviscous regions in an homogeneous or layered mantle was explored using the boundary element method based software bemearth the resulting dynamic behaviour was used to predict the absolute plate motion directions for the present day and a particular mid cretaceous 125 ma kinematic model we show how the methodology can be used to compare and revise kinematic reconstructions based on their effect on the balance of plate driving forces and the resulting euler poles of subducting plates as an example we compare the farallon plate dynamics at 125 ma in a global model with two reconstructions in the context of the evolution of the western north american cordillera our results suggest a method to identify episodes of absolute plate motions that are inconsistent with the expected plate dynamics

cenozoic global plate motions cenozoic global plate motions relative to the hot spots are investigated and compared to plate motions in a mean lithosphere reference frame plate motions were analyzed over six time intervals divided by ages 10 25 43 48 and 56 ma chosen as much as possible to coincide with key plate reorganizations alternative motion circuits and rotational parameters were considered and evaluated with paleomagnetic data from the pacific and north american plates the circuit found to be in best agreement with the paleomagnetic data is one in which the hot spots in the atlantic region are assumed to be fixed relative to the hot spots in the pacific region throughout the cenozoic the hot spot and mean lithosphere reference frames have been in continual slow relative motion the rate of motion is nonuniform however most of the motion having occurred during the middle cenozoic the net cenozoic rotation of the lithosphere relative to the hot spots is described by a right handed rotation of 7 about a euler pole at 46 s 87 e which yields a 5 displacement of the north poles of the two reference frames this motion is small enough that inferences drawn about plate speeds in one reference frame should be valid in the other analysis of the global motions resulting from our preferred model showed that many characteristics of current plate motions have persisted throughout the cenozoic plate speeds correlate with latitude plates moving faster near the equator than near the poles throughout the cenozoic as at present continental plates except for the indian plate moved slower than oceanic plates throughout the cenozoic even the structure of the velocity fields as revealed in a contour of root mean square velocities in equatorial bands persists throughout the cenozoic the migration of the paleomagnetic axis over time is also compared to the hot spot and mean lithosphere reference frames the paleomagnetic axis has shifted 5 10 relative to the hot spot frame and a lesser amount relative to the mean lithosphere frame

elastic imaging and time lapse migration based on adjoint methods we have drawn connections between imaging in exploration seismology adjoint methods and emerging finite frequency tomography all of these techniques rely on spatial and temporal constructive interference between observed and simulated waveforms to map locations of structural anomalies modern numerical methods and computers have facilitated the accurate and efficient simulation of 3d acoustic an elastic and poroelastic wave propagation using a 2d cross section of the seg eage salt model we have determined how such waveform simulations might be harnessed to improve onshore and offshore seismic imaging strategies and capabilities we have found that the density sensitivity kernel in adjoint tomography is related closely to the imaging principle in exploration seismology and that in elastic modeling the impedance kernel actually is a better diagnostic tool for reflector identification the shear and compressional wave speed sensitivity kernels in adjoint tomography are related closely to finite frequency banana doughnut kernels and these kernels are well suited for mapping larger scale structure i e for transmission tomography these ideas have been substantiated by addressing problems in subsalt time lapse migration

full waveform tomography of the upper mantle in the south atlantic region imaging a westward fluxing shallow asthenosphere abstract a prominent feature of the south atlantic region is its strongly asymmetric residual bathymetry across the ocean basin it has been suggested that the residual bathymetry is dynamic in nature arising from the large slow velocity seismic anomaly located in the lower mantle beneath the african plate unfortunately the pattern of mantle heterogeneity particularly in the upper mantle is not well known owing to the sparsity of seismic stations and the existence of large aseismic regions on the african and south american plates here we present a new seismic tomographic study of the south atlantic upper mantle our model is based on a full seismic waveform inversion of 4000 high quality seismograms for isotropic 3 d seismic structure using a powerful adjoint methodology capable of extracting maximum information from each seismogram the theory requires simulation of seismic wave propagation in 3 d heterogeneous earth models computed with a spectral element method where the differences between observed and synthetic seismograms are quantified using phase misfits obtained through a time frequency transform the model images a continuous channel of pronounced slow seismic velocity in the shallow sublithospheric mantle between 150 and 300 km depth that branches in between the cratonic roots under the african and south american continents at greater depth below 300 350 km the slow anomalies are less pronounced and a change in the convective planform is indicated by isolated round shaped patches in an overall faster mantle it is possible that the depthwise change of the convective planform from vertical to horizontal advection of hot buoyant material in a low viscosity asthenosphere can reconcile the anomalous residual bathymetry in the region and we present a simple fluid dynamic model of pressure driven flow to assess the feasibility of this scenario

uncertainty estimation of well catchments in heterogeneous aquifers 1 the uncertainty in the boundary of two dimensional steady state well catchments due to the uncertainty of the spatially variable hydraulic conductivity field is investigated the well discharge rate and the areal recharge rate are assumed constant the catchment boundary is traced by backward particle tracking in the velocity field the uncertainty bandwidth of the catchment boundary is approximated in first order by formulating the time dependent longitudinal and transversal second moments of the particle displacements along and normal to the mean particle trajectory applications of the approach are presented for a set of simple configurations the results are compared with the results from unconditional numerical monte carlo simulations the comparison allows an assessment of the accuracy the applicability and the limits of the method the approximation corresponds quite well with the monte carlo simulations provided that the distance to the domain boundary is sufficiently large

reconstruction of mid cenozoic extension in the rincon mountains area southeastern arizona usa and geodynamic implications nsf ear 1649254 u s geological survey national cooperative geologic mapping program under statemap grant 03hqag0114 statemap grant 06hqag0051 g09ac00199

the effect of the large scale mantle flow field on the iceland hotspot track abstract fluid dynamical simulations were carried out in order to investigate the effect of the large scale mantle flow field and the depth of the plume source on the structure of the iceland plume through time the time dependent location and shape of the plume in the earth s mantle was calculated in a global model and it was refined in the upper mantle using a 3d cartesian model box global flow was computed based on density heterogeneities derived from seismic tomography plate motion history served as a velocity boundary condition in both models hotspot tracks of the plume conduits and the plume head were calculated and compared to actual bathymetry of the north atlantic if a plume source in the lowermost mantle is assumed the calculated surface position of the plume conduit has a southward component of motion due to southward flow in the lower mantle depending on tomography model assumed plume age and buoyancy the southward component is more or less dominating plume models having a source at the 660 km discontinuity are only influenced by flow in the upper mantle and transition zone and hence rather yield westward hotspot motion many whole mantle plume models result in a v shaped track which does not match the straight greenland iceland faroe ridge models without strong southward motion such as for a plume source at 660 km depth match actual bathymetry better plume tracks were calculated from both plume conduits and plume heads a plume head of 120 k anomalous temperature gives the best match between plume head track and bathymetry

the geochemistry and tectonic significance of pre metamorphic minor intrusions of the central metasedimentary belt grenville province canada abstract more than 250 samples collected from dykes and sills intruded into the grenville supergroup have been analysed by xrf techniques for their major and trace element contents the ree contents of 43 of the samples have been determined by inaa using these data the rocks have been identified and placed in seven suites each characterized by its own trace element signature there are four tholeiitic suites the low zirconium suite which comprises a bimodal series of basalts and minor dacites the intermediate zirconium suite which is made up of basalts andesites dacites and rhyolites the high zirconium suite consisting of high iron basalts and rare highly fractionated tholeiites which comprise basalts characterized by high mg number high ni and cr contents and with strongly fractionated trace element patterns in addition a calc alkaline suite made up of basalts and andesites a transitional suite of andesites and trachyandesites and an ultra potassic suite of leucitites have been identified on chondrite normalized multi element plots all of the suites show negative nb and ti anomalies similar ranges of rock types with similar anomalies occur within volcanic arcs and back arc basins formed at collisional plate margins where the nb and ti anomalies are interpreted as subduction signatures and also in some continental flood basalt sequences in which the anomalies are commonly suggested to result from crustal contamination the geology of the central metasedimentary belt leads us to favour an interpretation in which the minor intrusions were emplaced in supracrustal rocks deposited upon attenuated continental crust in a back arc basin during a collisional orogeny

global plate motion frames toward a unified model 1 plate tectonics constitutes our primary framework for understanding how the earth works over geological timescales high resolution mapping of relative plate motions based on marine geophysical data has followed the discovery of geomagnetic reversals mid ocean ridges transform faults and seafloor spreading cementing the plate tectonic paradigm however so called absolute plate motions describing how the fragments of the outer shell of the earth have moved relative to a reference system such as the earth s mantle are still poorly understood accurate absolute plate motion models are essential surface boundary conditions for mantle convection models as well as for understanding past ocean circulation and climate as continent ocean distributions change with time a fundamental problem with deciphering absolute plate motions is that the earth s rotation axis and the averaged magnetic dipole axis are not necessarily fixed to the mantle reference system absolute plate motion models based on volcanic hot spot tracks are largely confined to the last 130 ma and ideally would require knowledge about the motions within the convecting mantle in contrast models based on paleomagnetic data reflect plate motion relative to the magnetic dipole axis for most of earth s history but cannot provide paleolongitudes because of the axial symmetry of the earth s magnetic dipole field we analyze four different reference frames paleomagnetic african fixed hot spot african moving hot spot and global moving hot spot discuss their uncertainties and develop a unifying approach for connecting a hot spot track system and a paleomagnetic absolute plate reference system into a hybrid model for the time period from the assembly of pangea 320 ma to the present for the last 100 ma we use a moving hot spot reference frame that takes mantle convection into account and we connect this to a pre 100 ma global paleomagnetic frame adjusted 5 in longitude to smooth the reference frame transition using plate driving force arguments and the mapping of reconstructed large igneous provinces to core mantle boundary topography we argue that continental paleolongitudes can be constrained with reasonable confidence

lagging mantle convection the geoid and mantle structure abstract in numerical models of convection incorporating migration of a simulated subduction zone the main descending flow lags far behind the migrating trench and a geoid low is associated with the main descending flow this provides physical plausibility for the suggestion by chase and sprowl that present very long wavelength degree 2 4 geoid lows are associated with mesozoic trench locations and suggests further that the present long wavelength geoid deep mantle structure and hotspot distribution may be straightforward consequences of plate evolution since the upper paleozoic

evidence for strong shear velocity reductions and velocity gradients in the lower mantle beneath africa we present data which indicate that the broad low shear velocity anomaly beneath southern africa is stronger and more extensive than previously thought recordings of earthquakes in the southwestern atlantic ocean at an array of broadband seismic stations in eastern africa show anomalously large propagation time delays of the shear phases s scs and sks which vary rapidly with epicentral distance by forward modeling we estimate that the low velocity anomaly extends from the core mantle boundary about 1500 km up into the mantle and that the average shear velocity within this structure is 3 lower than in standard models such as prem strong velocity contrasts exist at its margins 2 over about 300 km these seismic characteristic are consistent with recent numerical simulations of lower mantle mega plume formation

structural aspects of fluid rock interactions in detachment zones metamorphic core complexes and associated detachment faults of the north american cordillera represent gently dipping normal displacement shear zones detachment zones along which hot deeper levels of the crust were transported upward and outward from underneath a brittlely distended upper plate structures that formed during the ductile to brittle evolution of detachment zones can be used to reconstruct the relative magnitudes of fluid pressure and deviatoric stress at different levels within the shear zones mylonitization which occurred along deeper segments of detachment zones below the brittle ductile transition was locally accompanied by tensile failure indicative of low deviatoric stress and high fluid pressure this condition persisted into the earliest phases of brittle deformation after which shear fractures formed due to both a reduction in fluid pressure and an increase in deviatoric stress brittle deformation of upper plate rocks occurred largely under conditions of low fluid pressure structural and geochemical data suggest that normal displacement on detachment zones results in establishment of two fluid systems 1 an upper plate system driven by convection and dominated by meteoric and connate fluids at near hydrostatic pressures and 2 a system within deeper levels of the shear zone where fluids are largely derived from igneous sources and fluid migration is aided by dilatancy pumping the late phases of normal displacement on detachment zones structurally juxtaposed rocks affected by the two fluid systems and locally caused the shear zone rocks to be overprinted by mineralization related to the upper plate fluid system

changes of the earth s rotation axis owing to advection of mantle density heterogeneities polar wander the secular motion of the earth s rotation axis relative to its surface has been studied for many years dynamical arguments1 3 show that polar wander can arise from the redistribution of mass in a plastic deformable earth the rate depending on both the rate of mass redistribution and the rate at which the earth s rotational bulge can readjust to the changing rotation axis here we use a viscosity structure obtained through geoid modelling4 a mantle flow field consistent with tomographic anomalies5 and time dependent lithospheric plate motions6 to calculate the advection of mantle density heterogeneities and corresponding changes in the degree two geoid during the cenozoic era we show that the rotation axis will follow closely any imposed changes of the axis of maximum non hydrostatic moment of inertia the resulting path of the rotation axis agrees well with palaeomagnetic results7 with the model predicting a current rate of polar motion that explains 40 of that observed geodetically8

the geochemistry of the turriff metavolcanics grenville province southeastern ontario fifty seven samples of the turriff metavolcanic sequence from the hastings region of the grenville province have been chemically analyzed ten major element oxides and ten trace element values for each sample were determined by standard x ray fluorescence techniques the sampled sections consist predominantly of mafic flows subordinate intermediate flows and minor felsic flows and pyroclastics the sequence has been regionally metamorphosed to lower amphibolite facies the geochemical data indicate that the metavolcanics represent a tholeiitic mafic silicic bimodal sequence immobile element discriminant diagrams indicate that the turriff metabasalts are most similar to recent oceanic ridge basalts whereas the metabasalts from other published studies of grenville metavolcanics have an island arc tholeiite affinity however because of the many chemical similarities between continental and oceanic ridge tholeiites the bimodal nature of the sequence and the field relationships it is most likely that t

the role of the earth s mantle in controlling the frequency of geomagnetic reversals a series of computer simulations of the earth s dynamo illustrates how the thermal structure of the lowermost mantle might affect convection and magnetic field generation in the fluid core eight different patterns of heat flux from the core to the mantle are imposed over the core mantle boundary spontaneous magnetic dipole reversals and excursions occur in seven of these cases although sometimes the field only reverses in the outer part of the core and then quickly reverses back the results suggest correlations among the frequency of reversals the duration over which the reversals occur the magnetic field intensity and the secular variation the case with uniform heat flux at the core mantle boundary appears most earth like this result suggests that variations in heat flux at the core mantle boundary of the earth are smaller than previously thought possibly because seismic velocity anomalies in the lowermost mantle might have more of a compositional rather than thermal origin or because of enhanced heat flux in the mantle s zones of ultra low seismic velocity

global mantle shear velocity model developed using nonlinear asymptotic coupling theory we present a three dimensional shear velocity model of the whole mantle developed using s h waveform data the model is expressed horizontally in terms of spherical harmonics up to degree 12 and vertically in terms of legendre polynomials up to degrees 5 and 7 in the upper and lower mantle respectively what distinguishes this model from other tomographic models published to date is 1 the theoretical normal mode based wave propagation approach where we include across branch mode coupling terms in order to model the body wave sensitivity to structure along the path more accurately 2 the wave packet weighting scheme which allows to balance contributions from high amplitude and low amplitude phases increasing the resolution in some parts of the mantle we also relax the constraints on the moho depth which is allowed to vary in the inversion thus absorbing some uncertainties in crustal structure the resulting model is generally in good agreement with other recent global mantle s velocity models and with some regional models the rms profile with depth has more power than other models in the upper mantle lower mantle transition region and the zone of increased power and low degree structure near the base of the mantle is confined to the last 500 km in depth this model provides a particularly good fit to the non hydrostatic geoid through harmonic degree 12 79 variance reduction as well as good fits to observed splitting functions of s velocity sensitive mantle modes indicating that both large scale and small scale features are really well constrained

generalized inversion of tropical atmosphere ocean data and a coupled model of the tropical pacific abstract it is hypothesized that the circulation of the tropical pacific ocean and atmosphere satisfies the equations of a simple coupled model to within errors having specified covariances and that the tropical atmosphere ocean array tao measures the circulation to within errors also having specified covariances this hypothesis is tested by finding the circulation that is the weighted least squares best fit to the dynamics of the simple model to its initial and boundary conditions and to a year of monthly mean tao data for sea surface temperature for the depth of the 20 c isotherm and for surface winds the fit is defined over the entire tropical pacific and from 1 april 1994 to 31 march 1995 the best fit circulation or state estimate is calculated using variational methods posterior error covariances are estimated using statistical simulation the best fit is also subjected to a significance test it is found that although the fit to data is largely within standard errors the misfit to dynam