phase equilibria testing of a multiple pulse mechanism for origin of mafic ultramafic intrusions a case example of the shiant isles main sill nw scotland in this paper we examine the role of multiple emplacement of sills into partly solidified rocks an intrusive mechanism liquid into solid as a possible explanation for some textural and compositional anomalies of single cyclic mafic intrusions as a case study we used the shiant isles main sill that is widely regarded as a classical example of a multiple picrite picrodolerite crinanite alkaline sill this sill is currently interpreted as having been formed by several olivine phenocryst rich pulses of magma which were successively emplaced into their almost solidified predecessors such an intrusive mechanism is a random process in which many parameters vary independently and unpredictably among them are the number relative volume and bulk composition of magma pulses and their place sequence and timing of emplacement as well as modal abundance phase composition and distribution of intratelluric phenocrysts in magmas upon emplacement in terms of these variables one can envisage countless different profiles through alkaline sills produced from only three randomly intruded magma pulses of picritic picrodoleritic and crinanitic composition such multiple sills can readily be distinguished from simple ones formed from a single pulse of magma by anomalous compositional profiles with several prominent breaks in crystallization and compositional sequences the compositional profile of the shiant isles main sill is remarkably similar to an m shaped profile expected from fractional crystallization of a single pulse of olivine saturated magma along a crystallization path ol sp l picrite ol pl sp l picrodolerite troctolite ol pl cpx l crinanite the probability of the accidental formation of such a compositional profile by multiple intrusion liquid into solid is exceedingly small even for the single case of the shiant isles main sill the probability approaches zero when considering that exactly the same sequence of intrusive events must have been repeated in about 20 neighbouring alkaline sills with similar compositional profiles this can only be achieved by some universally operating differentiation process the best candidate for this is the classical fractional crystallization of magma constrained by liquidus phase equilibria this suggests that the shiant isles main sill can be best interpreted and modelled as a simple sill that crystallized from one large pulse of magma with possible involvement of minor refilling events further progress in our knowledge of intrachamber magma fractionation processes will probably enable us to interpret many anomalous textural and compositional features of mafic ultramafic intrusions in the frame of a single magma pulse model

a revised relaxation time spectrum for fennoscandia summary the fennoscandian relaxation time spectrum rts first derived by mcconnell 1968 is a classic data set in studies of glacial isostatic adjustment gia we outline a new method for estimating an rts from a set of strandline data which is based on a damped least squares solution for spherical harmonic coefficients associated with the strandline heights in contrast to the hankel transform approach outlined by mcconnell 1968 the method does not require interpolation or extrapolation of the data nor does it use the assumption that peripheral deformations are zero we begin by applying the new approach to a suite of synthetic strandlines these synthetic calculations quantify the effect on the rts estimates of the common assumptions of free decay uplift an axisymmetric fennoscandian deformation field and the uncertainty introduced by limited spatial and temporal sampling of this field recently the accuracy of the sauramo 1958 strandline data upon which the mcconnell 1968 rts was based has been questioned wolf 1996 accordingly we apply our new approach to a set of more robust strandline data published by donner 1964 1969 1980 1995 to compute a revised rts for fennoscandia at high harmonic degrees above 50 our new rts is characterized by weak constraints whereas mcconnell s 1968 rts suggests a significant reduction in relaxation times relative to the values at low degrees this reduction was the basis for mcconnell s 1968 inference of an elastic lithosphere in contrast to this we conclude that the trend is an artefact of the observational data set he adopted at lower degrees mcconnell s 1968 relaxation time estimates lie at the lower end of the range implied by the present analysis to complete our study we apply the techniques of linearized bayesian inference to invert our newly derived rts for mantle viscosity we find that the rts provides an estimate of 5 1020 pa s for the volumetric mean viscosity in a region extending from the base of the lithosphere to about 550 km depth target regions which extend from the transition zone to 1200 km depth are less well constrained however the average viscosity from the base of the lithosphere to 1200 km depth is consistent with the classic haskell 1935 value of 1021 pa s for mantle viscosity finally we demonstrate that viscosity models within the class inferred by mitrovica forte 1997 from joint inversions of postglacial relaxation times associated with gia and mantle convection observables simultaneously fit the revised fennoscandian rts

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

geodesy using the swedish permanent gps network effects of snow accumulation on estimates of site positions we have observed variations at the several centimeter level in estimates of the vertical coordinate of site position the estimates are obtained from our analysis of data acquired from the swedish permanent global positioning system gps network the observed variations are strongly correlated with changes in the indirectly inferred accumulation of snow which we assume collects on the radomes and pillars the gps sites could not be observed directly due to their remoteness numerical simulations which assume a simple geometry for the snow cover are used to study the effects of snow accumulation on gps phase observables and hence on estimates of the vertical coordinate of site position obtained from these observables our results indicate that the variations in the vertical coordinate of site position can be fully explained by reasonable accumulations of snow which retard the gps signals and enhance signal scattering effects

investigations of fennoscandian glacial isostatic adjustment using modern sea level records we present a new method for determining the rates from a network of regional tide gauge data the method involves using a model for the sea level observations annual averages of relative sea level that explicitly includes a term for the interannual sealevel variations which are assumed to be constant for all sites in the network the resulting simultaneous analysis of all the sea level observations yields sea level rates which are biased by the unknown temporal slope of the interannual variations by differencing sea level rate estimates with respect to one site site referenced sea level rates are calculated which are free from this bias the differencing procedure also removes any signal due to a common sea level rate such as might be associated with eustatic sea level rise the resulting site referenced sea level rates therefore in principle reflect only the relative vertical crustal motions of the tide gauge sites with respect to the geoid these site referenced sea level rates represent a potentially more accurate data set than have previously been used for sea level studies we have used these rates to investigate glacial isostatic adjustment gia in fennoscandia specifically we have used the site referenced sea level rates within the baltic sea to estimate adjustments to the ice history and earth model which are used to calculate vertical rates of adjustment due to gia a method never before used for fennoscandia the parameters selected were lithospheric thickness the viscosities of assumed isoviscous upper and lower mantles and a fennoscandian ice thickness scaling parameter we present the results of this estimation procedure for a specific test ice model we also find evidence that the sea level record for the site nearest the center of uplift furuogrund may be contaminated by systematic errors of unknown origin data from this site have previously been used to determine a rate for the maximum uplift that we find is perhaps 1 mm yr 1 or 10 too large

global geodesy using gps without fiducial sites baseline lengths and geocentric radii have been determined from gps data without the use of fiducial sites data from the first gps experiment for the iers and geodynamics gig 91 have been analyzed with a no fiducial strategy a baseline length daily repeatability of 2 mm 4 parts per billion was obtained for baselines in the northern hemisphere comparison of baseline lengths from gps and the global vlbi solution glb659 caprette et al 1990 show rms agreement of 2 1 parts per billion the geocentric radius mean daily repeatability for all sites was 15 cm comparison of geocentric radii from gps and sv5 murray et al 1990 show rms agreement of 3 8 cm given n globally distributed stations the n n 1 2 baseline lengths and n geocentric radii uniquely define a rigid closed polyhedron with a well defined center of mass geodetic information can be obtained by examining the structure of the polyhedron and its change with time

oxygen isotopes and sea level from the time that detailed oxygen isotope records derived from foraminifera living in the constant temperature environment of the abyssal ocean became available there has been a discrepancy between the ice volume record that these records imply and that derived from the altitude of dated coral terraces around the world here we re examine the data and conclude that the temperature of the abyssal ocean has been an actively varying component of the climate system

application of the global positioning system to crustal deformation measurement 1 precision and accuracy in this paper we assess the precision and accuracy of interstation vectors determined using the global positioning system gps satellites these vectors were between stations in california separated by 50 450 km using data from tracking the seven block i satellites in campaigns from 1986 through 1989 we examine the precision of gps measurements over time scales of a several days and a few years we characterize gps precision by constant and length dependent terms the north south component of the interstation vectors has a short term precision of 1 9 mm 0 6 parts in 108 the east west component shows a similar precision at the shortest distances 2 1 mm with a larger length dependence 1 3 parts in 108 the vertical precision has a mean value of 17 mm with no clear length dependence for long term precision we examine interstation vectors measured over a period of 2 2 to 2 7 years when we include the recent results of davis et al 1989 for distances less than 50 km we can describe long term gps precision for baselines less than 450 km in length as 3 4 mm 1 2 parts in 108 5 2mm 2 8 parts in 108 11 7mm 13 parts in 108 in the north south east west and vertical components accuracy has been determined by comparing gps baseline estimates with those derived from very long baseline interferometry vlbi a comparison of eight interstation vectors shows differences ranging from 5 to 30 mm between the mean gps and mean vlbi estimates in the horizontal components and less than 80 mm in the vertical a large portion of the horizontal differences can be explained by local survey errors at two sites in california a comparison which suffers less from such errors is between the rates of change of the baselines the horizontal rates estimated from over 4 years of vlbi data agree with those determined with 1 2 years of gps data to within one standard deviation in the vertical both gps and vlbi find insignificant vertical motion

modelling postglacial sea levels with power law rheology and a realistic ice model in the absence of ambient tectonic stress previous studies of postglacial rebound with power law rheology and simple ice models over laurentia have found that sea level data in the transition zone e g boston cannot be easily explained unless non linear rheology is restricted to lie within a thin layer between the lithosphere and the upper mantle the reason is the existence of a viscously stationary zone which is characteristic of non linear mantles in this study the simple ice model is replaced by a realistic ice history adapted from the ice 3g model which takes into account important effects such as retreating ice margins and eustatic ocean loading a 3 d finite element model is used to calculate the deformation and the relative sea levels in eastern canada and along the us east coast the purpose is to investigate whether the realistic load model allows sea level data near the centre of rebound and along the atlantic east coast of canada and the usa to be explained by non linear rheology simultaneously the assumptions made are that 1 postglacial rebound sees the steady state creep and not the transient creep 2 either ambient tectonic stresses do not interact with rebound stress or the ambient stress level is low 3 lateral heterogeneity of rock properties and anisotropic flow can be neglected results indicate that the retreating ice margin does make it easier for non linear rheology in the mantle to explain the sea level data in the transition zone around boston however reconciling all the sea level data near the centre of rebound and along the atlantic east coast simultaneously is still difficult for a non linear rheology so far two types of models with non linear rheology have been found to be able to explain the sea level data inside and outside laurentia simultaneously they are 1 earth models with a thin 270 km non linear zone overlying a 1021 pa s lower mantle 2 earth models with a linear upper mantle with an average viscosity of 1021 pa s overlying a non linear lower mantle with a 3 10 35 pa 3 s 1 and n 3

space geodetic constraints on glacial isostatic adjustment in fennoscandia analysis of global positioning system gps data demonstrates that ongoing three dimensional crustal deformation in fennoscandia is dominated by glacial isostatic adjustment our comparison of these gps observations with numerical predictions yields an earth model that satis es independent geologic constraints and bounds both the average viscosity in the upper mantle 5 x 10 20 to 1 x 10 21 pascal seconds and the elastic thickness of the lithosphere 90 to 170 kilometers we combined gps derived radial motions with fennoscandian tide gauge records to estimate a regional sea surface rise of 2 1 0 3 mm year furthermore ongoing horizontal tectonic motions greater than 1 mm year are ruled out on the basis of the gps derived three dimensional crustal velocity field

glacial isostatic adjustment i the forward problem summary the isostatic adjustment of a radially stratified visco elastic spheroid is treated using space time green functions for the associated surface mass load boundary value problem these impulse response functions are convolved with a heaviside function to give the time dependent deformation of the planet which would be produced by a unit point mass brought up from infinity at t 0 and allowed to remain on the surface the resulting heaviside green functions can be employed to simulate all of the important signatures of glacial isostatic adjustment given a space time dependent surface mass load consisting of ice sheet ablation histories and a model of the simultaneous filling of the ocean basins these source terms are simply convolved with the heaviside green function appropriate to a specific response signature a realistic model of the spatial distribution of the main late pleistocene ice loads and of their temporal disintegration is constructed the response of two visco elastic earth models is computed and compared to a global set of relaxation data relative sea level curves on the basis of this initial comparison of theory and observation the possibility that the lower mantle has a viscosity which is significantly in excess of the viscosity of the upper mantle is excluded in addition clear evidence of the presence of the lithosphere has been found in relaxation data from sites which were near the edge of the laurentide ice sheet such data should therefore prove useful as a basis for analysis of lateral variations in lithosphere thickness further extensions of the calculation are suggested

radial profile of mantle viscosity results from the joint inversion of convection and postglacial rebound observables we present new inferences of the radial profile of mantle viscosity that simultaneously fit long wavelength free air gravity harmonics associated with mantle convection and a large set of decay times estimated from the postglacial uplift of sites within previously glaciated regions hudson bay arctic canada and fennoscandia the relative sea level variation at these latter sites is constrained by age height pairs obtained by geological survey rather than the subjective trends which are commonly used in glacial isostatic adjustment gia studies our viscosity inferences are generated using two approaches first we adopt a relative viscosity profile which is known to provide a good fit to the free air gravity harmonics and determine an absolute scaling which yields a best fit to the gia decay time constraints second we perform an iterative nonlinear joint inversion of the two data sets in both cases our inferred profiles are characterized by a significant increase of viscosity 2 orders of magnitude with depth to values of 1022 pa s in the bottom half of the lower mantle the new viscosity profiles are shown to satisfy constraints based on the postglacial uplift of both fennoscandia the classic haskell 1935 number and hudson bay which have commonly been invoked to argue for an isoviscous mantle furthermore the models are used to predict a set of long wavelength signatures of the gia process these include predictions of gia induced variations in 1 the length of day over the late holocene period 2 the earth s precession constant and obliquity over the last 2 6 myr and 3 the present day zonal harmonics of the geopotential jl l 7 the predictions 1 and 3 bound the late holocene and ongoing mass flux between the large polar ice sheets greenland and antarctic and the global oceans to small values 0 4 mm yr equivalent eustatic sea level rise

glaciation induced perturbations in the earth s rotation a new appraisal we revisit the theory and predictions of glaciation induced perturbations in both the rotation rate of the earth or j 2 and the wander of the rotation pole with respect to the surface geography the two most common theoretical formulations associated with polar wander driven by the surface loading of a viscoelastic earth e g sabadini et al 1982 wu and peltier 1984 appear to disagree by one on the number of rotational normal modes associated with a surface gravitational response having n normal modes we show using a generalized theory that the two formalisms yield essentially equivalent predictions we next consider a benchmark comparison of recent predictions of present day polar wander speed due to glacial isostatic adjustment henceforth gia these comparisons confirm the validity of certain previous analyses e g spada et al 1992a they also reveal that predictions of polar wander speed can be sensitive to an assumption of incompressibility previous studies have noted that predictions of j 2 rotation rate as a function of lower mantle viscosity differ significantly in form from analogous predictions of polar wander speed we investigate these differences by considering the contribution to the predicted anomalies from the individual normal modes of relaxation we find that the normal mode structure of the j 2 rotation rate predictions is fundamentally different from that which characterizes the polar wander response and this difference reflects the distinct physical mechanisms which govern these anomalies finally using a large suite of forward computations as well as the calculation of a set of frechet kernels we investigate the sensitivity of our predictions to variations in the viscoelastic earth model we find for example that a previously noted sensitivity of polar wander speed predictions to variations in lithospheric thickness is only valid for earth models with relatively weak lower mantle viscosities 5 x 10 21 pa s

the inference of mantle viscosity from an inversion of the fennoscandian relaxation spectrum summary a formal inverse theory for mantle viscosity is here applied to a relaxation spectrum derived from the post glacial uplift of fennoscandia the spectrum represents the set of eigenfrequencies or inverse decay times for the fundamental mode of viscous gravitational relaxation between the spherical harmonic degrees 14 to 45 and 65 to 80 theoretical predictions of the eigenfrequencies are based upon the determination of the zeroes of the secular determinant function derived for a spherically symmetric self gravitating visco elastic planet differential kernels relating shifts in the eigenfrequencies to arbitrary perturbations in the radial viscosity profile i e frechet kernels are computed using the variational principle derived by peltier 1976 the inversions are performed within the framework of non linear bayesian inference and the problem has been parameterized in terms of the logarithm of viscosity the inversions have yielded a set of robust constraints which all models for the radial viscosity profile below fennoscandia must satisfy the a posteriori estimates and variance reduction are found to be insensitive to the a priori variance ascribed to the model layers the constraints have furthermore been summarized into a set of a posteriori estimates of the average model viscosity value in radial regions consistent with the resolving power of the data which decreases from a radial length scale of approximately 120km at the base of the lithosphere to 1200km at 1000km depth the data provide essentially no information regarding the mantle rheology below 1200km depth for example for earth models with a lithospheric thickness lt of 100 km the volumetric average logarithm of viscosity in regions in the depth ranges 1040 400 km 670 210 km and 235 100 km is constrained to be respectively 21 03 0 09 20 70 0 08 and 20 37 0 19 we have repeated the inversions for a number of assumed lithospheric thicknesses and have found that a relatively low viscosity layer in the sublithospheric region with respect to the underlying upper mantle is required for lt 120km in this respect we have quantified the previously described trade off between a decrease in the viscosity of this region and a decrease in lt cathles 1975 in forward analyses of the glacial isostatic adjustment data set it is common to use earth models with isoviscous upper and lower mantle regions to investigate this two layer case we have also performed inversions which assume perfect correlation amongst the model layers in the upper and separately the lower mantle under this strict model space limitation the inversions yield models with upper and lower mantle viscosities in the range 3 7 1020 4 5 1020 pa s and 2 2 1021 1 9 1021 pa s respectively the ranges are obtained from a suite of inversions using lithospheric thickness from 70 km to 145 km the a posteriori constraints generated from the bayesian inversions are used together with a statistic based on the computed misfit to the fennoscandian relaxation spectrum to rule out a number of previously published viscosity models

rheology of the upper mantle a synthesis rheological properties of the upper mantle of the earth play an important role in the dynamics of the lithosphere and asthenosphere however such fundamental issues as the dominant mechanisms of flow have not been well resolved a synthesis of laboratory studies and geophysical and geological observations shows that transitions between diffusion and dislocation creep likely occur in the earth s upper mantle the hot and shallow upper mantle flows by dislocation creep whereas cold and shallow or deep upper mantle may flow by diffusion creep when the stress increases grain size is reduced and the upper mantle near the transition between these two regimes is weakened consequently deformation is localized and the upper mantle is decoupled mechanically near these depths

viscosity and thickness of the asthenosphere detected from the fennoscandian uplift the earth s response to the deglaciation in fennoscandia is modelled using a layered viscous model with an elastic lithosphere the modelled tilting of palaeoshorelines at particular locations peripheral to the former ice load and the pattern of the present rate of uplift consistent with the observations strongly suggest a low viscosity asthenosphere earth models without a low viscosity asthenosphere give significant mismatch to the present rate of uplift and are unable to mimic the observed tilting of palaeoshorelines models with a viscosity of the lower mantle of 1 0 2 0 1021 pa s and a viscosity of the upper mantle of 0 7 1 0 1021 pa s overlain by low viscosity asthenosphere with a thickness ranging from 25 to 100 km fit equally well with the observations it is suggested strongly that the asthenosphere has a thickness of less than 150 km and a viscosity of less than 7 0 1019 pa s

geodesy using the global positioning system the effects of signal scattering on estimates of site position analysis of global positioning system gps data from two sites separated by a horizontal distance of only 2 2 m yielded phase residuals exhibiting a systematic elevation angle dependence one of the two gps antennas was mounted on an 1 m high concrete pillar and the other was mounted on a standard wooden tripod we performed elevation angle cutoff tests with these data and established that the estimate of the vertical coordinate of site position was sensitive to the minimum elevation angle elevation cutoff of the data analyzed for example the estimate of the vertical coordinate of site position changed by 9 7 0 8 mm when the minimum elevation angle was increased from 10 to 25 we performed simulations based on a simple ray tracing multipath model with a single horizontal reflector which demonstrated that the results from the elevation angle cutoff tests and the pattern of the residuals versus elevation angle could be qualitatively reproduced if the reflector were located 0 1 0 2 m beneath the antenna phase center we therefore hypothesized that the elevation angle dependent error was caused by scattering from the horizontal surface of the pillar located a distance of 0 2 m beneath the antenna phase center we tested this hypothesis by placing microwave absorbing material between the antenna and the pillar in a number of configurations and by analyzing the changes in apparent position of the antenna the results indicate that 1 the horizontal surface of the pillar is indeed the main scatterer 2 both the concrete and the metal plate embedded in the pillar are significant sources of scattering and 3 the scattering can be reduced greatly by the use of microwave absorbing materials these results have significant implications for the accuracy of global gps geodetic tracking networks which use pillar antenna configurations identical or similar to the one used for this study at the westford wfrd gps site

correlated errors in geodetic time series implications for time dependent deformation analysis of frequent trilateration observations from the two color electronic distance measuring networks in california demonstrate that the noise power spectra are dominated by white noise at higher frequencies and power law behavior at lower frequencies in contrast earth scientists typically have assumed that only white noise is present in a geodetic time series since a combination of infrequent measurements and low precision usually preclude identifying the time correlated signature in such data after removing a linear trend from the two color data it becomes evident that there are primarily two recognizable types of time correlated noise present in the residuals the first type is a seasonal variation in displacement which is probably a result of measuring to shallow surface monuments installed in clayey soil which responds to seasonally occurring rainfall this noise is significant only for a small fraction of the sites analyzed the second type of correlated noise becomes evident only after spectral analysis of line length changes and shows a functional relation at long periods between power and frequency of 1 where is frequency and 2 with 2 this type of correlated noise is termed random walk noise and its source is mainly thought to be small random motions of geodetic monuments with respect to the earth s crust though other sources are possible because the line length changes in the two color networks are measured at irregular intervals power spectral techniques cannot reliably estimate the level of 1 noise rather we also use here a maximum likelihood estimation technique which assumes that there are only two sources of noise in the residual time series white noise and random walk noise and estimates the amount of each from this analysis we find that the random walk noise level averages about 1 3 mm yr and that our estimates of the white noise component confirm theoretical limitations of the measurement technique in addition the seasonal noise can be as large as 3 mm in amplitude but typically is less than 0 5 mm because of the presence of random walk noise in these time series modeling and interpretation of the geodetic data must account for this source of error by way of example we show that estimating the time varying strain tensor a form of spatial averaging from geodetic data having both random walk and white noise error components results in seemingly significant variations in the rate of strain accumulation spatial averaging does reduce the size of both noise components but not their relative influence on the resulting strain accumulation model

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

glacial isostatic adjustment on a rotating earth summary we extend and complete previous work to compute the influence of perturbations to the rotation vector on a suite of observables associated with glacial isostatic adjustment gia we emphasize observables relevant to present and future geodetic missions for example present day 3 d crustal motions relative sea level change and geoid or absolute sea level variations our calculations adopt spherically symmetric self gravitating maxwell viscoelastic earth models while incorporating realistic mass ice plus ocean load and rotation variations the predicted rotation induced signals are dominated by the influence of true polar wander tpw the spatial geometry of the tpw induced relative sea level geoid and radial velocity fields is primarily that of a degree two order one surface spherical harmonic the spatial variation of the horizontal velocity vectors is given by the gradient of this harmonic the peak radial and horizontal velocities are of the order of 0 5 mm yr 1 however we show that this value is sensitive to the adopted profile of mantle viscosity we also demonstrate that an accurate prediction of tpw induced sea level and 3 d crustal deformation rates requires that a realistic number of glacial cycles be incorporated into the ice load history we conclude that geodetic observations of the gia process should be analysed using a gia theory valid for a rotating planet finally we also consider variations in rotation driven by simple present day polar melting scenarios and predict the influence of these variations on a suite of geophysical observables we find that the rotational feedback associated with greenland melting is capable of significantly perturbing both relative and absolute sea level variations

on postglacial geoid subsidence over the equatorial oceans we develop two new spectral formalisms for the gravitationally self consistent solution of the sea level equation which governs the redistribution of glacial meltwater on a visco elastic earth the first is a purely spectral technique based on an extension of theory outlined by dahlen 1976 for determining the equilibrium oceanic tide on an elastic planet using this technique with a feasible spherical harmonic truncation level l 30 we can obtain convergence in the computed sea level variations within the degree range l 10 we also develop a second pseudospectral technique however which permits the construction of gravitationally self consistent solutions to much higher degree and order l 100 the pseudospectral formalism is employed here to develop a comprehensive physical explanation for the global pattern of present day sea level variations due to ongoing glacial isostatic adjustment in particular we focus upon a mechanism which we term equatorial ocean syphoning that acts to draw water toward the oceanic portion of the collapsing peripheral bulge that encircles previously glaciated regions the collapse of the forebulge induces a flow of water which is required to maintain hydrostatic equilibrium the syphoning mechanism dominates the relative sea level rsl variation in oceans in the far field of the ice sheets that is beyond the peripheral bulge during periods such as the interglacial of the past 4000 years during which the volume of the ice sheets has not apparently changed appreciably while at the same time isostatic adjustment persists the rsl change in the near field is in contrast dominated by the local vertical displacement of the solid surface finally comparison of gravitationally self consistent predictions of rsl change in the far field with the observational data at small pacific island sites has provided an upper bound of 1 to 2 m for the eustatic sea level rise produced by any recent last 3000 years melting of the antarctic ice sheet

high primary productivity during the ediacaran period revealed by the covariation of paired c isotopic records from south china abstract remarkable carbonate carbon isotope 13ccarb excursions accompanied by invariant organic carbon isotope 13corg values have been observed in many late neoproterozoic successions this decoupled relationship between 13ccarb and 13corg in the precambrian differs from most phanerozoic records which have been substantially imprinted by aqueous photosynthesis and it has been tentatively interpreted as resulting from exotic organic matter inputs or diagenesis in this study we present high resolution 13corg records in combination with previously published 13ccarb data from a continuous drill core from the yangtze platform of south china the studied interval spans the cryogenian nantuo formation the ediacaran doushantuo and dengying formations and the base of the cambrian yanjiahe formation the 13ccarb profile of this drill core can be reliably correlated with contemporaneous sequences and it reveals multiple negative 13ccarb excursions associated with phosphorite deposits intriguingly the 13corg profile exhibits a co varying trend with the 13ccarb profile and the coupled relationship between 13ccarb and 13corg is rare in geological records of the precambrian the 13corg values of the drill core vary from 22 13 to 34 12 and the overall isotopic difference 13ccarb org between 13ccarb and 13corg ranges between 19 61 and 34 58 most of the 13corg and 13ccarb org data can be interpreted in terms of oxygenic photosynthesis probably mainly by eukaryotic algae however it is possible that exotic organic matter most likely doc from the deep ocean may also have contributed to the sedimentary organic matter composition of specific intervals studied herein moreover high primary productivity in shallow water may have been sustained for a long period in phosphate rich conditions and the organic matter generated by photosynthesis may have been quantitatively sufficient to overwhelm the doc buffering effect in the total 13corg signal throughout the ediacaran period the enhanced burial of organic matter in sediments would gradually result in the accumulation of oxygen both in the ocean and atmosphere which would likely have paved the way for macroscopic animal evolution

continuous gps measurements of postglacial adjustment in fennoscandia 1 geodetic results 1 data collected under the auspices of the bifrost gps project yield a geographically dense suite of estimates of present day three dimensional 3 d crustal deformation rates in fennoscandia johansson et al 2002 a preliminary forward analysis of these estimates milne et al 2001 has indicated that models of ongoing glacial isostatic adjustment gia in response to the final deglaciation event of the current ice age are able to provide an excellent fit to the observed 3 d velocity field in this study we revisit our previous gia analysis by considering a more extensive suite of forward calculations and by performing the first formal joint inversion of the bifrost rate estimates to establish insight into the physics of the gia response in the region we begin by decomposing a forward prediction into the three contributions associated with the ice ocean and rotational forcings from this analysis we demonstrate that recent advances in postglacial sea level theory in particular the inclusion of rotational effects and improvements in the treatment of the ocean load in the vicinity of an evolving continental margin involve peak signals that are larger than the observational uncertainties in the bifrost network the forward analysis is completed by presenting predictions for a pair of fennoscandian ice histories and an extensive suite of viscoelastic earth models the former indicates that the bifrost data set provides a powerful discriminant of such histories the latter yields bounds on the assumed constant upper and lower mantle viscosity nu um nu lm specifically we derive a 95 confidence interval of 5 x 10 20 less than or equal to nu um less than or equal to 10 21 pa s and 5 x 10 21 less than or equal to nu lm less than or equal to 5 x 10 22 pa s with some preference for elastic lithospheric thickness in excess of 100 km the main goal of the bayesian inverse analysis is to estimate the radial resolving power of the bifrost gps data as a function of depth in the mantle assuming a reasonably accurate ice history we demonstrate that this resolving power varies from similar to 200 km near the base of the upper mantle to similar to 700 km in the top portion of the lower mantle we conclude that the bifrost data are able to resolve structure on radial length scale significantly smaller than a single upper mantle layer however these data provide little constraint on viscosity in the bottom half of the mantle finally elements of both the forward and inverse analyses indicate that radial and horizontal velocity estimates provide distinct constraints on mantle viscosity

glacial isostatic adjustment and the radial viscosity profile from inverse modeling 1 a formal inverse procedure is used to infer radial mantle viscosity profiles from several observations related to the glacial isostatic adjustment process the data sets consist of late pleistocene and holocene sea level data from scandinavia the barents sea central europe canada and the far field as well as observations of changes in the earth s rotation and gravitational field and present day uplift and gravity changes in scandinavia inferences of mantle viscosity are robust against assumptions such as the a priori viscosity model and model discretization however the quality of ice sheet reconstruction remains crucial for the inverse inference the importance to discuss regional mantle viscosity models in view of the lateral variability in mantle properties has been evident our inference suggests a two order of magnitude increase of mantle viscosity with depth and volume averaged upper and lower mantle viscosities around 7 1020 and 2 1022 pa s respectively mantle viscosity does not need to increase sharply across the 660 km seismic discontinuity the viscosity profiles suggested are also able to reconcile the large scale geoid anomaly related to mantle convection

the itrf96 realization and its associated velocity field this text intends to present and to analyse the quality of the new 1996 edition of the international terrestrial reference system called the itrf96 the itrf96 represents a key step forward in the activity of the iers terrestrial system determinations a new physical combination model has been developed as well as a new stochastic model for the first time the level of accuracy has reached 1 cm or better in position for about 50 of itrf96 stations and 30 of the stations have their velocities determined free of any aditional tectonic plate model assumption with an uncertainty better than 3 mm yr the itrf96 also provides a more complete solution a new software has been developed which makes available the itrf96 full variance covariance matrix whereas this information was restricted to station positions in the previous itrf94 edition moreover the network coverage is clearly the largest set of globally distributed terrestrial space geodesy stations that have ever been computed 521 stations located among 290 sites in addition station velocities are also determined at a very accurate level allowing possible determination of kinematic plate motion models free of any geological assumption

rapid fluid disruption a source for self potential anomalies on volcanoes self potential sp anomalies observed above suspected magma reservoirs dikes etc on various volcanoes kilauea hawaii mount unzen japan piton de la fournaise reunion island miyake jima japan result from transient surface electric fields of tens of millivolts per kilometer and generally have a positive polarity these sp anomalies are usually attributed to electrokinetic effects where properties controlling this process are poorly constrained we propose an alternate explanation that contributions to electric fields of correct polarity should be expected from charge generation by fluid vaporization disruption as liquids are vaporized or removed as droplets by gas transport away from hot dike intrusions both charge generation and local increase in electrical resistivity by removal of fluids should occur we report laboratory observations of electric fields in hot rock samples generated by pulses of fluid water through the rock at atmospheric pressure these indicate the relative amplitudes of rapid fluid disruption rfd potentials and electrokinetic potentials to be dramatically different and the signals are opposite in sign above vaporization temperatures rfd effects of positive sign in the direction of gas flow dominate whereas below these temperatures effects of negative sign dominate this suggests that the primary contribution to observed self potential anomalies arises from gas related charge transport processes at temperatures high enough to produce vigorous boiling and vapor transport at lower temperatures the primary contribution is from electrokinetic effects modulated perhaps by changing electrical resistivity and rfd effects from high pressure but low temperature co 2 and so 2 gas flow ripping water molecules from saturated crustal rocks if charge generation is continuous as could well occur above a newly emplaced dike positive static potentials will be set up that could be sustained for many years and the simplest method for identifying these hot active regions would be to identify the sp anomalies they generate

constraining proposed combinations of ice history and earth rheology using vlbi determined baseline length rates in north america we predict the present day rates of change of the lengths of 19 north american baselines due to the glacial isostatic adjustment process contrary to previously published research we find that the three dimensional motion of each of the sites defining a baseline rather than only the radial motions of these sites needs to be considered to obtain an accurate estimate of the rate of change of the baseline length predictions are generated using a suite of earth models and late pleistocene ice histories these include specific combinations of the two which have been proposed in the literature as satisfying a variety of rebound related geophysical observations from the north american region a number of these published models are shown to predict rates which differ significantly from the vlbi observations

a comparison of vlbi data with the ice 3g glacial rebound model crustal motion predicted by the ice 3g glacial rebound model exhibits a pattern of tangential horizontal divergence away from the centres of uplift which in north america and europe are located around hudson bay and the gulf of bothnia tangential velocities reach peak magnitudes of 1 2 mm yr and must be included when predicting very long baseline interferometry vlbi baseline length change rates due to post glacial rebound out of 18 observed vlbi baselines examined 3 are situated such that their predicted length rates are around their 2 uncertainties or greater it is encouraging that 2 of these baselines exhibit predicted length rates within 2 of the observed rates

ice age cycles earth s rotation instabilities and sea level changes a new class of multilayered viscoelastic earth models based on prem is applied to the modeling of earth s rotation instabilities and associated sea level changes induced by the occurrence of pleistocene ice age cycles that match the oxygen isotope records over the last 0 8 myr the novelty of our approach stands on the usage for the first time in post glacial rebound induced sea level studies of a fully analytical scheme based on normal mode theory that allows to deal with complexities of the real earth such as lithospheric and mantle layering sphericity and self gravitation the ice models are based on ice 3g our results show that differences in true polar wander tpw and tpw induced sea level changes between earth models with a few layers and models having enough layers so that saturated continuum limits are reached can amount factors 2 to 3 this may change conclusions derived from some earlier studies on polar wander induced changes in climate that were based on earth models with a limited amount of layers the results indicate that models containing about 15 layers with a stratified lower mantle and transition zone have reached saturated continuum responses for both tpw and tpw induced sea level changes stratification of the lithosphere is not important this is in contrast with the sensitivity of post seismic deformation models this difference in sensitivity on the radial profile of the earth model can be explained with simple arguments on the dependence on zonal degree

ice 3g a new global model of late pleistocene deglaciation based upon geophysical predictions of post glacial relative sea level change a new high resolution global model of late pleistocene deglaciation is inferred on the basis of geophysical predictions of postglacial relative sea level variations in which the ice ocean solid earth interaction is treated in a gravitationally self consistent fashion for the purpose of these analyses the radial viscoelastic structure of the planet is assumed known on the basis of previously published sensitivity tests on solutions of the forward problem only radiocarbon controlled relative sea level histories from sites that were actually ice covered with one or two additions are employed to constrain the model leaving relative sea level rsl data from sites that were not ice covered to be employed to confirm its consistency results for these confirmatory analyses are reported elsewhere here the new deglaciation model referred to as ice 3g is compared to previous models derived by several independent means and tested against a number of additional observations other than sea level histories including geologically controlled retreat isochrones oxygen isotope data from deep sea sedimentary cores and coral terrace elevations the latter two observations strongly constrain the net sea level rise that has occurred since the onset of deglaciation and therefore the mass of ice that melted during the last glacial interglacial transition

geodesy using the swedish permanent gps network effects of signal scattering on estimates of relative site positions this paper presents results from a study of elevation angle dependent systematic effects on estimates of relative site positions within the swedish permanent global positioning system gps network two months of data from 16 sites have been analyzed with three different elevation cutoff angles namely 10 15 and 20 we present offsets between these solutions and demonstrate that estimates of the vertical component of several baselines strongly depend on the minimum elevation angle elevation cutoff angle of the data analyzed offsets of 22 3 1 6 mm in the vertical component are evident when the elevation cutoff angle is changed from 10 to 20 we investigate these offsets and conclude that a significant part is due to differential phase errors caused by scattering from structures associated with the mounting of the antenna to the pillar and with the pillar itself the horizontal components of baseline are less affected we found however that the offsets in the horizontal components increase with baseline length for the longest baselines 1500 km offsets of more than 5 mm are evident in the north component when the elevation cutoff angle is changed from 10 to 20 these offsets are most likely due to differential phase errors caused by nonuniform antenna phase patterns an effect that presumably increases with baseline length and which also might increase because of scattering from the pillars and the antenna mounts we identify the scattering structure and reduce associated errors in the vertical component of baseline to a significant degree on one of the sites by using microwave absorbing material the results presented are of importance for those analyzing data from existing networks and for those who intend to establish permanent gps geodetic networks

estimating present day postglacial rebound and horizontal movements in fennoscandia by repeated gps campaigns in 1993 and 1997 a well known geophysical phenomenon the postglacial rebound in fennoscandia is investigated by data from the baltic sea level project gps campaigns in 1993 and 1997 preliminary results indicate that the estimated uplift rates vary from 1 mm yr 1 to 11 mm yr 1 with standard errors of the order of 1 3 mm yr 1 which is partly consistent with traditional terrestrial data in addition there is a horizontal component of plate motion of 21 1 mm yr 1 towards northeast after subtracting the average velocity differential horizontal velocities suggest that there is a right hand strike slip fault with a relative velocity of about 1 5 0 5 mm yr 1 along a n s direction in the middle of the baltic sea which agrees with some geologists belief of n s trending 1 9 1 8 ga old strike slip megashears in the baltic shield

viscous gravitational relaxation summary this paper is concerned with a detailed examination of the response of maxwell models of the planet to surface mass loads particular attention is devoted to an examination of the factors which determine the isostatic response since the understanding of this response is crucial in a number of different geodynamic problems one particular example which we discuss in detail is concerned with the prediction of free air gravity anomalies produced by large scale deglaciation events using the methods developed here we are able to provide the first direct assessment of the importance of initial isostatic disequilibrium on the observed relative sea level variations and free air gravity anomalies forced by the melting of the laurentide ice sheet we are therefore able to estimate the extent to which such initial disequilibrium might influence the inference of mantle viscosity from isostatic adjustment data our calculations establish that free air gravity data although they are sensitive to the degree of initial disequilibrium provide an extremely high quality constraint upon the viscosity of the lower mantle

a spectral formalism for computing three dimensional deformations due to surface loads 2 present day glacial isostatic adjustment using a spherically symmetric self gravitating linear viscoelastic earth model we predict present day three dimensional surface deformation rates and baseline evolutions arising as a consequence of the late pleistocene glacial cycles in general we use realistic models for the space time geometry of the final late pleistocene deglaciation event and incorporate a gravitationally self consistent ocean meltwater redistribution the predictions of horizontal velocity presented herein differ significantly in both their amplitude and their spatial variation from those presented in an earlier analysis of others which adopted simplified models of both the late pleistocene ice history and the earth rheology an important characteristic of our predicted velocity fields is that the melting of the laurentide ice sheet over canada is capable of contributing appreciably to the adjustment in europe the sensitivity of the predictions to variations in mantle rheology is investigated by considering a number of different earth models and by computing appropriate frechet kernels these calculations suggest that the sensitivity of the deformations to the earth s rheology is significant and strongly dependent on the location of the site relative to the ancient ice sheet the effects on the predictions of three dimensional deformation rates of altering the ice history or adopting approximate models for the ocean meltwater redistribution have also been considered and found to be important the former especially so finally for a suite of earth models we provide predictions of the velocity of a number of baselines in north america and europe we find that in general both radial and tangential motions contribute significantly to baseline length changes and that these contributions are a strong function of the earth model we have furthermore found a set of earth models which together with the ice 3g deglaciation chronology produce predictions of baseline length changes that are consistent with very long baseline interferometry measurements of baselines within europe

pleistocene deglaciation and the earth s rotation a new analysis summary this paper is concerned with an analysis of the effect of the pleistocene glacial cycle upon the earth s rotation we demonstrate that two important geophysical observables may be explained as aspects of the rotational response to surface mass loading by ice sheets these are the astronomically observed non tidal component of the acceleration of planetary rotation and the secular drift of the rotation pole relative to the surface geography which is evident in the ils pole path the former observation is shown to provide an unambiguous constraint upon the viscosity of the planetary mantle and requires a depth dependence of this parameter which is the same as that which has previously been inferred in studies of the relative sea level variations and free air gravity anomalies associated with post glacial rebound the observed secular drift of the pole cannot provide an independent estimate of the viscosity of the mantle because it depends jointly upon mantle viscosity and lithospheric thickness with the viscosity profile fixed by the rebound data the observed speed of polar wander suggests a continental lithospheric thickness which is in excess of that appropriate for old ocean basins but nevertheless in accord with independent constraints

near field hydro isostasy the implementation of a revised sea level equation summary we describe how the existing sea level equation incorrectly predicts the change in sea level and thus the ocean load in ice covered subgeoidal geographic regions during periods of deglaciation we go on to present a new sea level equation that overcomes this problem and we describe how this equation can be solved in a gravitationally self consistent manner by employing a well known spectral technique application of the new theory to predict relative sea level rsl histories and present day 3 d solid surface deformation rates in northeastern canada based on a single earth model characterized by a lithospheric thickness of 100 km and upper and lower mantle viscosities of 5 1020 and 5 1021 pa s respectively demonstrates that a significant error is introduced when the original theory is employed to predict the oceanic component of the surface load predictions of rsl curves show a discrepancy of 40 per cent at sites where data have been obtained and employed to constrain models of earth viscosity structure and ice sheet histories this error will significantly bias estimates of mantle viscosity structure and ice thicknesses that are based on the original theory in addition predictions of 3 d deformation rates differ by up to 25 per cent in some regions and so future applications that employ these data to constrain models of the glacial isostatic adjustment process should adopt the improved sea level theory in contrast estimates of inverse decay times from the predicted rsl curves are insensitive to within the observational error to the improvement in the surface load introduced by the new theory thus viscosity structure inferences based on this parametrization and the original sea level equation are unaffected by the error in the ocean load finally the new theory predicts a eustatic i e globally uniform rise in sea level over the postglacial period that is 11 m lower than that determined via the original theory therefore estimates of the global ice budget at the last glacial maximum based on far field rsl data and the original sea level theory will be too small by 10 per cent

southern california permanent gps geodetic array spatial filtering of daily positions for estimating coseismic and postseismic displacements induced by the 1992 landers earthquake the june 28 1992 m w 7 3 landers california earthquake was the first earthquake to be surveyed by a continuously operating global positioning system gps array the coordinate time series of seven sites are evaluated for station displacements during an interval of 100 days centered on the day of the earthquake we employ a new spatial filtering technique that removes common mode errors from the coordinate time series this approach provides precise estimates of site specific displacements compared to the cumbersome method of analyzing baselines between pairs of stations all sites indicate significant coseismic horizontal displacements of 5 65 mm with uncertainties of 1 2 mm horizontal displacements are in general agreement with elastic dislocation models in particular for sites closer to the epicenter vertical displacements range from 13 to 7 mm with uncertainties of 2 4 mm the observed vertical displacements in all cases show 5 10 mm more subsidence than expected from geodetic and seismic geologic models significant postseismic horizontal displacements totaling 6 2 mm 10 20 of the coseismic displacement are detected at the three sites closest to the epicenter these displacements are modeled as a short term exponential relaxation with a decay time of 22 10 days superimposed on a longer term linear interseismic trend scaling the observed coseismic and postseismic displacements at one of the sites with the distance to the epicenter provides a measure of site strain which agrees well with the direction and magnitude determined from more precise laser strain meter data the time series do not show any detectable preseismic displacements

a parametrized solid earth tide model and ocean tide loading effects for global geodetic baseline measurements summary an observation model for earth tide displacements in application to very long baseline interferometry and similar precise geodetic techniques is developed it incorporates effects from anelasticity ellipsoidal figure and fluid core resonance based on a harmonic development of the external potential the model follows the familiar love number concept the transfer function of the earth to each harmonic is formulated in terms of coupled harmonics in the space domain and fulfils the causality condition in the time domain solve for parameters can be chosen flexibly the guideline however has been to provide a minimum set of well defined and well resolvable tide response parameters for analysis of observations the aim of accuracy for tide displacements prediction is below 1 mm being the major perturbation of the solid earth tide ocean tide loading effects are computed and the accuracy of the models involved is discussed it appears that the major error source relates to those ocean tide frequencies for which global models are not available these frequencies form a continuum with a power spectrum being largely a result of non linear tide interaction the associated loading effects cannot be reliably interpolated from global tide models which are available only for a few distinct frequencies and which disregard tidal intermodulation thus an accuracy of 1 mm for computed loading tide displacements cannot always be achieved

gps applications for geodynamics and earthquake studies geodetic measurements obtained with the global positioning system gps are increasingly more widely applied in geophysical studies in this paper we review the changes to the technology of gps geodesy over the last five years that are responsible for this increased applicability we survey geophysical investigations employing gps to measure coseismic postseismic and interseismic deformation plate motion and crustal deformation at plate boundaries volcano deformation and the deformation associated with glacial isostatic adjustment and its application to sea level studies we emphasize the use of gps determinations for the modeling of this wide variety of geophysical phenomena we also discuss the recent advent of permanent gps networks for regional geophysical studies as well as the possible future of gps surveying in light of the recent advances

polar wandering and the forced responses of a rotating multilayered viscoelastic planet changes in the earth s rotation produced by the waxing and waning of large mobile ice sheets can be used to infer the viscosity of the mantle from a comparison with the recent secular polar drift as revealed in the international latitude service data and also in the estimates of the nontidal acceleration of the length of the day we have developed by using an analytical approach a physical model of a rotating earth consisting of an elastic lithosphere a viscoelastic mantle and an inviscid core forcings from the two major ice sheets laurentide and fennoscandia have been considered sensitivity analysis of the parameters governing the external forcings such as the length and the time of termination of the deglaciation phase show in general that there exist two families of mean mantle viscosities 0 1022 p and 0 1023 p which can match the data satisfactorily however we find it an improvement to incorporate some amount of shrinkage from the antarctic ice sheet obtaining simultaneously a better fit with the two rotational data sets to the lower viscosity solutions hence forcings from the southern hemisphere may be able to remove the ambiguity associated with the extraction of mantle viscosity from rotational data we have also solved the initial value problem of the components of instantaneous angular velocity by means of the laplace transform for applied loads characterizing the continental ice sheets which since the mid pliocene have periodically expanded and contracted over the northern hemisphere in consequence of this continual forcing polar wander of around 5 10 degrees can take place for a mean mantle viscosity 0 1022 p recent reanalysis of paleomagnetic data in conjunction with hot spot tracks have revealed that several degrees of true polar wander could have occurred in the last 5 m y these calculations thus provide a physical explanation for the observed movement of the rotation axis membrane stresses of 0 10 bars can develop from this secular polar motion

inflation of long valley caldera from one year of continuous gps observations a permanent global positioning system receiver at casa diablo hot springs long valley caldera california was installed in january 1993 and has operated almost continuously since then the data have been transmitted daily to the jet propulsion laboratory for routine analysis with data from the fiducial laboratories for an international natural sciences network flinn by the jpl flinn analysis center results from these analyses have been used to interpret the on going deformation at long valley with data excluded from periods when the antenna was covered under 2 5 meters of snow and from some periods when anti spoofing was enforced on the gps signal the remaining time series suggests that uplift of the resurgent dome of long valley caldera during 1993 has been 2 5 1 1 cm yr and horizontal motion has been 3 0 0 7 cm yr at s53w in a no net rotation global reference frame or 1 5 0 7 cm yr at s14w relative to the sierra nevada block these rates are consistent with uplift predicted from frequent horizontal strain measurements spectral analysis of the observations suggests that tidal forcing of the magma chamber is not a source of the variability in the 3 dimensional station location these results suggest that remotely operated continuously recording gps receivers could prove to be a reliable tool for volcano monitoring throughout the world