Glacial isostatic adjustment in Fennoscandia for a laterally heterogeneous earth

Glaciation and deglaciation in Fennoscandia during the last glacial cycles has significantly perturbed the Earth's equilibrium figure. Changes in the Earth's solid and geoidal surfaces due to external and internal mass redistributions are recorded in sequences of ancient coastlines, now either submerged or uplifted, and are still visible in observations of present‐day motions of the surface and glacially induced anomalies in the Earth's gravitational field. These observations become increasingly sophisticated with the availability of GPS measurements and new satellite gravity missions.
Observational evidence of the mass changes is widely used to constrain the radial viscosity structure of the Earth's mantle. However, lateral changes in earth model properties are usually not taken into account, as most global models of glacial isostatic adjustment assume radial symmetry for the earth model. This simplifying assumption contrasts with seismological evidence of significant lateral variations in the Earth's crust and upper mantle throughout the Fennoscandian region.
We compare predictions of glacial isostatic adjustment based on an ice model over the Fennoscandian region for the last glacial cycle for both radially symmetric and fully 3‐D earth models. Our results clearly reveal the importance of lateral variations in lithospheric thickness and asthenospheric viscosity for glacially induced model predictions. Relative sea‐level predictions can differ by up to 10–20 m, uplift rate predictions by 1–3 mm yr⁻¹ and free‐air gravity anomaly predictions by 2–4 mGal when a realistic 3‐D earth structure as proposed by seismic modelling is taken into account.     

Pleistocene deglaciation and the Earth's rotation: implications for mantle viscosity

Summary. Recent results from the analysis of postglacial rebound data suggest that the viscosity of the Earth's mantle increases through the transition region. Models which fit both relative sea-level and free air gravity data have viscosities which increase from a value near 10²² poise in the upper mantle beneath the lithosphere to a value of about 10²³ poise in the lower mantle. In this paper we analyse the effect of deglaciation upon the Earth's rotation and thereby show that the observed secular trend (polar wander) evident in the ILS—IPMS pole path, and measurements of the non-tidal acceleration of the length of day, are both consistent with the viscosity profile deduced from postglacial rebound. The two analyses are therefore mutually reinforcing.     

Gravity anomalies, subsidence history and the tectonic evolution of the Malay and Penyu Basins (offshore Peninsular Malaysia)

The tectonic subsidence and gravity anomalies in the Malay and Penyu Basins, offshore Peninsular Malaysia, were analysed to determine the isostatic compensation mechanism in order to investigate their origin. These continental extensional basins contain up to 14  km of sediment fill which implies that the crust had been thinned significantly during basin development. Our results suggest, however, that the tectonic subsidence in the basins cannot be explained simply by crustal thinning and Airy isostatic compensation.
The Malay and Penyu Basins are characterized by broad negative free-air gravity anomalies of between −20 and −30  mGal. To determine the cause of the anomaly, we modelled four gravity profiles across the basins using a method that combines two-dimensional flexural backstripping and gravity modelling techniques. We assumed a model of uniform lithospheric stretching and Airy isostasy in the analysis of tectonic subsidence. Our study shows that the basins are probably underlain by relatively thinned crust, indicating that some form of crustal stretching was involved. To explain the observed gravity anomalies, however, the Moho depth that we calculated based on the free-air gravity data is about 25% deeper than the Moho predicted by assuming Airy isostasy (Backstrip Moho). This suggests that the Airy model overestimates the compensation and that the basins are probably undercompensated isostatically. In other words, there is an extra amount of tectonic subsidence that is not compensated by crustal thinning, which has resulted in the discrepancy between the gravity-derived Moho and the Backstrip Moho. We attribute this uncompensated or anomalous tectonic subsidence to thin-skinned crustal extension that did not involve the mantle lithosphere. The Malay and Penyu Basins are interpreted therefore as basins that formed by a combination of whole-lithosphere stretching and thin-skinned crustal extension.     

Regional three-dimensional gravity modelling of the NE Atlantic margin

A series of three‐dimensional models has been constructed for the structure of the crust and upper mantle over a large region spanning the NE Atlantic passive margin. These incorporate isostatic and flexural principles, together with gravity modelling and integration with seismic interpretations. An initial isostatic model was based on known bathymetric/topographic variations, an estimate of the thickness and density of the sedimentary cover, and upper mantle densities based on thermal modelling. The thickness of the crystalline crust in this model was adjusted to equalise the load at a compensation depth lying below the zone of lateral mantle density variations. Flexural backstripping was used to derive alternative models which tested the effect of varying the strength of the lithosphere during sediment loading. The models were analysed by comparing calculated and observed gravity fields and by calibrating the predicted geometries against independent (primarily seismic) evidence. Further models were generated in which the thickness of the sedimentary layer and the crystalline crust were modified in order to improve the fit to observed gravity anomalies. The potential effects of igneous underplating and variable upper mantle depletion were explored by a series of sensitivity trials. The results provide a new regional lithospheric framework for the margin and a means of setting more detailed, local investigations in their regional context. The flexural modelling suggests lateral variations in the strength of the lithosphere, with much of the margin being relatively weak but areas such as the Porcupine Basin and parts of the Rockall Basin having greater strength. Observed differences between the model Moho and seismic Moho along the continental margin can be interpreted in terms of underplating. A Moho discrepancy to the northwest of Scotland is ascribed to uplift caused by a region of upper mantle with anomalously low density, which may be associated with depletion or with a temperature anomaly.     

Iceocean mass balance during the Late Pleistocene glacial cycles in view of CHAMP and GRACE satellite missions

During the last glacial cycles, global sea level dropped several times by about 120 m and large ice sheets covered North America, northern Europe and Antarctica during the glacial stages. The changes in the iceocean mass balance have displaced mantle material mainly via viscous flow, and the perturbation of the equilibrium figure of the Earth by glacial isostatic adjustment is still observable today in timedependent changes of gravitational and rotational observations. Contemporary iceocean mass balance from volume changes of polar ice caps also contributes to secular variations of the Earth's gravitational field.
In the near future, several satellite gravity missions will significantly improve the accuracy of the observed timedependent gravitational field. In view of the expected improvements in the observations, we predict glacially induced perturbations of the gravitational field, induced by Late Pleistocene and contemporary ice volume changes, for a variety of radial mantle viscosity profiles. We assess the degree of uncertainty for the glacially induced contributions to gravitational and rotational parameters, both in the spectral and the spatial domain.
Predictions of power spectra for the glacially induced freeair gravity and geoid anomalies are about one order of magnitude lower than the observed values, and uncertainties arising from different plausible viscosity profiles are around 0.150.4 mGal and 0.21.5 m, respectively. Uncertainties from different ice models are of secondary importance for the predicted power spectra. Predicted secular changes in geoid anomalies in formerly glaciated areas are mainly controlled by the viscosity profile and contemporary ice volume changes. We also show that the simple threelayer viscosity profiles currently employed for the majority of postglacial rebound studies represent a limited subset for model predictions of the timedependent gravitational field.     

Post-glacial rebound and transient lower mantle rheology

Summary. Although post-glacial rebound data have been conventionally interpreted as being governed by the steady state component of the mantle viscosity spectrum, the radial profile of this parameter, which is then inferred by fitting a model to observations, is characterized by the fact that it exhibits rather slight variation with depth. This disagrees with expectations based upon microphysical models of the solid state creep process. It also disagrees with very recent inferences of the viscosity stratification based on isostatic geoid anomalies expected on the basis of the internal lateral heterogeneity of mantle density obtained from seismic tomographic analyses. The new calculations of the signatures of post-glacial rebound reported here show that these two types of information are easily reconciled if the previously inferred value of the lower mantle viscosity is interpreted as a transient value, as originally suggested by Weertman on the basis of qualitative considerations. In these new models considered here the steady state creep resistance of the lower mantle is not constrained at all by post-glacial rebound observations. It can be fixed only by an appeal to other geophysical data. Whether such models are actually required by the data should become clear in the very near future.     

A Bouguer anomaly map of India and its relation to broad tectonic elements of the sub-continent

Summary. A new Bouguer anomaly map of India and its generalized interpretation is presented in this paper. Bouguer anomalies in India show good correlation with the geology and tectonics. Isostatic anomalies in India are primarily geologic anomalies caused by intracrustal inhomogeneities. For example, the negative isostatic anomalies in southern India arise from large thicknesses of granitic bodies in the upper crust and the positive anomaly over the Himalaya may be attributed to a possible thickening of the basalt layer in the lower crust. The gravity data suggest that an overall isostatic equilibrium generally prevails in India and the Himalayan region. Crustal thickness estimates from DSS data in India are comparable to the values obtained from gravity data based on the Ahy's concept of isostatic compensation.     

Insights into the lithospheric structure and tectonic setting of the Barents Sea region from isostatic considerations

We study the tectonic setting and lithospheric structure of the greater Barents Sea region by investigating its isostatic state and its gravity field. 3-D forward density modelling utilizing available information from seismic data and boreholes shows an apparent shift between the level of observed and modelled gravity anomalies. This difference cannot be solely explained by changes in crustal density. Furthermore, isostatic calculations show that the present crustal thickness of 35–37 km in the Eastern Barents Sea is greater than required to isostatically balance the deep basins of the area (>19 km). To isostatically compensate the missing masses from the thick crust and deep basins and to adequately explain the gravity field, high-density material (3300–3350 kg m⁻³) in the lithospheric mantle below the Eastern Barents Sea is needed. The distribution of mantle densities shows a regional division between the Western and Eastern Barents and Kara Seas. In addition, a band of high-densities is observed in the lower crust along the transition zone from the Eastern to Western Barents Sea. The distribution of high-density material in the crust and mantle suggests a connection to the Neoproterozoic Timanide orogen and argues against the presence of a Caledonian suture in the Eastern Barents Sea. Furthermore, the results indicate that the basins of the Western Barents Sea are mainly affected by rifting, while the Eastern Barents Sea basins are located on a stable continental platform.     

Crustal structure and isostatic compensation near the Kane fracture zone from topography and gravity measurements—I. Spectral analysis approach

Summary. Six gravity and bathymetry profiles perpendicular to the Kane fracture zone, each more than 300 km long, were gathered to study the variation in crustal structure in the vicinity of a major fracture zone and the gravitational edge effect at the contact between lithosphere of two different ages. A spectral analysis of the gravity and bathymetric series as a function of wavelength shows that the gravitational edge effect is only significant at the longest wavelengths. For remaining wavelengths the admittance, the ratio of the amplitude of the gravity anomaly to the amplitude of the bathymetry, is best explained by a model of isostasy in which topographic loads are partially supported by the flexural rigidity of an elastic plate, about 6 km in thickness. After subtracting the gravitational attraction of the bathymetry and its compensation, substantial isostatic anomalies remain. We interpret these anomalies as being caused by variations in crustal thickness which have little correlation with surface topography, except at very long wavelengths. The apparent crustal thickness varies by as much as a factor of 2, but there is no evidence indicating systematic thinning of the crust beneath the fracture zone. Our data do suggest that such density variations within the plate are also compensated by the isostatic response of an elastic plate but with very different effect from those at the surface. This indicates that there are two different modes of crustal formation with different gravity and topographic signatures: effusive volcanism which loads the surface of the elastic plate producing both topographic relief and coherent gravity anomalies, and intrusive volcanism or underplating producing gravity anomalies but little topographic relief.     

Radial resolving power of far-field differential sea-level highstands in the inference of mantle viscosity

For two decades leading to the late 1980s, the prevailing view from studies of glacial isostatic adjustment (GIA) data was that the viscosity of the Earth's mantle increased moderately, if at all, from the base of the lithosphere to the core–mantle boundary. This view was first questioned by Nakada & Lambeck , who argued that differential sea-level (DSL) highstands between pairs of sites in the Australian region preferred an increase of approximately two orders of magnitude from the mean viscosity of the upper to the lower mantle, in accord with independent inferences from observables related to mantle convection. We use non-linear Bayesian inference to provide the first formal resolving power analysis of the Australian DSL data set. We identify three radial regions, two within the upper mantle (110–270 km and 320–570 km depth) and one in the lower mantle (1225–2265 km depth), over which the average of viscosity is well constrained by the data. We conclude that: (1) the DSL data provide a resolution in the inference of upper mantle viscosity that is better than implied by forward analyses based on isoviscous regions above and below the 670 km depth discontinuity and (2) the data do not strongly constrain viscosity at either the base or top of the lower mantle. Finally, our inversions also quantify the significant bias that may be introduced in inversions of the DSL highstands that do not simultaneously estimate the thickness of the elastic lithosphere.     

The Free Air Geoid for Australia

Summary The free air geoid, which is the co-geoid obtained by the use of free air anomalies in Stokes' integral, is computed for Australia from available gravity data. The set of anomalies used to represent the outer zones had been obtained previously using a combined solution from satellite data and terrestrial gravimetry. The solutions so obtained for the free air geoid are compared with the astrogeodetic determination of the geoid on the Australian Geodetic Datum by Fischer and Slutsky and the accuracy of the comparisons is estimated.     

Inference of mantle viscosity from GRACE and relative sea level data

Gravity Recovery And Climate Experiment (GRACE) satellite observations of secular changes in gravity near Hudson Bay, and geological measurements of relative sea level (RSL) changes over the last 10 000 yr in the same region, are used in a Monte Carlo inversion to infer-mantle viscosity structure. The GRACE secular change in gravity shows a significant positive anomaly over a broad region (>3000 km) near Hudson Bay with a maximum of ∼2.5 μGal yr⁻¹ slightly west of Hudson Bay. The pattern of this anomaly is remarkably consistent with that predicted for postglacial rebound using the ICE-5G deglaciation history, strongly suggesting a postglacial rebound origin for the gravity change. We find that the GRACE and RSL data are insensitive to mantle viscosity below 1800 km depth, a conclusion similar to that from previous studies that used only RSL data. For a mantle with homogeneous viscosity, the GRACE and RSL data require a viscosity between  1.4 × 10²¹  and  2.3 × 10²¹  Pa s. An inversion for two mantle viscosity layers separated at a depth of 670 km, shows an ensemble of viscosity structures compatible with the data. While the lowest misfit occurs for upper- and lower-mantle viscosities of  5.3 × 10²⁰  and  2.3 × 10²¹  Pa s, respectively, a weaker upper mantle may be compensated by a stronger lower mantle, such that there exist other models that also provide a reasonable fit to the data. We find that the GRACE and RSL data used in this study cannot resolve more than two layers in the upper 1800 km of the mantle.     

Small-scale instabilities below the cooling oceanic lithosphere

Interpretation of satellite altimetry data as well as ship bathymetry data revealed strongly elongated anomalies roughly perpendicular to the mid-ocean ridges in the Indian and east Pacific oceans. A spectral analysis of gravity altimetry data along profiles parallel to the East Pacific Rise indicated wavelengths of about 150–180  km close to the ridge and about 250  km further away. A simple model of Rayleigh–Taylor instabilities developing at the base of the cooling lithosphere is discussed and applied to the data. By considering thermal diffusion and comparing Rayleigh–Taylor growth rates to the velocity of the thermal front in the cooling lithosphere, we are able to explain the observed anomalies by instabilities developing below the lithosphere in a layer with a viscosity of about 10¹⁹  Pa  s above an asthenospheric layer with a viscosity reduction of 2–3 orders of magnitude.     

Crustal thicknesses in Fennoscandia

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As a supplement to seismic profiling surveys, crustal thicknesses have been estimated for 11 Fennoscandian seismograph stations equipped with three-component long period instruments, using the so-called spectral ratio technique of Phinney. The largest Moho depths, of the order of 45 km, were found for stations located in the north-east areas of Norway and Sweden and in Finland, with a local maximum in the Bothnian Bay. The coastal area of south-east Norway and Zealand, Denmark exhibit crustal thicknesses in the range 28–33 km. The agreement between our results and those obtained by conventional refraction profiling is good, when this comparison is restricted to profiles of lengths 300 km or more, and when the associated crustal thickness estimate is averaged over the central parts of the profiles in question. Also, a comparison between our results and other available geophysical information gives that the oldest tectonic provinces of the Baltic Shield also are characterized by relatively modest heat flow, and exhibit the greatest crustal thicknesses. Post-glacial uplift data and large wavelength free air gravity data appear to be uncorrelated with crustal thickness. The same partly applies to Bouguer gravity anomalies, thus implying that the isostatic compensation mechanism in Fennoscandia is of both Airy and Pratt type.     

Normal modes of the viscoelastic earth

Summary A uniformly valid linear viscoelastic rheology is described which takes the form of a 'generalized' Burgers' body and which appears capable of reconciling the behaviour of the Earth's mantle across the complete spectrum of geodynamic time-scales. This spectrum is bracketed by the short time-scales of body wave and free oscillation seismology on which anelastic effects are dominant, and the long time-scale of mantle convection on which the Earth behaves viscously. The parameters of the model which control the viscous response are fixed by post-glacial rebound data whereas those which govern the anelasticity are to be determined by fitting the model to observations of seismic Q. The paper is concerned primarily with a discussion of the normal mode spectrum of the Earth as a generalized Burgers' body. Focusing upon the homogeneous model, it includes an initial analysis of the accuracy of first-order perturbation theory as a method of calculating the respective Q s of the elastic gravitational free oscillations. Also considered are the quasi-static modes of relaxation which only exact eigenanalysis can reveal. The importance of these modes is assessed within the context of a discussion of the effect of viscoelasticity upon the efficiency of Chandler wobble excitation.     

Regional vertical tectonics in the Eastern Mediterranean

Summary. New gravity observations from a systematic survey of the Eastern Mediterranean Sea and from a reconnaissance land survey in Central and Western Turkey have been compiled with existing data. Lack of sufficient geological and geophysical information precludes an analysis of the local anomalies or crustal structure; however, implications of the topography and gravity field at long wavelengths have been examined. Negative free-air anomalies characterize almost the entire Eastern Mediterranean basin and positive anomalies predominate in Turkey and the Aegean Sea. The change in sign coincides with the northern boundary of the African plate, and the wavelength and amplitude of the gravity variation are of the order of 1000 km and 100 mgal respectively. The lithosphere is probably unable to support such anomalies because the implied shear stresses are too large. The source of the anomalies is concluded to be in the asthenosphere where the low finite strength of material suggests that some sort of flow must exist to maintain the stresses. A good correlation is observed between the gravity and topography at wavelengths greater than 300 km; and the relationship is the same as that observed in the North Atlantic and the Central Pacific, as well as that computed for simple models of mantle convection. The gravity and topography of the Eastern Mediterranean can be explained in terms of flow in the upper mantle. This is the first region of subsidence for which this interpretation has been made.     

The relationship between seismic velocity and density in the continental crust — a useful constraint?

Summary . Plots of seismic velocity and density of rock samples show that a range of densities is possible for rocks of each seismic velocity and vice versa. although a single linear relationship is often assumed in crustal gravity calculations. Because of the scatter, whenever rocks of known seismic velocity are converted to density using this relationship, a reduction is made to the resolving power of the resulting gravity calculation. If these rocks reach thicknesses of more than a few kilometres, then the uncertainties become significant when compared with the size of commonly observed gravity anomalies. Examples are considered from the North Sea, Mississippi and Carolina Trough. It is concluded that the use of a seismic velocity measurement as the only indication of rock density does not provide a useful constraint when attempting to reproduce observed gravity variations. An appropriate model for isostatic compensation is probably the most important factor for successful predictions of crustal structure on the basis of gravity data.     

On the existence of a second scale of convection in the upper mantle

Summary. This paper is concerned with an examination of the possibility that there might exist a small scale of convective circulation beneath the oceanic lithosphere. Recent suggestions that this might be the case have been made in an effort to understand why the bathymetry of the sea-floor deviates from the prediction of boundary layer theory for ages in excess of about 100 Ma. The energy source which sustains the secondary motion is supposed to be found in the steep temperature gradient near the planetary surface which is itself presumably maintained by the large-scale convective circulation associated with plate creation and destruction. Here we investigate the extent to which the temperature dependence of viscosity may act so as to stabilize the upper boundary layer against disruption by such secondary instability. If the viscosity profile is monotonie and the asymptotic upper mantle viscosity is about 10²²poise, as suggested by post-glacial rebound data, then the existence of the second scale is extremely unlikely. On the other hand, if a sufficiently pronounced low viscosity zone does exist under old sea-floor then the development of such a second scale cannot be ruled out completely. Some recently obtained geophysical evidence is reviewed which suggests that this is unlikely to be the case.     

Correlation between seismic anisotropy and Bouguer gravity anomalies in Tibet and its implications for lithospheric structures

As a baseline measurement for understanding the Himalayan–Tibetan orogen, a product of continent–continent collision between India and Eurasia, we analyse digital seismic data in order to constrain the seismic anisotropy of the Indian shield. Based on spatially sparse data that are currently available in the public domain, there is little shear-wave birefringence for SKS phases under the Indian shield, even though it is part of a fast-moving plate in the hotspot frame of reference. If most of the northern Indian mantle has little transverse anisotropy, the onset of significant anisotropy under Tibet marks the northern terminus of intact Indian lithosphere that is thrusting under the Himalayan–Tibetan orogen. Beyond this terminus, tectonic fabric such as that associated with the deforming lithospheric mantle of Eurasia must be present in the upper mantle. Along the profile from Yadong to Golmud, the only profile in Tibet where a number of shear-wave birefringence data are available, the amount of birefringence shows two marked increases, near 30° and 33°N, between which a local high in Bouguer gravity anomaly is observed. Such a correlation between patterns of shear-wave birefringence and gravity anomalies is explained by the juxtaposition of Indian lithosphere against the overlying Eurasian lithosphere: while the Eurasian lithospheric mantle appears only to the north of 30°N, the Indian lithospheric mantle extends northwards to near 33°N.     

Stress and Flow beneath Island Arcs

Summary. The flow pattern, stress distribution, topography, and gravity anomalies were computed from numerical models having density and viscosity distributions resemblant to the Aleutian arc. The results were compatible with the hypothesis that the excess density of the slab drives its descent and that hydrodynamic forces are responsible for topographic and gravity highs over the outer rise seaward of the trench and the frontal arc and lows over the trench. In models with simple distributions of rheological parameters, the force from the slab was transmitted directly upward producing a negative gravity anomaly over the arc. Material with low resistance to flow was needed along the fault plane above the slab or within the crust of the frontal arc and within the wedge of asthenosphere above the slab to reduce that force and to allow the horizontal lithosphere to move with the slab. Models with the resistance to flow thus reduced had outer rises, deep trenches, horizontal tension seaward of the trench, horizontal compression under the trench, and downdip tension in the slab. Free air gravity anomalies, which are the sum of between deflections of the free surface due to hydrodynamic forces and direct attractions from the masses driving the flow, were not fit excellently by any of the models, in part because the coarse grid used precluded accurate representation of the fault zone above the slab and the frontal arc. An alternate to the hypothesis that about 5 kb of stress on the fault plane is needed to produce an outer rise is offered by these models. Shear stress between the slab and the island arc was always below 700 bars in the more successful models if the density distribution was scaled to match the topography of the trench. This is much less than the 2000 bars stresses needed if frictional heating causes island arc volcanism.