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1.
Using the viscoelastic correspondence principle, we utilize the surface coseismic spheroidal deformation fields (i.e. vertical displacements, potential perturbations and gravity changes) of SNREI earth models caused by four typical types of point dislocation, derived by Sun & Okubo (1993 ), to deduce the fundamental formulas for spheroidal fields relevant to viscoelastic earth models. In computations, we employ a strike-slip dislocation on a vertical plane buried at the bottom of the lithosphere to estimate the maximal viscous relaxation responses to this kind of source that possibly exist on the surface of the earth. We take the seismic moment as 1022  N  m, which is characteristic of an average large earthquake. The numerical results demonstrate that, if we take the viscosity as 1019  Pa  s in the asthenosphere, and 1021  Pa  s in the other mantle layers, the rates of surface vertical displacements and gravity changes within about 2.5° for the 10 postseismic years are respectively 1.5–8.1  cm  yr−1 and 4.0–14.9  μgal  yr−1 : the viscous relaxation for this mantle viscosity profile proceeds much faster than for a constant mantle viscosity of 1021  Pa  s.  相似文献   

2.
In Paper I (Breuer & Wolf 1995), a preliminary interpretation of the postglacial land emergence observed at a restricted set of six locations in the Svalbard Archipelago was given. The study was based on a simple model of the Barents Sea ice sheet and suggested increases in lithosphere thickness and asthenosphere viscosity with increasing distance from the continental margin.
In the present paper, the newly developed high-resolution load model. BARENTS-2, and land-uplift observations from an extended set of 25 locations are used to study further the possibility of resolving lateral heterogeneity in the upper mantle below the northern Barents Sea. A comparison of the calculated and observed uplift values shows that the lithosphere thickness is not well resolved by the observations, although values above 110 km are most common for this parameter. In contrast to this, there are indications of a lateral variation of asthenosphere viscosity. Whereas values in the range 1018-1020Pas are inferred for locations close to the continental margin, 1020-1021 Pa s are suggested further away from the margin.
A study of the sensitivity of the values found for lithosphere thickness and asthenosphere viscosity to modifications of load model BARENTS-2 shows that such modifications can be largely accommodated by appropriate changes in lithosphere thickness, whereas the suggested lateral variation of asthenosphere viscosity is essentially unaffected. An estimate of the influence of the Fennoscandian. ice sheet leads to the conclusion that its neglect results in an underestimation of the thickness of the Barents Sea ice sheet by about 10 per cent.  相似文献   

3.
Previous investigations of the causal relationship between postglacial rebound and earthquakes in eastern Canada have focused on the mode of failure and the observed timing of the pulse of earthquake/faulting activity following deglaciation. In this study, the observational database has been extended to include observed orientations of the contemporary stress field and the rotation of stress since deglacial times. It is shown that many of these observations can be explained by a realistic ice history and a viscoelastic earth with a uniform 1021 Pa s mantle.
The effects of viscosity structure on the above predictions are also examined. It is shown that, since most of the above observations are found within the ice margin, they are not very sensitive to lithospheric thickness. Also, the inclusion of a 25 or 50 km ductile layer within the lithosphere will not decouple the seismogenic upper crust. High viscosity (1022 Pa s) in the lower mantle is rejected by the stress orientation and rotation observations. A low-viscosity (6 times 1020Pa s) upper mantle with 1.6 times 1021 Pa s in the upper part of the lower mantle and 3 times 1021 Pa s in the lower part of the lower mantle below 1200 km depth has been found to give predictions that are in general agreement with the observations.  相似文献   

4.
A decadal polar motion with an amplitude of approximately 25 milliarcsecs (mas) is observed over the last century, a motion known as the Markowitz wobble. The origin of this motion remains unknown. In this paper, we investigate the possibility that a time-dependent axial misalignment between the density structures of the inner core and mantle can explain this signal. The longitudinal displacement of the inner core density structure leads to a change in the global moment of inertia of the Earth. In addition, as a result of the density misalignment, a gravitational equatorial torque leads to a tilt of the oblate geometric figure of the inner core, causing a further change in the global moment of inertia. To conserve angular momentum, an adjustment of the rotation vector must occur, leading to a polar motion. We develop theoretical expressions for the change in the moment of inertia and the gravitational torque in terms of the angle of longitudinal misalignment and the density structure of the mantle. A model to compute the polar motion in response to time-dependent axial inner core rotations is also presented. We show that the polar motion produced by this mechanism can be polarized about a longitudinal axis and is expected to have decadal periodicities, two general characteristics of the Markowitz wobble. The amplitude of the polar motion depends primarily on the Y 12 spherical harmonic component of mantle density, on the longitudinal misalignment between the inner core and mantle, and on the bulk viscosity of the inner core. We establish constraints on the first two of these quantities from considerations of the axial component of this gravitational torque and from observed changes in length of day. These constraints suggest that the maximum polar motion from this mechanism is smaller than 1 mas, and too small to explain the Markowitz wobble.  相似文献   

5.
The deformation at the core–mantle boundary produced by the 2004 Sumatra earthquake is investigated by means of a semi-analytic theoretical model of global coseismic and postseismic deformation, predicting a millimetric coseismic perturbation over a large portion of the core–mantle boundary. Spectral features of such deformations are analysed and discussed. The time-dependent postseismic evolution of the elliptical part of the gravity field ( J 2) is also computed for different asthenosphere viscosity models. Our results show that, for asthenospheric viscosities smaller than 1018 Pa s, the postseismic J 2 variation in the next years is expected to leave a detectable signal in geodetic observations.  相似文献   

6.
Summary. The viscoelastic response of the Earth to the mass displacements caused by late Pleistocene deglaciation and concomitant sea level changes is shown to be capable of producing the secular motion of the Earth's rotation pole as deduced from astronomical observations. The calculations for a viscoelastic Earth yield a secular motion in the direction of 72° W meridian which is in excellent agreement with observed values. The average Newtonian viscosity and the relaxation time obtained from polar motion data are about (1.1 ± 0.6)1023 poise (P) and 104 (1 ± 0.5) yr. The non-tidal secular acceleration of the Earth can also be attributed to the viscoelastic response to deglaciation and results in an independent viscosity estimate of 1.6 × 1023 P with upper and lower limits of 1.1 × 1023 and 2.8 × 1023 P. These values are in agreement with those based on the polar drift analysis and indicate an average mantle viscosity of 1–2 × 1023 P.  相似文献   

7.
Observations of ice movements across the British Isles and of sea-level changes around the shorelines during Late Devensian time (after about 25 000 yr BP) have been used to establish a high spatial and temporal resolution model for the rebound of Great Britain and associated sea-level change. The sea-level observations include sites within the margins of the former ice sheet as well as observations outside the glaciated regions such that it has been possible to separate unknown earth model parameters from some ice-sheet model parameters in the inversion of the glacio-hydro-isostatic equations. The mantle viscosity profile is approximated by a number of radially symmetric layers representing the lithosphere, the upper mantle as two layers from the base of the lithosphere to the phase transition boundary at 400 km, the transition zone down to 670 km depth, and the lower mantle. No evidence is found to support a strong layering in viscosity above 670 km other than the high-viscosity lithospheric layer. Models with a low-viscosity zone in the upper mantle or models with a marked higher viscosity in the transition zone are less satisfactory than models in which the viscosity is constant from the base of the lithosphere to the 670 km boundary. In contrast, a marked increase in viscosity is required across this latter boundary. The optimum effective parameters for the mantle beneath Great Britain are: a lithospheric thickness of about 65 km, a mantle viscosity above 670 km of about (4-5) 1020 Pa s, and a viscosity below 670 km greater than 4 × 1021 Pa s.  相似文献   

8.
Previous studies of the wander of the rotation pole associated with the Late Pleistocene glacial cycles indicate that the predicted polar wander speed is sensitive to the density jump at the 670 km discontinuity, the thickness of the elastic lithosphere, and the lower mantle viscosity. In particular, the M1 mode related to the density jump at 670 km depth has been shown to contribute a dominant portion of predicted polar wander speed for sufficiently small lower mantle viscosities. In this study, we examine the sensitivity of polar wander to variations in the viscosity of the viscoelastic lithosphere using simplified compressible Maxwell viscoelastic earth models. Model calculations for earth models with a viscoelastic lithosphere of finite viscosity indicate that the contribution of the M1 mode is similar to those associated with the density discontinuity at the core–mantle boundary (C0 mode) and the lithosphere (L0 mode). We speculate that this is due to the interaction between the M1 mode and the transient mode associated with the viscoelastic lithosphere, which reduces the magnitude of polar wander rates. Therefore, the M1 mode does not contribute a dominant portion of the predicted polar wander speed for earth models with a viscoelastic lithosphere of finite viscosity. In this case, predictions of polar wander speed as a function of lower mantle viscosity exhibit the qualitative form of an 'inverted parabola', as predicted for the J ˙2 curve. We caution, however, that these results are obtained for simplified earth models, and the results for seismological earth models such as PREM may be complicated by the interaction between the M1 mode and the large set of transient modes.  相似文献   

9.
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.  相似文献   

10.
Summary. An empirical equation of state, assuming mineralogical equilibrium, is developed for the top 700 km of the mantle. Assuming a uniform viscosity, this equation of state is used to show that the stresses due to the changes in phase induced in a descending lithospheric plate in a subduction zone are an order of magnitude larger than those due to the negative buoyancy of the slab in the asthenosphere. The stresses predicted are well within the power law creep region for likely mantle materials and so the effective viscosity will vary within the slab. Consequently the stresses will be smaller than those of 7.0 × 108N/m2 obtained here using uniform viscosities. These stresses are relatively compressional near the sides of the slab and tensional in the centre.  相似文献   

11.
Viscous and viscoelastic models for a subduction zone with a faulted lithosphere and internal buoyancy can self-consistently and simultaneously predict long-wavelength geoid highs over slabs, short-wavelength gravity lows over trenches, trench-forebulge morphology, and explain the high apparent strength of oceanic lithosphere in trench environments. The models use two different free-surface formulations of buoyancy-driven flows (see, for example, Part I): Lagrangian viscoelastic and pseudo-free-surface viscous formulations. The lower mantle must be stronger than the upper in order to obtain geoid highs at long wavelengths. Trenches are a simple consequence of the negative buoyancy of slabs and a large thrust fault, decoupling the overriding from underthrusting plates. The lower oceanic lithosphere must have a viscosity of less than to24 Pa s in order to be consistent with the flexural wavelength of forebulges. Forebulges are dynamically maintained by viscous flow in the lower lithosphere and mantle, and give rise to apparently stiffer oceanic lithosphere at trenches. With purely viscous models using a pseudo-free-surface formulation, we find that viscous relaxation of oceanic lithosphere, in the presence of rapid trench rollback, leads to wider and shallower back-arc basins when compared to cases without viscous relaxation. Moreover, in agreement with earlier studies, the stresses necessary to generate forebulges are small (∼ 100 bars) compared to the unrealistically high stresses needed in classic thin elastic plate models.  相似文献   

12.
Analytical approach for the toroidal relaxation of viscoelastic earth   总被引：1，自引：0，他引：1  
This paper is concerned with post-seismic toroidal deformation in a spherically symmetric, non-rotating, linear-viscoelastic, isotropic Maxwell earth model. Analytical expressions for characteristic relaxation times and relaxation strengths are found for viscoelastic toroidal deformation, associated with surface tangential stress, when there are two to five layers between the core–mantle boundary and Earth's surface. The multilayered models can include lithosphere, asthenosphere, upper and lower mantles and even low-viscosity ductile layer in the lithosphere. The analytical approach is self-consistent in that the Heaviside isostatic solution agrees with fluid limit. The analytical solution can be used for high-precision simulation of the toroidal relaxation in five-layer earths and the results can also be considered as a benchmark for numerical methods. Analytical solution gives only stable decaying modes—unstable mode, conjugate complex mode and modes of relevant poles with orders larger than 1, are all excluded, and the total number of modes is found to be just the number of viscoelastic layers between the core–mantle boundary and Earth's surface—however, any elastic layer between two viscoelastic layers is also counted. This confirms previous finding where numerical method (i.e. propagator matrix method) is used. We have studied the relaxation times of a lot of models and found the propagator matrix method to agree very well with those from analytical results. In addition, the asthenosphere and lithospheric ductile layer are found to have large effects on the amplitude of post-seismic deformation. This also confirms the findings of previous works.  相似文献   

13.
Summary. A systematic approach is suggested for modelling the development of sedimentary basins. The theory, which partitions basin formation into initiating and isostatic adjustment processes, is applicable to all modes of basin formation if these processes are linear, or can he represented with sufficient accuracy in an incrementally linear form.
The dynamics of regional isostatic adjustment are characterized by the Heaviside space-time Green functions for the response of elastic and viscoelastic (Maxwell) thin plate models of the lithosphere. It is shown, by convolving the Heaviside—Green functions with cylindrical surface loads, that the rate of isostatic adjustment on a viscoelastic lithosphere is a function of the wavelength of the surface load, long wavelengths being compensated most rapidly.
Six archetypal initiating processes for sedimentary basin development are presented. These processes are those responsible for the subsidence of the Earth's surface which creates a depression in which water and sediments collect. Isostatic amplification of subsidence by sediment and water loads is cast in the form of an integral equation with isostatic Heaviside—Green functions as kernel.
Specific examples, the basins that result from a graben initiating process, are compared with the largest scale structure of the North Sea Basin, a basin that is known to be underlain by a graben system. A model, in which a 50-km wide graben subsides exponentially with a time constant of 5 × 107yr during the interval 180–100 Myr bp , is shown to be consistent with the largest scale structure of the North Sea Basin if the underlying lithosphere is viscoelastic with a flexural rigidity of ∼5 × 1025 Nm and relaxation time constant ∼ 106 yr.  相似文献   

14.
Summary. The thermal effect of a rapid injection of hot magmas into the lower part of the lithosphere is modelled as an increase in heat production through the invaded region. The change in surface heat flow and the uplift resulting from the thermal expansion are determined in three-dimensional axially symmetric geometry: they are expressed as the space time convolutions of a Green's function with the anomalous heat production.
The anomalies with shorter wavelength (compared to the lithospheric thickness) are attenuated. This filtering affects the surface uplift more than the heat flow anomaly; the attenuation effect is larger when only the lower part of the lithosphere is invaded.
The uplift time constant is of the same order as the heat conduction time if the lower lithosphere is invaded by magmas at a moderate rate (i.e. the rate of injection does not exceed the equivalent of 0.1 per cent of the lithospheric volume in 106yr). Fifty per cent of the total uplift takes place in about 80 × 106yr for a lithosphere 100 km thick. The uplift is slightly faster when the whole lithosphere is invaded. The heat flow anomaly is delayed when the lower part of the lithosphere is invaded.
The spatial extent and the timing of the uplift and heat flow anomalies are critical in determining the mechanism's feasibility. Magma injections explain rapid uplifts [> 100 m (106 yr)−1] only if the magma is supplied at a very high rate (i.e. at least 10 per cent of the lithosphere volume per 106yr). It is a feasible mechanism for uplifts that occur over longer periods of time (≊ 30 × 106yr) such as those that seem to have occurred when the African plate came to rest with respect to the mantle.  相似文献   

15.
Inference of mantle viscosity from GRACE and relative sea level data   总被引：12，自引：0，他引：12  
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.  相似文献   

16.
A spectral method is employed to study the response to surface loads of a Maxwell earth including lateral viscosity variations. In particular, we focus on the effects of lithospheric cratons on the long-wavelength time-dependent displacement field for simple earth models. The viscosity contrast of the craton with respect to the surrounding mantle is kept fixed, whereas its thickness is allowed to vary. We show that the long-wavelength vertical displacement is not greatly affected by the presence of a lithospheric craton, while the tangential displacement is severely modified for the case of a homogeneous mantle. With increasing harmonic degree and thickness of the craton, the load-deformation coefficients deviate from those pertaining to a homogeneous mantle with a viscosity of 1021 Pa s. These deviations are particularly enhanced on timescales larger than a few hundred years. These findings indicate that the interpretation of the viscosity structure of the mantle inferred from postglacial rebound signatures based on radially stratified models is affected by the presence of lateral viscosity variations.  相似文献   

17.
The   M w γ 9.0  2004 December 26 Sumatra-Andaman and   M w = 8.7  2005 March 28 Nias earthquakes, which collectively ruptured approximately 1800 km of the Andaman and Sunda subduction zones, are expected to be followed by vigorous viscoelastic relaxation involving both the upper and lower mantle. Because of these large spatial dimensions it is desirable to fully account for gravitational coupling effects in the relaxation process. We present a stable method of computing relaxation of a spherically-stratified, compressible and self-gravitating viscoelastic Earth following an impulsive moment release event. The solution is cast in terms of a spherical harmonic expansion of viscoelastic normal modes. For simple layered viscoelastic models, which include a low-viscosity oceanic asthenosphere, we predict substantial post-seismic effects over a region several 100s of km wide surrounding the eastern Indian Ocean. We compare observed GPS time-series from ten regional sites (mostly in Thailand and Indonesia), beginning in 2004 December, with synthetic time-series that include the coseismic and post-seismic effects of the 2004 December 26 and 2005 March 28 earthquakes. A viscosity structure involving a biviscous (Burgers body) rheology in the asthenosphere explains the pattern and amplitude of post-seismic offsets remarkably well.  相似文献   

18.
Simple models for the flexure of the lithosphere caused by the load of the Hawaiian-Emperor Seamount Chain have been determined for different values of the effective flexural rigidity of the lithosphere. The gravity effect of the models have been computed and compared to observed free-air gravity anomaly profiles in the vicinity of the seamount chain. The values of the effective flexural rigidity which most satisfactorily explain both the amplitude and wavelength of the observed profiles have been determined. Computations show that if the lithosphere is modelled as a continuous elastic sheet, a single effective flexural rigidity of about 5 × 1029 dyne-cm can explain profiles along the Hawaiian-Emperor Seamount Chain. If the lithosphere is modelled as a discontinuous elastic sheet an effective flexural rigidity of about 2 × 1030 dyne-cm is required. Since the age of the seamount chain increases from about 3 My near Hawaii to about 70 My near the northernmost Emperor seamount these results suggest there is apparently little decrease in the effective flexural rigidity of the lithosphere with increase in the age of loading. This suggests the lithosphere is rigid enough to support the load of the seamount chain for periods of time of at least several tens of millions of years. Thus the subsidence of atolls and guyots along the chain is most likely to be regional in extent and is unlikely to be caused by an inelastic behaviour of the lithosphere beneath individual seamounts.  相似文献   

19.
Surface velocities in parts of the India–Asia collision zone are compared to velocities calculated from equations describing fluid flow driven by topographically produced pressure gradients. A good agreement is found if the viscosity of the crust is ∼1020 Pa s in southern Tibet and ∼1022 Pa s in the area between the Eastern Syntaxis and the Szechwan Basin. The lower boundary condition of the flow changes between these two areas, with a stress-free lower boundary in the area between the Szechwan basin and the Eastern Syntaxis, and a horizontally rigid but vertically deformable boundary where strong Indian lithospheric material underlies southern Tibet. Deformation maps for olivine, diopside and anorthite show our findings to be consistent with laboratory measurements of the rheology of minerals. Gravitationally driven flow is also suggested to be taking place in the Indo–Burman Ranges, with a viscosity of ∼1019–1020 Pa s. Flow in both southern Tibet and the Indo–Burman Ranges provides an explanation for the formation of the geometry of the Eastern Himalayan Syntaxis. The majority of the normal faulting earthquakes in the Tibetan Plateau occur in the area of southern Tibet which we model as gravitationally spreading over the Indian shield.  相似文献   

20.
The dynamical origin of subduction zone topography   总被引：1，自引：0，他引：1  
Summary. Subduction zones are expressed topographically by long linear oceanic trenches flanked by a low outer rise on the seaward side and an island arc on the landward side. This topographic structure is reflected in free air gravity anomalies, suggesting that much of the topography originates from dynamical forces applied at the base of the crust. We have successfully reproduced the general topographic features of subduction zones by supposing that the stresses generated by the bending of the viscous lower lithosphere as it subducts are transmitted through the thin elastic upper portion of the lithosphere. The trench is due to a zone of extensional flow (associated with low pressure) in the upper part of the viscous lithosphere.
The stresses in the subducting slab are computed using a finite element technique, assuming a Maxwell viscoelastic constitutive relation. Various dips (10 to 90°) were investigated, as well as depth dependent and non-Newtonian (power law, n = 3) viscosities. Observed subduction zone dimensions are well reproduced by these models. The effective viscosity required at mid-depth in the lithosphere is about 6 × 1022 P. This low value is probably due to the stress dependence of the effective viscosity. However, these models also show that the topography of the subduction zone depends primarily upon the geometry of the subducting slab (dip, radius of curvature of the bend) rather than upon its rheology. Shear stresses beneath the trench reach maxima of approximately 50 MPa. An interesting feature of some solutions is a dynamically supported bench or platform between the trench and island arc.  相似文献   

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