共查询到20条相似文献，搜索用时 609 毫秒
1.
S.M. Nakiboglu 《Physics of the Earth and Planetary Interiors》1982,28(4):302-311
A second-order hydrostatic theory is developed on the assumption that the trace of the Earth's inertia tensor, its mass and mean radius are invariant under any process causing deviations from the hydrostatic state.The hydrostatic flattening and the zonal coefficients of the hydrostatic gravitational field are obtained as ??1 = 299.638, J2 = 1072.618 × 10?6 and J4 = ?2.992 × 10?6, respectively.The internal theory using the preliminary reference earth model (PREM) of Dziewonski and Anderson (1981) yields ??1 = 299.627, J2 = 1072.701 × 10?6 and J4 = ?2.992 × 10?6. The agreement between these and the hydrostatic values indicate that PREM is suitable as a reference model as it represents the spheroidal density distribution in a state of zero non-hydrostatic stress while satisfying the fundamental geodetic observations of the invariant quantities.The small discrepancy between the hydrostatic flattening and the value deduced from PREM suggests that the density is underestimated at large depths and/or it is slightly overestimated in shallow regions of the Earth.The discrepancies between the hydrostatic and observed quantities persist after the removal of the accountable effects of isostatically compensated topography, permanent tidal deformation and the present mass anomalies associated with the Late-Pleistocene deglaciation. These ‘corrected’ discrepancies point to a triaxial non-hydrostatic figure which cannot be explained by the delayed response of the Earth to tidal deceleration. 相似文献
2.
We present a geoid model for the area of Lake Vostok, Antarctica, from a combination of local airborne gravity, ice-surface and ice-thickness data and a lake bathymetry model. The topography data are used for residual terrain modeling (RTM) in a remove–restore approach together with GOCE satellite data. The quasigeoid is predicted by least-squares collocation (LSC) and subsequently converted to geoid heights. Special aspects of that method in presence of an ice sheet are discussed.It is well known that a body freely floating in water is in a state of hydrostatic equilibrium (HE). This usually applies, e.g., to ice shelves or sea ice. However, it has been shown that this is valid also for the ice sheet covering the subglacial Lake Vostok. Thus, we demonstrate the use of such a refined regional geoid model for glaciological and geophysical applications by means of the HE surface of that lake. The mean quadratic residual geoid signal (0.56 m) w.r.t. the GOCE background model exceeds the residual variations of the estimated apparent lake level (ALL) (0.26 m) within the central part of the lake. An approach considering the actual geopotential at the ALL has been derived and subsequently applied. In this context, downward continuation of the potential field within the ice sheet as well as the latitudinal tilt of off-geoid equipotential surfaces are discussed. In view of the accuracy of the ice-thickness measurements that dominate the total error budget of the estimated ALL these effects are negligible. Thus, the HE surface of subglacial lakes may safely be described by a constant height bias in small-scale regional applications. However, field continuation is significant with respect to the formal uncertainty of the quasigeoid, which is at the level of 5 cm given that accurate airborne gravity data (±2 mGal) are available. 相似文献
3.
A modified version of the 3D finite-element hydrostatic model QUODDY-4 is used to quantify the changes in the dynamics and energetics of the M 2 surface tide in the North European Basin, induced by the spatial variability in bottom roughness. This version differs from the original one, as it introduces a module providing evaluation of the drag coefficient in the bottom boundary layer (BBL) and by accounting for the equilibrium tide. The drag coefficient is found from the resistance laws for an oscillatory rotating turbulent BBL over hydrodynamically rough and incompletely rough underlying surfaces, describing how the wave friction factor as well as other resistance characteristics depend on the dimensionless similarity parameters for the BBL. It is shown that the influence of the spatial variability in bottom roughness is responsible for some specific changes in the tidal amplitudes, phases, and the maximum tidal velocities. These changes are within the model noise, while the changes in the averaged (over a tidal cycle) horizontal wave transport and the averaged dissipation of barotropic tidal energy may be of the same orders of magnitude as are the above energetic characteristics as such. Thus, contrary to present views, ignoring the spatial variability in bottom roughness at least in the North European Basin is only partially correct: it is valid for the tidal dynamics, but is liable to break down for the tidal energetics. 相似文献
4.
Abstract We have studied the behavior of nonlinear waves in isothermal atmospheres using an improved beam scheme method. It is shown that although the magnitude of the mass leakage due to side beams is significant, nevertheless in a motion close to hydrostatic equilibrium it can be suppressed, if special density distributions and/or suitable mesh intervals are selected. We adopt as the parameters for our model of the atmospheres M=1 M[odot], R=50 R[odot] and T=4864 K. The time variation of the physical quantities in each cell is found for several oscillation periods. The critical frequency for the model atmosphere in the case of waves with a weak nonlinearity seems to be consistent with that in the linear theory. 相似文献
5.
Michele Caputo 《Pure and Applied Geophysics》1964,57(1):66-82
Summary Adopting thePizzetti-Somigliana method and using elliptic integrals we have obtained closed formulas for the space gravity field in which one of the equipotential surfaces is a triaxial ellipsoid. The same formulas are also obtained in first approximation of the equatorial flattening avoiding the use of the elliptic integrals. Using data from satellites and Earth gravity data the gravitational and geometric bulge of the Earth's equator are computed. On the basis of these results and on the basis of recent gravity data taken around the equator between the longitudes 50° to 100° E, 155° to 180° E, and 145° to 180° W, we question the advantage of using a triaxial gravity formula and a triaxial ellipsoid in geodesy. Closed formulas for the space field in which a biaxial ellipsoid is an equipotential surface are also derived in polar coordinates and its parameters are specialized to give the international gravity formula values on the international ellipsoid. The possibility to compute the Earth's dimensions from the present Earth gravity data is the discussed and the value ofMG=(3.98603×1020 cm3 sec–2) (M mass of the Earth,G gravitational constant) is computed. The agreement of this value with others computed from the mean distance Earth-Moon is discussed. The Legendre polinomials series expansion of the gravitational potential is also added. In this series the coefficients of the polinomials are closed formulas in terms of the flattening andMG.Publication Number 327, and Istituto di Geodesia e Geofisica of Università di Trieste. 相似文献
6.
Qingsong Wang Xueliang Yuan Yanhua Lai Chunyuan Ma Wei Ren 《Stochastic Environmental Research and Risk Assessment (SERRA)》2012,26(7):887-898
In the logarithmic curves of the per capita GDP and the urbanization, with the traditional environmental Kuznets equation, this paper presented a coupling equation showing the relationship between urbanization and the atmospheric environment. Based on the “double exponential” coupling curve, the principles of flattening, advancing and fast-falling that new coupling curve should be followed were discussed. According to the two indicators of environmental assessment, namely the treatment cost and the deterioration degree of the environment, a new dual four times matrix model with the corresponding countermeasures and environment policy were introduced. Taking Shandong Province as an example, the coupling relationship between urbanization and atmospheric environment was investigated. The coupling curve showed that it was in running-in stage, and atmospheric quality tended to be improved. SO2 curve fluctuated more significantly compared with soot and industrial dust curves. The matrix model shows that the combination of flattening principle and advancing principle is preferable for SO2 emissions, but the fast-falling principle is recommended for soot and industrial dust emissions. 相似文献
7.
《Advances in water resources》1998,22(1):33-57
In this article we consider the transport of an adsorbing solute in a two-region model of a chemically and mechanically heterogeneous porous medium when the condition of large-scale mechanical equilibrium is valid. Under these circumstances, a one-equation model can be used to predict the large-scale averaged velocity, but a two-equation model may be required to predict the regional velocities that are needed to accurately describe the solute transport process. If the condition of large-scale mass equilibrium is valid, the solute transport process can be represented in terms of a one-equation model and the analysis is simplified greatly. The constraints associated with the condition of large-scale mass equilibrium are developed, and when these constraints are satisfied the mass transport process can be described in terms of the large-scale average velocity, an average adsorption isotherm, and a single large-scale dispersion tensor. When the condition of large-scale mass equilibrium is not valid, two equations are required to describe the mass transfer process, and these two equations contain two adsorption isotherms, two dispersion tensors, and an exchange coefficient. The extension of the analysis to multi-region models is straight forward but tedious. 相似文献
8.
采用武汉台超导重力仪(SG C032)14年多的长期连续观测资料,研究了固体地球对二阶和三阶引潮力的响应特征,精密测定了重力潮汐参数,系统研究了最新的固体潮模型和海潮模型在中国大陆的有效性.采用最新的8个全球海潮模型计算了海潮负荷效应,从武汉台SG C032的观测中成功分离出63个2阶潮汐波群和15个3阶潮汐波群信号,3阶潮波涵盖了周日、半日和1/3日三个频段.重力潮汐观测的精度非常高,标准偏差达到1.116 nm·s-2,系统反映了非流体静力平衡、非弹性地球对2阶和3阶引潮力的响应特征.结果表明,现有的武汉国际重力潮汐基准在半日频段非常精确,但在周日频段存在比较明显的偏差,需要进一步精化.对于中国大陆的大地测量观测,固体潮可以采用Dehant等考虑地球内部介质非弹性和非流体静力平衡建立的固体潮理论模型或Xu 等基于全球SG观测建立的重力潮汐全球实验模型作为参考和改正模型,海潮负荷效应应该采用Nao99作为改正模型. 相似文献
9.
The sea surface cannot be used as reference for Major Vertical Datum definition because its deviations from the ideal equipotential surface are very large compared to rms in the observed quantities. The quasigeoid is not quite suitable as the surface representing the most accurate Earth's model without some additional conditions, because it depends on the reference field. The normal Earth's model represented by the rotational level ellipsoid can be defined by the geocentric gravitational constant, the difference in the principal Earth's inertia moments, by the angular velocity of the Earth's rotation and by the semimajor axis or by the potential (U
0
) on the surface of the level ellipsoid. After determining the geopotential at the gauge stations defining Vertical Datums, gravity anomalies and heights should be transformed into the unique vertical system (Major Vertical Datum). This makes it possible to apply Brovar's (1995) idea of determining the reference ellipsoid by minimizing the integral, introduced by Riemann as the Dirichlet principle, to reach a minimum rms anomalous gravity field. Since the semimajor axis depends on tidal effects, potential U
0
should be adopted as the fourth primary fundamental geodetic constant. The equipotential surface, the actual geopotential of which is equal to U
0
, can be adopted as reference for realizing the Major Vertical Datum. 相似文献
10.
A variety of paleomagnetic data from the Mediterranean region show a strong bias toward shallow inclinations. This pattern of shallow inclinations has been interpreted to be the result of (1) major northward terrane displacement, (2) large nondipole components in the Earth's magnetic field, and (3) systematic inclination flattening of the paleomagnetic directions. Here, we use the observation that, in addition to the well-known variation of magnetic inclination with latitude, the N-S elongation of directional dispersion also varies, being most elongate at the equator and nearly symmetric at the poles. Assuming that inclination shallowing follows the relationship long known from experiment, we invert the inclinations using a range of “flattening factors” to find the elongation/inclination pair consistent with a statistical model for the paleosecular variation. We apply the so-called “elongation/inclination” method to the extensive paleomagnetic data sets from the Miocene sediments of the Calatayud basin (Spain) and the island of Crete (Greece). After correction, the Spanish data are in good agreement with the expected middle Miocene latitude of the region. The data from Crete suggest that it occupied a position in the late Miocene about 275 km north of the predicted location. This is in agreement with the geological and geodynamical models for the east Mediterranean region, which indicate that slab rollback processes in combination with Anatolian push generated southward migration of Crete. The 7.5 million year average displacement rate of Crete estimated by the E/I method is 37 mm/yr to the south, which closely coincides with present-day rates based on global positioning system (GPS) and model measurements. We also show that inappropriate tilt corrections lead to a shallow inclination bias as well, explaining that observed in studies of lava flows of the region. We conclude that the east Mediterranean inclination anomaly is caused by sedimentary inclination error and not by a persistent octupolar contribution to the geomagnetic field, or northward transport. 相似文献
11.
Chushiro Hayashi Kiyoshi Nakazawa Hiroshi Mizuno 《Earth and Planetary Science Letters》1979,43(1):22-28
When the proto-Earth was growing by the accretion of planetesimals and its mass became greater than about 0.1 ME, where ME is the present Earth's mass, an appreciable amount of gas of the surrounding solar nebula was attracted towards the proto-Earth to form an optically thick, dense atmosphere. We have studied the structure of this primordial atmosphere under the assumptions that (1) it is spherically symmetric and in hydrostatic equilibrium, and (2) the net energy outflow (i.e., the luminosity) is constant throughout the atmosphere and is given by GMM/R with M = M/106yr or M/107yr where M and R are the mass and the radius of the proto-Earth, respectively.The results of calculations show that the temperature at the bottom of the atmosphere, namely, at the surface of the proto-Earth increases greatly with the mass of the proto-Earth and it is about 1500°K for M = 0.25 ME. This high temperature is due to the blanketing effect of the opaque atmosphere. Thus, as long as the primordial solar nebula was existing, the surface temperature of the proto-Earth was kept high enough to melt most of the materials and, hence, the melted iron sedimented towards the center to form the Earth's core. 相似文献
12.
The Free Core Nutation (FCN) is an important eigenmode which affects both Earth rotation and body tide. The FCN parameters, the resonance period and the quality factor are important for understanding the dynamics of the Earth at nearly diurnal periods. Those parameters are usually estimated either from the Very Long Baseline Interferometry (VLBI) observations of nutation, or from the tidal gravity measurements. In this paper we investigate the determination of the FCN parameters from gravity records covering a period of more than three years, collected with the use of a LaCoste&Romberg Earth Tide no. 26 gravimeter, located at Józefos?aw observatory near Warsaw. From the resonant enhancements of gravimetric factors and phases of diurnal tidal gravity waves, we could infer the FCN period to be equal to 430 sidereal days. This result is in very good agreement with previous gravimetric and VLBI nutation results, confirming the discrepancy in the dynamic flattening of the outer liquid core from its theoretical value based on the hydrostatic equilibrium assumption. The estimated FCN quality factor (Q ≈ 1300) is considerably smaller than the VLBI nutation result, which confirms that the local gravity measurements are more sensitive than VLBI global analyses to site-dependent phenomena (such as atmospheric and indirect ocean tidal effects). We also investigated the importance of gravimetric corrections in the FCN analysis, including numerical tests and simulations. This allowed us to estimate the uncertainty of FCN parameters due to improper or incomplete set of environmental corrections. We took also into account the impact of gravimetric factor errors and tidal wave selection on estimated FCN parameters. We demonstrated that despite relatively noisy measurements due to unfavorable gravimeter location, we were able to obtain very good results in case when proper correction and tidal wave selection were applied. 相似文献
13.
14.
We develop a one-equation non-equilibrium model to describe the Darcy-scale transport of a solute undergoing biodegradation in porous media. Most of the mathematical models that describe the macroscale transport in such systems have been developed intuitively on the basis of simple conceptual schemes. There are two problems with such a heuristic analysis. First, it is unclear how much information these models are able to capture; that is, it is not clear what the model's domain of validity is. Second, there is no obvious connection between the macroscale effective parameters and the microscopic processes and parameters. As an alternative, a number of upscaling techniques have been developed to derive the appropriate macroscale equations that are used to describe mass transport and reactions in multiphase media. These approaches have been adapted to the problem of biodegradation in porous media with biofilms, but most of the work has focused on systems that are restricted to small concentration gradients at the microscale. This assumption, referred to as the local mass equilibrium approximation, generally has constraints that are overly restrictive. In this article, we devise a model that does not require the assumption of local mass equilibrium to be valid. In this approach, one instead requires only that, at sufficiently long times, anomalous behaviors of the third and higher spatial moments can be neglected; this, in turn, implies that the macroscopic model is well represented by a convection–dispersion–reaction type equation. This strategy is very much in the spirit of the developments for Taylor dispersion presented by Aris (1956). On the basis of our numerical results, we carefully describe the domain of validity of the model and show that the time-asymptotic constraint may be adhered to even for systems that are not at local mass equilibrium. 相似文献
15.
L. I. Lumb G. T. Jarvis K. D. Aldridge W. DeLandro-Clarke 《Physics of the Earth and Planetary Interiors》1995,90(3-4)
Indirect observations and theoretical predictions for the period of the free core nutation (FCN) differ by anywhere from 15 to 30 days, and various effects have been invoked in attempts to explain this difference. The favored explanation remains as much as 5% departure in the flattening of the core-mantle boundary (CMB) from that of its hydrostatic reference figure. This 5% ‘extra-flattening’ of the CMB is not seen at the Earth's surface, where the difference is only about 0.5%. In contrast to the a posteriori model adjustments used to determine this up to 5% value, and the kinematic results available from viscous flow modeling using the seismically determined lateral heterogeneity in density data, we consider this problem from the perspective of a forward-modeling dynamical study. More specifically, we investigate the related problem of flow-induced surface and CMB topography, arising from convection in the mantle. As such, we have completed a comparative and systematic study of relative surface and CMB topography resulting from numerical models of mantle convection. When effects resulting from boundary curvature are isolated, it appears that the magnitude of CMB topography produced is insufficient in producing a significant extra-flattening of the CMB. However, results concerning effects solely resulting from a depth-dependent mantle viscosity profile, indicate that this factor may indeed lead to enhanced topography at the CMB of the magnitude required to produce the extra-flattening there. 相似文献
16.
A modified version of the 3D finite-element hydrostatic model QUODDY-4 is used to quantify the changes in the dynamics and energetics of the M 2 surface tide in the North European Basin, induced by the spatial variability in bottom roughness. This version differs from the original one, as it introduces a module providing evaluation of the drag coefficient in the bottom boundary layer (BBL) and by accounting for the equilibrium tide. The drag coefficient is found from the resistance laws for an oscillatory rotating turbulent BBL over hydrodynamically rough and incompletely rough underlying surfaces, describing how the wave friction factor as well as other resistance characteristics depend on the dimensionless similarity parameters for the BBL. It is shown that the influence of the spatial variability in bottom roughness is responsible for some specific changes in the tidal amplitudes, phases, and the maximum tidal velocities. These changes are within the model noise, while the changes in the averaged (over a tidal cycle) horizontal wave transport and the averaged dissipation of barotropic tidal energy may be of the same orders of magnitude as are the above energetic characteristics as such. Thus, contrary to present views, ignoring the spatial variability in bottom roughness at least in the North European Basin is only partially correct: it is valid for the tidal dynamics, but is liable to break down for the tidal energetics.
相似文献17.
This work presents a validation study of global geopotential models (GGM) in the region of Fagnano Lake, located in the southern Andes. This is an excellent area for this type of validation because it is surrounded by the Andes Mountains, and there is no terrestrial gravity or GNSS/levelling data. However, there are mean lake level (MLL) observations, and its surface is assumed to be almost equipotential. Furthermore, in this article, we propose improved geoid solutions through the Residual Terrain Modelling (RTM) approach. Using a global geopotential model, the results achieved allow us to conclude that it is possible to use this technique to extend an existing geoid model to those regions that lack any information (neither gravimetric nor GNSS/levelling observations). As GGMs have evolved, our results have improved progressively. While the validation of EGM2008 with MLL data shows a standard deviation of 35 cm, GOCO05C shows a deviation of 13 cm, similar to the results obtained on land. 相似文献
18.
Summary The gravitational potential energy of the Sun and its corresponding internal energy have been estimated on the basis of the
standard model of the Sun's internal structure. It is demonstrated that the principal moment of inertia of the Sun, computed
from the model, does not fit the hydrostatic equilibrium limit. 相似文献
19.
M. Battaglia M. Di Bari V. Acocella M. Neri 《Journal of Volcanology and Geothermal Research》2011,199(1-2):153-164
Many volcanic edifices are subject to flank failure, usually produced by a combination of events, rather than any single process. From a dynamic point of view, the cause of collapse can be divided into factors that contribute to an increase in shear stress, and factors that contribute to the reduction in the friction coefficient μ of a potential basal failure plane. We study the potential for flank failure at Mount Etna considering a schematic section of the eastern flank, approximated by a wedge-like block. For such geometry, we perform a (steady state) limit equilibrium analysis: the resolution of the forces parallel to the possible basal failure plane allows us to determine the total force acting on the potentially unstable wedge. An estimate of the relative strength of these forces suggests that, in first approximation, the stability is controlled primarily by the balance between block weight, lithostatic load and magmatic forces. Any other force (sea load, hydrostatic uplift, and the uplift due to mechanical and thermal pore-fluid pressure) may be considered of second order. To study the model sensitivity, we let the inferred slope α of the basal surface failure vary between ?10° and 10°, and consider three possible scenarios: no magma loading, magmastatic load, and magmastatic load with magma overpressure. We use error propagation to include in our analysis the uncertainties in the estimates of the mechanics and geometrical parameters controlling the block equilibrium. When there is no magma loading, the ratio between destabilizing and stabilizing forces is usually smaller than the coefficient of friction of the basal failure plane. In the absence of an initiating mechanism, and with the nominal values of the coefficient of friction μ = 0.7 ± 0.1 proposed, the representative wedge will remain stable or continue to move at constant speed. In presence of magmastatic forces, the influence of the lateral restraint decreases. If we consider the magmastatic load only, the block will remain stable (or continue to move at constant speed), unless the transient mechanical and thermal pressurization significantly decrease the friction coefficient, increasing the instability of the flank wedge for α > 5° (seaward dipping decollement). When the magma overpressure contribution is included in the equilibrium analysis, the ratio between destabilizing and stabilizing forces is of the same order or larger than the coefficient of friction of the basal failure plane, and the block will become unstable (or accelerate), especially in the case of the reduction in friction coefficient. Finally, our work suggests that the major challenge in studying flank instability at Mount Etna is not the lack of an appropriate physical model, but the limited knowledge of the mechanical and geometrical parameters describing the block equilibrium. 相似文献
20.
Two diagnostic models, reproducing circulation generated in a marginal sea by variable density, have been developed. The models’ domain is a 2D transverse section for which analytical solutions have been obtained. They describe the winter situation in the northern Adriatic, with a strong vertical mixing present and the density maximum dominating the centre of the basin. Both models employ Boussinesq-type parametrisation of friction and linear slip at the bottom. The first model allows for frictional departure from hydrostatic equilibrium and includes vertical friction only. The second one is hydrostatic but allows for lateral friction as well. The results obtained by the two models are similar and to some extent dependent on the vertical and bottom friction. They reproduce several well known characteristics of the Adriatic circulation (cyclonic surface flow, downwelling in the central and larger part of the basin compensated by upwelling in the coastal zone) but also predict some phenomena that are still not well understood. A conspicuous feature of the model results are coastal jets, which were observed in the Adriatic on several occasions. The present models show that the distance of jets from the coasts depends on lateral friction: it is found to vary from 1 up to 10 km on the Italian side and between 2 and 15 km on the Croatian side. Both models reproduce the west–east asymmetry, with the wider current on the east side of the basin. The asymmetry is a subject on which conflicting empirical results exist in the Adriatic. In the two models cyclonic flow occupies the whole water column, which disagrees with some recent theoretical findings of the near-bottom anticyclonic flow and thus leaves the issue open. 相似文献