Transitions in the style of mantle convection at high Rayleigh numbers

The pattern and style of mantle convection govern the thermal evolution, internal dynamics, and large-scale surface deformation of the terrestrial planets. In order to characterize the nature of heat transport and convective behaviour at Rayleigh numbers, Ra, appropriate for planetary mantles (between 10⁴ and 10⁸), we perform a set of laboratory experiments. Convection is driven by a temperature gradient imposed between two rigid surfaces, and there is no internal heating. As the Rayleigh number is increased, two transitions in convective behaviour occur. First we observe a change from steady to time-dependent convection at Ra≈10⁵. A second transition occurs at higher Rayleigh numbers, Ra≈5×10⁶, with large-scale time-dependent flow being replaced by isolated rising and sinking plumes. Corresponding to the latter transition, the exponent β in the power law relating the Nusselt number Nu to the Rayleigh number (NuRa^β) is reduced. Both rising and sinking plumes always consist of plume heads followed by tails. There is no characteristic frequency for the formation of plumes.     

Regional compensation of subducted lithosphere: effects on geoid,gravity and topography from a preliminary model

It is proposed that the anomalous mass of subducted lithospheric slabs is partially compensated by two mechanisms: (a) by stresses transmitted up the slab to the surface lithosphere, causing the trench, and (b) by stresses transmitted through the mantle wedge overlying the slab, which cause a broad shallow depression. Results calculated from a preliminary two-dimensional model show that it can give a first-order account of observed topography, gravity and geoid anomalies. In particular, the model can reconcile the large mass anomaly predicted for the slab by thermal conduction theory with the smaller than expected gravity and geoid anomalies. Preliminary results indicate substantial compensation by mechanism (a), implying rather large stresses at the top of the slab: these could be important for theories of earthquake mechanisms and plate driving mechanisms. Roughly 50% of the possible compensation by mechanism (b) is indicated: the resulting depression, the order of 500 m deep and over 500 km wide, could explain anomalously deep marginal basins and some marine transgressions of continents.     

Lagging mantle convection,the geoid and mantle structure

In numerical models of convection incorporating migration of a simulated subduction zone, the main descending flow lags far behind the migrating trench, and a geoid low is associated with the main descending flow. This provides physical plausibility for the suggestion by Chase and Sprowl that present very long-wavelength (degree 2–4) geoid lows are associated with Mesozoic trench locations, and suggests further that the present long-wavelength geoid, deep mantle structure and hotspot distribution may be straightforward consequences of plate evolution since the Upper Paleozoic.     

Numerical simulation of nonstationary dissipative structures in 3D double-diffusive convection at large Rayleigh numbers

Numerical simulation of nonstationary dissipative structures in 3D double-diffusive convection has been performed by using the previously derived system of complex Ginzburg-Landau type amplitude equations, valid in a neighborhood of Hopf bifurcation points. Simulation has shown that the state of spatiotemporal chaos develops in the system. It has the form of nonstationary structures that depend on the parameters of the system. The shape of structures does not depend on the initial conditions, and a limited number of spectral components participate in their formation.     

Testing Stokes-Helmert geoid model computation on a synthetic gravity field: experiences and shortcomings

We report on testing the UNB (University of New Brunswick) software suite for accurate regional geoid model determination by use of Stokes-Helmert’s method against an Australian Synthetic Field (ASF) as “ground truth”. This testing has taken several years and has led to discoveries of several significant errors (larger than 5mm in the resulting geoid models) both in the UNB software as well as the ASF. It was our hope that, after correcting the errors in UNB software, we would be able to come up with some definite numbers as far as the achievable accuracy for a geoid model computed by the UNB software. Unfortunately, it turned out that the ASF contained errors, some of as yet unknown origin, that will have to be removed before that ultimate goal can be reached. Regardless, the testing has taught us some valuable lessons, which we describe in this paper. As matters stand now, it seems that given errorless gravity data on 1′ by 1′ grid, a digital elevation model of a reasonable accuracy and no topographical density variations, the Stokes-Helmert approach as realised in the UNB software suite is capable of delivering an accuracy of the geoid model of no constant bias, standard deviation of about 25 mm and a maximum range of about 200 mm. We note that the UNB software suite does not use any corrective measures, such as biases and tilts or surface fitting, so the resulting errors reflect only the errors in modelling the geoid.     

On calculation of the vertical deflection and the geoid undulation from gravity anomalies

Specific features of the calculation of the vertical deflection and the geoidal undulation in the Arctic from gravity anomalies are discussed. Basic requirements to the initial model of the anomalous field are described. The technique of calculating the vertical deflection with arbitrarily fine detail is proposed. The ways for improving the models of gravity anomalies for solving the stated problems are suggested.     

On the dynamics of 3-D single thermal plumes at various Prandtl numbers and Rayleigh numbers

Three-dimensional (3-D) numerical simulations of single turbulent thermal plumes in the Boussinesq approximation are used to understand more deeply the interaction of a plume with itself and its environment. In order to do so, we varied the Rayleigh and Prandtl numbers from Ra?～?10⁵ to Ra?～?10⁸ and from Pr?～?0.025 to Pr?～?70. We found that thermal dissipation takes place mostly on the border of the plume. Moreover, the rate of energy dissipation per unit mass ε _T has a critical point around Pr?～?0.7. The reason is that at Pr greater than ～0.7, buoyancy dominates inertia and thermal advection dominates wave formation whereas this trend is reversed at Pr less than ～0.7. We also found that for large enough Prandtl number (Pr?～?70), the velocity field is mostly poloidal although this result was known for Rayleigh–Bénard convection (see Schmalzl et al. [On the validity of two-dimensional numerical approaches to time-dependent thermal convection. Europhys. Lett. 2004, 67, 390--396]). On the other hand, at small Prandtl numbers, the plume has a large helicity at large scale and a non-negligible toroidal part. Finally, as observed recently in details in weakly compressible turbulent thermal plume at Pr?=?0.7 (see Plourde et al. [Direct numerical simulations of a rapidly expanding thermal plume: structure and entrainment interaction. J. Fluid Mech. 2008, 604, 99--123]), we also noticed a two-time cycle in which there is entrainment of some of the external fluid to the plume, this process being most pronounced at the base of the plume. We explain this as a consequence of calculated Richardson number being unity at Pr?=?0.7 when buoyancy balance inertia.     

基于重力卫星数据监测地表质量变化的三维点质量模型法

利用卫星重力测量手段监测全球质量变化取得了巨大成功,本文基于牛顿万有引力定律在三维空间直角坐标系中导出利用重力卫星观测数据监测全球质量变化的三维点质量模型法,该方法可直接利用重力卫星的轨道和星间观测数据或时变重力场模型计算全球质量变化,由于利用卫星观测数据计算地表质量变化的向下延拓过程以及观测数据噪声的影响,需要采用合适的空间约束方程或正则化技术对解算结果进行约束或平滑处理.利用合成全球质量变化模型模拟一个月的GRACE双星轨道和星间距离变率数据计算全球质量变化,对三维点质量模型法进行分析验证,采用零阶Tikhonov正则化技术处理病态问题.结果表明,三维点质量模型法可有效用于重力卫星观测数据监测全球质量变化,为利用重力卫星观测数据监测全球质量变化提供一种可选的途径.

     

Plume-induced geoid anomalies from 2D axi-symmetric temperature- and pressure-dependent mantle convection models

A collection of numerical simulations of 2D axi-symmetric thermal convection is presented here. The aim is to investigate the shape of geoid anomalies and dynamic topography above a plume. The simulation is based on the Boussinesq approximation and infinite Prandtl number and is carried out in the spherical shell with strongly temperature- and depth-dependent Arrhenius-type viscosity. According to the Arrhenius law, plume models with purely depth-dependent rheology are unphysical and should be taken with care. The strongly coupled temperature- and depth-dependent viscosity enables us to better understand the plume's behavior inside the Earth.The topography and geoid anomalies produced from plumes are sensitive to rheology of the mantle and rheology of the plume; both have effects on shape and amplitude of the geoid anomalies. We determined different categories of the geoid which are related to various rheology. Depth-dependent viscosity models show a geoid with a negative sign above the plume, and temperature-dependent viscosity models depict a bell-shaped geoid. We identified different behaviors in the combined model with temperature- and pressure-dependent viscosity.     

Statistical equilibrium distributions of baroclinic vortices in a rotating two-layer model at low Froude numbers

The point-vortex equilibrium statistical model of two-layer baroclinic quasigeostrophic vortices in an unbounded f-plane is examined. A key conserved quantity, angular momentum, serves to confine the vortices to a compact domain, thereby justifying the statistical mechanics model, and also eliminating the need for boundary conditions in a practical method for its resolution. The Metropolis method provides a fast and efficient algorithm for solving the mean field non-linear elliptic PDEs of the equilibrium statistical theory. A verification of the method is done by comparison with the exact Gaussian solution at the no interaction limit of zero inverse temperature. The numerical results include a geophysically and computationally relevant power law for the radii at which the most probable vortex distribution is non-vanishing: For fixed total circulation, and fixed average angular momentum, the radii of both layers are proportional to the square root of the inverse temperature β. By changing the chemical potentials μ of the runs, one is able to model the most probable vorticity distributions for a wide range of total circulation and energy. The most probable vorticity distribution obtained at low positive temperatures are consistently close to a radially symmetric flat-top profiles. At high temperatures, the radially symmetric vorticity profiles are close to the Gaussian distribution.     

Surface deformation and gravity changes caused by dilatancy in a layered elastic-vis-coelastic half space

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On the upper bounding approach to thermal convection at moderate rayleigh numbers

Abstract

Two upper bounding problems for thermal convection in a layer of fluid contained between perfectly conducting stress-free boundaries are treated numerically. Since the Euler equations resulting from this variational approach are simpler than the Navier-Stokes equations, they allow numerical calculations to be carried out economically to fairly large values of the Rayleigh number. The upper bounding problem formulated by Howard (1963), which yields a Nusselt number independent of Prandtl number, diverges from the correct behavior as the Rayleigh number increases. In hopes of coming closer to results of previous investigations of the Boussinesq equations of motion, a more restrictive upper bounding problem is formulated. For large Prandtl numbers the momentum equation is linearized and is used as an explicit side constraint on the variational problem, thereby forcing the solutions to more closely resemble the solutions of the Boussinesq equations. Numerical calculations at values of the Rayleigh number up to 1.5 × 10⁵ indicate that the additional constraint decreases the upper bound on the Nusselt number; it appears that this upper bound differs by only a multiplicative factor from that calculated from solutions of the full equations of motion and may be a reasonable approximation for large Rayleigh numbers.     

VHF radar observations of gravity waves at a low latitude

Wind observations made at Gadanki (13.5°N) by using Indian MST Radar for few days in September, October, December 1995 and January, 1996 have been analyzed to study gravity wave activity in the troposphere and lower stratosphere. Horizontal wind variances have been computed for gravity waves of period (2–6) h from the power spectral density (PSD) spectrum. Exponential curves of the form e^Z/H have been fitted by least squares technique to these variance values to obtain height variations of the irregular winds upto the height of about 15 km, where Z is the height in kilometers. The value of H, the scale height, as determined from curve fitting is found to be less than the theoretical value of scale height of neutral atmosphere in this region, implying that the waves are gaining energy during their passage in the troposphere. In other words, it indicates that the sources of gravity waves are present in the troposphere. The energy densities of gravity wave fluctuations have been computed. Polynomial fits to the observed values show that wave energy density increases in the troposphere, its source region, and then decreases in the lower stratosphere.     

A precise gravimetric geoid model in a mountainous area with scarce gravity data: a case study in central Turkey

In mountainous regions with scarce gravity data, gravimetric geoid determination is a difficult task that needs special attention to obtain reliable results satisfying the demands, e.g., of engineering applications. The present study investigates a procedure for combining a suitable global geopotential model and available terrestrial data in order to obtain a precise regional geoid model for Konya Closed Basin (KCB). The KCB is located in the central part of Turkey, where a very limited amount of terrestrial gravity data is available. Various data sources, such as the Turkish digital elevation model with 3 ?? × 3?? resolution, a recently published satellite-only global geopotential model from the Gravity Recovery and Climate Experiment satellite (GRACE) and the ground gravity observations, are combined in the least-squares sense by the modified Stokes?? formula. The new gravimetric geoid model is compared with Global Positioning System (GPS)/levelling at the control points, resulting in the Root Mean Square Error (RMS) differences of ±6.4 cm and 1.7 ppm in the absolute and relative senses, respectively. This regional geoid model appears to be more accurate than the Earth Gravitational Model 2008, which is the best global model over the target area, with the RMS differences of ±8.6 cm and 1.8 ppm in the absolute and relative senses, respectively. These results show that the accuracy of a regional gravimetric model can be augmented by the combination of a global geopotential model and local terrestrial data in mountainous areas even though the quality and resolution of the primary terrestrial data are not satisfactory to the geoid modelling procedure.     

孕震过程中重力位、重力、重力梯度变化的数值模拟研究

简要介绍了为探索和解释地震前后重力变化的各种孕震模式,推导了由孕震引起的密度变化和位移与地面重力位、重力、重力梯度之间的变化关系。摸拟计算了孕震位移和密度变化引起的重力位、重力、重力梯度变化的空间分布并分析了重力位、重力、重力梯度变化的空间分布特征。与此同时,采用广义司托克斯云积分和有限差分方法对云南丽江7. 0级地震前重力位、重力、重力水平梯度进行了计算。结果表明,强震前重力位、重力、重力梯度有其自身的变化特征,这对预测强震有实际意义。     

Surface deformation at the Krafla volcano,North Iceland, 1982–1992

Extensive measurements of ground deformation at the Krafla volcano, Iceland, have been made since the beginning in 1975 of a series of eruptions and intrusions into the fissure system that extends north and south of the volcano. I concentrate on measurements before and after the eruption of September 1984, the last event of this series when the largest volume of lava was erupted. The patterns of ground deformation associated with the 1984 eruption, determined by precision levelling, electronic distance measurements and lake level observations, were similar to earlier intrusions and eruptions, in that the surface of the volcano subsided and the fissure system widened as magma moved laterally from a shallow central reservoir into the fissure system. The shallow magma reservoir of Krafla continued to expand for about five years after the eruption, but a slow subsidence of the central area began in 1989. Besides the presence of an inflating and deflating shallow magma reservoir at a depth of 2.5 km beneath the Krafla caldera, another inflating magma reservoir may exist at much greater depth below Krafla. The accumulation of compressive strain by numerous rift intrusions and eruptions since 1975 along the flanks of the north-south Krafla fissure swarm is being released slowly and will probably be reflected in the results of deformation measurements near Krafla for the next several decades. The total horizontal extension of the Krafla rift system in 1975–1984 was about 9 m, equal to about 500 years of constant plate divergence. The extension is twice the accumulated divergence since previous rifting events and eruptions in 1724–1729     

Long-term crustal deformation monitored by gravity and space techniques at Medicina, Italy and Wettzell, Germany

Series of gravity recordings at the stations Medicina (Italy) and Wettzell (Germany) are investigated to separate seasonal gravity variations from long-term trends in gravity. The findings are compared to height variations monitored by continuous GPS observations. To study the origin of these variations in height and gravity the environmental parameters at the stations are included in the fact finding. In Medicina, a clear seasonal signal is visible in the gravity and height data series, caused by seasonal fluctuations in the atmosphere including mass redistribution, the ocean, groundwater but also by geo-mechanical effects such as soil consolidation and thermal expansion of the structure supporting the GPS antenna. In Wettzell, no seasonal effect could be clearly identified, and the long-term trend in gravity is mainly caused by ground water variations. The successful combination of height and gravity series with the derived ratio of gravity to height changes indicates that the long-term trends in height and gravity are most likely due to mass changes rather than to tectonic movements.     

从重力场识别与提取地壳变形带信息的方法研究

表面形貌识别是指用具体的参数表征表面各区段几何形态及属性并最终对不同类型的表面形貌进行识别,表面刻痕识别是其中的一种.以随机过程理论为基础的表面刻痕识别技术可以确切地识别表面形貌的各项特征,其各阶谱矩及统计不变量可以对表面的刻痕以及各向异性进行详细地刻画.区域重力场上的各向异性刻痕主要反映地壳线状变形带,它们常常是区域大地构造单元的边界.本文用重力场研究地壳变形带信息识别方法,将二阶谱矩、统计不变量等参数赋予一定的地质构造含义,并定义了脊形化系数、边界脊形化系数等,从而更详细地表征地壳变形带及大陆构造单元边界信息.理论模型与实际数据试验结果均表明,地壳变形带信息识别方法不但对重力场上地壳变形产生的线形刻痕进行了有效的刻画,而且提取出的刻痕信息,可为大陆构造单元划分提供客观依据.