基于配置法的局部重力场延拓模型构建与应用分析

在大地坐标系下利用Forsberg局部扰动位协方差模型（即DPM模型）导出了实用的局部重力异常协方差模型（即GAC模型）和局部扰动重力协方差模型（即GDC模型）,两种模型形式完全一致.针对GAC模型,提出了两种模型参数的拟合方法,即按照泊松积分向上延拓获得的不同高度数据进行拟合以及按照测量区域的平面实测数据进行拟合,通过某地区的实测数据检验得出两种参数拟合方法得到的参数值相差不大,这种差别在向上和向下延拓过程中的影响可以忽略.依据本文的算例,GAC模型作为配置法的协方差模型用于延拓时,其向上延拓的精度在1.8×10^－5 m·s^-2左右,向下延拓的精度在5×10^－5 m·s^-2左右,完全满足局部重力场在中等山区的延拓要求.通过对不同高度下GAC模型用于延拓效果的对比,可以得出基于GAC模型的延拓精度随着高度的增加而衰减,在满足测量精度要求下其最大向下延拓高度约为7 km.总体而言,本文推导的GAC模型能够很好地利用地形数据,较好地满足了航空重力测量在局部重力场的延拓要求.     

Adsorption of Cadmium Ions from Aqueous Solution Using Granular Activated Carbon and Activated Clay

The present study was aimed at removing cadmium ions from aqueous solution through batch studies using adsorbents, such as, granular activated carbon (GAC) and activated clay (A‐clay). GAC was of commercial grade where as the A‐clay was prepared by acid treatment of clay with 1 mol/L of H₂SO₄. Bulk densities of A‐clay and GAC were 1132 and 599 kg/m³, respectively. The surface areas were 358 m²/g for GAC and 90 m²/g for A‐clay. The adsorption studies were carried out to optimize the process parameters, such as, pH, adsorbent dosage, and contact time. The results obtained were analyzed for kinetics and adsorption isotherm studies. The pH value was optimized at pH 6 giving maximum Cd removal of 84 and 75.2% with GAC and A‐clay, respectively. The adsorbent dosage was optimized and was found to be 5 g/L for GAC and 10 g/L for A‐clay. Batch adsorption studies were carried out with initial adsorbate (Cd) concentration of 100 mg/L and adsorbent dosage of 10 g/L at pH 6. The optimum contact time was found to be 5 h for both the adsorbents. Kinetic studies showed Cd removal a pseudo second order process. The isotherm studies revealed Langmuir isotherm to better fit the data than Freundlich isotherm.     

Adsorption Characteristics of β‐Ionone in Water on Granular Activated Carbon

The adsorption performance of β‐ionone on four types of granular activated carbon (GAC) in water was investigated through batch experiments. The effect of initial β‐ionone concentrations and natural organic matter (NOM) adsorbed on GAC, adsorption kinetic and isothermal models were also studied. The results showed that four types of GAC all had good adsorption performance for β‐ionone, the equilibrium adsorption amount of the GAC employed was in the order of YK > GK > MZ‐A > MZ‐B. The adsorption amount increased with increasing initial concentrations. The presence of NOM could reduce adsorption of β‐ionone to a certain extent, and small molecular weight (MW) fractions (particularly <1000 Da) exhibited a remarkably competitive effect on the adsorption of β‐ionone. The experimental data showed good correlation with pseudo‐first‐order model. Furthermore, adsorption of β‐ionone on GAC fitted Freundlich, Langmuir, and Tempkin isotherms in the range of experimental concentrations, but followed Freundlich isothermal model most appropriate. The thermodynamic parameters were calculated by the results of the experiment, which showed adsorption of β‐ionone on GAC as being endothermic and spontaneous.     

基于随温度变化的热系数模拟板块俯冲动力学过程

热传导系数和热膨胀系数是影响板块俯冲动力学过程的两个重要参数. 由于地球介质的不均匀性,热系数也会随深度发生变化.然而,这种变化在地球动力学模拟研究中往往被忽略.本文针对随温度变化的热传导系数和热膨胀系数, 模拟板块俯冲的动力学过程,分析热系数、黏度对板块俯冲形态的影响及其对应的地幔对流特征.结果表明,依温度变化的热传导系数和热膨胀系数会影响地幔温度及黏度分布,进而改变板块的俯冲角度;黏度是控制板块俯冲动力学演化过程的重要因素;地幔对流受黏度结构的影响,呈现分层对流及局部多个对流环等多种不同形态的对流场特征.      

On a spectral method of solving the Stokes equation

A method of solving the Stokes equation for a spherical mantle model by expansion in spherical harmonics was developed by Hager and O’Connell [1979]. However, this method is applicable only if the viscosity depends solely on depth. In this case, the Stokes equation reduces to a system of independent equations for each harmonic. Given lateral variations in viscosity, the Stokes equation contains terms in the form of products of harmonics, which invalidates all advantages of harmonic expansion. Zhang and Christensen [1993] developed a perturbation method for the case when terms containing products of lateral viscosity variations are small. These terms are first calculated from the preceding iteration and are then expanded in a series of harmonic functions. As a result, equations for harmonics remain independent. An evident advantage of the spectral method is the simplicity of the technique of incorporating the self-gravitation and compressibility effects. Moreover, this method partially eliminates difficulties related to the singularities at poles. As yet, it has not been applied in practice, possibly because the equations presented in [Zhang and Christensen, 1993] contain misprints that have not been elucidated in the literature. In the present work, a system of equations is derived for the spectral-iterative method of solving the Stokes equation and the errata present in formulas of Zhang and Christensen [1993] and significantly affecting results of calculations are analyzed.     

Adsorption of Two Taste and Odor Compounds IPMP and IBMP by Granular Activated Carbon in Water

Granular activated carbon (GAC) adsorption of two representative taste and odor (T & O) compounds, 2‐isopropyl‐3‐methoxy pyrazine (IPMP), and 2‐isobutyl‐3‐methoxy pyrazine (IBMP), in drinking water was investigated. Results show that the modified Freundlich equation best fit the experimental data during the adsorption isotherm tests, and the pseudo first‐order kinetics and intra‐particle diffusion kinetics well described the adsorption kinetics pattern. The calculated thermodynamic parameters (ΔH⁰, ΔS⁰, and ΔG⁰) indicated a spontaneous and endothermic adsorption process. Factors affecting the treatment efficiency were carefully evaluated. Acidic and alkaline conditions both favored GAC adsorption of IPMP and IBMP, especially the former. With the GAC dosage increasing, the first order adsorption rates increased, while the intra‐particle adsorption rates decreased. Within 12 h, 200 mg/L GAC could remove >90% of 150 µg/L IPMP and IBMP via adsorption at pH 3–11. Therefore, GAC is a promising treatment technology to control the T & O compounds associated water pollution.     

Removal of Selenium by Adsorption onto Granular Activated Carbon (GAC) and Powdered Activated Carbon (PAC)

The present work involves the study of Se(IV) adsorption onto granular activated carbon (GAC) and powdered activated carbon (PAC). The adsorbents are coated with ferric chloride solution for the effective removal of selenium. The physico-chemical characterization of the adsorbents is carried out using standard methods, e. g., proximate analysis, scanning electron microscopy (SEM), fourier transform infrared spectroscopy (FTIR), thermo-gravimetric (TGA) and differential thermal analysis (DTA), etc. The FTIR spectra of the GAC and PAC indicate the presence of various types of functional groups, e. g., free and hydrogen bonded OH groups, silanol groups (Si-OH), alkenes, and CO group stretching from aldehydes and ketones on the surface of adsorbents. Batch experiments are carried out to determine the effect of various factors such as adsorbent dose (w), initial pH, contact time (t), and temperature (T) on the adsorption process. The optimum GAC and PAC dosage is found to be 10 g/L and 8 g/L, respectively, for Se(IV) removal with C₀ = 100 mg/L. The percent removal of Se(IV) increases with increasing adsorbent concentration, while removal per unit weight of adsorbent increases with decreasing adsorbent concentration. Se(IV) adsorption onto both the GAC and PAC adsorbents is high at low pH values, and decreases with increased initial pH. The results obtained are analyzed by various kinetic models. The parameters of pseudo-first order, pseudo-second order kinetics, and Weber-Morris intra particle kinetics are determined. It is seen that the sorption kinetics of Se(IV) onto GAC and PAC can be best represented by the pseudo-second order kinetic model.     

Application of a spectral model to the calculation of wind drift currents in an idealized stratified sea

The solution of the hydrodynamic equations describing wind drift currents in an idealized stratified sea is developed using a modal expansion in the vertical. The influence of the magnitude of wind induced surface eddy viscosity, within the surface mixed layer, and reduced eddy viscosity at depth associated with a stable pycnocline, upon wind induced current structure is examined.Changes in modal structure with eddy viscosity, mixed layer depth, pycnocline thickness and total water depth are considered. It is evident from the modal equations that the time variation of the contribution of each mode to current structure is determined by the modal eigenvalue, mean eddy viscosity, water depth and the vertical integral of the mode squared.Calculations show that the magnitude and direction of steady state surface currents under strongly stratified conditions, are significantly influenced by mixed layer depth and pycnocline thickness. Surface eddy viscosity is also important, and in weakly stratified conditions eddy viscosity within and below the pycnocline influences surface current.The presence of a thin near surface ‘wall layer’ is shown to influence significantly the direction of surface current, but to have little effect upon currents below this surface layer.     

A modal α2-dynamo in the limit of asymptotically small viscosity

Abstract

A spherical α²-dynamo is presented as an expansion in the free decay modes of the magnetic field. In the limit of vanishing viscosity the momentum equation yields various asymptotic expansions for the flow, depending on the precise form of the dissipation and boundary conditions applied. A new form for the dissipation is introduced that greatly simplifies this asymptotic expansion. When these expansions are substituted back into the induction equation, a set of modal amplitude equations is derived, and solved for various distributions of the α-effect. For all choices of α the solutions approach the Taylor state, but the manner in which this occurs can vary, as previously found by Soward and Jones (1983). Furthermore, as hypothesized by Malkus and Proctor (1975), but not previously demonstrated, the post-Taylor equilibration is indeed independent of the viscosity in the asymptotic limit, and depending on the choice of a may be either steady-state or oscillatory.     

Remediation of the Wells G & H Superfund Site,Woburn, Massachusetts

Remediation of ground water and soil contamination at the Wells G & H Superfund Site, Woburn, Massachusetts, uses technologies that reflect differences in hydrogeologic settings, concentrations of volatile organic compounds (VOCs), and costs of treatment. The poorly permeable glacial materials that overlie fractured bedrock at the W.R. Grace property necessitate use of closely spaced recovery wells. Contaminated ground water is treated with hydrogen peroxide and ultraviolet (UV) oxidation. At UniFirst, a deep well completed in fractured bedrock removes contaminated ground water, which is treated by hydrogen peroxide, UV oxidation, and granular activated carbon (GAC). The remediation system at Wildwood integrates air sparging, soil-vapor extraction, and ground water pumping. Air stripping and GAC are used to treat contaminated water; GAC is used to treat contaminated air. New England Plastics (NEP) uses air sparging and soil-vapor extraction to remove VOCs from the unsaturated zone and shallow ground water. Contaminated air and water are treated using separate GAC systems. After nine years of operation at W.R. Grace and UniFirst, 30 and 786 kg, respectively, of VOCs have been removed. In three years of operation, 866 kg of VOCs have been removed at Wildwood. In 15 months of operation, 36 kg of VOCs were removed at NEP. Characterization work continues at the Olympia Nominee Trust, Whitney Barrel, Murphy Waste Oil, and Aberjona Auto Parts properties. Risk assessments are being finalized that address heavy metals in the floodplain sediments along the Aberjona River that are mobilized from the Industri-Plex Superfund Site located a few miles upstream.     

Treatment of Arsenic Contaminated Groundwater Using Calcium Impregnated Granular Activated Carbon in a Batch Reactor: Optimization of Process Parameters

This paper is an experimental investigation into the removal of arsenic species from simulated groundwater by adsorption onto Ca²⁺ impregnated granular activated carbon (GAC‐Ca) in the presence of impurities like Fe and Mn. The effects of adsorbent concentration, pH and temperature on the percentage removal of total arsenic (As(T)), As(III) and As(V) have been discussed. Under the experimental conditions, the optimum adsorbent concentration of GAC‐Ca was found to be 8 g/L with an agitation time of 24 h, which reduced As(T) concentration from 188 to 10 μg/L. Maximum removal of As(V) and As(III) was observed in a pH range of 7–11 and 9–11, respectively. Removal of all the above arsenic species decreased slightly with increasing temperature. The presence of Fe and Mn increased the adsorption of arsenic species. Under the experimental conditions at 30°C, the maximum percentage removals of As(T), As(III), As(V), Fe, and Mn were found to be ca. 94.3, 90.6, 98.0, 100 and 63%, respectively. It was also observed that amongst the various regenerating liquids used, a 5 N H₂SO₄ solution exhibited maximum regeneration (ca. 91%) of the spent GAC‐Ca.     

The effect of cracks on the thermal expansion of rocks

Thermal expansion during the first heating cycle at atmospheric pressure was measured in several directions in seven igneous rocks between 25° and 400°C at slow heating rates. The coefficient of thermal expansion measured under these conditions increases more rapidly as temperature is increased than the average thermal expansion coefficient of the constituent minerals. The “extra” expansion is attributed to the formation of cracks by differential expansion of mineral grains. The presence of such cracks in the rocks during the cooling part of the cycle and during any subsequent heating and cooling cycles will result in a substantial decrease in the coefficient of thermal expansion as compared to that measured during the first heating cycles. The effect of cracks initially present in a rock was studied by measuring the full tensor of the coefficient of thermal expansion on two rocks with anisotropic crack distributions. In these two rocks the coefficient of thermal expansion is least in the direction perpendicular to the plane of greatest crack concentration. The implication of our data is that thermal expansion depends greatly on the fracture state of the rock. Both the fractures in the rock and the boundary conditions on the rock are significant for the interpretation of thermal expansion measurements and for their application to other problems.     

Analytical models for bubble growth during decompression of high viscosity magmas

Analytical models for decompressional bubble growth in a viscous magma are developed to establish the influence of high magma viscosity on vesiculation and to assess the time-scales on which bubbles respond to decompression. Instantaneous decompression of individual bubbles, analogous to a sudden release of pressure (e.g. sector collapse), is considered for two end-member cases. The infinite melt model considers the growth of an isolated bubble before significant bubble interaction occurs. The shell model considers the growth of a bubble surrounded by a thin shell and is analogous to bubble growth in a highly vesicular magmatic foam. Results from the shell model show that magmas less viscous than 10⁹ Pa s can freely expand without developing strong overpressures. The timescales for pressure re-equilibration are shortened by increased ratios of bubble radius to shell thickness and by larger decompression. Time-scales for isolated bubbles in rhyolitic melts (infinite melt model) are significantly longer, implying that such bubbles could experience internal pressures greater than the ambient pressure for at least a few hours following a sudden release of pressure. The shell model is developed to assess bubble growth during the linear decompression of a magma body of constant viscosity. For the range of decompression rates and viscosities associated with actual volcanic eruptions, bubble growth continues at approximately the equilibrium rate, with no attendant excess of internal pressure. The results imply that viscosity does not have any significant role in preventing the explosive expansion of high viscosity foams. However, for viscosities of >10⁹ Pa s there is the potential for a viscosity quench under the extreme decompression rates of an explosive eruption. It is proposed that the typical vesicularities of pumice of 0.7–0.8 are a consequence of the viscosity of the degassing magmas becoming sufficiently high to inhibit bubble expansion over the characteristic time-scale of eruption. For fully degassed silicic lavas with viscosities in the range 10¹⁰ to 10¹² Pa s time-scales for decompression of isolated bubbles can be hours to many months.     

Effect of sediment particles on the velocity profile of sediment-water mixtures in open-channel flow

The presence of sediment particles in open-channel flow has an important effect on turbulence; thus, an empirical, turbulent eddy viscosity formula was established for application in the limit for low concentrations. The current study establishes a theoretical relation for the mixture viscosity based on the two-phase mixture model. The percentage contribution of the three mechanisms of mixture viscosity,namely, fluid turbulence(FT), particle turbulence(PT), and inter-particle collisions(IPCs), w...     

A numerical model for simulation of fluid mud with different rheological behaviors

In this paper, a three-dimensional isopycnal approach is presented to simulate the dynamics of fluid mud covering the formation, development, transport, and disappearance of fluid mud. The basic assumption is the assignment of the fluid’s density as the indicating parameter for the rheological behavior. Considering stable stratification, as is usually the case for fluid mud, layers of constant density discretize the vertical domain. The non-Newtonian dynamics of fluid mud is simulated by solving the Cauchy equations for general continuum dynamics. Instead of using a turbulent viscosity approach, the viscosity is allowed to vary according to the rheological behavior of mud suspensions. This apparent viscosity can be determined for different rheological formulations in dependence of the volume solid fraction and the shear rate. An existing three-dimensional isopycnal hydrodynamic model was extended for vertical mass transport processes and was applied on a schematic system with hindered settling. For including the rheological behavior of fluid mud, the Worrall–Tuliani approach was parameterized and implemented. The resulting flow behavior is shown on a model application of fluid mud layers moving down an inclined plane. With these changes, it is demonstrated that the isopycnal model is capable of simulating fluid mud dynamics.     

New Perspectives on Mantle Dynamics from High-resolution Seismic Tomographic Model P1200

—Recently a high-resolution tomographic model, the P1200, based on P-wave travel times was developed, which allowed for detailed imaging of the top 1200 km of the mantle. This model was used in diverse ways to study mantle viscosity structure and geodynamical processes. In the spatial domain there are lateral variations in the transition zone, suggesting interaction between the lower-mantle plumes and the region from 600 km to 1000 km. Some examples shown here include the continental region underneath Manchuria, Ukraine and South Africa, where horizontal structures lie above or below the 660 km discontinuity. The blockage of upwelling is observed under central Africa and the interaction between the upwelling and the transition zone under the slow Icelandic region appears to be complex. An expansion of the aspherical seismic velocities has been taken out to spherical harmonics of degree 60. For degrees exceeding around 10, the spectra at various depths decay with a power-law like dependence on the degree, with the logarithmic slopes in the asymptotic portion of the spectra containing values between 2 and 2.6. These spectral results may suggest the time-dependent nature of mantle convection. Details of the viscosity structure in the top 1200 km of the mantle have been inferred both from global and regional geoid data and from the high-resolution tomographic model. We have considered only the intermediate degrees (l = 12–25) in the nonlinear inversion with a genetic algorithm approach. Several families of acceptable viscosity profiles are found for both oceanic and global data. The families of solutions for the two data sets have different characteristics. Most of the solutions asociated with the global geoid data show the presence of asthenosphere below the lithosphere. In other families a low viscosity zone between 400 and 600 km depth is found to lie atop a viscosity jump. Other families evidence a viscosity decrease across the 660 km discontinuity. Solutions from oceanic geoid show basically two low viscosity zones one lying right below the lithosphere; the other right under 660-km depth. All of these results bespeak clearly the plausible existence of strong vertical viscosity stratification in the top 1000 km of the mantle. The presence of the second asthenosphere may have important dynamical ramifications on issues pertaining to layered mantle convection. Numerical modelling of mantle convection with two phase transitions and a realistic temperature- and pressure-dependent viscosity demonstrates that a low viscosity region under the endothermic phase transition can indeed be generated self-consistently in time-dependent situations involving a partially layered configuration in an axisymmetric spherical-shell model.     

Dynamics of a spherical viscoelastic shell: Implications to a criterion for fragmentation/expansion of bubbly magma

This paper investigates dynamics of a spherical bubble surrounded by a viscoelastic fluid. The purpose of the study is to understand the parameters which control expansion and fragmentation of bubbly magma by decompression. In particular, we focus on which occurs first, fragmentation or expansion. Supposing that rupture of the bubble wall occurs in a critical stress condition, we calculate the change of the bubble radius and tensile stress at the bubble wall for various decompression rates. Conditions in which tensile stress is stored in the shell are represented in terms of dimensionless parameters. The results are interpreted as follows: when magma viscosity is larger than a critical value, and the decompression time is shorter than viscous expansion time, tensile stress is stored before expansion; when magma viscosity is smaller than the critical value, tensile stress is not stored, no matter how rapid the decompression. Although it is a generally accepted theory that fragmentation is effected by stress conditions and decompression time, exactly how decompression time (t₁) effects the fragmentation is not yet fully understood. This study demonstrates that the stress condition is controlled by the length of the decompression time not relative to the viscoelastic relaxation time (t₁ / τ), but relative to the viscous expansion time (t₁ / τ^l_rlx). As suggested by recent experimental studies, the decompression time relative to viscoelastic relaxation time (t₁ / τ) is also significant to the fragmentation process itself. It indicates that the decompression time effects the fragmentation not through the stress condition. However more work must be completed to fully understand the particular relationship between the decompression time and relaxation time in terms of its influence on fragmentation.     

Monitoring viscosity changes from time‐lapse seismic attenuation: case study from a heavy oil reservoir

Heating heavy oil reservoirs is a common method for reducing the high viscosity of heavy oil and thus increasing the recovery factor. Monitoring of these viscosity changes in the reservoir is essential for delineating the heated region and controlling production. In this study, we present an approach for estimating viscosity changes in a heavy oil reservoir. The approach consists of three steps: measuring seismic wave attenuation between reflections from above and below the reservoir, constructing time‐lapse Q and Q^?1 factor maps, and interpreting these maps using Kelvin–Voigt and Maxwell viscoelastic models. We use a 4D relative spectrum method to measure changes in attenuation. The method is tested with synthetic seismic data that are noise free and data with additive Gaussian noise to show the robustness and the accuracy of the estimates of the Q‐factor. The results of the application of the method to a field data set exhibit alignment of high attenuation zones along the steam‐injection wells, and indicate that temperature dependent viscosity changes in the heavy oil reservoir can be explained by the Kelvin–Voigt model.     

An implicit wave equation model for the shallow water equations

An implicit solution procedure for the wave equation form of the shallow water equations is presented. Efficiency is achieved through a Taylor expansion procedure applied to a time-varying matrix. This procedure allows matrix decompositions to be replaced by back substitutions. Isoparametric quadratic Lagrangian finite elements are employed for the spatial discretization. The Taylor expansion method is compared to different implicit and explicit solution procedures in an application to the southern part of the North Sea.     

Macrodynamics of α2 dynamos

Abstract

Two distributions of the α-effect in a sphere are considered. The inviscid limit is approached both by direct numerical solution and by solution of a simpler nonlinear eigenvalue problem deriving from asymptotic boundary layer analysis for the case of stress-free boundaries. The inviscid limit in both cases is dominated by the need to satisfy the Taylor constraint which states that the integral of the Lorentz force over cylindrical (geostrophic) contours in a homogeneous fluid must tend to zero. For a small supercritical range in α, this condition can only be met by magnetic fields which vanish as the viscosity goes to zero. In this range, the agreement of the two approaches is excellent. In a portion of this range, the method of finite amplitude perturbation expansion is useful, and serves as a guide for understanding the numerical results. For larger α, evidence from the nonlinear eigenvalue problem suggests both that the Taylor state exists, and that the transition from small to large amplitude can require a finite amplitude (oscillatory) instability in accord with the findings of Soward and Jones (1983). However, solutions of the full equations have not been found which are independent of viscosity at larger values of α.