Gravitational viscoelastic relaxation of eccentrically nested spheres

We present a semi-analytical solution to the 2-D forward modelling of viscoelastic relaxation in a heterogeneous model consisting of eccentrically nested spheres. Several numerical methods for 2-D and 3-D viscoelastic relaxation modelling have been applied recently, including finite-element and spectral-finite-difference schemes. The present semi-analytical approach provides a model response against which more general numerical algorithms can be validated. The eccentrically nested sphere solution has been tested by comparing it with the analytical solutions for viscoelastic relaxation in a homogeneous sphere and in two concentrically nested spheres, and good agreement was obtained.     

Post-seismic rebound of a spherical Earth: new insights from the application of the Post–Widder inversion formula

The post-seismic response of a viscoelastic Earth to a seismic dislocation can be computed analytically within the framework of normal-modes, based on the application of propagator methods. This technique, widely documented in the literature, suffers from several shortcomings; the main drawback is related to the numerical solution of the secular equation, whose degree increases linearly with the number of viscoelastic layers so that only coarse-layered models are practically solvable. Recently, a viable alternative to the standard normal-mode approach, based on the Post–Widder Laplace inversion formula, has been proposed in the realm of postglacial rebound models. The main advantage of this method is to bypass the explicit solution of the secular equation, while retaining the analytical structure of the propagator formalism. At the same time, the numerical computation is much simplified so that additional features such as linear non-Maxwell rheologies can be simply implemented. In this work, for the first time, we apply the Post–Widder Laplace inversion formula to a post-seismic rebound model. We test the method against the standard normal-mode solution and we perform various benchmarks aimed to tune the algorithm and to optimize computation performance while ensuring the stability of the solution. As an application, we address the issue of finding the minimum number of layers with distinct elastic properties needed to accurately describe the post-seismic relaxation of a realistic Earth model. Finally, we demonstrate the potentialities of our code by modelling the post-seismic relaxation after the 2004 Sumatra–Andaman earthquake comparing results based upon Maxwell and Burgers rheologies.     

Simulation of braided river flow using a new cellular routing scheme

Results are presented from a numerical simulation of two-dimensional flow patterns in a braided river using a simple cellular routing scheme. The results of the routing scheme are compared with field measurements of discharge per unit width obtained within the study reach at low flow and, for higher flows, with the predictions of a more sophisticated hydraulic model that solves the two-dimensional shallow water form of the Navier–Stokes equations. An assessment is made of the sensitivity of the routing scheme to variations in the values of its main parameters, and appropriate values are determined based on the physical characteristics of the study site and available flow measurements. It is shown that despite the simple approach adopted by the cellular routing scheme to simulate processes of water redistribution, it is able to replicate accurately both the field data and the results of the more sophisticated hydraulic model. These results indicate that the routing scheme outlined here is able to overcome some of the limitations of previous simple cellular automata models and may be suitable for use in modelling bedload transport and channel change in complex fluvial environments. As such this research represents a small and ongoing contribution to the field of numerical simulation of braided river processes.     

Geoelectromagnetic induction in a heterogeneous sphere:a new three-dimensional forward solver using a conservative staggered-grid finite difference method

A conservative staggered-grid finite difference method is presented for computing the electromagnetic induction response of an arbitrary heterogeneous conducting sphere by external current excitation. This method is appropriate as the forward solution for the problem of determining the electrical conductivity of the Earth's deep interior. This solution in spherical geometry is derived from that originally presented by Mackie et al. (1994 ) for Cartesian geometry. The difference equations that we solve are second order in the magnetic field H , and are derived from the integral form of Maxwell's equations on a staggered grid in spherical coordinates. The resulting matrix system of equations is sparse, symmetric, real everywhere except along the diagonal and ill-conditioned. The system is solved using the minimum residual conjugate gradient method with preconditioning by incomplete Cholesky decomposition of the diagonal sub-blocks of the coefficient matrix. In order to ensure there is zero H divergence in the solution, corrections are made to the H field every few iterations. In order to validate the code, we compare our results against an integral equation solution for an azimuthally symmetric, buried thin spherical shell model ( Kuvshinov & Pankratov 1994 ), and against a quasi-analytic solution for an azimuthally asymmetric configuration of eccentrically nested spheres ( Martinec 1998 ).     

An Analytic Model For A Mantle Plume Fed By A Boundary Layer

Summary. An approximate analytical solution for flow in a mantle plume of constant radius, viscosity, and density contrast is obtained in cylindrical coordinates. the differential equations for vertical velocity of the mantle surrounding the plume and for topography are homologous to the equation for flexure of an elastic plate. Although the model is too simple to be fully applicable to the Earth, one can conclude that the vertical velocity in the mantle changes significantly away from plumes, that the viscosity of the plume is important for controlling flow rate, and that the long-wavelength geoid anomalies are sensitive to the viscosity of the surrounding mantle. the first induced upwelling away from a plume is quite weak and unlikely to control the spacing of plumes.     

Length scales, patterns and origin of azimuthal seismic anisotropy in the upper mantle as mapped by Rayleigh waves

We measure the degree of consistency between published models of azimuthal seismic anisotropy from surface waves, focusing on Rayleigh wave phase-velocity models. Some models agree up to wavelengths of ∼2000 km, albeit at small values of linear correlation coefficients. Others are, however, not well correlated at all, also with regard to isotropic structure. This points to differences in the underlying data sets and inversion strategies, particularly the relative 'damping' of mapped isotropic versus anisotropic anomalies. Yet, there is more agreement between published models than commonly held, encouraging further analysis. Employing a generalized spherical harmonic representation, we analyse power spectra of orientational (2Ψ) anisotropic heterogeneity from seismology. We find that the anisotropic component of some models is characterized by stronger short-wavelength power than the associated isotropic structure. This spectral signal is consistent with predictions from new geodynamic models, based on olivine texturing in mantle flow. The flow models are also successful in predicting some of the seismologically mapped patterns. We substantiate earlier findings that flow computations significantly outperform models of fast azimuths based on absolute plate velocities. Moreover, further evidence for the importance of active upwellings and downwellings as inferred from seismic tomography is presented. Deterministic estimates of expected anisotropic structure based on mantle flow computations such as ours can help guide future seismologic inversions, particularly in oceanic plate regions. We propose to consider such a priori information when addressing open questions about the averaging properties and resolution of surface and body wave based estimates of anisotropy.     

Viscosity profile of the lower mantle

Summary. We determine the variation of effective viscosity η across the lower mantle from models of the Gibb's free energy of activation G * and the adiabatic temperature profile. The variation of G * with depth is calculated using both an elastic strain energy model, in which G * is related to the seismic velocities, and a model which assumes G * is proportional to the melting temperature. The melting temperature is assumed to follow Lindemann's equation. The adiabatic temperature profile is calculated from a model for the density dependence of the Grüneisen parameter. Estimates of η depend on whether the lower mantle is a Newtonian or power law fluid. In the latter case separate estimates of η are obtained for flow with constant stress, constant strain rate, and constant strain energy dissipation rate. For G * based on the melting temperature, increases in η with depth range from a factor of about 100 for Newtonian deformation or power-law flow with constant stress to about 5 for non-Newtonian deformation with constant strain rate. For G * based on elastic defect energy, increases in η with depth range from a factor of about 1500 for Newtonian deformation or power-law flow with constant stress to about 10 for non-Newtonian deformation with constant strain rate. Among these models, only a non-Newtonian lower mantle convecting with constant strain rate or constant strain energy dissipation rate is consistent with recent estimates of mantle viscosity from post-glacial rebound and true polar wander data.     

颠覆列车强风数值模式参数敏感性对比分析

新疆的三十里风区是著名的风口,兰新线和南疆铁路线横穿此地,时有列车被强风颠覆,对铁路运输影响很大,急需大风精细预报。数值模式中有许多参数,如何确定改进预报最显著的参数是个问题。采用MM5V3模式做模拟实验,设计3重嵌套,最小格距3km,用30″数字高程数据生成模式地形。分析表明,3km格距模式分辨率对地形有较为精确的表达。无论东西剖面还是南北剖面,3km所预报的风场更为详细,风速预报更准确;不仅可以预报出强的下坡风,亦可以预报出地形波列。对强风预报而言,模式水平分辨率是一个敏感因子。     

Two-dimensional modelling of subduction zone anisotropy with application to southwestern Japan

We present a series of 2-D numerical models of viscous flow in the mantle wedge induced by a subducting lithospheric plate. We use a kinematically defined slab geometry approximating the subduction of the Philippine Sea plate beneath Eurasia. Through finite element modelling we explore the effects of different rheological and thermal constraints (e.g. a low-viscosity region in the wedge corner, power law versus Newtonian rheology, the inclusion of thermal buoyancy forces and a temperature-dependent viscosity law) on the velocity and finite strain field in the mantle wedge. From the numerical flow models we construct models of anisotropy in the wedge by calculating the evolution of the finite strain ellipse and combining its geometry with appropriate elastic constants for effective transversely isotropic mantle material. We then predict shear wave splitting for stations located above the model domain using expressions derived from anisotropic perturbation theory, and compare the predictions to ∼500 previously published shear wave splitting measurements from seventeen stations of the broad-band F-net array located in southwestern Japan. Although the use of different model parameters can have a substantial effect on the character of the finite strain field, the effect on the average predicted splitting parameters is small. However, the variations with backazimuth and ray parameter of individual splitting intensity measurements at a given station for different models are often different, and rigorous analysis of details in the splitting patterns allows us to discriminate among different rheological models for flow in the mantle wedge. The splitting observed in southwestern Japan agrees well with the predictions of trench-perpendicular flow in the mantle wedge along with B-type olivine fabric dominating in a region from the wedge corner to about 125 km from the trench.     

Effect of 3-D viscoelastic structure on post-seismic relaxation from the 2004 M= 9.2 Sumatra earthquake

The 2004 M = 9.2 Sumatra–Andaman earthquake profoundly altered the state of stress in a large volume surrounding the ∼1400 km long rupture. Induced mantle flow fields and coupled surface deformation are sensitive to the 3-D rheology structure. To predict the post-seismic motions from this earthquake, relaxation of a 3-D spherical viscoelastic earth model is simulated using the theory of coupled normal modes. The quasi-static deformation basis set and solution on the 3-D model is constructed using: a spherically stratified viscoelastic earth model with a linear stress–strain relation; an aspherical perturbation in viscoelastic structure; a 'static' mode basis set consisting of Earth's spheroidal and toroidal free oscillations; a "viscoelastic" mode basis set; and interaction kernels that describe the coupling among viscoelastic and static modes. Application to the 2004 Sumatra–Andaman earthquake illustrates the profound modification of the post-seismic flow field at depth by a slab structure and similarly large effects on the near-field post-seismic deformation field at Earth's surface. Comparison with post-seismic GPS observations illustrates the extent to which viscoelastic relaxation contributes to the regional post-seismic deformation.     

Spectral-finite-element approach to two-dimensional electromagnetic induction in a spherical earth

We present a spectral-finite-element approach to the 2-D forward problem for electromagnetic induction in a spherical earth. It represents an alternative to a variety of numerical methods for 2-D global electromagnetic modelling introduced recently (e.g. the perturbation expansion approach, the finite difference scheme). It may be used to estimate the effect of a possible axisymmetric structure of electrical conductivity of the mantle on surface observations, or it may serve as a tool for testing methods and codes for 3-D global electromagnetic modelling. The ultimate goal of these electromagnetic studies is to learn about the Earth's 3-D electrical structure.
Since the spectral-finite-element approach comes from the variational formulation, we formulate the 2-D electromagnetic induction problem in a variational sense. The boundary data used in this formulation consist of the horizontal components of the total magnetic intensity measured on the Earth's surface. In this the variational approach differs from other methods, which usually use spherical harmonic coefficients of external magnetic sources as input data. We verify the assumptions of the Lax-Milgram theorem and show that the variational solution exists and is unique. The spectral-finite-element approach then means that the problem is parametrized by spherical harmonics in the angular direction, whereas finite elements span the radial direction. The solution is searched for by the Galerkin method, which leads to the solving of a system of linear algebraic equations. The method and code have been tested for Everett & Schultz's (1995) model of two eccentrically nested spheres, and good agreement has been obtained.     

地理学多视角研究方法——Braess网络车流分配过程的理论分析与数值计算

对复杂的地理系统采用多种方法从不同的视角开展分析,可以降低错误结论的概率。本文以Braess交通网络为例,提出一个地理系统多视角分析的研究案例。首先借助La氏乘数法预测奇对称Braess网络的车流优化分配的结果。然后采用数值计算和模拟方法论证,在该网络中,车流会通过自组织过程自动向着优化分配的方向演化,并且利用Markov链预测各个阶段的车流分配数值。最后借助最大熵原理从理论上证明,上述最优化过程的本质是地理系统的熵最大化;运用对偶规划和对称思想揭示,熵最大化的实质是车流运行的耗时总量最小。不同的方法给出的结果殊途同归、互相印证。这一套研究方法可以推广到多维不对称的交通网络,进而推广应用于地理学其他方面的理论分析和应用研究。     

Groundwater flow regime under natural conditions as inferred from past evidence and contemporary field observations in a semi-arid basin: Cuenca de la Independencia, Guanajuato, México

This study was carried out in the Cuenca de la Independencia, a semi-arid basin in Central Mexico. The objective is to describe the main features of a groundwater flow regime under natural conditions, based on groundwater discharge manifestations. Information obtained from paleoecological, paleontological, archaeological and historical data suggests that, prior to heavy development (starting in the 1950s), the hydrogeologic regime was characterized by a larger groundwater availability in a more humid and colder climate. Manifestations associated to groundwater discharges are springs, lagoons, wetlands, saline soils, chalcedony deposits, phreatophytes, thermalism, and artesianism. The different types of manifestations and their position in the basin indicate the influence of groundwater flow systems hierarchically nested, forming concentric zones at ground level. The groundwater flow regime corresponds to a classical gravity-induced flow system with generation of local, intermediate and regional patterns. Integrating several types of data to establish the flow geometry and its dynamics has proven a useful tool to increase understanding of the original groundwater regimes. This approach can also be applied in other over-exploited semi-arid basins.     

Groundwater flow regime under natural conditions as inferred from past evidence and contemporary field observations in a semi-arid basin: Cuenca de la Independencia,Guanajuato, México

This study was carried out in the Cuenca de la Independencia, a semi-arid basin in Central Mexico. The objective is to describe the main features of a groundwater flow regime under natural conditions, based on groundwater discharge manifestations. Information obtained from paleoecological, paleontological, archaeological and historical data suggests that, prior to heavy development (starting in the 1950s), the hydrogeologic regime was characterized by a larger groundwater availability in a more humid and colder climate. Manifestations associated to groundwater discharges are springs, lagoons, wetlands, saline soils, chalcedony deposits, phreatophytes, thermalism, and artesianism. The different types of manifestations and their position in the basin indicate the influence of groundwater flow systems hierarchically nested, forming concentric zones at ground level. The groundwater flow regime corresponds to a classical gravity-induced flow system with generation of local, intermediate and regional patterns. Integrating several types of data to establish the flow geometry and its dynamics has proven a useful tool to increase understanding of the original groundwater regimes. This approach can also be applied in other over-exploited semi-arid basins.     

A critical assessment of viscous models of trench topography and corner flow

Summary. We obtain stresses for Newtonian viscous flow in simple geometries (e.g. corner flow, bending flow) in order to study the effect of imposed velocity boundary conditions. Stress for a delta function velocity boundary condition decays as 1/ r ²; for a step function velocity, stress goes as 1/ r ; for a discontinuity in curvature, the stress singularity is logarithmic. For corner flow, which has a discontinuity of velocity at a certain point, the corresponding stress has a 1/ r singularity. However, for a more realistic circular-slab model, the stress singularity becomes logarithmic. Thus the stress distribution is very sensitive to the boundary conditions, and in evaluating the applicability of viscous models of trench topography it is essential to use realistic geometries.
Topography and seismicity data from northern Honshu, Japan, were used to construct a finite element model, with flow assumed constant speed and tangent to the top of the grid, for both Newtonian and non-Newtonian flow (power law 3 rheology). Normal stresses at the top of the grid are compared to the observed trench topography. There is poor agreement. Purely viscous models of subducting slabs with simple, geometrically consistent velocity boundary conditions do not predict normal stress patterns compatible with observed topography. Elasticity and plasticity appear to be important in determining trench topography.     

A COMPARISON OF HYDROLOGY AND VEGETATION BETWEEN A CHANNELIZED STREAM AND A NONCHANNELIZED STREAM IN WESTERN TENNESSEE

The purpose of this study was to provide baseline data on floodplain forest structure, composition, and function that would be needed to predict and monitor the consequences of a proposed stream restoration project. This project would involve the “dechannelization” of Stokes Creek, a stream in western Tennessee that was channelized and leveed in the first half of the 1900s. To this end, we collected data on surface hydrology, soil redox potential (Eh), and the structure and composition of the floodplain vegetation of Stokes Creek. To place our findings into a regional context, we also collected comparable vegetation data from plots located along a nonchannelized stream reach of the Wolf River near Moscow, Tennessee. While hydrologic fluctuations of floodplain sites were synchronous with river dynamics for the Wolf River, the hydrology of floodplain sites at Stokes Creek was constrained by the influence of beaver dams, backflooding, and ponding of overland flow behind levees. Consequently, composition of the forest overstory, understory, and herbaceous strata was significantly different between the two sites. For example, Stokes Creek had a noticeable lack of cypress and tupelo sites, and a greater abundance of red maple. Analyses of size-class structure and woody debris quantity reinforced the existing differences between the more natural and human-impacted systems. While the current hydrology apparently has a negative affect on bottomland hardwoods, scattered regeneration stems and soil redox measurements indicate that a dechannelization effort that yielded lower water tables in the Stokes Creek floodplain potentially could increase bottomland hardwood establishment. [Key words: channelization, western Tennessee, bottomland hardwoods, hydrology.]     

基于高分辨率遥感影象的城市泥石流灾害损失评估

文章探讨了城市泥石流灾害损失评估的系统方法,该方法包括了泥石流堆积泛滥区危险区划、城市土地覆盖类型遥感解译、损失评估模型构建和价值核算4个主要内容。以美国高分辨率的"快鸟"卫星影象为数据源完成了研究区的土地覆盖类型遥感解译,根据泥石流危险程度和土地覆盖类型特征,构建了城市泥石流灾害的损失评估模型。最后,应用GIS提供的分析工具完成了研究区不同土地覆盖类型的泥石流灾害损失计算和评价。     

区域气候模式对中国沙尘天气气候特征的模拟研究

现有的沙尘天气数值预报模式多选用中尺度天气模式单向耦合起沙模式的方式,不适合用来模拟沙尘气溶胶的长距离输送过程,也无法研究沙尘气溶胶辐射效应对气象场的反馈及气候变化的影响。利用一个耦合沙尘模式的高分辨率区域气候模式,模拟了2001年中国北方沙尘天气爆发的时空分布特征。模拟结果与站点观测结果对比发现,模式能够较好地模拟出中国北方主要的沙尘源地分布及沙尘天气爆发的季节变率。分析不同粒径沙尘颗粒的垂直分布特征发现,沙源地表土壤粒子特征、地形对起沙颗粒的大小都有影响;直径超过5 μm的大粒子是北方沙尘天气的主要成分,而影响长江以南的沙尘天气主要以1 μm以下的小粒子为主。对沙尘传输路径的模拟结果和实况观测发现,来自于不同沙源的沙尘天气其影响的范围有显著差异,模式能够较好地模拟出中国主要沙尘传输路径。     

A new class of stratified viscoelastic models by analytical techniques

Multilayer, spherically stratified, self-gravitating relaxation models with a large number of layers (more than 100) can be dealt with analytically. Relaxation processes are studied for both Heaviside surface loads and tidal forcings. Simulations of the relaxation process of a realistic earth model with an incompressible Maxwell rheology show that models containing about 30 to 40 layers have reached continuum limits on all timescales and for all harmonic degrees up to at least 150 whenever an elastic lithosphere is present, irrespective of the viscosity profile in the mantle. In particular, fine-graded stratification of the shallow layers proves to be important for high harmonic degrees in these models. The models produce correct long-time (fluid) limits. It is shown that differences in the transient behaviour of the various models are due to the applied volume-averaging procedure of the rheological parameters. Our earlier proposed hypothesis that purported shortcomings in the fundamental physics of (discrete) normal-mode theory are artificial consequences of numerical inaccuracies, theoretical misinterpretations and the use of incomplete sets of normal modes is reinforced by the results presented. We show explicitly that the models produce both continuous behaviour resulting from continuous rheological stratifications and discrete behaviour resulting from sharp density contrasts, as at the outer surface and the core-mantle boundary. The differences between volume-averaged models and fixed-boundary contrast models are outlined. Reducing many-layer models with a volume-averaging procedure before employing a normal mode analysis is both economical and highly accurate on all timescales and for all spherical harmonic degrees. The procedure minimizes the chances of missing contributing modes, while using models with more layers will not result in any substantial increase of accuracy.     

基于高速公路联网收费数据的江苏省交通流动特征与影响因素

高速交通网络是一种十分重要的地区间联系形式,对区域空间结构的重构有着显著的推动作用。高速公路联网收费数据为从高速公路流量视角探讨区域交通流动提供了有效的数据支撑。以江苏省为案例区,以江苏省内高速公路网络2014年的收费站点间出发地—目的地（O-D）数据为支撑,探究区域交通流动特征,并运用地理加权回归（GWR）模型分析方法探讨流动的影响因素。结果表明：① 江苏省内部交通流动存在较大的不均衡性,核心节点（收费站、县域节点）主要位于江苏省南部,在空间上呈现出以核心节点为中心的放射性结构。② 流量总体上呈现距离衰减特征,空间间隔尺度越大,距离衰减规律特征越明显,且衰减规律符合幂律分布。③ 常住人口、经济发展、公路里程可有效解释县域流量分布,经济发展对各县域交通流量的影响在江苏北部地区表现的更为强烈,人口对江苏南部地区交通流量影响具有局部优势,公路里程对苏南地区存在较弱的负向影响。