Interpolation by regularized spline with tension: I. Theory and implementation

Bivariate and trivariate functions for interpolation from scattered data are derived. They are constructed by explicit minimization of a general smoothness functional, and they include a tension parameter that controls the character of the interpolation function (e.g., for bivariate case the surface can be tuned from a membrane to a thin steel plate), Tension can be applied also in a chosen direction, for modeling of phenomena with a simple type of anisotropy. The functions have regular derivatives of all orders everywhere. This makes them suitable for analysis of surface geometry and for direct application in models where derivatives are necessary. For processing of large datasets (thousands of data points), which are now common in geosciences, a segmentation algorithm with a flexible size of overlapping neighborhood is presented. Simple examples demonstrating flexibility and accuracy of the functions are presented.On leave from the Department of Physical Geography and Cartography, Comenius University, Mlynská dolina, Bratislava, Czechoslovakia.On leave from the Institute of Physics, Dúbravská cesta 9, Bratislava, Czechoslovakia.     

相律的应用:蒸发结晶过程自由度

在连续原理和浓度限制条件的基础上,分析了卤水蒸发过程的自由度,提出了“蒸发结晶过程自由度”这一概念。发现蒸发结晶过程自由度在整个过程中不是1便是0,在1和0之间交替变化,与选择的组分数和析出固相数目无关。蒸发结晶过程自由度为1,物理意义是在不引起新相产生旧相不消失的前提下过程连续地变化(水分的连续蒸失),几何意义是指在适当的坐标系中的一条线,一条直线或曲线;0的物理意义是指新相的产生和旧相的即将消失或者前一段的连续变化过渡到后一段的连续变化,几何意义是指一点,两蒸发阶段的交点或者过程的终点。简单地讨论了过程的单向性和连续件。     

新疆地区夏季平流层低层风场特征分析及数值模拟

利用2017年6—8月的FNL再分析资料分析了新疆地区夏季平流层低层风场的时空演变特征，开展了平流层低层风场的高分辨率数值模拟和检验。结果表明：新疆地区夏季平流层纬向风随时间的变化存在经向差异，同时准零风层开始和结束的时间也存在经向差异，准零风层开始时间南部地区早于北部地区，而准零风层结束时间则相反。整个夏季新疆地区上空的准零风层处于70～40 hPa之间，其高度随时间呈先降低而后升高的变化趋势。准零风层数值模拟结果表明，模拟的准零风层参数与探空资料分析结果相比二者存在一致的变化趋势，准零风层起始高度的平均绝对误差为467 m，该高度对应的风速均方根误差为1.75 m/s。     

利用主成分分析改善土地利用变化的遥感监测精度——以珠江三角洲城市用地扩张为例

近年来,珠江三角洲由于经济的快速发展,城市用地急剧增加,利用多时相的遥感图,可以定量地监测这种城市化的现象。但理,由一般的遥感动态监测方法所得的结果往往夸大变化的程度,以及获得一些不合理的结论．该文提出主成分分析的方法来改善遥感动态监测的精度。将该方法应用应用于珠江三角洲发展最快的东莞市,获得了较满意的结果。     

北京云蒙山地区花岗岩穹隆及伸展构造的探讨

北京云蒙山花岗岩为一中生代侵入的花岗岩穹隆,花岗岩穹隆的叶理普遍发育,叶理轨迹基本平行于穹隆的外部边界,并显示出从核部到边部逐渐增强,东南侧明显强于西北侧的特点。变形构造研究显示,花岗岩穹隆的边部及围岩中普遍存在不同层次及不同运动方向的伸展构造。东南侧以具河防口－水峪伸展型韧性剪切带为特征,剪切运动标志显示为从ＮＷ－ＳＥ的正剪切运动,有限应变分析估算其剪切位移量在１０ｋｍ以上,剪切带上部被河防口正     

Research on temporal and spatial distribution, evolutionary character and mechanism of crustal deformation field before and after the Tangshan earthquake

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Efficient generation of conditional simulations by chebyshev matrix polynomial approximations to the symmetric square root of the covariance matrix

Consider the problem of generating a realization y₁ of a Gaussian random field on a dense grid of points ₁ conditioned on field observations y₂ collected on a sparse grid of points ₂. An approach to this is to generate first an unconditional realization y over the grid =_{1 2}, and then to produce y₁ by conditioning y on the data y₂. As standard methods for generating y, such as the turning bands, spectral or Cholesky approaches can have various limitations, it has been proposed by M. W. Davis to generate realizations from a matrix polynomial approximations to the square root of the covariance matrix. In this paper we describe how to generate a direct approximation to the conditional realization y₁, on ₁ using a variant of Davis' approach based on approximation by Chebyshev polynomials. The resulting algorithm is simple to implement, numerically stable, and bounds on the approximation error are readily available. Furthermore we show that the conditional realization y₁ can be generated directly with a lower order polynomial than the unconditional realization y, and that further reductions can be achieved by exploiting a nugget effect if one is present. A pseudocode version of the algorithm is provided that can be implemented using the fast Fourier transform if the field is stationary and the grid ₁ is rectangular. Finally, numerical illustrations are given of the algorithm's performance in generating various 2-D realizations of conditional processes on large sampling grids.     

Characterizing heterogeneous permeable media with spatial statistics and tracer data using sequential simulated annealing

Characterizing heterogeneous permeable media using flow and transport data typically requires solution of an inverse problem. Such inverse problems are intensive computationally and may involve iterative procedures requiring many forward simulations of the flow and transport problem. Previous attempts have been limited mostly to flow data such as pressure transient (interference) tests using multiple observation wells. This paper discusses an approach to generating stochastic permeability fields conditioned to geologic data in the form of a vertical variogram derived from cores and logs as well as fluid flow and transport data, such as tracer concentration history, by sequential application of simulated annealing (SA). Thus, the method incorporates elements of geostatistics within the framework of inverse modeling. For tracer-transport calculations, we have used a semianalytic transit-time algorithm which is fast, accurate, and free of numerical dispersion. For steady velocity fields, we introduce a transit-time function which demonstrates the relative importance of data from different sources. The approach is illustrated by application to a set of spatial permeability measurements and tracer data from an experiment in the Antolini Sandstone, an eolian outcrop from northern Arizona. The results clearly reveal the importance of tracer data in reproducing the correlated features (channels) of the permeability field and the scale effects of heterogeneity.     

Regional Seas and Sustainable Development Results of an International Workshop

Reports

Regional Seas and Sustainable Development Results of an International Workshop     

Estimation for partially observed Markov processes

Many stochastic process models for environmental data sets assume a process of relatively simple structure which is in some sense partially observed. That is, there is an underlying process (X_n, n 0) or (X_t, t 0) for which the parameters are of interest and physically meaningful, and an observable process (Y_n, n 0) or (Y_t, t 0) which depends on the X process but not otherwise on those parameters. Examples are wide ranging: the Y process may be the X process with missing observations; the Y process may be the X process observed with a noise component; the X process might constitute a random environment for the Y process, as with hidden Markov models; the Y process might be a lower dimensional function or reduction of the X process. In principle, maximum likelihood estimation for the X process parameters can be carried out by some form of the EM algorithm applied to the Y process data. In the paper we review some current methods for exact and approximate maximum likelihood estimation. We illustrate some of the issues by considering how to estimate the parameters of a stochastic Nash cascade model for runoff. In the case of k reservoirs, the outputs of these reservoirs form a k dimensional vector Markov process, of which only the kth coordinate process is observed, usually at a discrete sample of time points.