融合海域多源重力数据的正则化点质量方法

泰勒级数展开是实施位场向下延拓解算的主要方法之一。该方法的有效性主要取决于位场延拓参量各阶垂向（或径向）偏导数的求取精度及其可靠性。为了避免使用封闭解析核函数在球边界面出现奇异性带来的不确定性问题,依据各类重力观测经滤波处理后均表现为一类有限频谱带宽信号的特点,提出将地球外部重力异常泊松积分式的核函数表示为球谐级数展开式,并将其截断为与重力观测值频谱范围相一致的带限求和式,进而通过直接求导方法,推导得到一组与带限核函数相对应的重力异常高阶径向导数带限计算公式,同时对该组公式进行了实用性改化,并将其应用于重力异常向下延拓泰勒级数展开式计算。使用超高阶地球位模型EGM2008设计两个阶段的数值计算检验方案,分别对重力异常高阶径向偏导数带限模型及其泰勒级数展开向下延拓模型的计算精度进行了检核评估,表明新模型具有良好的可靠性和有效性,在解算稳定性和计算精度两个方面都优于其他同类模型。

     

Some modifications of Stokes' formula that account for truncation and potential coefficient errors

 Stokes' formula from 1849 is still the basis for the gravimetric determination of the geoid. The modification of the formula, originating with Molodensky, aims at reducing the truncation error outside a spherical cap of integration. This goal is still prevalent among various modifications. In contrast to these approaches, some least-squares types of modification that aim at reducing the truncation error, as well as the error stemming from the potential coefficients, are demonstrated. The least-squares estimators are provided in the two cases that (1) Stokes' kernel is a priori modified (e.g. according to Molodensky's approach) and (2) Stokes' kernel is optimally modified to minimize the global mean square error. Meissl-type modifications are also studied. In addition, the use of a higher than second-degree reference field versus the original (Pizzetti-type) reference field is discussed, and it is concluded that the former choice of reference field implies increased computer labour to achieve the same result as with the original reference field. Received: 14 December 1998 / Accepted: 4 October 1999     

Water balance modelling in lateritic terrain

An analytical approximate model for unsaturated flow in a spatially variable field, coupled with infiltration and evapotranspiration at the upper boundary and a fluctuating water-table at the lower boundary, has been developed. The unsaturated flow equations depend on parameterizations of θ(Φ) and K(Φ). They are based on the notion of a moving, discontinuous front. The field heterogeneity refers to saturated hydraulic conductivity only. Horizontal variability is considered, and the flow medium is approximated as a set of uncorrelated, vertically homogeneous columns. Expectations and variances obtained with this approach have been compared with observations of the field hydrological processes. Three important aspects of the hydrology in this lateritic terrain are rapid water-table response, Hortonian surface runoff generation and soil suction variability. The stochastic conceptualization used explains to a high degree these characteristics, although some limitations are demonstrated.     

Inverse modeling of lichen growth curves and implications for lichenometric dating

Lichenometric dating represents a quick and affordable surface exposure dating method that has been widely used to provide a minimum age constraint on tectonic and geomorphic landscape changes as well as buildings and anthropogenic landscape changes in various settings during the late Holocene. Despite its widespread usage, this method has several limitations. Major problems relate to the sampling of lichen population on any given rock surface and the modeling of growth curves. In order to overcome these issues, it has been suggested to subdivide the rock surface into some areas and measure the largest lichen thallus on each one. However, how to express the data in terms of a probability distribution function and link it to an age of last exposure of the rock surface are still a matter of debate. Here, we propose a novel approach to the modeling of lichen growth curves by treating lichen growth as a continuous-time Markov process with a time-varying rate and additive Brownian noise. Given the growth rates, the probability distribution of the lichen population at any time can then be obtained by solving the Fokker–Planck equation. This method is illustrated using a dataset from the Huashan area of eastern China, which consists of measurements of the largest thalli on 12 rock surfaces of known age. We first build up the probability distribution of the lichen population for each rock surface based on extreme value theory and then use these to optimize the growth curve by minimizing the Jensen–Shannon divergence. A new method is also proposed to use the growth curve to map a sample of size data from an undated rock surface to the calendar age domain so as to yield a fully probabilistic estimate of the exposure age of the undated rock surface rather than a point estimate.     

基于逆Stokes公式的测高重力反演中央区效应计算

为提高利用逆Stokes公式反演测高重力的精度,将中央区大地水准面高表示成双三次多项式插值形式,引入了非奇异变换,推导出了重力异常的计算公式。大地水准面高理论模型下的分析表明,该公式有较高的精度。以分辨率为2′×2′的大地水准面高数据为背景场进行了实际计算,结果说明中央区对反演重力异常有不容忽视的贡献。本文导出的公式可为高精度重力异常的反演提供理论依据。     

广义反距离加权空间推估法

提出了k阶广义反距离加权空间推估法。首先,估计空间函数在已知点处的各阶偏导数;然后,利用泰勒级数逼近原理计算待估点处的函数值,根据空间函数偏导数估值的方差协方差评价推估精度;最后,对待估点处的这些推估值进行最小二乘平差。引入了确定k阶广义反距离加权空间推估法阶次k的BIC准则,并以GPS水准推估为例进行了实验。     

测高数据在计算海平面时的取权

根据卫星测高数据分布所具有的低纬时稀疏、高纬时密集的特点,提出了计算平均海平面时非交叉点数据的解析定权公式和交叉点数据的解析定权公式。     

地震活动的随机标度和非线性标度律

把地震作为一个复杂系统,研究了地震活动的随机性质．当不考虑震级范围时,全球地震活动、人震的余震和区域震群均有以幂次律为特征的长尾现象．地震的强度由震级确定,具有一特定震级的地震可形成一个地震活动系列,很多这样的地震活动系列就形成具有各种震级的地震的集合．不同地震系列间的统计特征由随机标度来表征,随机标度表明了由地震震级分类的不同地震系列间统计时刻的标度关系．为了统一地方、区域和全球地震活动性的统计特性,引入了非线性标度率．     

风沙运动中MAGNUS效应的数值研究

在风沙运动中,跃移沙粒一般都会伴随高速旋转,同时引起一种升力效应,即Magnus效应。采用数值模拟的方法计算了0.1Re400,转速ω为100~1000 rev.s-1范围时均匀来流中单个球形沙粒受到的Magnus力,并与Rubinow和Keller推导的Magnus力公式进行了比较。计算结果表明,在0.1Re200范围内,升力和沙粒的旋转速度成正比,随雷诺数的增大而减小。同时,Magnus效应和固定沙粒在均匀来流中的流动结构也有关系,即计算结果和Magnus力公式的升力系数比K在沙粒流动是附体的时随Re数增加逐渐减小,在Re=20~30时达到最小值,然后在沙粒流动是对称分离的时K随着Re数增加逐渐增大。当雷诺数继续增大到超过200时,沙粒本身流动状态非对称所引起的升力超过Magnus效应产生的升力,但Magnus效应的作用也不可以忽略。根据计算结果,对Magnus力公式进行了修正。另外,还发现流场速度梯度与Magnus效应并没有耦合作用,速度梯度对升力的影响可以和Magnus效应线性叠加。