Zonal-Harmonics Perturbations

A recently developed iterative technique for solving the perturbed Kepler problem is explained, in a step-by-step detail, using the simple example of oblateness perturbations. The results are then extended to deal with higher-degree zonal harmonics.     

A bimodal four‐parameter lognormal linear model of soil water repellency persistence

Soil water repellency may be characterized in terms of the delayed infiltration time of a water droplet resting on the soil surface, which is, water drop penetration time (WDPT), or repellency persistence. Such repellency persistence varies nonlinearly with soil water content (θ_g), although no models have been proposed to reproduce the variation of WDPT with θ_g in soils. Dynamic factor analysis (DFA) is used to identify two common patterns of unexplained variability in a scattered dataset of WDPT versus θ_g measurements. A four‐parameter lognormal distribution was fitted to both common patterns obtained by DFA, and these were combined additively in a weighted multiple linear bimodal model. We show how such an empirical model is capable of reproducing a large variety of WDPT versus θ_g curve shapes (N = 80) both within a wide range of measured WDPTs (0–17 000 s) and for samples with organic matter content ranging from 21·7 to 80·6 g (100 g)^?1. Copyright © 2009 John Wiley & Sons, Ltd.     

考虑应变局部化的粗粒料剪切损伤力学机制

针对粗粒料的应变软化、剪胀等力学特性,通过考虑以剪切带为标志的应变局部化现象,建立了具有广泛适用性的剪切损伤力学模型。损伤模型采用了包体理论中的剪切带数学简化,基于应变等价原理、Weibull分布,推导了粗粒料的应力-应变关系方程。从剪胀作用的机制出发,提出可以描述剪胀弱化的轴向塑性应变和体积塑性应变的非线性函数关系。结合粗粒料三轴压缩试验中的伺服过程,提出了基于遗传算法的损伤模型参数确定方法。通过开展不同围压下的粗粒料三轴压缩试验,对剪切损伤力学模型进行验证,进一步分析了参数演化对粗粒料强度和变形特征的影响。研究结果表明,考虑应变局部化特征的剪切损伤力学模型可以高精度的模拟粗粒料的应变软化和剪胀等特征,有效揭示剪切带内部变形对试样整体宏观变形的影响机制,模型中剪切带参数和围压的关系与粗粒料细观机制一致,计算得到强度组成与颗粒破碎、重组特征较为吻合。     

顺层岩质边坡溃屈变形机制及失稳判定方法

溃屈型破坏是一种常见的顺层岩质边坡破坏模式,溃屈变形发展机制及失稳破坏的定量研究对滑坡工程勘查和防治指导十分重要。本文根据边坡的地质环境和力学作用机制,建立了三维受压板简化模型,其能够考虑岩层自身重力、地震力、静水压力的共同作用和岩体材料塑性变形的影响。基于弹塑性受压板稳定理论,利用能量法推导得到了边坡溃屈变形破坏的临界方程。对于溃屈型边坡的结构失稳和滑动失稳分别提出了相应的稳定性判定方法,并针对不同状态的边坡提出了相应的防治措施建议。以四川省甘孜藏族自治州巴塘县下归哇边坡为例,对所提判定方法的正确性进行了验证。计算结果表明,边坡的临界溃屈长度（a1）为483.8 m,说明下归哇边坡能够发生溃屈变形;现场勘查得知边坡实际溃屈长度（a′）为530.0 m,a′＞a1,可知边坡是稳定的。这与实际情况相吻合,由此证明本文所提出的判定方法可行。     

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.     

POS与DEM辅助机载SAR多普勒参数估计

由于机载SAR多普勒参数受载机不稳定飞行和复杂地形影响明显,目前仍缺少有效的矢量估计法。本文对POS和DEM数据及其误差对机载多普勒参数的影响进行了分析,以距离-共面方程构建的SAR几何关系为基础,在POS和DEM数据支持下,建立了一种多普勒参数矢量估计法,并通过仿真对提出的方法进行了验证和分析。理论和仿真表明,本文方法在高山地形、不稳飞行及大斜视角等复杂条件下,亦能够为机载SAR瞬时多普勒中心提供高精度估计。     

基于单位四元数的单独像对相对定向

目前对单位四元数描述空间旋转的应用,基本上是将其转换成旋转矩阵的形式,而忽略了单位四元数描述空间向量旋转具有描述几何关系的直观性以及运算简洁的优势。基于此提出一种基于单位四元数的单独像对相对定向法,方法首先采用向量描述同名光线,然后利用单位四元数描述立体像对中左右影像同名光线的变换关系,建立单位四元数共面条件方程模型,再按照带有约束条件的间接平差原理进行最小二乘平差,确定相对定向元素。针对RC30航空影像和低空无人机影像采用单位四元数法分别进行单独像对相对定向实验,结果表明单位四元数相对定向方法计算精度较高,为解决摄影测量中坐标变换问题提供更多选择。     

基于原始观测值的单频精密单点定位算法

研究了一种基于GPS原始观测值的单频PPP算法。该算法通过增加电离层延迟先验信息、空间和时间约束的虚拟观测方程,将电离层延迟当作未知参数与其他定位参数一并进行估计来高效修正电离层延迟误差。通过使用全球178个IGS站1d的实测数据对本算法的收敛速度、定位精度和电离层VTEC的精度进行检验与分析。结果表明,该算法的收敛速度和稳定性均得到了改善,其静态单频单天PPP解的精度可达2~3cm、模拟动态单频单天PPP解的精度可达2~3dm,并且单频PPP与双频PPP提取的电离层总电子含量平均偏差小于5个TECU,可作为一种附属定位产品使用。     

GRAPES区域扰动预报模式动力框架设计及检验

设计了适用于四维变分同化系统的扰动预报模式GRAPES_PF。根据GRAPES的地形追随坐标非静力原始方程组,采用小扰动分离方法推导微分形式的线性扰动预报方程组,并利用与GRAPES非线性模式相似的数值求解方案求解线性扰动微分方程组。在设计扰动预报模式时采用了两个时间层半隐式半拉格朗日方案对动量方程、热力学方程、水汽方程和连续方程进行时间差分,空间差分方案的变量分布水平方向采用Arakawa C跳点网格,垂直方向采用Charney/Phillips跳层。利用代数消元法进一步推导得到只包含未来时刻扰动Exner气压的亥姆霍兹方程,进而通过广义共轭余差法（GCR）求解,在此基础上得到未来时刻扰动量的预报值。基于所开发的扰动模式开展了数值试验。首先在非线性模式中施加一个中尺度初始扰动高压,得到初始扰动在非线性模式中的后续演变,然后将相同的初始扰动作为扰动模式的初值进行时间积分,将扰动模式预报的结果与非线性模式的结果做了对比。结果表明,所开发的扰动模式GRAPES_PF较好地模拟了惯性重力内波的传播过程:初始高压扰动激发了一个迅速向外传播的惯性重力内波,在气压场向风场适应的过程中,水平风场、垂直运动、位温和湿度等变量均出现了扰动增量,与非线性模式得到的结果相当接近。GRAPES_PF作为GRAPES非线性模式的合理线性模式为建立基于线性扰动预报的区域四维变分同化系统奠定了科学基础。