High-precision geoid determination in small areas: A case study in Doñana National Park (Spain)

Doñana National Park is an area of approximately 500 km² located on the SW coast of Spain that shows one of the greatest geoid gradients on the entire Iberian Peninsula, due to its peculiar tectonic characteristics. So, it is necessary to elaborate an accurate geoid model that can be used with GPS for precise surveying, since the existing ones are insufficient, due to their poor resolution and their limited adaptation to a small area with such a strong gradient. The least squares prediction method was tested in order to obtain the undulation from GPS/orthometric points. The results obtained were unsatisfactory because of the strong geoid gradient. In order to improve accuracy the remove-restore technique was used. Global geopotential model EIGEN-CG01C and a Digital Elevation Model (DEM) with a 25 × 25 m resolution and an accuracy better than 3 m were used. Thus, the final geometrical geoid obtained reaches the precision required by other disciplines (3 cm in any point within the Park). Particularly, the geoid model has allowed for the acquisition of a precision DEM that is essential to formulate a hydrodynamic model for the Doñana marsh functions.     

Determining useful benchmarks for the bioassessment of highly disturbed areas based on diatoms

Modern ecological assessments of running waters are based on the a priori definition of ecological benchmarks, given by reference-quality sites. Such benchmarks are established at the level of ecoregions, typologies, or site. Yet, in highly disturbed regions, such as coastal areas of European countries, the assessment of streams’ water quality based on the reference condition concept is very difficult, due to the lack of undisturbed sites. Among others, the reduced number of reference sites may have as a consequence the definition of imprecise ecological benchmarks. Here we tested the hypotheses that (1) the increase in the number of potential reference sites (2) the definition of more precise abiotic thresholds using the least disturbed condition approach (LDC), and (3) the use of diatom assemblages, as the most ubiquitous element in lowland areas, would result in refinement and eventual sub-division of existing river types of a highly disturbed area, such as the Portuguese centre-western region. For this purpose, abiotic data characterising natural conditions of 55 sites from a littoral highly disturbed region were used in a hierarchical classification analysis that revealed the existence of three different sub-groups. In addition, a three-step approach was used to define thresholds for the pressure variables in LDC. Based on these new thresholds, sites in LDC were selected. A hierarchical classification performed to the LDC diatom spring assemblages revealed the existence of two sub-groups, concordant with two of the abiotic sub-groups. Several species contributed to the dissimilarity between the two sub-groups (e.g., Achnanthidium minutissimum and Karayevia oblongella). Differences between the sub-groups were also found in the trait proportions of stalked species. New benchmark values for these two sub-groups, based on the scores of the official diatom index, the Indice de Polluosensibilité Spécifique (IPS), were different from the previous reference value used. Yet, no biological benchmark values were established for one of the groups due to the absence of sites in the LDC. Our study suggests that streambed substrate is an important characterisation variable in the river type definition and highlights that, in spite of the potential refinement in reference conditions and typology obtained, an alternative approach that does not require the use of reference sites should be explored in the future.     

基于Remez迭代算法求解差分系数的双相介质自适应有限差分正演模拟

利用传统有限差分方法对基于Biot理论的双相介质波动方程进行数值求解时,由于慢纵波的存在,数值频散效应较为明显,影响模拟精度.相对于声学近似方程及普通弹性波方程,Biot双相介质波动方程在同等数值求解算法和精度要求条件下,其地震波场正演模拟需要更多的计算时间.本文针对Biot一阶速度-应力方程组发展了一种变阶数优化有限差分数值模拟方法,旨在同时提高其正演模拟的精度和效率.首先结合交错网格差分格式推导Biot方程的数值频散关系式.然后基于Remez迭代算法求取一阶空间偏导数的优化差分系数,并用于Biot方程的交错网格有限差分数值模拟.在此基础上把三类波的平均频散误差参数限制在给定的频散误差阈值和频率范围内,此时优化有限差分算子的长度就能自适应非均匀双相介质模型中的不同速度区间.数值频散曲线分析表明：基于Remez迭代算法的优化有限差分方法相较传统泰勒级数展开方法在大波数范围对频散误差的压制效果更明显;可变阶数的优化有限差分方法能取得与固定阶数优化有限差分方法相近的模拟精度.在均匀介质和河道模型的数值模拟实验中将本文变阶数优化有限差分算法与传统泰勒展开算法、最小二乘优化算法进行比较,进一步证明其在复杂地下介质中的有效性和适用性.

     

Spatial interpolation using nonlinear mathematical programming models for estimation of missing precipitation records

Abstract

New mathematical programming models are proposed, developed and evaluated in this study for estimating missing precipitation data. These models use nonlinear and mixed integer nonlinear mathematical programming (MINLP) formulations with binary variables. They overcome the limitations associated with spatial interpolation methods relevant to the arbitrary selection of weighting parameters, the number of control points within a neighbourhood, and the size of the neighbourhood itself. The formulations are solved using genetic algorithms. Daily precipitation data obtained from 15 rain gauging stations in a temperate climatic region are used to test and derive conclusions about the efficacy of these methods. The developed methods are compared with some naïve approaches, multiple linear regression, nonlinear least-square optimization, kriging, and global and local trend surface and thin-plate spline models. The results suggest that the proposed new mathematical programming formulations are superior to those obtained from all the other spatial interpolation methods tested in this study.

Editor D. Koutsoyiannis; Associate editor S. Grimaldi

Citation Teegavarapu, R.S.V., 2012. Spatial interpolation using nonlinear mathematical programming models for estimation of missing precipitation records. Hydrological Sciences Journal, 57 (3), 383–406.     

基于不等式约束的三维电阻率探测混合反演方法

三维电阻率探测的线性反演和非线性反演中均存在着多解性的固有难题.电阻率线性反演方法的效率较高,但反演结果对初始模型的依赖性较强,易陷入局部极小;而非线性反演方法不依赖初始模型,但搜索效率极低,尚未见到关于三维电阻率非线性反演的文献.针对上述问题,融合线性与非线性反演方法的互补优势,提出了最小二乘法（线性方法）与改进遗传算法（非线性方法）相结合的混合反演方法的概念和思想.首先,提出了将介质电阻率变化范围作为不等式约束引入反演方程的思路,以实现压制多解性、提高可靠性的目标.提出了宽松不等式约束和基于钻孔推断的局部严格不等式约束的获取及定义方法.在此基础上,分别提出了基于不等式约束的最小二乘线性反演方法和遗传算法非线性反演方法.其次,对于遗传算法在变异搜索方向控制、初始群体产生等方面进行了改进,优化了其搜索方向和初始群体多样性.然后,提出了混合反演方法及其实现方案,利用改进遗传算法进行第一阶段反演,发挥其对初始模型的依赖程度低的优势,搜索到最优解附近的空间,输出当前最优个体;利用最小二乘法进行第二阶段反演,将遗传算法得到的当前最优个体作为初始模型,在最优解附近空间执行高效率的局部线性搜索,最终实现地电结构的三维成像.最后,开展了合成数据与实际工程算例验证,与传统最小二乘方法进行了对比,发现混合反演方法在压制多解性、摆脱初始模型依赖和提高反演效果方面有较好效果.

     

地壳形变分析的抗差最小二乘配置迭代解法

利用最小二乘配置进行地壳形变分析,其结果的合理性关键在于经验协方差函数的拟合.考虑到观测数据存在粗差的情况,提出基于观测值中位数初值的抗差最小二乘配置方法和基于中位参数法的抗差最小二乘配置方法.两种方法首先分别利用观测值中位数给出观测值初始权阵以及利用中位参数法给出最小二乘配置初始解,然后均在给定协方差函数参数初始值的情况下,应用合适的等价权进行抗差估计并通过迭代计算,最终获得稳健的协方差函数参数估值及最小二乘配置解.利用本文提出的两种方法以及传统方法分别对庐山地震的GPS垂直位移数据和意大利L'Aquila地震的InSAR同震位移数据进行处理分析.结果表明：相对传统方法,基于观测值中位数初值的抗差最小二乘配置方法效果更好,更具稳健性.

     

基于热点参考系的板块绝对运动模型

本文在最新一代板块相对运动模型（MORVEL模型）的基础上,通过最小二乘反演观测热点方向数据建立板块绝对运动模型.经过对前人用于约束板块绝对运动模型的所有热点数据与MORVEL模型的一致性作系统的统计学检验,发现存在离群数据.相应地,提出两种系统剔除离群数据的新方法：逐一剔除法和全局搜索法.结合对总残差的卡方检验和对残差频率分布的正态检验,逐步筛选最优模型,最终得到一个基于热点参考系的板块绝对运动新模型（T87模型）.该模型能够合理拟合全球分布的87个热点方向数据,而模型预测的板块绝对运动速率比观测热点火山的迁移速率系统偏小,最大偏差达到4 cm·a^-1.这样的偏差可由观测热点速率的系统误差或地幔返回流造成的热点间运动解释.不论是哪种解释成立,本文结果表明热点方向数据能够独立、有效地定义全球热点参考系.这样定义的热点参考系可方便地应用于板块绝对运动、地幔对流及真极移的研究.

     

地震预警现地PGV连续预测的最小二乘支持向量机模型

为提升现地仪器地震烈度预测的准确性与连续性,研究面向地震预警的PGV连续预测模型.以中国仪器地震烈度标准的计算参数：0.1~10 Hz带通滤波三分向矢量合成速度峰值PGV为预测目标,利用日本K-net与KiK-net台网P波触发后1~10 s强震数据,基于人工智能中的机器学习方法-最小二乘支持向量机,选取7种特征参数作为输入构建最小二乘支持向量机PGV预测模型LSSVM-PGV.结果表明,本文建立的LSSVM-PGV模型在训练数据集与测试数据集上的预测误差标准差变化趋于一致,具备泛化性能;P波触发后3 s预测PGV与实测PGV即可整体符合1：1关系,随着时间窗的增长,PGV预测的误差标准差显著减小、并在P波触发后6 s趋向收敛,具备准确连续预测能力;对比同为P波触发后3 s的常用Pd-PGV模型,LSSVM-PGV模型的PGV预测误差标准差明显减小,"小值高估"与"大值低估"现象明显改善,预测准确性得到提升.熊本地震序列的震例分析表明,对于6.5级以下地震,LSSVM-PGV模型最多在P波触发后3 s即可预测出与实测PGV整体符合1：1关系的PGV;对于7.3级主震,由于其破裂过程的复杂性,P波触发后3 s的预测结果出现一定程度的低估,但随着时间窗增长至6 s时,预测PGV与实测PGV符合1：1关系、并直到10 s整体趋势保持一致.本文构建的LSSVM-PGV模型可用于现地地震预警仪器地震烈度的预测.     

长白山天池火山区长白-敦化剖面结晶基底的探测和研究

时间项分析法中，应用广义最小二乘法进行反演，对长白山天池火山区岩浆系统的长白—敦化(L1)剖面的Pg波到时进行了计算处理，得到了Pg波时间项及基底速度值；取上部地壳的介质平均速度为4．5km/s，经反演求得了各点的深度值，给出了长白山天池火山区结晶基底的厚度分布。结晶基底厚度一般在2．0km左右，而在长白山天池下方结晶基底最厚处接近4．0km；在万宝和敦化附近各有一不太明显的凹陷，其原因可能与在这两个位置处有几条断裂穿过有关。     

混合LS-TLS的GM（1,1）模型在基坑水平位移监测中的应用

通过分析传统GM（1,1）模型的局限性,提出了混合整体最小二乘法（混合LS-TLS）的GM（1,1）模型,并将其应用于宁夏某深基坑水平位移的监测中。同时,将此模型与最小二乘法（LS）的GM（1,1）模型及整体最小二乘法（TLS）的GM（1,1）模型进行了对比,分析了3种模型所求水平位移的预测值。结果表明,混合LS-TLS的GM（1,1）模型更符合工程实际,预测精度更高,在深基坑水平位移监测中具有一定的实用性。