大地坐标系应变张量表达及其与地心直角坐标系的相互转换

推导并给出了不同正交曲线坐标系应变张量和转动张量的普适表达和在旋转椭球坐标系下的应变张量表达,给出了不同正交曲线坐标系之间应变张量转换的普适表达式,以及在大地坐标系与地心直角坐标系这两种坐标系之间应变张量矩阵相互转换的具体表达,可供实际研究工作应用。     

旋转椭球面上的应变与转动张量表达

以旋转椭球体面上某点为原点建立一个大地坐标单位活动坐标架. 通过平移, 使活动坐标架的原点与以椭球中心为原点的笛卡尔单位标架的原点相重合. 然后再通过两次标架旋转, 使活动坐标架与笛卡尔单位标架完全重合. 本文给出了使两个单位标架相重合的转换关系式, 以及该点位移在两个单位标架中的坐标转换式; 在此基础上, 考虑该点的位移及活动坐标架皆为该点大地坐标的函数, 经复杂推导, 分别给出了该点位移向量的微分在大地坐标系中的分量以及该点分别沿坐标曲线的弧微分表达式, 继而导出了该点的位移梯度矩阵; 最后推导出了椭球坐标系的应变张量与转动张量表达式, 并对转动张量的几何含义进行了较详细的解释, 且采用曲面理论对球面与椭球面的应变张量间的内在关系进行了讨论.      

泰安地震台洞体应变与钻孔体应变参数解算结果对比分析

基于泰安台2013年洞体应变观测资料,首先利用维涅第科夫(Venedikov)调和分析方法计算洞体应变测项的潮汐因子和相位滞后,并以潮汐因子的稳定性对观测资料进行了质量评价。同时对观测仪器的2个测项进行解算,并提取相关应变参数进行对比。在此基础上,选取泰安台资料质量较稳定的体应变数据进行了应变参数时间序列计算,并对2套仪器观测数据进行了对比。通过分析,认定应力场存在异常,并对比分析了应力场异常与重力场异常的对应关系。     

曲线坐标系下的块体运动与应变模型研究

本文建立了顾及地球扁率和局部切标架随点变化特性的椭球坐标系下的刚体运动模型和块体运动与应变模型,以及球坐标系下顾及局部切标架随点变化特性的严密的块体运动与应变模型,分析了球坐标系下块体运动与应变模型及椭球坐标系下的块体运动与应变模型间的差异;通过计算具体讨论了地球扁率和曲线坐标系的局部切标架随点变化特性对欧拉矢量与应变张量的影响.结果表明：地球扁率对刚体欧拉矢量和应变参数的影响甚小,具体计算时可以不予考虑,但曲线坐标系的局部切标架随点变化特性对两者的影响较大,在建模过程中需要顾及,常用的Savage模型需要修正.     

铁岭地震台洞体应变参数解算与分析

针对铁岭地震台洞体应变观测资料,利用Venedikov调和分析方法计算铁岭地震台站洞体应变测项的潮汐因子和相位滞后,并以潮汐因子的稳定性对观测资料进行了质量评价;以铁岭地震台洞体应变讨论两分量观测解算平面应变参数,结果表明：铁岭洞体应变的最大剪应变T和面应变s在2006年和2009年出现了明显同步转折,可能反映了铁岭地震台及附近地区的应变出现了调整。     

地震的应变张量观测与应用前景

地震发生时的动态应变场,在研究地震触发、地震破裂、地面破坏、水文和岩浆变化等方面都具有重要应用意义.地震的应变张量观测和现有的惯性地震仪观测的物理量不同.前者可以直接记录到地震发生时震源辐射的应变（应力）波,而后者记录到的是位移、速度或加速度.地震频率的应变测量在地震学中的应用前景主要表现在：①测量震源机制解理论预言的辐射4象限分布;②测量库仑应力变化;③换算成动态应力以评估地震烈度;④测量地震波的能量密度;⑤测量地震断层形变加速和形变局部化过程.用惯性地震仪的记录虽然在理论上也可以解算出动态应变值,然而种种原因导致计算结果的误差很大,往往不可接受.应变张量地震仪若能与现有的惯性地震仪配套起来,形成大规模台阵,则有可能推动应变地震学的诞生,在地震观测和地震学科领域引起重大革新.

     

地壳应变主体单元模型及其与中强地震关系研究

讨论了目前利用GPS观测结果研究块体及其边界带应变状态的研究进展,阐明了与地震相关的块体边界活动构造附近是地壳应变主体区域的认识. 利用Scholz断层能量动态平衡过程,建立了断层周边应变累积与断层面构造力的一般物理关系,据此提出以断裂带为主体的地壳应变主体单元模型. 并利用GPS基准站连续观测资料讨论了模型力学状态演化与2001年11月14日昆仑山口西8.1级地震过程的关系. 结果表明,强烈压剪背景中出现的相对松弛变化,可能有利于触发型中等强度地震的发生.      

GPS应变率场解算方法的对比分析及其可靠性研究

利用GPS速度场资料进行应变率场计算存在多种不同的计算方法,虽然理论上速度场与应变率为简单的偏导关系,但由于GPS观测为点测量方式,如何构建逼近真实的速度场进而计算可靠的应变率场就有其复杂的一面,因此实际计算中不同研究者即使利用相同的数据也很难得到相同的结果,究竟如何评价不同计算方法的可靠性和适用性就显得尤为重要.     

位移观测值协方差矩阵模拟及其在整体解算地壳应变场中的应用

借助高斯型函数模拟分散分布的不同监测网点位移观测值的协方差矩阵,并将其应用于广东新丰江地区地壳应变场的计算中．结果表明：本文的方法不仅计算简便,模拟效果及计算稳定性较好,而且对联系分散分布的单元有一定的意义     

Computation of strain and rotation tensor as well as their uncertainties for small arrays in spherical coordinate system

Based on Taylor series expansion and strain components expressions of elastic mechanics, we derive formulae of strain and rotation tensor for small arrays in spherical coordinates system. By linearization process of the formulae, we also derive expressions of strain components and Euler vector uncertainties respectively for subnets using the law of error propagation. Taking GPS velocity field in Sichuan-Yunnan area as an example, we compute dilation rate and maximum shear strain rate field using the above procedure, and their characteristics are preliminarily car- ried on. Limits of the strain model for small array are also discussed. We make detailed explanations on small array method and the choice of small arrays. How to set weights of GPS observations are further discussed. Moreover relationship between strain and radius of GPS subnets is also analyzed.     

Expression of strain and rotation tensor in geodetic coordinates

In this paper, unit moving trihedron is first constructed for a point on the surface of a revolution ellipsoid. Via translation, the origin of the trihedron coincides with that of Cartesian coordinates established at the center of the ellipsoid, and then through two coordinate rotations, the trihedron completely coincides with the Cartesian coordi-nates. Transformation formulae between the moving trihedron and unit Cartesian coordinate frameworks as well as transformation of point displacement between two unit coordinate frameworks are presented. Based on the above transformation formulae between two different coordinate frameworks, due to the fact that the displacement and moving trihedron of the point are both functions of the geodetic coordinates, components in the corresponding axis for differential of displacement vector and geodetic curves arc differential at the point in geodetic system can be obtained through complicated derivation. Displacement gradient matrix at the point in geodetic system is also given. Finally, expressions of strain and rotation tensor in geodetic coordinates are presented. Geometric meanings of the rotation tensor are explained in detail. The intrinsic relationship between strain tensors of sphere and ellip-soid are also discussed.     

Standardized uncertainty analysis for hydrometry: a review of relevant approaches and implementation examples

Abstract

The water-centric community has continuously made efforts to identify, assess and implement rigorous uncertainty analyses for routine hydrological measurements. This paper reviews some of the most relevant efforts and subsequently demonstrates that the Guide to the expression of uncertainty in measurement (GUM) is a good candidate for estimation of uncertainty intervals for hydrometry. The demonstration is made by implementing the GUM to typical hydrometric applications and comparing the analysis results with those obtained using the Monte Carlo method. The results show that hydrological measurements would benefit from the adoption of the GUM as the working standard, because of its soundness, the availability of software for practical implementation and potential for extending the GUM to hydrological/hydraulic numerical simulations.

Editor D. Koutsoyiannis

Citation Muste, M., Lee, K. and Bertrand-Krajewski, J.-L., 2012. Standardized uncertainty analysis for hydrometry: a review of relevant approaches and implementation examples. Hydrological Sciences Journal, 57 (4), 643–667.     

Parameter and rating curve uncertainty propagation analysis of the SWAT model for two small Mediterranean catchments

Abstract

The SWAT model was tested to simulate the streamflow of two small Mediterranean catchments (the Vène and the Pallas) in southern France. Model calibration and prediction uncertainty were assessed simultaneously by using three different techniques (SUFI-2, GLUE and ParaSol). Initially, a sensitivity analysis was conducted using the LH-OAT method. Subsequent sensitive parameter calibration and SWAT prediction uncertainty were analysed by considering, firstly, deterministic discharge data (assuming no uncertainty in discharge data) and secondly, uncertainty in discharge data through the development of a methodology that accounts explicitly for error in the rating curve (the stage?discharge relationship). To efficiently compare the different uncertainty methods and the effect of the uncertainty of the rating curve on model prediction uncertainty, common criteria were set for the likelihood function, the threshold value and the number of simulations. The results show that model prediction uncertainty is not only case-study specific, but also depends on the selected uncertainty analysis technique. It was also found that the 95% model prediction uncertainty interval is wider and more successful at encompassing the observations when uncertainty in the discharge data is considered explicitly. The latter source of uncertainty adds additional uncertainty to the total model prediction uncertainty.

Editor D. Koutsoyiannis; Associate editor D. Gerten

Citation Sellami, H., La Jeunesse, I., Benabdallah, S., and Vanclooster, M., 2013. Parameter and rating curve uncertainty propagation analysis of the SWAT model for two small Mediterranean watersheds. Hydrological Sciences Journal, 58 (8), 1635?1657.     

曲线坐标系因式分解程函方程及其走时计算

地震波走时广泛应用于静校正、层析成像、Kirchhoff偏移成像、地震定位等研究.复杂地表条件是影响走时计算精度的重要因素.近年来,发展的曲线坐标系程函方程为精细刻画起伏地表条件下的地震波走时场特征提供了新的思路.然而,基于有限差分程函方程的求解方法不可避免地受到震源奇异性的影响,即震源附近波前的曲率较大,此时使用平面波近似假设的差分格式会导致较大误差.而震源误差会随着波前的传播到达整个计算区域,从而影响整个区域的求解精度.针对该问题,本文借鉴因式分解的思想,推导建立了曲线坐标系因式分解程函方程,并针对性地发展了其数值求解方法,从根源上解决了复杂模型走时计算中的震源奇异性问题.数值实例表明因式分解法能够有效降低震源误差,显著提高起伏地表走时计算的精度和效率,为起伏地表地震波走时计算提供更佳的选择,在复杂模型的地震资料处理中展现出广泛的应用前景.

     

Discharge and nutrient uncertainty: implications for nutrient flux estimation in small streams

The measurement of discharge is fundamental in nutrient load estimation. Because of our ability to monitor discharge routinely, it is generally assumed that the associated uncertainty is low. This paper challenges this preconception, arguing that discharge uncertainty should be explicitly taken into account to produce robust statistical analyses. In many studies, paired discharge and chemical datasets are used to calculate ‘true’ loads and used as the benchmark to compare with other load estimates. This paper uses two years of high frequency (daily and sub‐hourly) discharge and nutrient concentration data (nitrate‐N and total phosphorus (TP)) collected at four field sites as part of the Hampshire Avon Demonstration Test Catchment (DTC) programme. A framework for estimating observational nutrient load uncertainty was used which combined a flexible non‐parametric approach to characterising discharge uncertainty, with error modelling that allowed the incorporation of errors which were heteroscedastic and temporally correlated. The results showed that the stage–discharge relationships were non‐stationary, and observational uncertainties from ±2 to 25% were recorded when the velocity–area method was used. The variability in nutrient load estimates ranged from 1.1 to 9.9% for nitrate‐N and from 3.3 to 10% for TP when daily laboratory data were used, rising to a maximum of 9% for nitrate‐N and 83% for TP when the sensor data were used. However, the sensor data provided a better representation of the ‘true’ load as storm events are better represented temporally, posing the question: is it more beneficial to have high frequency, lower precision data or lower frequency but higher precision data streams to estimate nutrient flux responses in headwater catchments? Copyright © 2015 John Wiley & Sons, Ltd.     

库尔勒体应变观测资料可靠性分析

剔除库尔勒体应变观测资料中地震波、仪器标定及明确原因的干扰数据,计算应变潮汐因子、高频信息和非潮汐速率,结果显示：O1波、半日波潮汐因子在轮台5.4级、新源-和静交界6.6级地震前存在明显的异常反应,潮汐因子曲线形态、周期均发生明显的异常变化,异常结束后2-3个月内发震.总结体应变观测资料的异常特征,可有效捕捉前兆异常变化信息,有助于提高台站的地震短临预报水平.     

Temporal sampling strategies and uncertainty in calibrating a conceptual hydrological model for a small boreal catchment

How much data is needed for calibration of a hydrological catchment model? In this paper we address this question by evaluating the information contained in different subsets of discharge and groundwater time series for multi‐objective calibration of a conceptual hydrological model within the framework of an uncertainty analysis. The study site was a 5·6‐km² catchment within the Forsmark research site in central Sweden along the Baltic coast. Daily time series data were available for discharge and several groundwater wells within the catchment for a continuous 1065‐day period. The hydrological model was a site‐specific modification of the conceptual HBV model. The uncertainty analyses were based on a selective Monte Carlo procedure. Thirteen subsets of the complete time series data were investigated with the idea that these represent realistic intermittent sampling strategies. Data subsets included split‐samples and various combinations of weekly, monthly, and quarterly fixed interval subsets, as well as a 53‐day ‘informed observer’ subset that utilized once per month samples except during March and April—the months containing large and often dominant snow melt events—when sampling was once per week. Several of these subsets, including that of the informed observer, provided very similar constraints on model calibration and parameter identification as the full data record, in terms of credibility bands on simulated time series, posterior parameter distributions, and performance indices calculated to the full dataset. This result suggests that hydrological sampling designs can, at least in some cases, be optimized. Copyright © 2009 John Wiley & Sons, Ltd.     

基于多尺度球面小波解算GPS应变场的方法及应用

提出了利用多尺度球面小波解算GPS应变场的方法,该方法通过建立不规则分布的小波基函数以凸显测站非均匀分布的特征,获取不同空间尺度的应变场.通过对模拟数据进行对比分析验证该方法的有效性,模拟结果显示,多尺度球面小波应变计算方法稳健性较好.在位移场中加入高斯随机误差(均值为0.0 mm,标准差为0.5 mm)对应变计算结果的影响可忽略不计.从原有位移场随机抽取的60%的数据解算应变场时,仍然能够获取比较可靠的结果,但如果出现大范围的数据空缺,则会对应变结果产生明显影响.基于华北地区GPS测站原始观测数据,通过高精度数据处理方法解算了该区域GPS速度场,根据多尺度球面小波方法,解算了该区域的应变率场及其误差,并分析了其空间分布特征.