Determination of the polynomial moments of the seismic moment rate density distribution with positivity constraints

We present a new formulation of the inverse problem of determining the temporal and spatial power moments of the seismic moment rate density distribution, in which its positivity is enforced through a set of linear conditions. To test and demonstrate the method, we apply it to artificial data for the great 1994 deep Bolivian earthquake. We use two different kinds of faulting models to generate the artificial data. One is the Haskell-type of faulting model. The other consists of a collection of a few isolated points releasing moment on a fault, as was proposed in recent studies of this earthquake. The positions of 13 teleseismic stations for which P - and SH -wave data are actually available for this earthquake are used. The numerical experiments illustrate the importance of the positivity constraints without which incorrect solutions are obtained. We also show that the Green functions associated with the problem must be approximated with a low approximation error to obtain reliable solutions. This is achieved by using a more uniform approximation than Taylor's series. We also find that it is necessary to use relatively long-period data first to obtain the low- (0th and 1st) degree moments. Using the insight obtained into the size and duration of the process from the first-degree moments, we can decrease the integration region, substitute these low-degree moments into the problem and use higher-frequency data to find the higher-power moments, so as to obtain more reliable estimates of the spatial and temporal source dimensions. At the higher frequencies, it is necessary to divide the region in which we approximate the Green functions into small pieces and approximate the Green functions separately in each piece to achieve a low approximation error. A derivation showing that the mixed spatio-temporal moments of second degree represent the average speeds of the centroids in the corresponding direction is given.     

Single station and regional analysis of daily rainfall extremes

A peaks over threshold (POT) method of analysing daily rainfall values is developed using a Poisson process of occurrences and a generalised Pareto distribution (GPD) for the exceedances. The parameters of the GPD are estimated by the method of probability weighted moments (PWM) and a method of combining the individual estimates to define a regional curve is proposed.     

Grain yield reliability analysis with crop water demand uncertainty

A new method of reliability analysis for crop water production function is presented considering crop water demand uncertainty. The procedure uses an advanced first-order second moment (AFOSM) method in evaluating the crop yield failure probability. To determine the variance and the mean of actual evapotranspiration as the component of interest for AFOSM analysis, an explicit stochastic optimization model for optimal irrigation scheduling is developed based on the first and second-order moment analysis of the soil moisture state variables. As a result of the study, the violation probabilities of crop yield at different levels were computed from AFOSM method. Also using the optimization results and the double bounded density function estimation methodology, the weekly soil moisture density function is derived which can be used as a short term reliability index. The proposed approach does not involve any discretization of system variables. The results of reliability analysis and optimization model compare favorably with those obtained from simulation.     

Multivariate homogeneity testing in a northern case study in the province of Quebec,Canada

In regional frequency analysis, the examination of the regional homogeneity represents an important step of the procedure. Flood events possess multivariate characteristics which can not be handled by classical univariate regional procedures. For instance, classical procedures do not allow to assess regional homogeneity while taking into consideration flood peak, volume and duration. Chebana and Ouarda proposed multivariate discordancy and homogeneity tests. They carried out a simulation study to evaluate the performance of these tests. In the present paper, practical aspects are investigated jointly on flood peak and flood volume of a data set from the Côte‐Nord region in the province of Quebec, Canada. It is shown that, after removing the discordant sites, the remaining ones constitute a homogeneous region for the volumes and heterogeneous region for the peaks. However, if both variables are jointly considered, the obtained region is possibly homogeneous. Furthermore, the results demonstrate the usefulness of the bivariate test to take into account the dependence structure between the variables representing the event, and to take advantage of more information from the hydrograph. Copyright © 2009 John Wiley & Sons, Ltd.     

内核晃动对地球主惯性矩的时变性影响

高密度内核相对于地幔的晃动将改变地球内部物质的密度分布并导致地球主惯性矩随时间变化。本文在重力场球谐分析理论的基础上,给出了时变的地球主惯性矩A、B、C及主惯性轴,并研究了内核晃动对A、B、C的时变性影响。计算结果表明,A、B、C平均每年增大约4.5×1027kg m2,而内核晃动使A、B、C均表现出振幅为1022~1024kg m2的似正弦式变化,不足以维持其长期增大趋势,这进一步支持了"地球在膨胀"的结论。     

谱矩方法在磁源体深度反演中的应用研究

谱矩方法可以对数据的表面形貌做较为细致的描述.它以随机过程为理论基础,用各阶谱矩及统计不变量等具体的参数表征表面的几何形态,算术平均顶点曲率是一种基于四阶谱矩的统计不变量.通常,埋深不同的场源所引起的磁异常尺度不同,从曲率的角度来理解即为磁异常曲面的弯曲程度不同.因此,本文应用算术平均顶点曲率提取磁异常的几何信息,并将所提取的信息用于场源深度的反演.理论上推导了基于谱矩的球状磁源体和板状磁源体的反演公式,得到了场源深度与磁异常、曲率之间的关系式.结合理论模型计算验证了方法的有效性,并与欧拉反褶积方法进行对比.与传统的方法相比,该方法快速简单,无需调节参数,且有较好的反演精度.最后,将该方法用于塔里木盆地航磁异常的反演和解释中,反演出的磁源体深度可满足区域磁异常数据分析和解释的要求,为克拉通沉积盆地磁异常源的深度划分提供丰富的信息.

     

边界时刻一致性判别方法在北京市出租车运量生成机制中的实证应用

以北京市出租车运量生成机制研究为例,探索时间基本单元大小对交通时段划分及运量生成机制的影响。基于北京市出租车轨迹数据,按10 min步长,采用10 min至60 min共6种时间基本单元对全天数据在交通小区尺度进行划分得到切片数据,应用系统聚类法将切片聚合得到时段划分,得到6种时段划分结果,进而对具有交集的时段采用边界时刻进行一致性判别。在时段划分基础上,应用地理加权回归模型比较分析了不同时间基本单元在上班时段的出租车运量影响因子的差异。结果显示,时间基本单元小于40 min时,上班时段的起始时刻不具有一致性;如果考虑所有时段的起始和结束时刻,则小于50 min时不具有一致性。上班时段的运量生成机制模型结果与时刻一致性判别类似,当时间基本单元在50 min及以上时,回归得到的解释变量具有一致性,小于50 min后则会有所变化。这些结果说明,基本时间单元的大小会影响交通运量时段划分和生成机制研究的结果;考虑到结果一致性和整点划分习惯,推荐采用60 min为基本划分单元。提出的边界时刻一致性判别方法也可以用到其它交通模式和其他相似的大数据研究。     

基于高阶概率权重矩的广义极值分布参数估计

研究基于高阶概率权重矩的广义极值分布参数估计。根据高阶概率权重矩法原理,建立了广义极值分布高阶概率权重矩估算参数模型。以陕北地区4个水文测站的年最大洪峰流量序列为例,结果表明:高阶概率权重矩法能赋予大洪水值更多的权重。蒙特卡洛试验表明:适当提高阶数可以减小误差,但阶数过高反而会增大误差。     

The PWM large quantile estimates of heavy tailed distributions from samples deprived of their largest element / Estimation des grands quantiles de distributions à queue à décroissance lente par la méthode des moments pondérés par les probabilités à partir d'échantillons amputés de leur plus grande valeur

Abstract

Extremes of streamflow are usually modelled using heavy tailed distributions. While scrutinising annual flow maxima or the peaks over threshold, the largest elements in a sample are often suspected to be low quality data, outliers or values corresponding to much longer return periods than the observation period. In the case of floods, since the interest is focused mainly on the estimation of the right-hand tail of a distribution function, sensitivity of large quantiles to extreme elements of a series becomes the problem of special concern. This study investigated the sensitivity problem using the log-Gumbel distribution by generating samples of different sizes and different values of the coefficient of L-variation by means of Monte Carlo experiments. Parameters of the log-Gumbel distribution were estimated by the probability weighted moments (PWM) method, both for complete samples and the samples deprived of their largest element. In the latter case Hosking's concept of the “A” type PWM with Type II censoring was employed. The largest value was censored above the random threshold T corresponding to the non-exceedence probability F _T. The effect of the F _T value on the performance of the quantile estimates was then examined. Experimental results show that omission of the largest sample element need not result in a decrease in the accuracy of large quantile estimates obtained from the log-Gumbel model by the PWM method.