Histogram and variogram inference in the multigaussian model

Several iterative algorithms are proposed to improve the histogram and variogram inference in the framework of the multigaussian model. The starting point is the variogram obtained after a traditional normal score transform. The subsequent step consists in simulating many sets of gaussian values with this variogram at the data locations, so that the ranking of the original values is honored. The expected gaussian transformation and the expected variogram are computed by an averaging operation over the simulated datasets. The variogram model is then updated and the procedure is repeated until convergence. Such an iterative algorithm can adapt to the case of tied data and despike the histogram. Two additional issues are also examined, referred to the modeling of the empirical transformation function and to the optimal pair weighting when computing the sample variogram.     

Characteristics of the low energy seismicity of central Apulia (southern Italy) and hazard implications

The central part of the Apulia region, in southern Italy, has been generally considered practically free from significant level of seismicity, but historical documentation, geological indicators and recent instrumental observations suggest that the activity of local minor tectonic structures could have been masked (and partly also induced) by that of major seismogenic structures located in the neighbouring regions. A revision of the central Apulia seismicity characteristics was conducted considering its space and time distribution, energy release rate and focal mechanisms, in view of possible hazard implications. To better constrain the seismicity rates inferable from the set of available historical data, special attention was paid to the declustering of a catalogue of low energy events (magnitude < 3.5) instrumentally detected in about 20 years: a new declustering procedure, useful for cases like to the one at hand, was purposely devised taking into account the peculiarity of local seismicity characteristics and the limitations of the available database. The results obtained by combining instrumental and historical data show that this area is affected by a rather sporadic seismicity, likely associated to a general tensional regime and possibly stimulated by the interaction with Apenninic and northern Apulia seismogenic activity. Even though less energetic, the local seismicity contributes to increase the moderately damaging shaking probability due to the activity of seismic sources located in the near areas, so to justify the adoption of at least a minimum level of caution in relation to the local definition of seismic protection measures.     

泰森多边形在地质数据去丛聚中的应用

钻井总是被优先设计在有利储层的部位,导致获取的地质数据分布不均匀。为了使地质数据的统计结果更客观地反映实际情况,需要对地质数据进行去丛聚处理,其核心思想就是给密集的数据赋较小的权值,给稀疏的数据赋较大的权值。笔者用泰森多边形法求取钻井的控制范围,以此确定该井数据统计时的权值大小,为多边形去丛聚法中多边形的确定提供了新思路。应用本方法对石南油田某井区的孔隙度分布进行了分析,验证了该方法的可行性。     

Reducing fluctuations in the sample variogram

In the analysis of regionalized data, irregular sampling patterns are often responsible for large deviations (fluctuations) between the theoretical and sample semi-variograms. This article proposes a new semi-variogram estimator that is unbiased irrespective of the actual multivariate distribution of the data (provided an assumption of stationarity) and has the minimal variance under a given multivariate distribution model. Such an estimator considerably reduces fluctuations in the sample semi-variogram when the data are strongly correlated and clustered in space, and proves to be robust to a misspecification of the multivariate distribution model. The traditional and proposed semi-variogram estimators are compared through an application to a pollution dataset.     

Spatial declustering weights

Because of autocorrelation and spatial clustering, all data within a given dataset have not the same statistical weight for estimation of global statistics such mean, variance, or quantiles of the population distribution. A measure of redundancy (or nonredundancy) of any given regionalized random variable Z(u_α)within any given set (of size N) of random variables is proposed. It is defined as the ratio of the determinant of the N X Ncorrelation matrix to the determinant of the (N - 1) X (N - 1)correlation matrix excluding random variable Z(u_α).This ratio measures the increase in redundancy when adding the random variable Z(u_α)to the (N - 1 )remainder. It can be used as declustering weight for any outcome (datum) z(u_α). When the redundancy matrix is a kriging covariance matrix, the proposed ratio is the crossvalidation simple kriging variance. The covariance of the uniform scores of the clustered data is proposed as a redundancy measure robust with respect to data clustering.     

A New Model of Peaks over Threshold for Multivariate Extremes

The peaks over threshold（POT） methods are used for the univariate and multivariate extreme value analyses of the wave and wind records collected from a hydrometric station in the South China Sea. A new multivariate POT method： Multivariate GPD（MGPD） model is proposed, which can be built easily according to developed parametric models and is a natural distribution of multivariate POT methods. A joint threshold selection approach is used in the MGPD model well. Finally, sensitivity analyses are carried out to calculate the return values of the base shear, and two declustering schemes are compared in this study.     

Permeability Heterogeneity in a Fractured Sandstone–Mudstone Rock Mass in Xiaolangdi Dam Site, Central China

Abstract: Heterogeneity of permeability in fractured media is a hot research topic in hydrogeology. Numerous approaches have been proposed to characterize heterogeneity in the last several decades. However, little attention has been paid to correlate permeability heterogeneity with geological information. In the present study, several causes of permeability heterogeneity, that is, lithology, tectonism, and depth, are identified. The unit absorption values (denoted as ω), which are results obtained from the packer test, are employed to represent permeability. The variability of permeability in sandstone–mudstone is so significant that the value of unit absorptions span 3–4 orders of magnitude at any depth with several test sections. By declustering, it has been found that under a similar tectonic history, the means of permeability differ greatly at different formations as a result of different mudrock contents. It has also been found that in the same formation, permeability can be significantly increased as a result of faulting. The well-known phenomenon, the decrease in permeability with depth, is found to be caused by the fractures in the rock mass, and the relationship between permeability and depth can be established in the form of logω–logd. After subtracting the trend of ω with absolute depth, the mean of the residual value at each relative depth can be well correlated with the distribution of mudstone. The methods proposed in this paper can be utilized to research in similar study areas.     

Scaling properties of the spatio–temporal distribution of earthquakes: a multifractal approach applied to a Californian catalogue

We study the spatio–temporal scaling properties of the NCSN California catalogue for the period 1975–1995 (about 137 000 events) using a multifractal approach. The study is based on a new method of declustering earthquake catalogues based on looking for independent events. This technique makes use of the properties of the multifractal distribution of the inter-event times. A comparison test between our method and the Gardner and Knopoff (GK hereafter) approach reveals that our method produces a catalogue of independent events (monofractal Poissonian catalogue), while the GK declustered catalogue remains multifractal. The main difference lies in the assumption that the events can be considered to be correlated at large distances. The spatial properties of the declustered catalogue reveal a distribution of epicentres that is more complex than the distribution for the complete catalogue. We suggest that such results are very similar to the scaling properties of fully developed turbulence.     

蒙古国及其周边地区地震目录初步分析

本文以蒙古国及其周边地区M≥3.5级以上地震目录为基础数据,对该目录做了余震删除、时间完整性分析以及时间统计分布特征分析.结果表明,蒙古国M≥3.5级地震完整记录起始时间为1977年;M≥5.0级地震完整记录起始时间为1945年;M≥6.0级地震完整记录起始时间为1900年.删除余震后,蒙古国地震活动随时间变化基本平稳,时间统计分布特征符合泊松分布.并且在删除余震后,蒙古国地震活动仍有6年左右的丛集周期.