Spatial Breakdown Point of Variogram Estimators

In the context of robust statistics, the breakdown point of an estimator is an important feature of reliability. It measures the highest fraction of contamination in the data that an estimator can support before being destroyed. In geostatistics, variogram estimators are based on measurements taken at various spatial locations. The classical notion of breakdown point needs to be extended to a spatial one, depending on the construction of most unfavorable configurations of perturbation. Explicit upper and lower bounds are available for the spatial breakdown point in the regular unidimensional case. The difficulties arising in the multidimensional case are presented on an easy example in IR² , as well as some simulations on irregular grids. In order to study the global effects of perturbations on variogram estimators, further simulations are carried out on data located on a regular or irregular bidimensional grid. Results show that if variogram estimation is performed with a 50% classical breakdown point scale estimator, the number of initial data likely to be contaminated before destruction of the estimator is roughly 30% on average. Theoretical results confirm the previous statement on data in IR^d , d 1.     

Optimized and robust experimental design: a non-linear application to EM sounding

Pragmatic experimental design requires objective consideration of several classes of information including the survey goals, the range of expected Earth responses, acquisition costs, instrumental capabilities, experimental conditions and logistics. In this study we consider the ramifications of maximizing model parameter resolution through non-linear experimental design. Global optimization theory is employed to examine and rank different EM sounding survey designs in terms of model resolution as defined by linearized inverse theory. By studying both theoretically optimal and heuristic experimental survey configurations for various quantities of data, it is shown that design optimization is critical for minimizing model variance estimates, and is particularly important when the inverse problem becomes nearly underdetermined. We introduce the concept of robustness so that survey designs are relatively immune to the presence of potential bias errors in important data. Bias may arise during practical measurement, or from designing a survey using an appropriate model.     

General absorbing boundary conditions for dynamic analysis of fluid-saturated porous media

General absorbing boundary conditions based on Biot's two-phase mixture theory and paraxial approximation is presented for the dynamic analysis of fluid-saturated porous media with isotropic, transverse isotropic, and anisotropic properties. For the last two cases, the equivalent Lame's constants, under conditions of uniqueness, are introduced to facilitate the analytical solutions. The numerical results show that the proposed absorbing boundary can greatly suppress spuriously reflected waves and efficiently model the far field of the system with sufficient accuracy.     

The inner Galaxy resolved at IJK using DENIS data

We present the analysis of three-colour optical/near-infrared images, in IJK , taken for the DEep Near Infrared Southern Sky Survey (DENIS) project. The region considered covers 17.4 deg² and lies within <5°, b <1.°5. The adopted methods for deriving photometry and astrometry in these crowded images, together with an analysis of the deficiencies nevertheless remaining, are presented. The numbers of objects extracted in I , J and K are 748 000, 851 000 and 659 000 respectively, to magnitude limits of 17, 15 and 13. Eighty per cent completeness levels typically fall at magnitudes 16, 13 and 10 respectively, fainter by about 2 mag than the usual DENIS limits as a result of the crowded nature of these fields. A simple model to describe the disc contribution to the number counts is constructed, and parameters for the dust layer are derived. We find that a formal fit of parameters for the dust plane, from these data in limited directions, gives a scalelength and scaleheight of 3.4±1.0 kpc and 40±5 pc respectively, and a solar position 14.0±2.5 pc below the plane. This latter value is likely to be affected by localized dust asymmetries. We convolve a detailed model of the systematic and random errors in the photometry with a simple model of the Galactic disc and dust distribution to simulate expected colourmagnitude diagrams. These are in good agreement with the observed diagrams, allowing us to isolate those stars from the inner disc and bulge. After correcting for local dust-induced asymmetries, we find evidence for longitude-dependent asymmetries in the distant J and K sources, consistent with the general predictions of some Galactic bar models. We consider complementary L -band observations in the companion paper.     

Development of longitudinal profiles of alluvial channels in response to base-level lowering

Degradation of alluvial channels in cohesive sediments was studied in 15 m and 20 m long flumes with a slope of 0°01 cm/cm. Degradation was initiated by lowering base level to a fixed position, and the development of the longitudinal profile of the channel is analysed through a model formulated as a heat (diffusion) equation. It is based on the equation of sediment continuity, combined with an assumption regarding sediment transport, namely that sediment discharge is linearly proportional to the channel slope. In accordance with the boundary and initial conditions imposed by the experimental setup and procedure, the basic equation is amenable to an analytical solution, which defines bed elevation at any distance and time, as a function of the amount of base-level lowering and a ‘diffusion’ coefficient. Additional problems arising from bank erosion and channel armouring are also treated successfully within the framework of the same model. The results show that in homogeneous alluvial sediments, not subject to armouring, the ultimate result of base-level lowering by a certain amount is degradation all along the channel by the same amount. The main impact of erosion is felt in the early stages after initiation of the process, and mainly near the mouth. The rate of degradation at any station along the channel reaches a peak and then slowly decreases with time, and the peak rate is attenuated with distance from the outlet. The model permits the prediction of intermediate stages of profile development at any distance from the outlet and at different times.     

数值预报产品动力-统计释用方法与寒潮预报

从气温变化的物理过程出发,设计了一种数值预报产品的动力－统计释用方法,开发了一套四川盆地寒潮入侵时间和降温幅度的释用方案,并利用ＥＣＭＷＦ产品建立四川盆地寒潮自动预报系统,滚动预报未来１～６日内的寒潮过程。１９９５～１９９７年投入中短期业务运行,取得了显著效果。     

Point-block covariance: A general solution for the two-dimensional stationary random functions

The application of the theory of random functions to problems of ore evaluation may involve computations of the covariance between the mean value of a given block and the functional value at a given point. However, an analytical solution for such a covariance does not exist for nonspherical blocks and for commonly applied models of covariance functions. Further, because this covariance is a function of the spatial arrangements of the block and the point, it has to be evaluated numerically each time for given point—block arrangements. This paper presents a readily available general solution to this problem in the form of a series of graduated curves which, together with some geometric manipulations, may be used to compute the covariance between a pointand a two-dimensional block for all possible point—block arrangements. The availability of the graph thus eliminates the necessity of using the time-absorbing programs on computers for such computations. Finally, many of the approximations that are made in order to avoid cumbersome covariance evaluations are no longer necessary due to the ease of such computations with the help of the graph provided.     

Some methods for statistical analysis of multimodal distributions and their application to grain-size data

Some of the methods used in the resolution of mixed normal distributions are discussed under three headings: analytical, graphical, and numerical methods. Attention is given to their applicability in the analysis of grain-size data as derived from sieving. Comparisons are made by applying several methods to published data. It is concluded that the numerical methods offer most scope, especially the method of nonlinear least squares. Some analyses of beach sediments, using this method, are presented. The adoption of a convention for the number of individuals in the sample increases ease of interpretation.     

Correlations among color,morphology, and luminosity for the luminous red galaxy (LRG) sample of the SDSS data release 5

We have investigated the correlations among color, morphology and luminosity for all LRGs, cut I LRGs, cut II LRGs, and Main galaxies that are also classified as LRGs. It is found that the morphology of LRGs is tightly correlated with luminosity. The rest-frame u-g color of cut I LRGs and cut II LRGs is nearly independent of luminosity, but the color of Main galaxies is correlated with luminosity. For cut I LRGs and Main galaxies, the early type proportion apparently changes with color: at the rest-frame u-g < 1.3 it increases strongly with increasing color, while at the rest-frame u-g > 1.3 it decreases with increasing color. We also notice that the morphology of cut II LRGs is only a weak function of color. Published in Astrofizika, Vol. 50, No. 3, pp. 335–345 (August 2007).     

Mid-to-Far Infrared Spectral Energy Distribution of Galaxies in the Spitzer First Look Survey Field

We made model fitting to the mid-to-far infrared spectral energy distributions (SEDs) for different categories of galaxies in the main extragalactic field of the Spitzer First Look Survey with the aid of spectroscopic information from the Sloan Digital Sky Survey. We find that the mid-to-far infrared SEDs of HII galaxies, mixture type galaxies and LINERs can be well fitted by the one-parameter (α) dust model of Dale et al. plus the 13 Gyr dust-free elliptical galaxy model. The statistics of α values indicates that all these galaxies tend to be quiescent, although the HII galaxies are relatively more active than the LINERs. The mid- infrared SEDs of absorption galaxies are well fitted simply by the 13 Gyr dust-free elliptical galaxy template, and the near-to-mid infrared SEDs of QSOs can be represented by AGN NGC 5506.