The Tau Model for Data Redundancy and Information Combination in Earth Sciences: Theory and Application

Many decision-making processes in the Earth sciences require the combination of multiple data originating from diverse sources. These data are often indirect and uncertain, and their combination would call for a probabilistic approach. These data are also partially redundant with each other or with all others taken jointly. This overlap in information arises due to a variety of reasons—because the data arises from the same geology, because they originate from the same location or the same measurement device, etc. The proposed tau model combines partially redundant data, each taking the form of a prior probability for the event being assessed to occur given that single datum. The parameters of that tau model measure the additional contribution brought by any single datum over that of all previously considered data; they are data sequence-dependent and also data value-dependent. Data redundancy depends on the sequence in which the data is considered and also on the data values themselves. However, for a given sequence, averaging the tau model parameters over all possible data values leads to exact analytical expressions and corresponding approximations and inference avenues. Information on multiple-point connectivity of permeability arrives from core data, well-test data and seismic data which are defined over varying supports with complex redundancy between these information sources. In order to compute these tau weights for determining connectivity, one needs a model of data redundancy, here expressed as a vectorial training image (Ti) constructed using a prior conceptual knowledge of geology and the physics of data measurement. From such a vectorial Ti, the tau weights can be computed exactly. Neglecting data redundancy leads to an over-compounding of individual data information and the possible risk of making extreme decisions.     

Group Time Delay in the Reflection of P-Polarized Electromagnetic Plane Waves at a Stratigraphic Interface

The group time delay (GTD) formulae of quasi-total reflection of inhomogeneous P-polarized electromagnetic waves (P-PEW, whose electric field parallels to the plane of incidence), caused by the Goos–Hänchen effect, is derived by the phase shift of the wave. A numerical example where the frequency equals to 1 GHz is given. The curves of calculating results show that there are three discontinuous points at the critical angle of phase shift vector, the critical angle of attenuation vector and 90^○. When the angle of incidence is equal to one of these three angles, the GTD will become infinite, and the electromagnetic wave will propagate along the interface. The GTD will be very large, when the angle of incidence is close to one of these three angles. The results indicate that there is an important relationship between the two critical angles and the conductivity and permittivity of the two strata, and that the GTD has an important relationship with the angle of incidence. These results can be used to determine the lithology of the strata and to delimit the interfaces of strata more effectively. It is suggested that this research may prove useful in electromagnetic logging analysis and, perhaps, in the design of logging instruments.     

Stability Analysis and Numerical Simulation of Differential Frost Heave

Differential frost heave is often implicated in the formation of patterned ground in regions subject to recurrent freezing and thawing. A linear stability analysis (LSA) indicates that a continuum model of frost heave is linearly unstable under typical natural freezing conditions of silty-clay soils. A two-dimensional non-linear numerical analysis corroborates the frozen time LSA results, and also indicates the importance of non-linear and time-dependent terms that ultimately lead to a preferred mode, which the LSA fails to predict. Instability of the one-dimensional solution occurs at shallow freezing depths and near-zero surface loads when positive perturbations in the ice content at the freezing front lead to a concomitant increase in thermomolecular pressure and upward ice velocity. Differential frost heave can then occur because of the increased heat flux from the perturbed surfaces. A three-dimensional model using random initial surface perturbations indicates that regular surface patterns will evolve with a length scale in the order of 2–4 meters, which corresponds quite closely with naturally-occurring non-sorted patterned ground.     

Non-Linear Theory and Power-Law Models for Information Integration and Mineral Resources Quantitative Assessments

Singular physical or chemical processes may result in anomalous amounts of energy release or mass accumulation that, generally, are confined to narrow intervals in space or time. Singularity is a property of different types of non-linear natural processes including cloud formation, rainfall, hurricanes, flooding, landslides, earthquakes, wildfires, and mineralization. The end products of these non-linear processes can be modeled as fractals or multifractals. Hydrothermal processes in the Earth’s crust can result in ore deposits characterized by high concentrations of metals with fractal or multifractal properties. Here we show that the non-linear properties of the end products of singular mineralization processes can be applied for prediction of undiscovered mineral deposits and for quantitative mineral resource assessment, whether for mineral exploration or for regional, national and global planning for mineral resource utilization. In addition to the general theory and framework for the non-linear mineral resources assessment, this paper focuses on several power-law models proposed for characterizing non-linear properties of mineralization and for geoinformation extraction and integration. The theories, methods, and computer system discussed in this paper were validated using a case study dealing with hydrothermal Au mineral potential in southern Nova Scotia, Canada.     

Inversely-Mapped Analytical Solutions for Flow Patterns around and within Inclined Elliptic Inclusions in Fluid-Saturated Rocks

In this paper, an inverse mapping is used to transform the previously-derived analytical solutions from a local elliptical coordinate system into a conventional Cartesian coordinate system. This enables a complete set of exact analytical solutions to be derived rigorously for the pore-fluid velocity, stream function, and excess pore-fluid pressure around and within buried inclined elliptic inclusions in pore-fluid-saturated porous rocks. To maximize the application range of the derived analytical solutions, the focal distance of an ellipse is used to represent the size of the ellipse, while the length ratio of the long axis to the short one is used to represent the geometrical shape of the ellipse. Since the present analytical solutions are expressed in a conventional Cartesian coordinate system, it is convenient to investigate, both qualitatively and quantitatively, the distribution patterns of the pore-fluid flow and excess pressure around and within many different families of buried inclined elliptic inclusions. The major advantage in using the present analytical solution is that they can be conveniently computed in a global Cartesian coordinate system, which is widely used in many scientific and engineering computations. As an application example, the present analytical solutions have been used to investigate how the dip angle of an inclined elliptic inclusion affects the distribution patterns of the pore-fluid flow and excess pore-fluid pressure when the permeability ratio of the elliptic inclusion is of finite but nonzero values.     

Spatial orientation of the spin vectors of the disk galaxies in the Virgo cluster I. A catalogue of the disk galaxies in the Virgo cluster

Based on four UK Schmidt Telescope (UKST) IIIa-j direct plates which had been digitized by the Automated Plate Measuring System (APM), a detailed identification of the disk galaxies in the Virgo cluster has been carried out. The certain and possible member galaxies are mainly selected from the updated Catalogue of 2096 Galaxies in the Virgo Cluster Area (VCC). The area of this identification covers a 85 square degree region centered on this cluster. As a result, we compiled a new catalogue of 340 certain and possible member disk galaxies, including 85 lenticulars (SO), 136 spirals (S) and 119 irregulars (Irr), where the APM-measured values of the position angle (P.A.) and diameters of 299 disk galaxies are provided. For at least 149 galaxies, the values of the P.A. and diameters are published for the first time.Comparison between the APM-measured P.A. and diameters of galaxies and those given by the Uppsala General Catalog of Galaxies (UGC) demonstrates the reliability of our data. The statistical properties and completeness of this database are also discussed. Compared with the UGC-given P.A. and diameters which were determined by eyes, our data has no selection effect owing to the instrument measurements. Within our searching region, this might be the largest and relatively complete photometric database published so far for investigating the spatial orientation of the spin vectors of galaxies in the Virgo cluster.     

SOME NEW UNDERSTANDINGS OF LAND-SURFACE PROCESSES IN ARID AREA FROM THE HEIFE*

The survey for the HEIFE(Atmosphere-Land Surface Processes Experiment at Heihe River Basin,Western China) is given in the paper.The following basic subjects for land-surface processes in arid areas are studied:(1) the general characteristics of the energy budget on ground surface in arid areas;(2) the parameterization of the land surface processes;(3) the interaction between oasis and its desert circumstances,a special phenomenon in arid areas.The analysis shows that the sensible heat flux in the surface energy budget is in the majority,and the latent heat flux may be neglected.The influence of atmospheric stratification stability on the turbulent transfer of energy and substance must be considered in parameterization of land surface processes in arid areas.The "cold island effect" phenomenon in oasis and the "humidity inversion" phenomenon in desert near oasis are the result of the interaction between them.The results would improve the understanding of land surface processes in arid areas.     

暖切变型江淮梅雨锋结构及其形成和维持机制

对在1991年7月上旬特别稳定的梅雨形势下持续10天的特大暴雨期作了合成和典型过程研究,并进一步探讨了暖切变型江淮梅雨锋天气系统模型。它在自由大气层表现为结构竖立的相当正压切变线和一种不同于经典地转动量近似的带状准二维运动场。边界层的浅层锋生倾斜环流以及偏于切变线轴以南的Ekman抽吸与自由大气层中基本上由积云对流加热驱动的竖直环流相互依存和耦合,造成持续的大暴雨。这种系统的初生和中断后复苏的机制可能是由斜压性极弱的副热带高空东移的短波扰动在低层“湿度锋”带紧南侧触发导致的一种带状CISK。     

Arctic haze: Perturbation to the radiation field

Summary A model of the polluted arctic troposphere is constructed to estimate the magnitude and seasonal variation of the climate forcing function of arctic haze. Using a pill-box bathtub model for the Arctic and envisioning it to be filled with pollution from industrial sources in Eurasia, we estimate that maximum climate perturbation from arctic contamination occurs in the spring months. The major perturbation to the radiation budget is a lowering of the albedo (heating) of the earth-atmosphere system around the vernal equinox and is due to a trace amount (about 5% by mass) of black carbon associated with the removal-resistant submicron mode of aerosols. The black carbon over the reflecting polar ice/snow introduces a heating of about 1.5 degree per day into the haze layer.With 8 Figures     

地铁施工对济南白泉泉群流量的影响

为研究地铁建设对济南白泉泉群的影响，在综合分析白泉泉域地质、水文地质条件的基础上，假定研究区岩溶强径流带位置及水力性质，利用FEFLOW软件建立地下水流数值模型。以规划地铁M1号线为研究对象，分析了济南东站、梁王站、梁王东站分别施工及3个站同时施工4种情景下，采用施工降水或施工降水+人工回灌两种施工方式对白泉泉群流量的影响。结果表明：单独采用施工降水的施工方式使得白泉泉群流量衰减，其中3个站同时施工对泉流量的影响最大，泉流量最大衰减达5.48%；各站分别施工时，济南东站对泉流量影响最大，泉流量较未施工时减少了0.043×10⁴ m³/d。采用施工降水+人工回灌的施工方式，能够有效缓解泉流量的衰减，各车站施工时的泉流量衰减由仅施工降水时的2.26%~5.48%降低至0.08%~1.21%。岩溶强径流带有利于地下水形成优势径流，促进白泉泉群补给，一定程度上缓解因地铁施工引起的泉流量衰减。