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.     

扬州市6－7月份天气预报服务业务化系统

从地（市）级气象台的业务工作出发,试图建立通过微机实现的对上接收信息、对外预报服务、对下预报指导的三位一体的天气预报服务业务化系统,以发挥地（市）级气象台在经济建设和防灾减灾中的作用,推动天气预报和服务的现代化建设,把基层气象工作推向一个新的台阶。     

A dynamic box model of bioactive elements in the southern Taiwan Strait

A dynamic box model was applied to study the characteristics of biogeochemical cycling of PO_4-P,NO_3-N,AOU,POC and PON in the southern Taiwan Strait region based on field data of the"Minnan Taiwan Bank Fishing Ground Upwelling Ecosystem Study" during the period of Dec.1987-Nov.1988.According to the unique hydrological and topographical features of the region,six boxesand three layers were considered in the model.The variation rates and fluxes of elements induced by hor-izontal current,upwelling,by diffusion,sinking of particles and biogeochemical processes were estimatedrespectively.Results further confirmed that upwellings had important effects in this region.Thenearshore upwelling areas had net input fluxes of nutrients brought by upwelling water,also had high de-pletion rates of nutrients and production rates of particulate organic matter and dissolved oxygen.Theabnormal net production of nutrients in the middle layer(10-30m) indicated the important role of bacte-ria in this high production region.Th     

矿产预测中成矿信息的提取和强化

成矿信息的提取是矿产预测的重要手段,其方法的有效性直接影响到预测成果的可靠性。在成矿规律研究的基础上,有意识地干预模型的构成,突出与成矿有关的信息;抑制某些成矿意义不明显和属干扰的信息,有目的地使模型向反映成矿信息的方向逼近,提高模型与矿床实际赋存地质环境的吻合程度,均是成矿信息提取和强化的内涵。本文从研究实践中总结了先验约束模型和非先验约束模型的强化方法,在新疆阿勒泰地区的地质－找矿工作中已取得     

The elastic properties of single-crystal fayalite as determined by dynamical measurement techniques

We present new elasticity measurements on single-crystal fayalite and combine our results with other data from resonance, pulse superposition interferometry, and Brillouin scattering to provide a set of recommended values for the adiabatic elastic moduliC _ij and their temperature variations. We use a resonance method (RPR) with specimens that were previously investigated by pulse superposition experiments. The nineC _ij of fayalite are determined from three new sets of measurements. One set of our newC _ij data is over the range 300–500 K. We believe that the relatively large discrep ncies found in someC _ij are due in large part to specimen inhomogeneities (chemical and microstructural) coupled with differences in the way various techniques sample, rather than only systematic errors associated with experimental procedures or in the preparations of the specimens.Our recommendeaC _ij's (GPa) and (C _ij/T) _p (GPa/K) are: The resulting values for the isotropic bulk and shear moduli,K _s and , and their temperature derivatives are:K _s=134(4) GPa; =50.7(0.3) GPa; (K _s/T) _p =–0.024(0.005) GPa/K; and (/T) _p =–0.013(0.001) GPa/K. An important conclusion is thatK _s increases as the Fe/(Fe+Mg) ratio in olivine is increased.     

新疆地震预报研究

新疆的地震预报是1970年开始的。二十多年来在“边观测、边研究、边预报”、“多路探索、多兵种联合作战”、“走综合预报之路”的方针指导下取得了长足的进展。建设了43个地震台站,投入189套仪器,建成了遍布全疆的地震无线通讯网,开展了历史地震调查和地震烈度区划工作,建立健全了地震会商预报制度,进行了多方面的地震预报研究。实际地震预报统计分析表明,扣除自然发震概率之后,趋势预报的成功率约0.3,短临预报的成功率约0.1。在前兆台网控制范围内取得了一些震例,说明地震确实是有前兆的,但又是非常复杂的。地震预报作为科学难题还有漫长的路要走。作者简要地讨论了地震观测的间接性和地震异常的离散性、难以区别的地震异常和地壳变动异常、建立在复杂现象基础上的地震前兆以及地震的混沌性对地震预报的影响等科学问题。