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.     

研究“源兆”的若干问题及途径分析

从位场理论的观点讨论了场和源的概念,建议将“场兆”改称为构造前兆,将“源兆”称为震源前兆。文中还分析了震源体与各种前兆观测方法探测的深度,并根据地磁与重力观测方法不同的物理基础和地质基础,指出震磁效应对于研究震源前兆的特殊意义,文中还介绍了１９７６唐山地震观测到震源前兆的部分实际地磁资料。     

北京及邻区微震活动的初步分析

通过对北京遥测地震台网近年来记录到的北京及邻区地震的震中分布,地震活动频度及能量释放强度的分析,得到本区地震活动在时间分布上具有“聚堆性”。在年发震频度,地震强度和能释放方面均具有双峰值特征,并且具有较好的一致性和同步性,在空间分布上具有条带特征,且形成北东～南西和北西～南东的两条相互交汇的条带。又通过统计分析得到本区发震概率最大的时间段是每年的１０月前后,而地震主要发生在北西～南东带上。     

皖南变质岩中的疑源类、孢粉化石组合及其地质意义

皖南变质岩区地层原被认为属江南古陆的一部分,时代定为中、晚元古代。本文根据其中所含的Asperatopsophosphaera?sp.,Trachysphaeridium sp.,Nucellosphaeridium sp.,Lophosphaeridium sp.,Leiosphaeridia sp.,Baltisphaeridium spp.,Micrhystridium spp.和scolecodonts等疑源类和其它微体化石及笔者等以前发现的Lingulacea总面貌反映的时代,判断其中部分变质地层的时代应为晚元古代—早古生代和早古生代。同时还根据Crassispora sp.,Kraeuselisporites sp.和Lueckisporites ef.virkkiae Potonie ＆ Klaus,Triquitritessp.等孢粉化石组合面貌反映的时代,推断其中尚有一部分为晚古生代地层。因此认为本区是一个从晚元古代—早古生代开始到中生代结束的碰撞型造山带,而不是一个古陆。     

热液脉动与岩浆涌动控制机理浅论

热液脉动与岩浆涌动的控制机理,是基础地质理论所涉及的两个重要议题。本文首先对当今流行的构造控制机理提出了质疑,其后借助＂间歇喷泉＂原理和＂吹气球＂机制,分别对热浪的脉动和岩浆的涌动进行了必要的探讨。     

首都减灾圈的思考与建议

首都减灾圈,系首都减轻自然灾害预测防治圈。1991年12月20—21日在北京召开了《首都圈自然灾害及其减灾对策研讨会》。本文根据这次会议所提供的材料,在从整体上实现减灾的思想指导下,就首都减灾圈的“成灾背景”、“首都减灾圈的组成”、“首都减灾圈的灾害预测与防治状况”、“首都减灾圈的灾害关联性分析”、“首都减灾圈的减灾实效预估”和“首都减灾圈的减灾对策与实施”等六个带有共同性的问题,进行了讨论。供制定首都圈减灾方案时参考。