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.     

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。     

A planetary boundary-layer numerical model containing third-order derivative terms

In this paper, the third-order derivative of velocity with respect to height is included in the traditional motion equations of the neutral PBL. The nonlinear equations are solved numerically to obtain the vertical distribution of wind in the PBL and some PBL characteristic parameters. Reasonable simulations of the Leipzig wind profile using these parameters show the success of this kind of nonlocal closure in a real PBL simulation.     

热液成矿作用的地质地球化学动力学——以胶东牟平-乳山金矿带为例

通过对胶东牟平—乳山热液脉状金,铅锌矿床成矿动力学控制规律的研究,说明了建立热液成矿反应体系的方法,并得出以下认识:（1）区域断裂构造活动,通过影响成矿反应体系的热力学性质和条件,控制元素的富集和分散。（2）热液成矿过程中容矿断裂活动可划分为两种作用方式:脆性破裂和韧—脆性张开,构成热液成矿的两种构造动力学环境。（3）热液成矿反应体系是一种开放的动态的热力学体系。断裂的脆性破裂阶段,使体系处于强烈的过饱和状态,矿质在远离平衡状态下快速结晶,加剧物质分异;在脆—韧性张开阶段,矿质在接近平衡态体系中缓慢晶出。（4）热液演化晚期,金在残余溶液中富集;当断裂再次发生构造脉动震颤时,早期形成的块状黄铁矿矿石碎裂,富金溶液充填其中,形成含裂隙金和晶隙金的富矿石。成矿体系热力学演化与构造动力学条件有利的匹配控制着富矿石的形成。     

论南岭成矿带大宝山斑岩型铜矿的特殊性及其勘查意义

广东省大宝山矿床是南岭成矿带唯一的大型铜多金属矿床，此次研究在矿区中南部发现了细脉浸染状铜矿的新类型。为确定其是否为斑岩型铜矿的成因类型，本文在梳理南岭成矿带铜成矿条件和成矿规律的基础上，查明了矿区中南部英安斑岩的蚀变和铜矿化特征。综合研究认为南岭成矿带早侏罗世中酸性斑岩的小岩体较多，叠加多期断裂构造和碳酸盐岩建造，非常有利于铜多金属成矿物质的运移、富集。大宝山英安斑岩发育黑云母化、钾长石化、青磐岩化、绢英岩化、泥化等蚀变类型，铜矿化与绢英岩化、绿泥石化关系密切。大宝山铜矿中的英安斑岩沿逆冲推覆构造侵位并呈岩墙状产出，冷却过程中受区域构造应力产生了一组平行裂隙，岩浆房去气作用排出的热液沿裂隙蚀变围岩并充填成矿。大宝山斑岩型铜矿取得的找矿勘查成果表明，“全位成矿，缺位找矿”理念可以有效指导靶区圈定和老矿山外围（深部）找矿勘查，早侏罗世的南岭具有形成较大规模斑岩型铜矿的条件。