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.     

Trace metals in suspended particulate matter and in sediment trap material from a permanently anoxic fjord — Framvaren, South Norway

Geochemical studies of the trace metal concentrations in suspended particulate matter (SPM) and sediment trap material from a permanently anoxic fjord, Framvaren, South Norway in 1989 and 1993 indicate that extremely high concentrations of zinc (max = 183920 mg/kg), copper (max = 4130 mg/kg), lead (max = 2752 mg/kg), and cadmium (max= 8.1 mg/kg) sometimes (1993) occur in the SPM collected in the anoxic water layer. The highest concentrations of Zn occur just below the redoxcline at 22 m water depth (in 1993), and copper, lead and cadmium have maximum concentrations between 30 and 80 m depth, where the amount of total SPM is at a minimum (about 0.3 mg/L). On a mass per volume (g/L) basis, the maximum concentrations of Cd, Cu and Fe occur at the interface (21m) and those of Zn occur just below the redoxcline (22 m depth). The SPM and sediment trap data suggest that the metals are precipitated as sulfide minerals in the anoxic water. The presence of particulate sulfides was confirmed by SEM studies that show the occurrence of discrete metal (Cu, Fe, Pb, and Zn) sulfide particles in size from 10–20 m as well as framboidal pyrites (1–5 m in size). Higher levels of metal sulfides at intermediate depths rather than in the deep water of Framvaren (> 100 m), may be due to input of trace metals by water exchange over the sill in the upper part of the water column. In the deep water, less metal sulfide precipitation takes place due to depletion of trace metals, and the dilution of particulate metal concentrations by organic matter and by the chemogenic formation of calcite.     

Petrogenesis of anomalous K-enriched MORB from the Southwest Indian Ridge: 11°53′E to 14°38′E

Glassy pillow basalts with unusual geochemical characteristics for mid-ocean ridge basalt (MORB) have been dredge sampled from the Southwest Indian Ridge between 12 and 15°E during Leg ANT IV/4 of the F.S. POLARSTERN. Lavas from 4 of 6 dredges are moderately nepheline normative, highly K-enriched (0.5–1.77 wt% K₂O) alkali basalts and hawaiites. Mg-numbers indicate that many of the lavas are fairly primitive (Mg No.=63–67), yet show extreme enrichment in incompatible elements; e.g. Nb (24–60 ppm), Ba (170–470 ppm) and Sr (258–460 ppm). Incompatible-element ratios such as Zr/Nb (3–5) and Y/Nb (0.46–1.1) are extremely low even for E-type (enriched) MORB, whereas (La/Yb)_n ratios are particularly high (3.4–7.8). ⁸⁷Sr/⁸⁶Sr (0.70290–0.70368), ¹⁴³Nd/¹⁴⁴Nd (0.51302–0.51284) and ²⁰⁶Pb/²⁰⁴Pb (18.708–19.564) isotopic ratios further indicate the geochemically enriched nature of these lavas, which range from the compositional field for depleted N-type (normal) MORB towards the composition of Bouvet Island lavas. Mutually correlated incompatible-element and Sr-, Nd- and Pb-isotopic ratios allow a fairly well constrained model to be developed for the petrogenesis of these unusually alkalic mid-ocean ridge lavas. The alkalic nature and degree of enrichment in incompatible elements is ascribed to particularly low degrees of partial melting (3–5 wt%), at greater than usual depth, of a source region that has experienced prior geochemical enrichment (by veining) related to the upwelling Bouvet mantle plume. To account for the observed compositional variations, a model is proposed whereby mixing between partial melts derived from these geochemically enriched silicate veins, and an incipient to low percentage (±2%) melt from the surrounding geochemically depleted suboceanic asthenosphere occurs as a consequence of increasing degree of melting with adiabatic upwelling. Eruption of these alkalic lavas in this spreading ridge environment is attributed to a temporary hiatus in tholeiitic volcanism and associated spreading along this section of the Southwest Indian Ridge, related to readjustment of spreading direction to a more stable plate geometry.     

斜交型不稳定谱点分布侧半圆定理及其增长率上界的估计

本对斜交型扰动不稳定谱点的分布做了理论分析，得到了该谱点分布的半圆定理一该谱点分布在复一面上以原点为圆心以R0为半径的上半平面上，同时还对该不稳定增长率的上界作了估计。发现水平永度越小，模式顶越高则该估计值越大；垂直风切变的增大和纬度的增高对该增长率的增大有正贡献；当层结稳定度减小时，最大增长率随相对最大增长率得增大而减小。     

青藏高原近地面层微气象学特征

利用1998年5月-7月在改则、当雄和昌都三测站获得的近地面层气象要素变化的观测资料，分析了青藏高原近地面层风速、温度和湿度日变化特征及廓线规律，发现高原近地面层微气象学特征具有自己的特点；同时还讨论了高原近地面层白天出现的逆湿现象。     

一类广义Hamilton系统的辛格式

通过引人泊松括号，分析了无限维Hamilton的性质，并将其推广到广义Hamilton系统，且从理论和实用角度讨论了这类广义Hamilton系统的辛格式构造问题，从而为辛几何算法在一般的时间发展方程的数值求解提供新的具体途径。