Multi-Scale Texture Modeling

Patterns of crystallographic preferred orientation are referred to as texture. The specific subject of texture analysis is the experimental determination and interpretation of the statistical distribution of orientations of crystals within a specimen of polycrystalline material, which could be metals or rocks. The objective is to relate an observed pattern of preferred orientation to its generating processes and vice versa. In geosciences, texture of minerals in rocks is used to infer constraints on their tectono-metamorphic history. Since most physical properties of crystals, such as elastic moduli, the coefficients of thermal expansion, or chemical resistance to etching depends on crystal symmetry and orientation, the presence of texture imparts directional properties to the polycrystalline material. A major issue of mathematical texture analysis is the resolution of the inverse problem to determine a reasonable orientation density function on SO(3) from measured pole intensities on , which relates to the inverse of the totally geodesic Radon transform. This communication introduces a wavelet approach into mathematical texture analysis. Wavelets on the two-dimensional sphere and on the rotational group SO(3) are discussed, and an algorithms for a wavelet decomposition on both domains following the ideas of Ta-Hsin Li is given. The relationship of these wavelets on both domains with respect to the totally geodesic Radon transform is investigated. In particular, it is shown that the Radon transform of these wavelets on SO(3) are again wavelets on . A novel algorithm for the inversion of experimental pole intensities to an orientation density function based on this relationship is developed.     

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.     

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.     

Mt. Melbourne volcano,antarctica: Evidence of seismicity related to volcanic activity

Characterization of the microseismic activity (M _L <2.0) has been performed at Mt. Melbourne since 1990. We recorded a group of low frequency events with common morphological characteristics, i.e., an emerging onset, an unclear second phase and a sharply dropping coda. Spectral analysis of events recorded at more than one station indicates that the seismogram characteristics and spectral content are largely due to source effects. A polarization filter applied to a set of three component data revealed a first phase made up ofP waves followed (after about 0.9–1.4 sec.) by a second phase probably composed ofSH-type waves. Particle motion analysis detected a seismic ray angle direction mainly between N70°E and N110°E and apparent angle of incidence between 35° and 48° for the first phase. The studied seismicity was localized in an area on the eastern slope of Mt. Melbourne Volcano which presents a surface temperature anomaly (Mazzarini andSalvini, 1994). We formulate two hypotheses for the type of earthquakes recorded: 1) long-period events involving active presence of magmatic fluids in the source processes; 2) or the result of fracturing processes (shear?) in a medium characterized by transition between brittle and plastic behaviors. In the latter hypothesis the superficial thermal anomaly may be a symptom of this behavior at depth and is confirmed by the lown values observed for the exponential fit in the codaQ analysis.     

Towards a nonperturbation transport theory in hetereogeneous aquifers

A large body of existing theories of flow and contaminant transport in aquifers ignore the presence of recharge, eliminate the boundary conditions, neglect transient conditions in groundwater flow, conceive hydraulic gradients as linear, and require parameter variability to be stationary and Gaussian. The most outstanding and difficult to justify assumption is the subjective small size of the stochastic terms (i.e., small perturbation methods), which usually is forced by considering the logarithm of the hydraulic conductivity. Several problems in flow and contaminant subsurface hydrology, such as the enhanced dispersion parameters with plume size or time after injection, remain to be observed in the light of a stochastic theory that allows a more realistic consideration of physical and hydrologic properties. In this article, an attempt is made to reformulate a contaminant transport equation (the variable dispersion equation, VDE) with transport parameters in terms of regional hydrologic and aquifer hydraulic properties, such as recharge rate, spatially random transmissivity, hydraulic gradient, aquifer thickness, and soil porosity. Subsequently, a general analytic procedure, the method of decomposition, is used to derive a solution to the VDE. This procedure does not require small perturbation, logarithmic transformations, or specific probability law assumptions. Comparison tests with existing theoretical and field results are given. The tests illustrate the enhanced dispersion and shifting concentration effects produced by the variable dispersion equation. Finally a generalization of the method to nonstationary dispersion in three-dimensional domains is proposed.     

Hierarchical decomposition of variance with applications in environmental mapping based on satellite images

A quadtree-based image segmentation procedure (HQ) is presented to map complex environmental conditions. It applies a hierarchical nested analysis of variance within the framework of multiresolution wavelet approximation. The procedure leads to an optimal solution for determining mapping units based on spatial variability with constraints on the arrangement and shape of the units. Linkages to geostatisiics are pointed out, but the HQ decomposition algorithm does not require any homogeneity criteria. The computer implementation can be parameterized by either the number of required mapping units or the maximum within-unit variance, or it can provide a spectrum of significances of nested ANOVA. The detailed mathematical background and methodology is illustrated by a salt-affected grassland mapping study (Hortobágy, Hungary), where heterogeneous environmental characteristics have been sampled and predicted based on remotely sensed images using these principles.     

Palaeolimnological studies of the eutrophication of volcanic Lake Albano (Central Italy)

We use palaeolimnological techniques to reconstruct the eutrophication history of a volcanic lake (Lake Albano, central Italy) over the past three centuries. The presence of annual varves down to the bottom of the core (c. 1700 A.D.) indicated the lack of bioturbation and likely long-term meromixis. Sedimentation rates were estimated by varve counts (calcite/diatom couplets), indicating a mean rate of 0.15 cm yr^–1. The reconstruction of eutrophication was traced using past populations of algal and photosynthetic bacteria (through their fossil pigment), and geochemistry, as well as fossil remains of chironomids. Phaeophorbidea and the red carotenoid astaxanthin were used to detect past zooplankton development.The first sign of trophic change related to human activities is datedc. 1870 A.D. From that period onward a sharp increase of authigenic CaCO₃, nitrogen, N:P ratio, and dinoxanthin, a characteristic carotenoid of Chrysophyceae and Dinophyceae, is observed.Chironomid analyses showed the near absence of a deep water fauna throughout the core length. The populations of chironomid larvae are restricted to oxygenated littoral zones. In fact, the few fossil remains found are primarily of littoral origin, representing shallow water midges that were transported to profundal waters. The reduction of total chironomid in the uppermost layers of the core is to be related to human land uses.     

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。     

Palaeoclimatic studies in South Shetland Islands,Antarctica, based on numerous stratigraphic variables in lake sediments

The hitherto longest found lake sediment sequence on Byers Peninsula, Livingston Island, South Shetland Islands, was analysed with respect to lithology, chronology, diatoms, Pediastrum, pollen and spores, mosses, mineralogy, and sediment chemistry. During the ca. 5000 year long development the sediments were influenced by frequent tephra fall-outs. This volcanic impact played a major role in the lake's history during two periods, 4700–4600 and 2800–2500 BP, but was of importance during the lake's entire history with considerable influence on many of the palaeoenvironmentally significant indicators. The large and complex data set was analysed and zonated with different types of multivariate analysis. This resulted in a subdivision of the sequence into 8 time periods and 21 variables. Redundancy analysis (RDA) of this data set, both without and with the tephra periods, and with 4–6 of the variables as explanatory environmental variables, reveal that climatic/environmental signals are detectable. The palaeoclimatic picture that emerged out of the tephra noise suggests that the first 100 years were characterized by mild, humid conditions. This was followed by a less mild and humid climate until ca. 4000 BP when a gradual warming seems to have started, coupled with increased humidity. These mild and humid conditions seem to have reached an optimum slightly after 3000 BP. At ca. 2500 BP a distinct climatic deterioration occurred with colder and drier conditions and long seasons with ice cover. This arid, cold phase probably reached its optimum conditions at ca. 1500 BP, when slightly warmer conditions might have prevailed for a while. Except for the modern sample with rather mild climate, the last 1400 years seem to have been fairly arid and cold, and the effects of the frequent volcanic activity during this period is only vaguely seen in the records.     

A comparison between 2D and 3D wavelet analysis method for asteroid family dynamical study

As found in previous studies (Bendjoyaet al. 1991) the wavelet analysis is a reliable tool for the determination of asteroid families. A comparison between the 2D and a newly developed 3D wavelet analysis is performed on 14 fictitious families numerically generated the members of which area priori known. It clearly appears that the 3D method brings improvements to the 2D approach. Indeed the 3D analysis appears well suited for all cases even for those corresponding to the very dense Flora region and for exotic families such as filamentar ones. With the 2D method, satisfying results are obtained for the simulations which correspond to 70% of the real asteroid families previously found. The aim of this paper is to show quantitatively the improvement of the 3D method versus the 2D one.