Mathematical Analysis of a Model of River Channel Formation

The study of overland flow of water over an erodible sediment leads to a coupled model describing the evolution of the topographic elevation and the depth of the overland water film. The spatially uniform solution of this model is unstable, and this instability corresponds to the formation of rills, which in reality then grow and coalesce to form large-scale river channels. In this paper we consider the deduction and mathematical analysis of a deterministic model describing river channel formation and the evolution of its depth. The model involves a degenerate nonlinear parabolic equation (satisfied on the interior of the support of the solution) with a super-linear source term and a prescribed constant mass. We propose here a global formulation of the problem (formulated in the whole space, beyond the support of the solution) which allows us to show the existence of a solution and leads to a suitable numerical scheme for its approximation. A particular novelty of the model is that the evolving channel self-determines its own width, without the need to pose any extra conditions at the channel margin.     

弹性波正演模拟中PML吸收边界条件的改进

在弹性波有限差分正演模拟中, 完全匹配层(PML) 吸收边界条件是使用广泛、吸收效果最好的吸收边界条件.在目前的两种PML实现方法中, 分裂形式的完全匹配层(SPML) 方法计算存储量大、编程实现复杂; 非分裂形式的完全匹配层(NPML) 方法计算效率低、计算过程复杂.针对传统PML吸收边界条件在实现过程中存在的问题, 推导出了一种简洁有效的非卷积实现的NPML吸收边界条件, 既不需要对场分量进行分裂, 也不需要做复杂的卷积运算.分析结果表明, 本文实现的NPML吸收边界条件不仅具有良好的吸收衰减性能, 而且计算方程简单, 编程实现容易, 占有内存更小.      

大陆盆地的聚敛-闭合过程研究:以塔里木盆地为例

印度与欧亚大陆第三纪以来碰撞汇聚,造成亚洲大陆内部强烈缩短变形。塔里木盆地如何发生相应的变形调节和应变分解,成为中亚板内构造的重要问题。塔里木陆块新生代以来被板内造山带及走滑断裂系环绕,盆地内部以刚性为特征,未发生强烈构造变形。区域大断裂与塔里木盆地的冲断、走滑构造边界共同作用,形成盆地边缘复杂的构造系。其新生代构造变形主要集中于盆地的构造边界上,4条构造边界显示差异性的运动特征和构造交切关系。盆地边缘构造带叠加并向盆内扩展,造成盆地总体上水平缩短,并发生应变分解。盆地内部发生沉积-构造分异,发育前陆盆地、前缘隆起、复合前陆盆地、拉分盆地等单元。其中,盆地西北缘及西南缘发生陆内俯冲,形成前陆盆地及前陆冲断带,对盆内构造演化有重要影响。区域构造研究表明,塔里木盆地新生代主要发生了4期区域构造变形,第三纪以来还发生顺时针旋转。大陆盆地构造边界上的运动组合、盆内不均匀阻挡和滑脱拆离,造成其变形扩展方式的差异,并影响盆内单元构造演化。因此,塔里木盆地是认识大陆盆地聚敛与闭合过程的天然实验室。     

Significance of ichnofossils to genetic stratigraphy--Examples from the Cretaceous of Alberta, Canada

Trace fossils represent both sedimentological and paleontological entities, representing a unique blending of potential environmental indicators in the rock record. Trace fossils and trace fossil suites can be employed effectively to aid in the recognition of various discontinuity types and to assist in their genetic interpretation. Ichnology may be employed to resolve surfaces of stratigraphic significance in two main ways: 1) through the identification of discontinuities using substrate-controlled ichnofacies, and 2) through careful analysis of vertical softground (penecontemporaneous) ichnologic successions (analogous to facies successions). Ichnological analysis is a valuable tool in genetic stratigraphic studies. Integrating the data derived from substrate-controlled ichnofacies with paleoecological data from vertical ichnologic successions greatly enhances the recognition and interpretation of a wide variety of stratigraphic surfaces. When this is coupled with conventional facies analysis and sequence stratigraphy, a powerful approach to the interpretation of the rock record is generated.     

岩溶区地表水与地下水资源及环境统一评价的流域边界划分研究

岩溶地区地表水流域与地下水流域边界的分异形式有三类,即：地表分水岭与地下水流域边界在平面分布上基本一致;地表分水岭超出了地下水流域边界;地下水流域边界超出了地表分水岭。岩溶区地表水与地下水耦合流域的顶界为地表水流域的水面及下垫面,底界为浅循环潜水含水层或潜水—承压含水层下伏的隔水层顶面,在大厚度岩溶含水层分布区,可以弱岩溶发育带的顶面作为底界。其中地表水与地下水两个子系统间的次级边界,为地表水流域的下垫面。结合专门调查（勘查）评价和区域调查评价的特性,提出评价单元划分的原则及方法。这有助于在新一轮自然资源调查评价中,以流域为单元系统地开展水资源及环境调查评价,实行地表水和地下水资源及环境的统一管理。     

Voronoi tessellation on the ellipsoidal earth for vector data

Voronoi tessellation, and its dual the Delaunay triangulation, provide a cohesive framework for the study and interpretation of phenomena of geographical space in two and three dimensions. The planar and spherical solutions introduce errors in the positional accuracy of both Voronoi vertices and Voronoi edges due to errors in distance computations and the path connecting two locations with planar lines or great circle arcs instead of geodesics. For most geospatial applications the introduction of the above errors is insignificant or tolerable. However, for applications where the accuracy is of utmost importance, the ellipsoidal model of the Earth must be used. Characteristically, the introduction of any positional error in the delimitation of maritime zones and boundaries results in increased maritime space for one state at the expense of another. This is a situation that may, among others, have a serious impact on the financial activities and the relations of the states concerned. In the context of previous work on maritime delimitation we show that the Voronoi diagram constitutes the ideal solution for the development of an automated methodology addressing the problem in its entirety. Due to lack of a vector methodology for the generation of Voronoi diagram on the ellipsoid, the aforementioned solution was constrained by the accuracy of existing approaches. In order to fill this gap, in this paper we deal with the inherent attributes of the ellipsoidal model of the Earth, e.g. the fact that geodesics are open lines, and we elaborate on a methodology for the generation of the Voronoi diagram on the ellipsoid for a set of points in vector format. The resulting Voronoi diagram consists of vertices with positional accuracy that is only bounded by the user needs and edges that are comprised of geodesics densified with vertices equidistant to their generators. Finally, we present the implementation of the proposed algorithm in the Python programming language and the results of two case studies, one on the formation of closest service areas and one on maritime boundaries delimitation, with the positional accuracy set to 1 cm.     

Environmental evaluation of MODIS-derived land units

A land stratification of the French territory had been previously performed based on time series of vegetation and texture indices. This stratification led to 300 radiometrically homogenous regions that were considered as land units (LUs). In this paper, we present a quantitative analysis of the LUs, with the aim of testing if these LUs are linked to landscape. In this sense, an evaluation of their thematic meaning in terms of environmental variables and land cover was performed. In order to achieve this, we first conducted a statistical analysis at national scale using a set of environmental variables and land cover by means of Moran’s autocorrelation index and Spearman rank correlation index. Second, to analyze the quality of the boundaries between neighboring LUs, we developed a method based on the Spearman rank correlation index calculated on test areas across the boundaries. The first analyses showed that the most explanatory variables of the LUs were land cover, topography and parent material. The boundaries analysis was applied at a regional scale (Pyrenean region), and showed that 89% of the boundaries were well explained by the land cover compositions. The results obtained support the hypothesis that time series of broad resolution remote-sensing images can capture landscape identities and produce LUs maps that have an environmental and land occupation sense.     

The role of subgrain boundaries in partial melting

Evidence for partial melting along subgrain boundaries in quartz and plagioclase is documented for rocks from the Lost Creek Gneiss of the Llano Uplift, central Texas, the Wet Mountains of central Colorado, and the Albany-Fraser Orogen, southwestern Australia. Domains of quartz or plagioclase crystals along subgrain boundaries are preferentially involved in partial melting over unstrained domains of these minerals. Material along subgrain boundaries in quartz and plagioclase has the same morphology as melt pseudomorphs present along grain boundaries and is commonly laterally continuous with this former grain boundary melt, indicating the material along subgrain boundaries can also be categorized as a melt pseudomorph. Subgrain boundaries consist of arrays of dislocations within a crystal lattice, and unlike fractures would not act as conduits for melt migration. Instead, the presence of former melt along subgrain boundaries requires that partial melting occurred in these locations because it is kinetically more favorable for melting reactions to occur there. Preferential melting in high strain locations may be attributed to strain energy, which provides a minor energetic contribution to the reaction and leads to preferential melting in locations with weakened bonds, and/or the presence of small quantities of water associated with dislocations, which may enhance diffusion rates or locally lower the temperature needed for partial melting.     

Fluid Borders: Rethinking Historical Geography and Fixed Map Boundaries in Contested Regions

This article introduces a quantitative methodology for analyzing contested map borders. The article applies the new analytical technique to a data set of thirty maps showing Bulgaria in ca. 800 CE, a disputed state and period in medieval historiography with relevance to modern national politics and territorial claims. Based on the data set, we generate a series of new maps that make explicit the fluid medieval boundaries and general disagreement among geographers and historiographers. Our analysis begins with a simple point-in-polygon procedure to create a majority map that depicts the points included within the borders of the Bulgarian polity in sixteen or more of the maps (>50 percent). The majority map is then combined with percentage maps, confidence interval map boundaries, and cluster maps. The confidence interval maps are created via a spatial bootstrapping procedure and measure the uncertainty in the majority map. The cluster maps are developed via a radial basis function and provide insight into the potential affectivity based on the cartographers' countries of origin. The final map reflects the general modern consensus of the borders of the Bulgarian polity around 800 CE. Besides its quantitative contribution to medieval and modern cartographic, historiographical, and political debates, this article has developed a widely applicable methodology for synthesizing map borders and territories in cases of cartographic disagreement.