Comparison of methods to model the gravitational gradients from topographic data bases

A number of methods have been developed over the last few decades to model the gravitational gradients using digital elevation data. All methods are based on second-order derivatives of the Newtonian mass integral for the gravitational potential. Foremost are algorithms that divide the topographic masses into prisms or more general polyhedra and sum the corresponding gradient contributions. Other methods are designed for computational speed and make use of the fast Fourier transform (FFT), require a regular rectangular grid of data, and yield gradients on the entire grid, but only at constant altitude. We add to these the ordinary numerical integration (in horizontal coordinates) of the gradient integrals. In total we compare two prism, two FFT and two ordinary numerical integration methods using 1" elevation data in two topographic regimes (rough and moderate terrain). Prism methods depend on the type of finite elements that are generated with the elevation data; in particular, alternative triangulations can yield significant differences in the gradients (up to tens of Eötvös). The FFT methods depend on a series development of the topographic heights, requiring terms up to 14th order in rough terrain; and, one popular method has significant bias errors (e.g. 13 Eötvös in the vertical–vertical gradient) embedded in its practical realization. The straightforward numerical integrations, whether on a rectangular or triangulated grid, yield sub-Eötvös differences in the gradients when compared to the other methods (except near the edges of the integration area) and they are as efficient computationally as the finite element methods.     

Spherical Slepian functions and the polar gap in geodesy

The estimation of potential fields such as the gravitational or magnetic potential at the surface of a spherical planet from noisy observations taken at an altitude over an incomplete portion of the globe is a classic example of an ill-posed inverse problem. We show that this potential-field estimation problem has deep-seated connections to Slepian's spatiospectral localization problem which seeks bandlimited spherical functions whose energy is optimally concentrated in some closed portion of the unit sphere. This allows us to formulate an alternative solution to the traditional damped least-squares spherical harmonic approach in geodesy, whereby the source field is now expanded in a truncated Slepian function basis set. We discuss the relative performance of both methods with regard to standard statistical measures such as bias, variance and mean squared error, and pay special attention to the algorithmic efficiency of computing the Slepian functions on the region complementary to the axisymmetric polar gap characteristic of satellite surveys. The ease, speed, and accuracy of our method make the use of spherical Slepian functions in earth and planetary geodesy practical.     

A traveltime reciprocity discrepancy in the Podvin & Lecomte time3d finite difference algorithm

We have found that the extensively used finite difference scheme time3d produces time fields which are 'asymmetric' in the sense that traveltimes computed to the right of the source are faster than traveltimes computed to the left. All finite difference schemes will, as they are approximations to the wave equation, to some extent fail to obey reciprocity perfectly. We show, however, that the errors in time3d may be significant—and unnecessarily large. An asymmetry in the point source initialization has been identified, and after correction time3d produces time fields with an improved reciprocity.     

Effects of fracture lineaments and in-situ rock stresses on groundwater flow in hard rocks: a case study from Sunnfjord, western Norway

Systematic field mapping of fracture lineaments observed on aerial photographs shows that almost all of these structures are positively correlated with zones of high macroscopic and mesoscopic fracture frequencies compared with the surroundings. The lineaments are subdivided into zones with different characteristics: (1) a central zone with fault rocks, high fracture frequency and connectivity but commonly with mineral sealed fractures, and (2) a damage zone divided into a proximal zone with a high fracture frequency of lineament parallel, non-mineralized and interconnected fractures, grading into a distal zone with lower fracture frequencies and which is transitional to the surrounding areas with general background fracturing. To examine the possible relations between lineament architecture and in-situ rock stress on groundwater flow, the geological fieldwork was followed up by in-situ stress measurements and test boreholes at selected sites. Geophysical well logging added valuable information about fracture distribution and fracture flow at depths. Based on the studies of in-situ stresses as well as the lineaments and associated fracture systems presented above, two working hypotheses for groundwater flow were formulated: (i) In areas with a general background fracturing and in the distal zone of lineaments, groundwater flow will mainly occur along fractures parallel with the largest in-situ rock stress, unless fractures are critically loaded or reactivated as shear fractures at angles around 30° to σ_H; (ii) In the influence area of lineaments, the largest potential for groundwater abstraction is in the proximal zone, where there is a high fracture frequency and connectivity with negligible fracture fillings. The testing of the two hypotheses does not give a clear and unequivocal answer in support of the two assumptions about groundwater flow in the study area. But most of the observed data are in agreement with the predictions from the models, and can be explained by the action of the present stress field on pre-existing fractures.     

基于土质边坡塑性极限分析条分法的可靠度计算方法研究

从土塑性极限分析上限定理出发,以土质边坡塑性极限分析条分法为基础,在引入可靠性分析方法(JC法)后,建立了土质边坡塑性极限分析条分法可靠度极限状态方程,并推导得到了塑性极限分析条分法可靠度计算公式。这种方法实现了定值计算向不确定性计算的转变,同时可靠度指标的计算结果具有概率的意义。     

我国水资源承载力研究现状及展望

概要说明了我国水资源承载力的研究现状,阐述了水资源承载力的概念、内涵及影响因素,探讨了目前几种常用的水资源承载力评价方法,并对当前研究中存在的问题进行了初步分析,进而提出了我国水资源承载力的研究趋势。     

基于GIS的城镇土地定级信息系统建模方法探讨

基于GIS的城镇土地定级信息系统在建设过程中,定级方法确定、定级单元大小确定和定级因素/子权重值的生成是关键,且三者都具有不同的确定方法,因此选择什么样的方法决定了系统建立的优劣。本文着重归纳、总结了城镇土地定级信息系统定级方法,通过对比分析,探讨了最优定级方法、最优网格单元大小划分方法和最优因素/子权重值计算方法。     

我国西部1∶5万地形图空白区地物解译研究——以西藏那曲其香错地区为例

我国西部部分地区1∶5万地形图数据尚未完成,给区域和国家经济发展带来极大不便。空间技术、计算机技术和信息技术的高速发展为遥感技术应用提供了技术支持,高分辨率影像获取能力的提高为大比例尺地物特征的提取提供了数据可能。本文采用SPOT5遥感影像,以1∶5万地形图图式标准为依据,进行青藏高原其香错地区地物判读,结果表明SPOT5能基本满足1∶5万地形图制图要求。为进一步提高判读结果,可采用多时相、多分辨率影像进行1∶5万地形图地物判读。     

ODP204航次天然气水合物的可能有利储层——浊积层

为了解岩性在天然气水合物分布中的作用, 利用岩矿鉴定、扫描电镜和能谱法对ODP204航次的 4个站位 10个钻孔共计 115个沉积物样品进行分析, 发现沉积物中矿物成分基本相近, 以粘土矿物为主, 含少量以石英为主的陆源碎屑。样品中含有丰富的硅藻和有孔虫等微体化石, 可形成硅藻粘土—硅藻土、有孔虫硅藻土或凝灰质硅质生物粘土。石英碎屑大多呈棱角状, 粒径小、含量少, 同时, 样品中可见透镜体、团块或旋涡状层状结构以及杂乱堆积的斑杂构造。上述特征表明沉积物为含有大量深海或半深海的浊流沉积物或其夹层。由于钻井岩心中有相当部分的天然气水合物样品分布在上述沉积物中, 推断这些浊流沉积物很可能是ODP204航次天然气水合物的有利储层。