Finite cube elements method for calculating gravity anomaly and structural index of solid and fractal bodies with defined boundaries

In this paper, we present the finite cube elements method (FCEM); a novel numerical tool for calculating the gravity anomaly g and structural index SI of solid models with defined boundaries and variable density distributions, tilted or in normal position (e.g. blocks, faulted blocks, cylinders, spheres, hemispheres, triaxial ellipsoids). Extending the calculation to fractal objects, such as Menger sponges of different orders and bodies defined by polyhedrons, demonstrates the robustness of FCEM. In addition, approximating the cube element by a sphere of equal volume makes the calculation of gravitation and related derivatives much simpler. In gravity modelling of a sphere, cubes with edges of 100 m and 200 m achieve a good compromise between running time and overall error.
Displaying the distribution of SI of the studied models on contour maps and profiles will have a strong impact on the forward and inverse modelling of potential field data, especially for Euler deconvolution.
For Menger sponges, plots of gravity elements g and its derivatives show similar patterns independent of fractal order. Moreover, both the pattern and magnitude of SI are independent of fractal order, allowing the use of SI as a new invariant measure for fractal objects. However, SI pattern and magnitude strongly depend on the depth to the buried bodies as do other elements
In this study, we also present a new type of plot; the structural index against distance variation diagrams from which we extract the three critical SI ( CSI ) values, one per axis. The inversion of gravity anomaly data at CSI values gives the optimal mean location of the buried body.     

城市形态的分维估算与分形判定

城市形态的分形是城市发育到一定阶段涌现出的有序格局和复杂结构,其基本特征是空间分布的无尺度性质。当研究者基于某个显著性水平推断城市分维存在时,实际上就是基于相应的置信度判断分形特征。虽然分形城市研究已经多年,但大量有关维数测算的基础问题依然悬而未决。本文根据分形几何学的基本思想论证城市形态分维测算的若干问题。分维测量的准则是最佳覆盖——不多不少、恰到好处的覆盖。盒子覆盖是最容易理解的测量方法。采用盒子覆盖法测量城市形态分维时,应考虑三个标准：一是快速逼近,二是简便操作,三是稳定拟合。直观估计分维的办法是利用双对数坐标图。由于城市形态不是严格意义的分形,而是类似于文献中的“前分形”,测量尺度与相应测度的幂律关系通常仅在一定尺度范围内有效,从而形成所谓标度区。本文围绕城市形态的分维测量和分形判断开展一系列讨论,包括尺度选取、标度区识别和统计标准等问题,对今后城市分形研究具有理论启示和方法论的参考价值。     

Estimating gambling venue catchments for impact assessment using a calibrated gravity model

Gambling using electronic gaming machines (EGMs) has emerged as a significant public health issue. While social impact assessments are required prior to the granting of new gaming machine licenses in Australia, there are a few established techniques for estimating the spatial distribution of a venue’s clientele. To this end, we calibrated a Huff model of gambling venue catchments based on a geocoded postal survey (n = 7040). We investigated the impact of different venue attractiveness measures, distance measures, distance decay functions, levels of spatial aggregation and venue types on model fit and results. We then compared model estimates for different behavioural subgroups. Our calibrated spatial model is a significant improvement on previously published models, increasing R² from 0.23 to 0.64. Venue catchments differ radically in size and intensity. As different population subgroups are attracted to different venues, there is no single best index of venue attractiveness applicable to all subpopulations. The calibrated Huff model represents a useful regulatory tool for predicting the extent and composition of gambling venue catchments. It may assist in decision-making with regard to new license applications and evaluating the impact of health interventions such as mandated reductions in EGM numbers. Our calibrated parameters may be used to improve model accuracy in other jurisdictions.     

3-D magnetotelluric inversion and model validation with gravity data for the investigation of flood basalts and associated volcanic rifted margins

20 magnetotelluric (MT) soundings were collected on the Isle of Skye, Scotland to provide a high-resolution three-dimensional (3-D) electrical resistivity model of a volcanic province within the framework of a project jointly interpreting gravity, seismic, geological and MT data. The full 3-D inversion of the MT data jointly interpreted with gravity data reveals upper crustal structure. The main features of the model are interpreted in conjunction with previous geological mapping and borehole data. Our model extends to 13 km depth, several kilometres below the top of the Lewisian basement. The top of the Lewisian basement is at approximately 7–8 km depth and the topography of its surface was controlled by Precambrian rifting, during which a 4.5 km thick sequence of Torridonian sediments was deposited. The Mesozoic sediments above, which can reach up to 2.2 km thick, have small-scale depocentres and are covered by up to 600 m of Tertiary lava flows. The interpretation of the resistivity model shows that 3-D MT inversion is an appropriate tool to image sedimentary structures beneath extrusive basalt units, where conventional seismic reflection methods may fail.     

基于引力模型的中德双边贸易现状及潜力评价

德国是中国在欧洲最大的贸易伙伴,研究中德双边贸易潜力对中德及时调整对外贸易战略、推进"一带一路"建设具有十分重要的理论价值与现实意义。首先利用双边贸易数据和贸易结合度指数分析中德双边贸易现状,继而用2014年37个主要国家的贸易数据,从两国GDP、人均GDP、两国首都之间距离、是否加入WTO和是否加入APEC五方面,运用EViews软件建立贸易引力模型对中德贸易发展潜力进行预测,得出以下结论:中德双边贸易规模较大,增长速度较快,贸易逐渐深化;中德商品结构有较强的互补性;德国对中国的贸易结合度正由弱变强,中国对德国的贸易结合度有减弱趋势;中德双边贸易潜力值在波动中增大,且大于1.2,属于"潜力再造型",贸易潜力已经得到充分发挥,上升空间狭小。