Spatial statistics for urban analysis: A review of techniques with examples

Traditionally, urban analysis has been quick to adopt and benefit from developments in technology (e.g., microcomputer, GIS) and techniques (e.g., statistics, mathematical programming). This has not been the case, however, with newer methods of spatial analysis — in particular, spatial statistics. Only recently has this situation started to change. This paper documents the confluence of spatial statistics and urban analysis by first reviewing developments in spatial statistics, and then presenting examples of recent applications in urban analysis. The developments reviewed fall under the rubric of global and local forms of spatial analysis, and cover three major technical issues: spatial association, spatial heterogeneity and the modifiable areal unit problem. The examples highlight the relevance and usefulness of the techniques reviewed for urban transportation and land-use applications. The paper concludes with conjectures concerning future developments at the intersection of spatial statistics and urban analysis.     

Underground geotechnical and geological investigations at Ekati Mine–Koala North: case study

Since 1998, BHP Billiton has mined diamonds at the Ekati Diamond Mine™ near Lac de Gras in the Northwest Territories of Canada. Current operations are based on mining multiple pipes by the open-pit method, but as some pits deepen, converting to underground mining is being considered.

As a test of underground mining methods and to provide access to the lower elevations of the Panda and Koala pipes, the Koala North pipe is being developed for underground mining. Initially, the top 40 m of the pipe were mined as an open pit to provide grade information and a prepared surface for the transition to underground mining. Currently, Koala North is being developed as an open-benching, mechanized, trackless operation. Although the method was successfully used at several De Beers diamond operations in South Africa, it has never been tested in an Arctic environment.

This case study describes basic geology, mining method layout and ongoing geological and geotechnical investigation. From the beginning of underground development, geotechnical daily routines have been fully integrated within the technical services department, which supports the operation. Geotechnical, geological and structural information obtained from underground mapping and core logging is compiled, processed, reviewed and analyzed on site by the geotechnical staff. Conclusions and recommendations are implemented as part of the operations in a timely manner. This ongoing “live” process enables the operators to make the most efficient use of resources both for ground support and excavations as well as to address safety issues, which are the top priority.     

Spatial statistics for urban analysis: A review of techniques with examples

Traditionally, urban analysis has been quick to adopt and benefit from developments in technology (e.g., microcomputer, GIS) and techniques (e.g., statistics, mathematical programming). This has not been the case, however, with newer methods of spatial analysis — in particular, spatial statistics. Only recently has this situation started to change. This paper documents the confluence of spatial statistics and urban analysis by first reviewing developments in spatial statistics, and then presenting examples of recent applications in urban analysis. The developments reviewed fall under the rubric of global and local forms of spatial analysis, and cover three major technical issues: spatial association, spatial heterogeneity and the modifiable areal unit problem. The examples highlight the relevance and usefulness of the techniques reviewed for urban transportation and land-use applications. The paper concludes with conjectures concerning future developments at the intersection of spatial statistics and urban analysis.     

Subglacial tunnel channels, Porcupine Hills, southwest Alberta, Canada

At some time close to the Last Glacial Maximum (LGM) high-energy, subglacial, Laurentide, meltwater flows eroded a series of discontinuous tunnel channels into the northeastern flanks of the Porcupine Hills and adjacent parts of the high plains near Nanton, Stavely and Claresholm. Discrete channel segments, kilometers long, up to about 1 km wide, and 100 m deep, were carved into Paleocene sandstone and shale of the Porcupine Hills Formation. Floors of Pine, Boneyard, and Crocodile channels all occur at elevations between 1050 and 1175 m a.s.l., and share the characteristic of strongly convex-up long profiles. Intrachannel drainage divides on each channel floor are tens of meters above the water entry and exit points. Formative flows, therefore, must have been pressurized in the subglacial Nye-channels. Prominent scour-holes at some major bends in the channels now host ephemeral ponds or lakes. During the channel erosion, the overlying Laurentide ice surface was probably close to its local LGM maximum elevation of ca. 1400–1500 m a.s.l. Misfit modern streams now drain in opposite directions within the tunnel channels, and there are only minor, local, distal accumulations of sediment derived from the tunnel channel erosion.     

Chronology of the Pueblo Viejo epithermal gold–silver deposit,Dominican Republic: formation in an Early Cretaceous intra-oceanic island arc and burial under ophiolite

The Pueblo Viejo deposit (production to 1996: 166 t Au, 760 t Ag) is located in the Dominican Republic on the Caribbean island of Hispaniola and ranks as one of the largest high-sulfidation/acid-sulfate epithermal deposits (reserves in 2007: 635 t Au, 3,648 t Ag). One of the advanced argillic ore bodies is cut by an inter-mineral andesite porphyry dike, which is altered to a retrograde chlorite–illite assemblage but overprinted by late-stage quartz–pyrite–sphalerite veins and associated low-grade Au, Ag, Zn, Cd, Hg, In, As, Se, and Te mineralization. The precise TIMS U–Pb age (109.6 ± 0.6 Ma) of the youngest zircon population in this dike confirms that the deposit is part of the Early Cretaceous Los Ranchos intra-oceanic island arc. Intrusion-related gold–sulfide mineralization took place during late andesite–dacite volcanism within a thick pile (>200 m) of carbonaceous sand- and siltstones deposited in a restricted marine basin. The high-level deposit was shielded from erosion after burial under a late Albian (109–100 Ma) ophiolite complex (8 km thick), which was in turn covered by the volcano-sedimentary successions (>4 km) of a Late Cretaceous–Early Tertiary calc-akaline magmatic arc. Estimates of stratigraphic thickness and published alunite, illite, and feldspar K-Ar ages and closure temperatures (alunite 270 ± 20°C, illite 260 ± 30°C, K-feldspar 150°C) indicate a burial depth of about 12 km at 80 Ma. During peak burial metamorphism (300°C and 300 MPa), the alteration assemblage kaolinite + quartz in the deposit dehydrated to pyrophyllite. Temperature–time relations imply that the Los Ranchos terrane then cooled at a rate of 3–4°C/Ma during slow uplift and erosion.     

A laser-ablation ICP-MS study of Apollo 15 low-titanium olivine-normative and quartz-normative mare basalts

Apollo 15 low-Ti mare basalts have traditionally been subdivided into olivine- and quartz-normative basalt types, based on their different SiO₂, FeO, and TiO₂ whole-rock compositions. Previous studies have reconciled this compositional diversity by considering the olivine- and quartz-normative basalts as originating from different lunar mantle source regions. To provide new information on the compositions of Apollo 15 low-Ti mare basalt parental magmas, we report a study of major and trace-element compositions of whole rocks, pyroxenes, and other phases in the olivine-normative basalts 15016 and 15555 and quartz-normative basalts 15475 and 15499. Results show similar rare-earth-element patterns in pyroxenes from all four basalts. The estimated equilibrium parental-melt compositions from the trace-element compositions of pyroxenes are similar for 15016, 15555 and 15499. Additionally, an independent set of trace-element distribution coefficients has been determined from measured pyroxene and mesostasis compositions in sample 15499. These data suggest that fractional crystallization may be a viable alternative to compositional differences in the mantle source to explain the 25% difference in whole-rock TiO₂, and corresponding differences in SiO₂ and FeO between the Apollo 15 olivine- and quartz-normative basalts. In this model, the older (3.35 Ga) quartz-normative basalts, with lower TiO₂ experienced olivine, chromite, and Cr-ulvöspinel fractionation at ‘crustal levels’ in magma chambers or dikes, followed by limited near-surface mineral fractionation, within the lava flows. In contrast, the younger (3.25 Ga) olivine-normative basalts experienced only limited magmatic differentiation at ‘crustal-levels’, but extensive near-surface mineral fractionation to produce their evolved mineral compositions. A two-stage mineral-fractionation model is consistent with textural and mineralogical observations, as well as the mineral trace-element constraints developed by this study.     

Quantitative Analysis of H2OComa Images Using a Multiscale MHD Model with Detailed Ion Chemistry

The observation of ions created by ionization of cometary gas, either by ground-based observations or byin situmeasurements can give us useful information about the gas production and composition of comets. However, due to the interaction of ions with the magnetized solar wind and their high chemical reactivity, it is not possible to relate measured ion densities (or column densities) directly to the parent gas densities. In order to quantitatively analyze measured ion abundances in cometary comae it is necessary to understand their dynamics and chemistry. We have developed a detailed ion–chemical network of cometary atmospheres. We include production of ions by photo- and electron impact-ionization of a background neutral atmosphere, charge exchange of solar wind ions with cometary atoms/molecules, reactions between ions and molecules, and dissociative recombination of molecular ions with thermal electrons. By combining the ion–chemical network with the three-dimensional plasma flow as computed by a new fully three-dimensional MHD model of cometary plasma environments (Gombosiet al.1996) we are able to compute the density of the major cometary ions everywhere in the coma. The input parameters for our model are the solar wind conditions (density, speed, temperature, magnetic field) and the composition and production rate of the gas. We applied our model to Comet P/Halley in early March 1986, for which the input parameters are reasonably well known. We compare the resulting column density of H₂O⁺with ground-based observations of H₂O⁺from DiSantiet al.(1990). The results of our model are in good agreement with both the spatial distribution and the absolute abundance of H₂O⁺and with their variations with the changing overall water production rate between two days. The results are encouraging that it will be possible to obtain production rates of neutral cometary constituents from observations of their ion products.