On maximum likelihood estimation of parameters in incorrectly specified models of covariance for spatial data

The analysis of, and from, models of spatial data usually proceeds under the assumption, often implicit, that the correct model has been specified. However, any model identification procedures based on sample data are subject to error, and consequences of such errors then permeate subsequent analysis. Thus, an attempt to quantify some of these consequences is of interest. A standard framework for analysis is extended here, by introduction of information theory, to permit the study of effects of model misspecification on maximum likelihood estimators of parameters of model covariance. Asymptotically valid theoretical results are presented, and the relevance of these results to samples of finite sizes met in practice is assessed in a series of simulation experiments. The effect of model misspecification, and use of estimators of parameters of misspecified covariance models, on the practical problem of prediction at a previously unsampled location is considered briefly, and further areas for possible investigation are outlined.     

Power spectrum shape from peculiar velocity data

We constrain the velocity power spectrum shape parameter Γ in linear theory using the nine bulk flow and shear moments estimated from four recent peculiar velocity surveys. For each survey, a likelihood function for Γ was found after marginalizing over the power spectrum amplitude  σ₈Ω^0.6_m  using constraints obtained from comparisons between redshift surveys and peculiar velocity data. In order to maximize the accuracy of our analyses, the velocity noise σ_* was estimated directly for each survey. A statistical analysis of the differences between the values of the moments estimated from different surveys showed consistency with theoretical predictions, suggesting that all the surveys investigated reflect the same large-scale flows. The peculiar velocity surveys were combined into a composite survey yielding the constraint  Γ= 0.13^+0.09_−0.05  . This value is lower than, but consistent with, values obtained using redshift surveys and cosmic microwave background data.     

The spatial distribution of economic activity in Melbourne, 1971–2006

This paper reports an empirical analysis of the distribution of employment by industry in Melbourne and how this changes over time. Depending on the nature of the industry being considered, two main patterns of spatial behavior are found, population-related dispersion and centralization. A methodology for estimating the benefits of centralization is developed and applied. Centralization benefits are highest for business services and other high-level services, supporting the view that the benefits of concentrating in the central business district are related to knowledge creation and exchange. Other forces, such as competitive pressure, land prices, and colocation with other industries, play only a minor role in determining the spatial distribution of industries, at least at the spatial levels used here. The implications of these findings are discussed.     

Diffusion-controlled spherulite growth in obsidian inferred from H<Subscript>2</Subscript>O concentration profiles

Spherulites are spherical clusters of radiating crystals that occur naturally in rhyolitic obsidian. The growth of spherulites requires diffusion and uptake of crystal forming components from the host rhyolite melt or glass, and rejection of non-crystal forming components from the crystallizing region. Water concentration profiles measured by synchrotron-source Fourier transform spectroscopy reveal that water is expelled into the surrounding matrix during spherulite growth, and that it diffuses outward ahead of the advancing crystalline front. We compare these profiles to models of water diffusion in rhyolite to estimate timescales for spherulite growth. Using a diffusion-controlled growth law, we find that spherulites can grow on the order of days to months at temperatures above the glass transition. The diffusion-controlled growth law also accounts for spherulite size distribution, spherulite growth below the glass transition, and why spherulitic glasses are not completely devitrified. An erratum to this article can be found at     

Evolution of the Cretaceous calcareous nannofossil genus Eiffellithus and its biostratigraphic significance

The calcareous nannofossil genus Eiffellithus is an important taxon of mid- to Upper Cretaceous marine sediments in biostratigraphy and paleoceanography. The definition of species within Eiffellithus have been both broadly interpreted and variably applied by nannofossil workers. This is particularly true for the Eiffellithus eximius plexus. While the taxonomy of mid-Cretaceous Eiffellithus species has recently been well-defined, the remaining 35 m.y. history of the genus has not been closely examined. Our investigation of Cenomanian to Maastrichtian sediments from the Western Interior Seaway, Gulf of Mexico, and Western Atlantic gives rise to six new species of Eiffellithus that can be reliably differentiated. In this paper the hitherto used biostratigraphic markers (E. turriseiffelii and E. eximius) have been redefined in a more restricted sense to increase their utility. These refinements in taxonomy reveal an obvious shift in abundance both within the genus and within the nannofossil assemblage as a whole through the Late Cretaceous. In the Cenomanian and Maastrichtian the genus is composed exclusively of coccoliths bearing an X-shaped central cross, such as E. turriseiffelii, while in the Coniacian through Campanian axial-cross forms such as E. eximius comprise more than 60% of the genus. Within the nannofossil assemblage the genus has low abundances in the Cenomanian but increases to >15% of the assemblage in well-preserved samples in the Santonian. In addition, the pattern of diversification of this genus, whereby a x-shaped, diagonal cross repeatedly gives rise to an axial cross by rotation about the central axis, is an excellent example of iterative evolution that may be related to repetitive shifts in Late Cretaceous climatic and paleoceanographic regimes.     

Primary oxidation variation and petrogenesis in a single lava

Oxidation variation between the cooling faces of a single lava has been studied by polished section examination, and Fe₂O₃: FeO chemical analysis. The oxidation state, which is at a maximum toward the center of the lava, developed during the initial cooling, and has very marked magnetic expression. The Th: U ratio varies in harmony with the oxidation state emphasizing the problem of resentative sampling of the body. Examination of thirteen additional bodies suggests that in lavas there exists at least a partial dependence of the oxidation variation development on the lava thickness or interior cooling rate.     

Assessing agricultural drought management strategies in the Northern Murray–Darling Basin

Natural Hazards - The Northern Murray–Darling Basin (MDB) is a key Australian agricultural region requiring efficient Agricultural Drought Management (ADM), focused on resilience. Although a...