Analytical methods for error propagation in planar space–time prisms

The space–time prism demarcates all locations in space–time that a mobile object or person can occupy during an episode of potential or unobserved movement. The prism is central to time geography as a measure of potential mobility and to mobile object databases as a measure of location possibilities given sampling error. This paper develops an analytical approach to assessing error propagation in space–time prisms and prism–prism intersections. We analyze the geometry of the prisms to derive a core set of geometric problems involving the intersection of circles and ellipses. Analytical error propagation techniques such as the Taylor linearization method based on the first-order partial derivatives are not available since explicit functions describing the intersections and their derivatives are unwieldy. However, since we have implicit functions describing prism geometry, we modify this approach using an implicit function theorem that provides the required first-order partials without the explicit expressions. We describe the general method as well as details for the two spatial dimensions case and provide example calculations.     

Sedimentation on the Ionian active margin (Hellenic arc) — Provenance of sediments and mechanisms of deposition

Lithological, sedimentological, mineralogical and faunal analyses of twenty cores from the western Peloponnesus margin and adjacent Matapan Trench permit the origin of the sediments and the processes of sedimentation to be defined in some detail.Except for the ash layers derived from the Ischian Province, the major part of the sediment is local in origin (Peloponnesus). Analyses of heavy, light and clay minerals enable three main provinces to be distinguished. Each of these provinces includes one or more slope basins and a portion of trench, without lateral connection between them and mixing of inputs.The diversity and complexity of sedimentary structures, the granulometric characters, the mixed fauna (molluscs and ostracods) and the variability of rates of sedimentation all testify to the prevalence of reworking phenomena and gravitative processes.These data confirm and elaborate on the model of sedimentation deduced from seismic studies in which sediments are successively trapped, released by the slope basins and transferred via channels and canyons towards the underlying trench basins. This “cascade feeding” appears characteristics of this subductive sedimentary environment.     

FORWARD MODELING IN THE FREQUENCY-SPACE DOMAIN*

Forward modeling of zero-offset data is performed in the frequency-space domain using a one-way extrapolation equation. The use of the frequency domain offers several advantages over conventional time domain methods. The greatest advantage of the frequency domain is that all time derivatives are evaluated exactly by a simple multiplication. Synthetic zero-offset sections are computed with a high degree of accuracy for arbitrary velocity and reflectivity structures. Examples are shown for realistic complicated models and compared with results from physical modeling.     

Tropospheric Ozone in a Global-Scale Three-Dimensional Lagrangian Model and Its Response to NOX Emission Controls

A three-dimensional Lagrangian tropospheric chemistry modelis used toinvestigate the impact of human activities on the tropospheric distributionofozone and hydroxyl radicals. The model describes the behaviour of 50 speciesincluding methane, carbon monoxide, oxides of nitrogen, sulphur dioxide andnineorganic compounds emitted from human activities and a range of other sources.Thechemical mechanism involves about 100 chemical reactions of which 16 arephotochemical reactions whose diurnal dependence is treated in full. The modelutilises a five minute chemistry time step and a three hour advection timestepfor the 50,000 air parcels. Meteorological data for the winds, temperatures,clouds and so on are taken from the UK Meteorological Office global model for1994 onwards. The impacts of a 50% reduction in European NO_Xemissions onglobal ozone concentrations are assessed. Surface ozoneconcentrations decrease in summertime and rise in wintertime, but to differentextents.     

A NEW APPROACH TO THE INVERSION OF SEISMIC DATA*

A new inversion method for seismic reflection data is based on impedance concepts and uses transformations to reduce the essentially non-linear problem to a linear eigenvalue formulation without approximation. A set of reflection data has been inverted using this method. The characteristic impedances of the layers so determined are compared with log data from a reference borehole.     

Non-Linear Theory and Power-Law Models for Information Integration and Mineral Resources Quantitative Assessments

Singular physical or chemical processes may result in anomalous amounts of energy release or mass accumulation that, generally, are confined to narrow intervals in space or time. Singularity is a property of different types of non-linear natural processes including cloud formation, rainfall, hurricanes, flooding, landslides, earthquakes, wildfires, and mineralization. The end products of these non-linear processes can be modeled as fractals or multifractals. Hydrothermal processes in the Earth’s crust can result in ore deposits characterized by high concentrations of metals with fractal or multifractal properties. Here we show that the non-linear properties of the end products of singular mineralization processes can be applied for prediction of undiscovered mineral deposits and for quantitative mineral resource assessment, whether for mineral exploration or for regional, national and global planning for mineral resource utilization. In addition to the general theory and framework for the non-linear mineral resources assessment, this paper focuses on several power-law models proposed for characterizing non-linear properties of mineralization and for geoinformation extraction and integration. The theories, methods, and computer system discussed in this paper were validated using a case study dealing with hydrothermal Au mineral potential in southern Nova Scotia, Canada.     

The effect of composition,temperature and pressure on the stability of the 1Tc and 2M polytypes of sapphirine

Microprobe analyses and structural characterisation by means of transmission electron microscopy and powder X-ray diffraction are presented for a suite of natural and synthetic sapphirines. Most sapphirines appear to consist of intergrowths of the common 2M polytype with minor amounts of the 1Tc phase, although the converse situation is found in some cases. Attempts to correlate the structural state of the mineral with other factors reveal that: (i) There is no strong relationship between mean tetrahedral cation radius or mean octahedral cation radius and the preferred polytype. The Tschermak substitution M²⁺M⁴⁺-M³⁺M³⁺ does not appreciably influence the 1Tc-2M equilibrium, (ii) However, the total content and mean oxidation state of iron in sapphirine are important in this respect. Fe²⁺ stabilises the 2M phase, whereas Fe³⁺ stabilises the 1Tc phase. (iii) P-T estimates for the host rocks, and estimates for the conditions of sapphirine crystallisation, where obtainable, suggest that the 1Tc phase is stable at lower T and higher P than the 2M phase. Some quantitative constraints are inferred.     

TEM study of a special grain boundary in a synthetic K-feldspar bicrystal: Manebach Twin

 A monoclinic KAlSi₃O₈ feldspar Manebach twin boundary was synthesized by diffusion bonding and examined using high-resolution transmission electron microscopy. The sharp (001) twin boundary is straight and free of strain. The boundary width is smaller than d₀₀₁. There is no rigid body shift observed at the twin boundary, and the feldspar structure is arranged symmetrically across (001). The twin boundary structure consists of bridged tetrahedral crankshafts, which are characteristic of the feldspar lattice. The grain boundary structure is in good agreement with the geometrical model of Taylor et al. (1934). The grain boundary composition of K_1/2H_1/2AlSi₃O₈ differs from their model. Received: 13 February 2002 / Accepted: 24 December 2002 Acknowledgements We thank M. Rühle, S. Hutt, J. Mayer, A. Strecker and U. Salzberger at MPI, Stuttgart, for their support and valuable advice in preparing TEM sections of bicrystals.