Compound compositional data processes

Compositional data is non-negative data subject to the unit sum constraint. The logistic normal distribution provides a framework for compositional data when it satisfies sub-compositional coherence in that the inference from a sub- composition should be the same based on the full composition or the sub-composition alone. However, in many cases sub-compositions are not coherent because of additional structure on the compositions, which can be modelled as process(es) inducing change. Sometimes data are collected with a model already well validated and hence with the focus on estimation of the model parameters. Alternatively, sometimes the appropriate model is unknown in advance and it is necessary to use the data to identify a suitable model. In both cases, a hierarchy of possible structure(s) is very helpful. This is evident in the evaluation of, for example, geochemical and household expenditure data. In the case of geochemical data, the structural process might be the stoichiometric constraints induced by the crystal lattice sites, which ensures that amalgamations of some elements are constant in molar terms. The choice of units (weight percent oxide or moles) has an impact on how the data can be modelled and interpreted. For simple igneous systems (e.g. Hawaiian basalt) mineral modes can be calculated from which a valid geochemical interpretation can be obtained. For household expenditure data, the structural process might be how teetotal households have distinct spending patterns on discretionary items from non-teetotal households. Measurement error is an example of another underlying process that reflects how an underlying discrete distribution (e.g. for the number of molecules in a sample) is converted using a linear calibration into a non-negative measurement, where measurements below the stated detection limit are reported as zero. Compositional perturbation involves additive errors on the log-ratio space and is the process that does show sub-compositional coherence. The mixing process involves the combination of compositions into a new composition, such as minerals combining to form a rock, where there may be considerable knowledge about the set of possible mixing processes. Finally, recording error may affect the composition, such as recording the components to a specified number of decimal digits, implying interval censoring, which implies error is close to uniform on the simplex.postprin

Using surface regolith geochemistry to map the major crustal blocks of the Australian continent

Multi-element near-surface geochemistry from the National Geochemical Survey of Australia has been evaluated in the context of mapping the exposed to deeply buried major crustal blocks of the Australian continent. The major crustal blocks, interpreted from geophysical and geological data, reflect distinct tectonic domains comprised of early Archean to recent Cenozoic igneous, metamorphic and sedimentary rock assemblages. The geochemical data have been treated as compositional data to uniquely describe and characterize the geochemistry of the regolith overlying the major crustal blocks across Australia according to the following workflow: imputation of missing/censored data, log-ratio transformation, multivariate statistical analysis, multivariate geospatial (minimum/maximum autocorrelation factor) analysis, and classification. Using cross validation techniques, the uniqueness of each major crustal block has been quantified. The ability to predict the membership of a surface regolith sample to one or more of the major crustal blocks is demonstrated. The predicted crustal block assignments define spatially coherent regions that coincide with the known crustal blocks. In some areas, inaccurate predictions are due to uncertainty in the initial crustal boundary definition or from surficial processes that mask the crustal block geochemical signature. In conclusion, the geochemical composition of the Australian surface regolith generally can be used to map the underlying crustal architecture, despite secondary modifications due to physical transport and chemical weathering effects. This methodology is however less effective where extensive and thick sedimentary basins such as the Eromanga and Eucla basins overlie crustal blocks

Biplots for compositional data derived from generalized joint diagonalization methods

Biplots constructed from principal components of a compositional data set are an established means to explore its features. Principal Component Analysis (PCA) is also used to transform a set of spatial variables into spatially decorrelated factors. However, because no spatial structures are accounted for in the transformation the application of PCA is limited. In geostatistics and blind source separation a variety of different matrix diagonalization methods have been developed with the aim to provide spatially or temporally decorrelated factors. Just as PCA, many of these transformations are linear and so lend themselves to the construction of biplots. In this contribution we consider such biplots for a number of methods (MAF, UWEDGE and RJD transformations) and discuss how and if they can contribute to our understanding of relationships between the components of regionalized compositions. A comparison of the biplots with the PCA biplot commonly used in compositional data analysis for the case of data from the Northern Irish geochemical survey shows that the biplots from MAF and UWEDGE are comparable as are those from PCA and RJD. The biplots emphasize different aspects of the regionalized composition: for MAF and UWEDGE the focus is the spatial continuity, while for PCA and RJD it is variance explained. The results indicate that PCA and MAF combined provide adequate and complementary means for exploratory statistical analysis

Recognition of geochemical footprints of mineral systems in the regolith at regional to continental scales

Understanding the character of Australia's extensive regolith cover is crucial to the continuing success of mineral exploration. We hypothesise that the regolith contains geochemical fingerprints of processes related to the development and preservation of mineral systems at a range of scales. We test this hypothesis by analysing the composition of surface sediments within greenfield regional-scale (southern Thomson Orogen) and continental-scale (Australia) study areas. In the southern Thomson Orogen area, the first principal component (PC1) derived in our study [Ca, Sr, Cu, Mg, Au and Mo at one end; rare earth elements (REEs) and Th at the other] is very similar to the empirical vector used by a local company (enrichment in Sr, Ca and Au concomitant with depletion in REEs) to successfully site exploration drill holes for Cu-Au mineralisation. Mapping of the spatial distribution of PC1 in the region reveals several areas of elevated values and possible mineralisation potential. One of the strongest targets in the PC1 map is located between Brewarrina and Bourke in northern New South Wales. Here, exploration drilling has intersected porphyry Cu-Au mineralisation with up to 1 wt% Cu, 0.1 g/t Au, and 717ppm Zn. The analysis of a comparable geochemical dataset at the continental scale yields a compositionally similar PC1 (Ca, Sr, Mg, Cu, Au and Mo at one end; REEs and Th at the other) to that of the regional study. Mapping PC1 at the continental scale shows patterns that (1) are spatially compatible with the regional study and (2) reveal several geological regions of elevated values, possibly suggesting an enhanced potential for porphyry Cu-Au mineralisation. These include well-endowed mineral provinces such as the Curnamona and Capricorn regions, but also some greenfield regions such as the Albany-Fraser/western Eucla, western Murray and Eromanga geological regions. We conclude that the geochemical composition of Australia's regolith may hold critical information pertaining to mineralisation within/beneath it.The studies reported here would not have been possible without Commonwealth funding through the Cooperative Research Centre Program, the Onshore Energy Security Program, and Geoscience Australia appropriation

State-of-the-art analysis of geochemical data for mineral exploration

Multi-element geochemical surveys of rocks, soils, stream/lake/floodplain sediments and regolith are typically carried out at continental, regional and local scales. The chemistry of these materials is defined by their primary mineral assemblages and their subsequent modification by comminution and weathering. Modern geochemical datasets represent a multi-dimensional geochemical space that can be studied using multivariate statistical methods from which patterns reflecting geochemical/geological processes are described (process discovery). These patterns form the basis from which probabilistic predictive maps are created (process validation). Processing geochemical survey data requires a systematic approach to effectively interpret the multi-dimensional data in a meaningful way. Problems that are typically associated with geochemical data include closure, missing values, censoring, merging, levelling different datasets and adequate spatial sample design. Recent developments in advanced multivariate analytics, geospatial analysis and mapping provide an effective framework to analyse and interpret geochemical datasets. Geochemical and geological processes can often be recognized through the use of data discovery procedures such as the application of principal component analysis. Classification and predictive procedures can be used to confirm lithological variability, alteration and mineralization. Geochemical survey data of lake/till sediments from Canada and of floodplain sediments from Australia show that predictive maps of bedrock and regolith processes can be generated. Upscaling a multivariate statistics-based prospectivity analysis for arc-related Cu-Au mineralization from a regional survey in the southern Thomson Orogen in Australia to the continental scale, reveals a number of regions with a similar (or stronger) multivariate response and hence potentially similar (or higher) mineral potential throughout Australia.The National Geochemical Survey of Australia project was supported by Commonwealth funding through the Onshore Energy Security Program, and Geoscience Australia appropriation (http://www.ga.gov. au/ngsa)

Remote Predictive Mapping 3. Optical Remote Sensing – A Review for Remote Predictive Geological Mapping in Northern Canada

Optical remotely sensed data have broad application for geological mapping in Canada’s North. Diverse remote sensors and digital image processing techniques have specific mapping functions, as demonstrated by numerous examples and associated interpretations. Moderate resolution optical sensors are useful for discriminating rock types, whereas sensors that offer increased spectral resolution (i.e. hyperspectral sensors) allow the geologist to identify certain rock types (mainly different types of carbonates, Fe-bearing rocks, sulphates and hydroxyl-(clay-) bearing rocks) as opposed to merely discriminating between them. Increased spatial resolution and the ability to visualize the earth’s surface in stereo are now offered by a host of optical sensors. However, the usefulness of optical remote sensing for geological mapping is highly dependent on the geologic, surficial and biophysical environment, and bedrock predictive mapping is most successful in areas not obscured by thick drift and vegetation/lichen cover, which is typical of environments proximal to coasts. In general, predictive mapping of surficial materials has fewer restrictions. Optical imagery can be enhanced in a variety of ways and fused with other geo-science datasets to produce imagery that can be visually interpreted in a GIS environment. Computer processing techniques are useful for undertaking more quantitative analyses of imagery for mapping bedrock, surficial materials and geomorphic or glacial features. SOMMAIRE Les données recueillies par télédétection optique offrent beaucoup de possibilités pour la cartographie géologique des régions nordiques canadiennes. La diversité des télécapteurs et des techniques de traitement numérique des données permet la définition de fonctions de cartographie spécifique, tel que l’illustre de nombreux exemples et interprétations associées. Des capteurs optiques de moyenne résolution sont utiles pour différencier les types de roche, alors que les capteurs à plus fines résolutions (les capteurs hyperspectraux, par ex.) permettent au géologue de subdiviser certains types de roches (principalement différents types de carbonates, roches ferrugineuses, roches à sulfates et à hydroxyle (argile). Une meilleure résolution spatiale et la fonction de vision stéréoscopique sont maintenant offertes sur une gamme de capteurs optiques. Cela dit, l’utilité de la télédétection optique pour la cartographie géologique est fortement tributaire des conditions de la géologie de surface et de son environnement biophysique, le potentiel prédictif de la télécartographie étant maximal pour les régions exemptes d’une couverture épaisse de dépôts glaciaires ou d’une couverture végétale/lichen caractéristique typique des environnements longeant les côtes. Divers procédés permettent de rehausser l’imagerie optique et de réaliser des fusions avec d’autres jeux de données géoscientifiques et de produire une imagerie visuellement inter-prétable en environnement de SIG. Les techniques de traitement de données par ordinateur sont utiles pour d’autres types d’analyse quantitative d’imagerie pour la cartographie des matériaux de couverture du socle et pour répertorier des formes glaciaires et géomorphologiques

Report of the President of the Academy for the year 1928

Volume: 17Start Page: 297End Page: 30

A contribution to the climatology of the Ice Age

Volume: 16Start Page: 53End Page: 8