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AbstractAbstract

[en] Isotopic dating is subject to uncertainties arising from counting statistics and experimental errors. These uncertainties are additive when an isotopic age difference is calculated. If large, they can lead to no significant age difference by classical statistics. In many cases, relative ages are known because of stratigraphic order or other clues. Such information can be used to establish a Bayes estimate of age difference which will include prior knowledge of age order. Age measurement errors are assumed to be log-normal and a noninformative but constrained bivariate prior for two true ages in known order is adopted. True-age ratio is distributed as a truncated log-normal variate. Its expected value gives an age-ratio estimate, and its variance provides credible intervals. Bayesian estimates of ages are different and in correct order even if measured ages are identical or reversed in order. For example, age measurements on two samples might both yield 100 ka with coefficients of variation of 0.2. Bayesian estimates are 22.7 ka for age difference with a 75% credible interval of [4.4, 43.7] ka

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MGUS '87; Redwood City, CA (USA); 13-15 Apr 1987; CONF-8704137--

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AbstractAbstract

[en] Recent studies have shown that internal surfaces of porous geological materials, such as rocks and lignite coals, can be described by fractals down to atomic length scales. In this paper, the basic properties of self-similar and self-affine fractals are reviewed and how fractal dimensions can be measured by small-angle scattering experiments are discussed

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MGUS '87; Redwood City, CA (USA); 13-15 Apr 1987; CONF-8704137--

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BARYONS, BREMSSTRAHLUNG, CARBONACEOUS MATERIALS, COAL, ELECTROMAGNETIC RADIATION, ELEMENTARY PARTICLES, ENERGY SOURCES, FERMIONS, FOSSIL FUELS, FUELS, HADRONS, INTEGRAL TRANSFORMATIONS, INVARIANCE PRINCIPLES, IONIZING RADIATIONS, MATERIALS, MATHEMATICAL MODELS, MATHEMATICS, MECHANICS, NUCLEONS, RADIATIONS, SCATTERING, TRANSFORMATIONS

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AbstractAbstract

[en] Difficulties in applying disjunctive kriging (D.K.) with an anamorphosis to a normal distribution have led to an interest in D.K. based on other distributions. After reviewing Gaussian D.K., this paper reviews other types of D.K. based on other infinitely divisible distributions (gamma, Poisson, and negative binomial)

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DATA COVARIANCES, DISTRIBUTION, GAUSS FUNCTION, GEOLOGIC DEPOSITS, GEOLOGIC MODELS, HERMITE POLYNOMIALS, HILBERT SPACE, INFORMATION NEEDS, LAGUERRE POLYNOMIALS, LAPLACE TRANSFORMATION, POISSON EQUATION, PROBABILISTIC ESTIMATION, PROBABILITY, RESERVES, RESOURCES, STATISTICAL MODELS, STATISTICS, URANIUM DEPOSITS

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AbstractAbstract

[en] The modeling of fracture networks is useful for fluid flow and rock mechanics studies. About 6600 fracture traces were recorded on drifts of a uranium mine in a granite massif. The traces have an extension of 0.20-20 m. The network was studied by fractal and by geostatistical methods but can be considered neither as a fractal with a constant dimension nor a set of purely randomly located fractures. Two kinds of generalization of conventional models can still provide more flexibility for the characterization of the network: (a) a nonscaling fractal model with variable similarity dimension (for a 2-D network of traces, the dimension varying from 2 for the 10-m scale to 1 for the centimeter scale, (b) a parent-daughter model with a regionalized density; the geostatistical study allows a 3-D model to be established where: fractures are assumed to be discs; fractures are grouped in clusters or swarms; and fracturation density is regionalized (with two ranges at about 30 and 300 m). The fractal model is easy to fit and to simulate along a line, but 2-D and 3-D simulations are more difficult. The geostatistical model is more complex, but easy to simulate, even in 3-D

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MGUS '87; Redwood City, CA (USA); 13-15 Apr 1987; CONF-8704137--

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Journal Article

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Conference

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COMPUTERIZED SIMULATION, DATA COVARIANCES, DIAGRAMS, FRACTALS, FRACTURE MECHANICS, GEOLOGIC FRACTURES, GEOLOGIC SURVEYS, GRANITES, ONE-DIMENSIONAL CALCULATIONS, STATISTICAL MODELS, STOCHASTIC PROCESSES, TECTONICS, THREE-DIMENSIONAL CALCULATIONS, TWO-DIMENSIONAL CALCULATIONS, URANIUM DEPOSITS, URANIUM MINES

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AbstractAbstract

[en] The proposed objective of limited sample geologic site characterization is to minimize the chance of unknown and unexpected extremes. This problem proves to be extremely difficult when the data are spatially correlated. A generalization of the classical one-sided nonparametric tolerance interval, based upon the statistical concept of associated random variables, establishes a rigorous, almost distribution-free, tool for computing the minimum required sample size for site characterization. An upper bound on the required number of samples follows from a heuristic measure for the quantity of information in a spatially dependent sample; the measure presented is the equivalent number of uncorrelated samples and is calculated using an estimated variogram. An empirical check of the upper and lower bounds, using more than 2 million simulations and seven real data sets produces a heuristic rule for quantifying the required number of samples

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ACCURACY, BOUNDARY CONDITIONS, COMPUTERIZED SIMULATION, DATA COVARIANCES, DATA PROCESSING, GEOLOGIC FORMATIONS, GEOLOGIC FRACTURES, GEOLOGY, HIGH-LEVEL RADIOACTIVE WASTES, MATRICES, MAXIMUM-LIKELIHOOD FIT, PROBABILISTIC ESTIMATION, RADIOACTIVE WASTE DISPOSAL, RANDOMNESS, SAMPLING, SITE SELECTION, SITE SURVEYS, SIZE, STATISTICAL MODELS, STATISTICS, UNDERGROUND DISPOSAL

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AbstractAbstract

[en] A hierarchy of models is being developed to represent the changes in climate that could occur in the next 10,000 years at proposed nuclear waste repository sites in the US. Three levels of modeling of the global aspects of climate change are included. At the broadest level a multitude of theoretical representations are being considered, most based upon the Milankovitch theory. A set of at least 150 situations will be examined, and those of concern for site stability will be screened for more thorough analysis at the next level of detail. The screening criteria include estimation of the probability of the event; the level of probability which must be considered (0.0001) requires use of the most detailed paleoclimatic records available. Uncertainty in the results will be evaluated by comparison of model reconstructions to the paleoclimatic record and by Monte Carlo analyses

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AERODYNAMICS, ATMOSPHERIC PRECIPITATIONS, CLIMATES, DATA COVARIANCES, EARTH ATMOSPHERE, GEOLOGIC FORMATIONS, GROUND WATER, HANFORD RESERVATION, HIGH-LEVEL RADIOACTIVE WASTES, HYDROLOGY, LAW, METEOROLOGY, MONTE CARLO METHOD, NEVADA TEST SITE, PROBABILISTIC ESTIMATION, PROBABILITY, RADIOACTIVE WASTE DISPOSAL, RADIONUCLIDE MIGRATION, REGULATIONS, RISK ASSESSMENT, SEISMIC EFFECTS, SITE SURVEYS, STATISTICAL MODELS, TECTONICS, TEXAS, UNDERGROUND DISPOSAL, US DOE, USA, VARIATIONS, WEATHER

DEVELOPED COUNTRIES, ENVIRONMENTAL TRANSPORT, FLUID MECHANICS, HYDROGEN COMPOUNDS, MANAGEMENT, MASS TRANSFER, MATERIALS, MATHEMATICAL MODELS, MECHANICS, NATIONAL ORGANIZATIONS, NORTH AMERICA, OXYGEN COMPOUNDS, POLAR SOLVENTS, RADIOACTIVE MATERIALS, RADIOACTIVE WASTES, SOLVENTS, US ORGANIZATIONS, WASTE DISPOSAL, WASTE MANAGEMENT, WASTES, WATER

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[en] Advantages of robust procedures over ordinary least-squares procedures in geochemical data analysis is demonstrated using NURE data from the Hot Springs Quadrangle, South Dakota, USA. Robust principal components analysis with 5% multivariate trimming successfully guarded the analysis against perturbations by outliers and increased the number of interpretable factors. Regression with SINE estimates significantly increased the goodness-of-fit of the regression and improved the correspondence of delineated anomalies with known uranium prospects. Because of the ubiquitous existence of outliers in geochemical data, robust statistical procedures are suggested as routine procedures to replace ordinary least-squares procedures

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[en] In order to find distributions other than infinitely divisible distributions which are suitable for disjunctive kriging, infinitesimal generators are used. In addition to distributions developed in Part I, this leads to development of suitable models for the beta (β), hypergeometric, and binomial distributions

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AbstractAbstract

[en] Federal regulations governing the disposal of high-level radioactive waste in deep, geologic repositories require an assessment of performance over thousands of years. Because of the long regulatory period involved and the complex nature of the events and processes of interest, prediction of the performance of the disposal system will inevitably include uncertainties. These uncertainties come from a variety of sources, and some are quantifiable and others are not. This paper discusses these uncertainties and outlines approaches for their treatment. Recommendations for the potential resolution of current limitations in the treatment of uncertainties in performance assessment are made. Some general issues as well as a suggested approach for incorporating expert judgment into quantitative performance assessment analysis, are discussed also

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COMPUTER CODES, COMPUTERIZED SIMULATION, DATA COVARIANCES, FORECASTING, GEOCHEMISTRY, GEOLOGIC FORMATIONS, GEOLOGY, GEOPHYSICAL SURVEYS, HIGH-LEVEL RADIOACTIVE WASTES, HYDROLOGY, INTERPOLATION, LAW, MATHEMATICAL MODELS, MONTE CARLO METHOD, PERFORMANCE, RADIOACTIVE WASTE DISPOSAL, REGULATIONS, SENSITIVITY ANALYSIS, SITE SURVEYS, STATISTICS, STOCHASTIC PROCESSES, UNDERGROUND DISPOSAL

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[en] A mathematical model for determining solute concentrations at a point within a cylindrically symmetrical conduit-porous matrix system is described. Both convection and diffusion are considered within the conduit subsystem, whereas only diffusion is considered within the porous matrix subsystem. The two subsystems are coupled through continuity conditions imposed at their interface boundary. The transport equations are solved utilizing an alternating-direction implicit-method technique. The solute concentration profiles resulting from this model are then sketched and discussed

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BOUNDARY CONDITIONS, BUILDUP, DIFFUSION, FINITE DIFFERENCE METHOD, GEOLOGIC FORMATIONS, GEOLOGIC FRACTURES, LEACHING, LIQUID FLOW, MATHEMATICAL MODELS, MATRIX MATERIALS, NUMERICAL SOLUTION, POROSITY, RADIOACTIVE WASTE DISPOSAL, RADIOACTIVE WASTES, RADIOECOLOGICAL CONCENTRATION, RADIONUCLIDE MIGRATION, ROCK-FLUID INTERACTIONS, ROCKS, SITE SURVEYS, UNDERGROUND DISPOSAL, WASTE-ROCK INTERACTIONS

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