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11.
P. A. Dowd 《Mathematical Geosciences》1982,14(5):475-499
A theoretical study of the general case of the estimation of regionalized variables with a lognormal distribution is presented. The results of this study are compared to those obtained assuming conservation of lognormality. The numerical significance of the different solutions is illustrated by several simple examples. 相似文献
12.
Empirical Maximum Likelihood Kriging: The General Case 总被引：4，自引：0，他引：4
Although linear kriging is a distribution-free spatial interpolator, its efficiency is maximal only when the experimental data follow a Gaussian distribution. Transformation of the data to normality has thus always been appealing. The idea is to transform the experimental data to normal scores, krige values in the “Gaussian domain” and then back-transform the estimates and uncertainty measures to the “original domain.” An additional advantage of the Gaussian transform is that spatial variability is easier to model from the normal scores because the transformation reduces effects of extreme values. There are, however, difficulties with this methodology, particularly, choosing the transformation to be used and back-transforming the estimates in such a way as to ensure that the estimation is conditionally unbiased. The problem has been solved for cases in which the experimental data follow some particular type of distribution. In general, however, it is not possible to verify distributional assumptions on the basis of experimental histograms calculated from relatively few data and where the uncertainty is such that several distributional models could fit equally well. For the general case, we propose an empirical maximum likelihood method in which transformation to normality is via the empirical probability distribution function. Although the Gaussian domain simple kriging estimate is identical to the maximum likelihood estimate, we propose use of the latter, in the form of a likelihood profile, to solve the problem of conditional unbiasedness in the back-transformed estimates. Conditional unbiasedness is achieved by adopting a Bayesian procedure in which the likelihood profile is the posterior distribution of the unknown value to be estimated and the mean of the posterior distribution is the conditionally unbiased estimate. The likelihood profile also provides several ways of assessing the uncertainty of the estimation. Point estimates, interval estimates, and uncertainty measures can be calculated from the posterior distribution. 相似文献
13.
Mathematical Geosciences - Fractal analysis has, for some time, been used to evaluate the roughness of both natural and engineered surfaces. Since the introduction of fractal geometry, evidence of... 相似文献
14.
Laboratory and field experiments demonstrated that solid state pressure transducers are accurate and reliable devices for frequent measurements of soil suction. However, each transducer had to be individually calibrated before use and a hanging column procedure designed for this purpose is described. Analysis showed that each transducer had a linear response and that environmental conditions such as temperature had minimal influence. Twenty four tensiometers with pressure transducers were intalled in a forest soil to test their operation and their output was monitored by a data logger. An example of soil suction results measured during four storms is given to demonstrate their stability and their rapid response. The transducers were found to perform accurately and were only affected by temperatures below 0°C. 相似文献
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Neural networks offer a non-algorithmic approach to geostatistical simulation with the possibility of automatic recognition of correlation structure. The paper gives a brief overview of neural networks and describes a feedforward, back-propagation network for geostatistical simulation. The operation of the network is illustrated with two simple one-dimensional examples which can be followed through with hand calculations to give an insight into the operation of the network. The convergence of the network is described in terms of the variogram calculated from the values at each of the output nodes at each iteration. 相似文献
17.
S. Seifollahi P. A. Dowd C. Xu A. Y. Fadakar 《Rock Mechanics and Rock Engineering》2014,47(4):1225-1235
Fracture network modelling plays an important role in many application areas in which the behaviour of a rock mass is of interest. These areas include mining, civil, petroleum, water and environmental engineering and geothermal systems modelling. The aim is to model the fractured rock to assess fluid flow or the stability of rock blocks. One important step in fracture network modelling is to estimate the number of fractures and the properties of individual fractures such as their size and orientation. Due to the lack of data and the complexity of the problem, there are significant uncertainties associated with fracture network modelling in practice. Our primary interest is the modelling of fracture networks in geothermal systems and, in this paper, we propose a general stochastic approach to fracture network modelling for this application. We focus on using the seismic point cloud detected during the fracture stimulation of a hot dry rock reservoir to create an enhanced geothermal system; these seismic points are the conditioning data in the modelling process. The seismic points can be used to estimate the geographical extent of the reservoir, the amount of fracturing and the detailed geometries of fractures within the reservoir. The objective is to determine a fracture model from the conditioning data by minimizing the sum of the distances of the points from the fitted fracture model. Fractures are represented as line segments connecting two points in two-dimensional applications or as ellipses in three-dimensional (3D) cases. The novelty of our model is twofold: (1) it comprises a comprehensive fracture modification scheme based on simulated annealing and (2) it introduces new spatial approaches, a goodness-of-fit measure for the fitted fracture model, a measure for fracture similarity and a clustering technique for proposing a locally optimal solution for fracture parameters. We use a simulated dataset to demonstrate the application of the proposed approach followed by a real 3D case study of the Habanero reservoir in the Cooper Basin, Australia. 相似文献
18.
The integration of geological and geometallurgical data can significantly improve decision-making and optimize mining production due to a better understanding of the resources and their metallurgical performances. The primary-response rock property framework is an approach to the modelling of geometallurgy in which quantitative and qualitative primary properties are used as proxies of metallurgical responses. Within this framework, primary variables are used to fit regression models to predict metallurgical responses. Whilst primary rock property data are relatively abundant, metallurgical response property data are not, which makes it difficult to establish predictive response relationships. Relationships between primary input variables and geometallurgical responses are, in general, complex, and the response variables are often non-additive which further complicates the prediction process. Consequently, in many cases, the traditional multivariate linear regression models (MLR) of primary-response relationships perform poorly and a better alternative is required for prediction. Projection pursuit is a powerful exploratory statistical modelling technique in which data from a number of variables are projected onto a set of directions that optimize the fit of the model. The purpose of the projection is to reveal underlying relationships. Projection pursuit regression (PPR) fits standard regression models to the projected data vectors. In this paper, PPR is applied to the modelling of geometallurgical response variables. A case study with six geometallurgical variables is used to demonstrate the modelling approach. The results from the proposed PPR models show a significant improvement over those from MLR models. In addition, the models were bootstrapped to generate distributions of feasible scenarios for the response variables. Our results show that PPR is a robust technique for modelling geometallurgical response variables and for assessing the uncertainty associated with these variables. 相似文献
19.
The statistical technique of functional data analysis (FDA) is applied to a time series analysis of plankton monitoring data. The analysis is focused on revealing patterns in the seasonal cycle to assess interannual variability of several different taxonomic groups of plankton. Cell concentrations of diatom, dinoflagellate and zooplankton abundances from the Bay of Fundy, Canada provide the observations for analysis. FDA was performed on the log-transformed abundance data as a new approach for treating such types of sparse and noisy data. Differences in the seasonal progression were seen, with peak numbers, timings and abundance levels varying for the three groups as determined by curve registration and higher order derivatives using the objectively fit FDA curves. Nonmetric multidimensional scaling was used to capture seasonal variation among years. These results were further assessed in terms of dominant species and the relationships between groups for different seasons and years. It is anticipated that the easy to use, general and flexible technique of FDA could be applied to a wide variety of marine ecological data that are characterized by missing values and non-Gaussian distributions. 相似文献
20.
In studies that involve a finite sample size of spatial data it is often of interest to test (statistically) the assumption that the marginal (or univariate) distribution of the data is Gaussian (normal). This may be important per se because, for example, a data transformation may be desired if the normality hypothesis is rejected, or it may provide a way of testing other hypotheses, such as lognormality, by testing the normality of the logarithms of the observations. The most commonly used tests, such as the Kolmogorov–Smirnov (K–S), chi-square (2), and Shapiro–Wilks (S–W) tests, are designed on the assumption that the observations are independent and identically distributed (iid). In geostatistical applications, however, this is not usually the case unless the spatial covariance (semivariogram) function is a pure nugget variance. If the covariance structure has a (practical) range greater than the minimum distance between observations, the data are correlated and the standard tests cannot be applied to the probability density function (pdf) or cumulative probability function (cdf) estimated directly from the data. The problem with correlated data arises not from the correlation per se but from cases in which correlated data are clustered rather than being located on a regular grid. In these cases inferences requiring iid assumptions may be seriously biased because of the spatial correlation among the observations. If unbiased (i.e., de-clustered) estimates of the pdf or cdf are obtained, then normality tests, such as K-S, 2, or S–W, can be applied using the unbiased estimates and an effective number of samples equivalent to the iid case. There are three questions to be addressed in these cases: Is the distribution ergodic? 相似文献