Change of Support for Estimating Local Block Grade Distributions     

Xavier Emery 《Mathematical Geosciences》2008,40(6):671-688

An important aspect in mineral resource evaluation is the reduction of variance when post-processing the grade distributions defined on the support (volume) of the available data into distributions defined on the support of the proposed selective mining units. Although the volume-variance relationship is well understood for the estimation of global grade distributions, it is still an unsolved issue for local estimation studies based on non-parametric geostatistical methods, such as indicator kriging, for which the support correction is not inherent to the method. To clarify this relationship, the local change of support problem is examined in the scope of two parametric models (multi-Gaussian and discrete Gaussian models). It is shown that the variance reduction factor between point and block-support local distributions depends on the block being considered and is less than the global variance reduction factor. As a consequence, post-processing the local point-support grade distributions on the basis of the latter systematically understates the importance of the change of support at the local scale and makes selective mining appear more economically attractive than it really is. In the light of these results, a methodology is proposed to post-process the local point-support distributions obtained via non-parametric (indicator) methods into block-support distributions. An application to simulated data indicates that this methodology provides an accurate estimation at the block support when dealing with diffusion-type random fields.  相似文献   

Modelling Positional Uncertainty of Line Features by Accounting for Stochastic Deviations from Straight Line Segments   总被引：1，自引：0，他引：1  

Sytze de Bruin 《Transactions in GIS》2008,12(2):165-177

The assessment of positional uncertainty in line and area features is often based on uncertainty in the coordinates of their elementary vertices which are assumed to be connected by straight lines. Such an approach disregards uncertainty caused by sampling and approximation of a curvilinear feature by a sequence of straight line segments. In this article, a method is proposed that also allows for the latter type of uncertainty by modelling random rectangular deviations from the conventional straight line segments. Using the model on a dense network of sub‐vertices, the contribution of uncertainty due to approximation is emphasised; the sampling effect can be assessed by applying it on a small set of randomly inserted sub‐vertices. A case study demonstrates a feasible way of parameterisation based on assumptions of joint normal distributions for positional errors of the vertices and the rectangular deviations and a uniform distribution of missed sub‐vertices along line segments. Depending on the magnitudes of the different sources of uncertainty, not accounting for potential deviations from straight line segments may drastically underestimate the positional uncertainty of line features.  相似文献   

Optimizing interpolation of shoot density data from a Posidonia oceanica seagrass bed   总被引：1，自引：0，他引：1  

Michele Scardi  Lorenzo A. Chessa  Eugenio Fresi  Antonio Pais  & Simone Serra 《Marine Ecology》2006,27(4):339-349

A case study on the optimization of Posidonia oceanica density interpolation, using a data set from a large meadow at Porto Conte Bay (NW Sardinia, Italy), is presented. Ordinary point kriging, cokriging and a weighted average based on inverse square distance were used to interpolate density data measured in 36 sampling stations. The results obtained from different methods were then compared by means of a leave‐one‐out cross‐validation procedure. The scale at which interpolation was carried out was defined on the basis of the Hausdorff dimension of the variogram. Optimizing spatial scale and data points search strategy allowed obtaining more accurate density estimates independently of the interpolation method.  相似文献   

On the geologic structure of the Explora Escarpment (Weddell Sea,Antarctica) revealed by satellite and Shipboard data evaluation     

Ute Christina Herzfeld  Arnold L. Brodscholl 《Marine Geophysical Researches》1994,16(5):325-345

Bathymetric, gravity, and magnetic data from Antarctic expeditions with RV POLARSTERN and satellite altimeter data from the Geosat Geodetic Mission are analysed using methods from geostatistics and geophysical inverse theory.The Explora Escarpment represents the edge between the Antarctic Continental Shelf and the Weddell Abyssal Plain. It is an important link in the reconstruction of Gondwana breakup, but a feature as large as the 2000 m deep Wegener Canyon was only discovered in 1984, when extensive bathymetric, gravimetric, and magnetic surveys with RV POLARSTERN began.Geostatistics, the theory of regionalized variables, is applied to integrate dense surveys of Wegener Canyon and sparse observations in adjacent areas into maps with full coverage of the 230 km by 330 km area at 10°–20° W/70°–72° S. The resultant highresolution bathymetric and gravity maps reveal detailed structures of the Explora Escarpment. Using geophysical inversion, the gravity terrain effect is calculated. Satellite data are used for their better coverage, but have much lower resolution. Nevertheless, the structures of Wegener Canyon and other more prominent features appear with surprisingly good correlation also in the Geosat altimeter data. While it was initially supposed that Wegener Canyon is purely an erosional structure, the magnetic map now provides evidence of the canyon's tectonic origin.  相似文献   

Geostatistical analysis of variations in soil salinity in a typical irrigation area in Xinjiang, northwest China     

Mamattursun Eziz  Mihrigul Anwar  XinGuo Li 《寒旱区科学》2016,8(2):147-155

Characterizing spatial and temporal variability of soil salinity is tremendously important for a variety of agronomic and environmental concerns in arid irrigation areas. This paper reviews the characteristics and spatial and temporal variations of soil salinization in the Ili River Irrigation Area by applying a geostatistical approach. Results showed that:(1) the soil salinity varied widely, with maximum value of 28.10 g/kg and minimum value of 0.10 g/kg, and was distributed mainly at the surface soil layer. Anions were mainly SO_4~(2-) and Cl~-, while cations were mainly Na~+ and Ca~(2+);(2) the abundance of salinity of the root zone soil layer for different land use types was in the following order: grassland cropland forestland. The abundance of salinity of root zone soil layers for different periods was in the following order: March June September;(3) the spherical model was the most suitable variogram model to describe the salinity of the 0–3 cm and 3–20 cm soil layers in March and June, and the 3–20 cm soil layer in September, while the exponential model was the most suitable variogram model to describe the salinity of the 0–3 cm soil layer in September. Relatively strong spatial and temporal structure existed for soil salinity due to lower nugget effects; and(4) the maps of kriged soil salinity showed that higher soil salinity was distributed in the central parts of the study area and lower soil salinity was distributed in the marginal parts. Soil salinity tended to increase from the marginal parts to the central parts across the study area. Applying the kriging method is very helpful in detecting the problematic areas and is a good tool for soil resources management. Managing efforts on the appropriate use of soil and water resources in such areas is very important for sustainable agriculture, and more attention should be paid to these areas to prevent future problems.  相似文献   

Prediction of local ore recoveries and ore-waste ratios at the silver bell uranium mine     

R. Froidevaux  A. G. Journel 《Mathematical Geology》1982,14(6):645-660

Geostatistical estimation techniques were customized to allow forecasting of production figures at the Silver Bell uranium mine (Uravan District).Surface drill hole data were used to provide a block model of kriged estimators of average uranium grades. Figures for recoverable ore grade and the ore-waste ratio are then deduced from regressive curves previously obtained from underground information and production data. Cross-validations of the entire model were performed and were found positive.  相似文献   

Sequential sampling to contour an uncertain function     

Daniele Veneziano  Peter K. Kitanidis 《Mathematical Geology》1982,14(5):387-404

Sampling exploration of uncertain functions to locate critical contour levels is most effective if sampling decisions are made sequentially. A simple sequential exploration strategy, based on pseudo-Bayesian second-moment analysis, is proposed and compared with non-sequential systematic sampling. Repeated application to functions simulated pseudorandomly from stationary random processes on the line and on the plane indicates uniform superiority of the sequential strategy. The method is particularly advantageous when the function of interest,h(X), has an uncertain trend, and in general when the random process that quantifies prior uncertainty onh(X) is highly correlated.  相似文献   

Testing variograms for positive-definiteness     

Margaret Armstrong  Phil Diamond 《Mathematical Geology》1984,16(4):407-421

A method based on Bochner's theorem is described for demonstrating the positive-definiteness of variogram models and for generating classes of valid variogram functions.Work performed while on leave at the Centre de Géostatistique et de Morphologie Mathématique.  相似文献   

    

Scott Painter 《Mathematical Geology》1995,27(7):813-830

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Bias in estimating fractal dimension with the rescaled-range (R/S) technique     

Colin P. North  David I. Halliwell 《Mathematical Geology》1994,26(5):531-555

Fractal geostatistics are being applied to subsurface geological data as a way of predicting the spatial distribution of hydrocarbon reservoir properties. The fractal dimension is the controlling parameter in stochastic methods to produce random fields of porosity and permeability. Rescaled range (R/S)analysis has become a popular way of estimating the fractal dimension, via determination of the Hurst exponent (H). A systematic investigation has been undertaken of the bias to be expected due to a range of factors commonly inherent in borehole data, particularly downhole wireline logs. The results are integrated with a review of previous work in this area. Small datasets. overlapping samples, drift and nonstationariry of means can produce a very large bias, and convergence of estimates of H around 0.85–0.90 regardless of original fractal dimension. Nonstationarity can also account for H>1, which has been reported in the literature but which is theoretically impossible for fractal time series. These results call into question the validity of fractal stochastic models built using fractal dimensions estimated with the R/Smethod.  相似文献