A. Erhan Tercan

Estimation of lignite reserve in the Kalburcayiri field, Kangal basin, Sivas, Turkey

Abstract This paper addresses a case study on global estimation of lignite reserve in the Kalburcayiri field from the Sivas–Kangal basin, which is one of the most productive lignite basins in eastern Anatolia, Turkey. The two lignite seams, which were developed in a fresh-water lacustrine depositional environment during the Pliocene time, are currently being exploited in the Kalburcayiri open-cast mine for feed coal to a power plant with 300-MW capacity. Tonnage, thickness and quality parameters (ash yield, total sulphur content, and calorific value) of the lignite are variables considered in this study. The global estimates of these variables together with 95% confidence limits are obtained using the approximation principle of global estimation. A random stratified grid is fitted to available boreholes; the variograms for thickness and lignite quality parameters are estimated and modeled. The models are used in calculating estimation error variances that will later be used in constructing 95% confidence intervals for the true values.

Optimally Locating Additional Drill Holes in Three Dimensions Using Grade and Simulated Annealing

Average kriging variance is a standard tool used in optimization of the location of additional drill holes. However, this tool cannot distinguish between areas with different priorities. This limitation could be eliminated by using weighted average kriging variance. This paper extends the problem of optimal location to three dimensional cases, use grade as a weight and search optimum locations by simulated annealing. Weighted average kriging variance is used as objective function. The method is applied to a copper deposit. Results have shown that weighting of the estimation variance with “grade” is effective only when the difference among the grades estimated for different blocks is considerable.

Use of genetic algorithm in optimally locating additional drill holes

Optimally locating additional drill holes depends on initial data configuration, spatial structure of the variable under study, the number of additional drill holes and shape of deposit. Several approaches have been proposed for this problem using geostatistics and optimization methods, but all of them treat the mineral deposit in 2D. An optimization procedure that is based on genetic algorithm is presented for optimally locating additional drill holes in 3D. A case study in an industrial mineral deposit using Al2O3 % grade illustrates the procedure. The results showed that this procedure is in effect in the case of varying thickness.

Local spatial regression models : a comparative analysis on soil contamination

Spatial data analysis focuses on both attribute and locational information. Local analyses deal with differences across space whereas global analyses deal with similarities across space. This paper addresses an experimental comparative study to analyse the spatial data by some weighted local regression models. Five local regression models have been developed and their estimation capacities have been evaluated. The experimental studies showed that integration of objective function based fuzzy clustering to geostatistics provides some accurate and general models structures. In particular, the estimation performance of the model established by combining the extended fuzzy clustering algorithm and standard regional dependence function is higher than that of the other regression models. Finally, it could be suggested that the hybrid regression models developed by combining soft computing and geostatistics could be used in spatial data analysis.

Global Recoverable Reserve Estimation by Covariance Matching Constrained Kriging

A central problem in mining practice is estimation of global recoverable reserves, i.e., recovered tonnage and mean quality varying with cut-off value over the whole deposit. This article describes the application of covariance matching constrained kriging to the estimation of the global recoverable reserves in a lignite deposit in Turkey. Thickness and calorific value are the variables used in this study. The deposit is divided into 180 panels with 200 m × 200 m size and the mean calorific value of the panels is estimated by covariance matching constrained kriging. Quality tonnage curve is constructed based on the estimated mean values. For comparison, quality tonnage curve from ordinary kriging is also provided.

Evaluating geo-environmental variables using a clustering based areal model

Global regression models do not accurately reflect the spatial heterogeneity which characterises most geo-environmental variables. In analysing the relationships between such variables, an approach is required which allows the model parameters to vary spatially. This paper proposes a new framework for exploring local relationships between geo-environmental variables. The method is based on extended objective function based fuzzy clustering with the environmental parameters estimated through on a locally weighted regression analysis. The case studies and prediction evaluations show that the fuzzy algorithm yields well-fitted models and accurate predictions. In addition to an increased accuracy of prediction relative to the widely-used geographically weighted regression (GWR), the proposed algorithm provides the search radius (bandwidth) and weights for local estimation directly from the data. The results suggest that the method could be employed effectively in tackling real world kernel-based modelling problems.

Constrained multiple indicator kriging using sequential quadratic programming

Multiple indicator kriging (MIK) is a nonparametric method used to estimate conditional cumulative distribution functions (CCDF). Indicator estimates produced by MIK may not satisfy the order relations of a valid CCDF which is ordered and bounded between 0 and 1. In this paper a new method has been presented that guarantees the order relations of the cumulative distribution functions estimated by multiple indicator kriging. The method is based on minimizing the sum of kriging variances for each cutoff under unbiasedness and order relations constraints and solving constrained indicator kriging system by sequential quadratic programming. A computer code is written in the Matlab environment to implement the developed algorithm and the method is applied to the thickness data.

A Geostatistical Study of Tertiary Coal Fields in Turkey

The majority of lignite and sub-bituminous coal resources known in Turkey are of Tertiary age. Therefore Tertiary coals in Turkey are of great importance in terms of coal potential and production. This paper presents a study of spatial distributions of calorific value, ash content and moisture content over Tertiary fields. For this purpose data collected from 187 coal fields in Turkey are used. The experimental variograms of three quality attributes are computed from these data and models are fitted. These models are used in estimation of spatial distributions of the corresponding variables by ordinary kriging. In addition, the probabilities of calorific value being less than 1,600 kCal/kg at estimation nodes are computed by using Direct- Sequential Simulation. Finally, additional sampling locations are proposed especially for the fields in which further information are required.

Geostatistics: Modeling Spatial Uncertainty, Jean-Paul Chilès, Pierre Delfiner. Second ed., Wiley Series in Probability and Statistics, John Wiley & Sons, Inc., Hoboken, New Jersey (2012). 699pp. ISBN: 978-0-470-18315-1

Geostatistics basically concerns with the description of a characteristic that varies in space and is originally developed to deal with mineral resource estimation problem in mining. Due to the spatial feature of the characteristic, geostatistical applications are now extended to many fields in the earth sciences other than mining, including the subsurface, the land, the atmosphere, and the oceans. A recent study made by Hengl et al. (2009) on the bibliometric indices of geostatistics shows that it is an active scientific field, expanding fast. Considering new perspectives, new developments and an explosion in the applications of geostatistical methods, the authors revised and updated the first edition without increasing the size of the book. The most noticeable change is the removal of the chapter related to stochastic hydrology and the distribution of some material included in it throughout the relevant chapters. Some chapters (e.g., multivariate methods) are largely rewritten with a number of additions and some (nonlinear methods and conditional simulations) are restructured and updated. Some chapters such as preliminaries and intrinsic model of order k remain the same. Another change to the second edition is that footnotes are given immediately at the bottom of the page, not at the end of the chapter, providing reader with great comfort. The first edition of Geostatistics: Modeling Spatial Uncertainty appeared in 1999, and in reviewing it in Computers & Geosciences, 2001, vol. 27, pp. 121–123, L. Zheng wrote, ‘y it covers a wide range of theoretical and technical issues involved in modeling spatial uncertainty and performing geostatistical analyses. Its major features include its comprehensive scope, the rich content and full details, the clear presentation, and a good balance between theory and application. Although this book may not be a good choice for beginners, it is no doubt a must-read for anyone who wants to gain a comprehensive view and an insightful understanding of this specialized discipline’. I strongly agree and during the review process, I have used it as a reference for my research and gained some interesting research ideas. The book begins with an introductory chapter defining types of problems considered in each chapter and presenting a striking example demonstrating that geostatistical methods are rather descriptive. Chapter 1 defines basic mathematical, statistical and philosophical properties of random functions that are useful models for regionalized variables. These are needed for the subsequent chapters. In particular, shaking jar example illustrating a notion of random functions is very instructive and memorable. Throughout the book it is easy to find such kind of interesting examples. Chapter 2, one of the most voluminous chapters, is devoted to structural analysis of a regionalized variable. The variogram is the fundamental tool. To characterize

The Ranked Tile Resampling in Assessing Accuracy for the Global Coal Reserve Estimates

Global estimation is the first and most important step in evaluating a coal deposit. Assessing accuracy for estimates constitutes the most difficult stage of this procedure. In this study, I introduce the ranked tile resampling method to assess uncertainty for the global means. It is based on producing a simulated version of the original field. The simulation is achieved by dividing the observation field into tiles, resampling them at random with replacement, and joining them together in a ranked order. The method is applied to thickness and ash yield of a simulated coal deposit. The simulation results show that the ranking significantly improves the correlation structure of the resampled field, especially over short tile sizes.Global estimation is the first and most important step in evaluating a coal deposit. Assessing accuracy for estimates constitutes the most difficult stage of this procedure. In this study, I introduce the ranked tile resampling method to assess uncertainty for the global means. It is based on producing a simulated version of the original field. The simulation is achieved by dividing the observation field into tiles, resampling them at random with replacement, and joining them together in a ranked order. The method is applied to thickness and ash yield of a simulated coal deposit. The simulation results show that the ranking significantly improves the correlation structure of the resampled field, especially over short tile sizes.