Margaret Armstrong

Plurigaussian simulations in geosciences

Simulations are the fastest developing branch in geostatistics, and simulating the acies inside reservoirs and ore bodies is the most exciting part of this. Several methods have been developed to do this (sequential indicator simulations, Boolean methods, Markov chains and plurigaussian simulations). This book focusses on the last type of simulation. It develops the theory required to understand the method together and presents practical examples of applications in mining and petroleum, plus tutorial examples. An accompanying CD-ROM featuring demonstration software and color images complements the printed book.

Robustness of variograms and conditioning of kriging matrices

Current ideas of robustness in geostatistics concentrate upon estimation of the experimental variogram. However, predictive algorithms can be very sensitive to small perturbations in data or in the variogram model as well. To quantify this notion of robustness, nearness of variogram models is defined. Closeness of two variogram models is reflected in the sensitivity of their corresponding kriging estimators. The condition number of kriging matrices is shown to play a central role. Various examples are given. The ideas are used to analyze more complex universal kriging systems.

Variogram models must be positive-definite

The aim of this short article is to stress the importance of using only positive-definite functions as models for covariance functions and variograms.The two examples presented show that a negative variance can easily be obtained when a nonadmissible function is chosen for the variogram model.

Geostatistical case studies

Computing Variograms on Uranium Data.- The Comparison Between the Gamma Logs and the Grades in the Estimation of a Uranium Deposit.- Geostatistical Estimation of a Section of the Perseverance Nickel Deposit.- Multipurpose Geostatistical Modelling of a Bauxite Orebody in Sardinia.- Application of Kriging to the Mapping of a Reef from Wireline Logs and Seismic Data A Case History.- Study of a Gas Reservoir Using the External Drift Method.- The Grade-Tonnage Curves for a Zinc Mine in France.- Conditioning by the Panel Grade for Recovery Estimation of Non-Homogeneous Orebodies.- Recoverable Reserves Estimation at an Australian Gold Project.- Comparing Estimated Uranium Grades with Production Figures.- Global Recoverable Reserves: Testing Various Changes of Support Models on Uranium Data.- Calculating Ore Reserves Subject to Mining Constraints, for a Uranium Deposit.

Testing variograms for positive-definiteness

A method based on Bochners theorem is described for demonstrating the positive-definiteness of variogram models and for generating classes of valid variogram functions.

Towards a practical approach to responsible innovation in finance: New Product Committees revisited

The purpose of this paper is to highlight the potentials offered by New Product Committees for the development of responsible innovation in the financial services industry; and to provide grounds for policy recommendations. The paper takes the form of collective, interdisciplinary reflection and experience within the industry. New Product Committees can serve a practical approach to responsible innovation in finance.

Scenario Reduction Applied to Geostatistical Simulations

Having a large number of geostatistical simulations of a mineral or petroleum deposit provides a better idea of its upside potential and downside risk; however, large numbers of simulated realizations of a deposit may pose computational difficulties in subsequent decision-making phases. Hence, depending on the specific case, there can be a need to select a representative subset of conditionally simulated deposit realizations. This paper examines and extends an approach developed by the stochastic optimization community based on stochastic mathematical programming with recourse and is discussed here in the context of mineral deposits while it is possibly suitable for other earth science applications. The approach is based on measuring the “distance” between simulations and the introduced distance measure between simulated realizations of a mineral deposit is based on the metal above a given set of cutoff grades while a pre-existing mine design is available. The approach is tested on 100 simulations of the Walker Lake data with promising results.

Comparison between different kriging estimators

Six different geostatistical estimators (linear kriging, lognormal kriging, and disjunctive kriging, each with and without a nonbias, i.e., universality condition) were compared using data from a polymetallic deposit in Algeria. The differences between estimators with and without the nonbias condition were far more pronounced than between the different kriging methods. This highlights the importance of choosing an appropriate stationarity model for the data. The criterion concerning kriging weight of the mean in simple kriging, proposed by Remacre (1984, 1987) and Rivoirard (1984) was found to be helpful for determining blocks where the choice of the stationarity hypothesis was critical.

Geostatistics Rio 2000

Preface R. Olea. Introduction M. Armstrong, et al. Petroleum Papers. Using Quantitative Outcrop Databases As a Guide for Geological Reservoir Modelling R. Eschard, et al. Quantification of facies relationships via proportion curves C. Ravenne, et al. Geologic Modelling of External and Internal Reservoir Architecture of Fluvial Depositional Systems P.E. Patterson, et al. Impact of Seismic Constraints on a Stochastic Reservoir Model and Fluid Flow Simulation I. Azpiritxaga, et al. Practical Workflows for Reservoir Modelling J.M. Yarus, et al. Mining Papers. Simulating the Geometry of a Granite-hosted Uranium Orebody T. Skvortsova, et al. Simulation of Weathered Iron Ore Facies: Integrating Leaching Concepts and Geostatistical Models D.T. Ribeiro, R.M. Carvalho. Geostatistical Simulation of Structurally Controlled Low Grade High Tonnage Gold Ores: A Strategy for Targeting Genuine Enriched Zones A.H.M. Silva, et al. Geostatistical Framework for Modelling Clay Deposits: Nova Veneza Case Study in Southern Brazil R.L. Stangler, et al. Risk Assessment of Reserve Calculation during Milestones of a Mine Life F. Silva, et al. Successful Incorporation of Geological Controls into Reserve Evaluation: Recent Examples from Giant Copper Mines in Chile N. Champigny, et al. Geological Conditions for a Correct Geostatistical Evaluation: Example 177 from the Elatsite Copper Deposit in Bulgaria J. Todorov, et al. Evaluation of Kriging and Cokriging for Asbestos Ore Reserve Estimation at the Cana Brava Mine, Goias, Brazil R.P. Conde, J.K. Yamamoto. Geostatistical Evaluation of the Mineral Resources of the Cajati Mine, State of Sao Paulo, Brazil G. Barros, J.K. Yamamoto. Variographic Trends of Gold in the Alluvial Sediments Associated with the QuartzLodes in the Princesa Isabel Region, Paraiba, Brazil S.R. Lanusse, T.R. Gopinath.

COMPARISON OF THREE METHODS FOR EVALUATING OIL PROJECTS

SUMMARY Option pricing, decision trees, and Monte Carlo simulations are three methods used to evaluate projects. In this paper, we compare their similarities and differences from three points of view—how they handle uncertainty in the values of key parameters, such as reserves, oil price, and costs; how they incorporate the time value of money; and whether they allow for managerial flexibility. We show that, despite their obvious differences, they are in fact different facets of a general project-evaluation framework that has the static base-case scenario as its simplest form. Compromises have to be made when modeling the complexity of the real world. These three approaches can be obtained from the general framework by focusing on certainty aspects.