Modeling the Semivariogram: New Approach, Methods Comparison, and Simulation Study
A. Gribov, K. Krivoruchko, J. M. Ver Hoef, 2006. "Modeling the Semivariogram: New Approach, Methods Comparison, and Simulation Study", Stochastic Modeling and Geostatistics: Principles, Methods, and Case Studies, Volume II, T. C. Coburn, J. M. Yarus, R. L. Chambers
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This chapter proposes some new methods for computing empirical semivariograms and covariances and for fitting semivariogram and covariance models to empirical data. Grid-based empirical semivariograms and covariances are described, in which the grid values are smoothed using triangular kernels. A model-fitting procedure using modified iterative weighted least squares is presented. This algorithm is shown to be reliable for a wide range of data types and conditions, and its implementation in commercial software is discussed. Comparisons to restricted maximum likelihood estimation are also discussed.
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Since publication of the first volume of Stochastic Modeling and Geostatistics in 1994, there has been an explosion of interest and activity in geostatistical methods and spatial stochastic modeling techniques. Many of the computational algorithms and methodological approaches that were available then have greatly matured, and new, even better ones have come to the forefront. Advances in computing and increased focus on software commercialization have resulted in improved access to, and usability of, the available tools and techniques. Against this backdrop, Stochastic Modeling and Geostatistics Volume II provides a much-needed update on this important technology. As in the case of the first volume, it largely focuses on applications and case studies from the petroleum and related fields, but it also contains an appropriate mix of the theory and methods developed throughout the past decade. Geologists, petroleum engineers, and other individuals working in the earth and environmental sciences will find Stochastic Modeling and Geostatistics Volume II to be an important addition to their technical information resources.