Iterative algorithms for fitting a linear model of coregionalization
In geostatistical applications, automated or semi-automated procedures are often used for modeling the spatial correlation structure (simple and cross variograms) of multivariate data. This paper deals with the well-known linear model of coregionalization and presents three iterative algorithms to f...
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| Published in | Computers & geosciences Vol. 36; no. 9; pp. 1150 - 1160 |
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| Format | Journal Article |
| Language | English |
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01.09.2010
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| Abstract | In geostatistical applications, automated or semi-automated procedures are often used for modeling the spatial correlation structure (simple and cross variograms) of multivariate data. This paper deals with the well-known linear model of coregionalization and presents three iterative algorithms to find out coregionalization matrices that minimize a weighted sum of the squared deviations between sample and modeled variograms. The first one is a variation of Goulard and Voltz’s proposal for variogram fitting with no constraint other than mathematical consistency. The second one uses simulated annealing for fitting subject to constraints on the simple variogram sills. The third one is a nonlinear least squares algorithm for fitting a plurigaussian model. In all three algorithms, the sample variogram matrices need not be entirely known for every lag vector, a situation of interest with heterotopic samplings. To demonstrate the capabilities of the proposed algorithms, a set of computer programs is provided and applied to case studies in mineral resources evaluation. |
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| AbstractList | In geostatistical applications, automated or semi-automated procedures are often used for modeling the spatial correlation structure (simple and cross variograms) of multivariate data. This paper deals with the well-known linear model of coregionalization and presents three iterative algorithms to find out coregionalization matrices that minimize a weighted sum of the squared deviations between sample and modeled variograms. The first one is a variation of Goulard and Voltz's proposal for variogram fitting with no constraint other than mathematical consistency. The second one uses simulated annealing for fitting subject to constraints on the simple variogram sills. The third one is a nonlinear least squares algorithm for fitting a plurigaussian model. In all three algorithms, the sample variogram matrices need not be entirely known for every lag vector, a situation of interest with heterotopic samplings. To demonstrate the capabilities of the proposed algorithms, a set of computer programs is provided and applied to case studies in mineral resources evaluation. |
| Author | Emery, Xavier |
| Author_xml | – sequence: 1 givenname: Xavier surname: Emery fullname: Emery, Xavier email: xemery@ing.uchile.cl organization: Department of Mining Engineering, University of Chile, Avenida Tupper 2069, Santiago, Chile |
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| Keywords | Multi-Gaussian model Cross variogram Multivariate variogram analysis Simulated annealing Plurigaussian model Cross covariance Heterotopic sampling algorithms iterative methods computer programs variograms covariance case studies multivariate analysis sills copper polymetallic ores computers geostatistics mineral resources sampling data processing least-squares arsenic linear models correlation silver |
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| SubjectTerms | Algorithms Cross covariance Cross variogram Deviation Earth sciences Earth, ocean, space Exact sciences and technology Fittings Heterotopic sampling Iterative algorithms Mathematical analysis Mathematical models Matrices Matrix methods Metal geology Metallic and non-metallic deposits Multi-Gaussian model Multivariate variogram analysis Plurigaussian model Proposals Simulated annealing |
| Title | Iterative algorithms for fitting a linear model of coregionalization |
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