Analysis and Estimation of Natural Processes with Nonhomogeneous Spatial Variation Using Secondary Information |
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| Authors: | Giorgio Cassiani and George Christakos |
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| Institution: | (1) Department of Civil and Environmental Engineering, Duke University, Durham, North Carolina 27708, U.S.A;(2) Department of Environmental Sciences and Engineering, University of North Carolina, 111 Rosenau Hall, Chapel Hill, North Carolina 27599-, 7400;(3) Present address: Agip S.p.A.-GEDA, Via Emilia 1, San Donato Milanese, Milan, Italy |
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| Abstract: | Natural processes encountered in mining, hydrogeologic, environmental, etc. applications usually are poorly known because of scarcity of data over the area of interest. Therefore, stochastic estimation techniques are the tool of choice for a careful accounting of the heterogeneity and uncertainty involved. Within such a framework, a better utilization of all available data concerning the process of interest and all other natural processes related to it, is of primary importance. Because many natural processes show complicated spatial trends, the hypothesis of spatial homogeneity cannot be invoked always, and the more general theory of intrinsic spatial random fields should be employed. Efficient use of secondary information in terms of the intrinsic model requires that suitable permissibility criteria for the generalized covariances and cross-covariances are satisfied. A set of permissibility criteria are presented for the situation of two intrinsic random fields. These criteria are more general and comprehensive than the ones currently available in the geostatistical literature. A constrained least-square technique is implemented for the inference of the generalized covariance and cross-covariance parameters, and a synthetic example is used to illustrate the methodology. The numerical results show that the use of secondary information can lead to significant reductions in the estimation errors. |
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| Keywords: | vector random fields generalized covariances permissibility criteria kriging |
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