ANALYSIS AND ESTIMATION OF NATURAL PROCESSES WITH NONHOMOGENEOUS SPATIAL VARIATION USING SECONDARY INFORMATION

Natural processes encountered in mining, hydrogeologic, environmental, etc. applications usually are poorly known because of scarcity of dat a over the area of interest. Therefore, stochastic estimation techniqu es are the tool of choice for a careful accounting of the heterogeneit y and uncertainty involved. Within such a framework, a better utilizat ion of all available data concerning the process of interest and all o ther natural processes related to it, is of primary importance. Becaus e many natural processes show complicated spatial trends, the hypothes is of spatial homogeneity cannot be invoked always, and the more gener al theory of intrinsic spatial random fields should be employed. Effic ient use of secondary information in terms of the intrinsic model requ ires that suitable permissibility criteria for the generalized covaria nces and cross-covariances are satisfied. A set of permissibility crit eria are presented for the situation of two intrinsic random fields. T hese criteria are more general and comprehensive than the ones current ly available in the geostatistical literature, A constrained least-squ are technique is implemented for the inference of the generalized cova riance and cross-covariance parameters, and a synthetic example is use d to illustrate the methodology. rite numerical results show that the use of secondary information can lead to significant reductio,ls in th e estimation errors.