Sequential kriging and cokriging: Two powerful geostatistical approaches

A sequential linear estimator is developed in this study to progressively i ncorporate new or different spatial data sets into the estimation. It begin s with a classical linear estimator (i.e., kriging or cokriging) to estimat e means conditioned to a given observed data set. When an additional data s et becomes available, the sequential estimator improves the previous estima te by using linearly weighted sums of differences between the new data set and previous estimates at sample Locations. Like the classical linear estim ator, the weights used in the sequential linear estimator are derived from a system of equations that contains covariances and cross-covariances betwe en sample locations and the location where the estimate is to be made. Howe ver, the covariances and cross-covariances are conditioned upon the previou s data sets. The sequential estimator is shown to produce the best, unbiased linear esti mate, and to provide the same estimates and variances as classic simple kri ging or cokriging with the simultaneous use of the entire data set. However , by using data sets sequentially, this new algorithm alleviates numerical difficulties associated with the classical kriging or cokriging techniques when a large amount of data are used. It also provides a new way to incorpo rate additional information into a previous estimation.