Optimal contour mapping using universal kriging


  • Ricardo A. Olea


Currently available procedures for automatic contouring are unsatisfactory from both theoretical and practical viewpoints. The theory of regionalized variables allows formulation of a superior contouring algorithm. The theory of regionalized variables has been developed by G. Matheron to allow the drawing of statistical inferences, not only sample values but also implicit relationships in the geometry of the sample space being considered. Universal kriging is an estimation procedure within the context of the regionalized variable theory; it is presented and used here as an alternative method for grid generation in automatic contouring procedures, where spatial relationships must be considered. Universal kriging is more general and reliable than empirical contouring methods and is unbiased if the assumptions of the regionalized variable theory are met. In addition, kriged values have minimum estimation variance. Universal kriging is an exact interpolation procedure and, probably the most important feature, yields a measure for the estimation error at every point in the sample space.